ESA-Prima Win STEEL AND TIMBER DESIGN BENCHMARKSdocumentatie.nemetschek.ro/documentatie/7scia/tutoriale/en/STEEL... · ESA-Prima Win Steel and timber design benchmarks ... EXAMPLE

ESA-Prima Win Steel and timber design benchmarks

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ESA-Prima Win

STEEL AND TIMBER DESIGN BENCHMARKS SCIA Scientific Application Group


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___________________________________________________________ Release : 3.20.xx Module : Manual : Design benchmarks Revision : June 2000

___________________________________________________________ SCIA Group n.v. Scientific Application Group Industrieweg 1007 B-3540 Herk-de-Stad (België) Tel.(+32) (0)13/55 17 75 Fax.(+32) (0)13/55 41 75 ___________________________________________________________ SCIA W+B Software b.v. Postbus 330 NL-6860 AH Oosterbeek (Nederland) Tel.(+31) 26-3338008 Fax.(+31) 26-3341949 ___________________________________________________________ SCIA sarl Parc Club des Prés Rue Papin 29 - F-59650 Villeneuve d'Asq (Frankrijk) Tel.(+33) (0) 3.20.04.10.60 Fax.(+33) (0) 3.20.04.03.36 ___________________________________________________________ SCIA GmbH Giesestraße 3 D 58636 Iserlohn (Duitsland) Tel.(+49) 2371-4944 Fax.(+49) 2371-4904


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ABOUT THIS BENCHMARKS All benchmarks are presented in the following form : Description Short description of the benchmark. Project data All necessary data to calculate the project. Reference The reference from which the results are taken or the analytical solution. Result Comparison between ESA-Prima Win and the reference result. Version Version number of the version with which the verification was done. Input file + calculation note Name of the corresponding ESA-Prima Win file. Modules Name of the commercial modules needed to calculate this example. Author Initials of the author of the benchmark Information in this document is subject to change without notice. No part of this document may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of the publisher. SCIA Software is not responsible for direct or indirect damage as a result of imperfections in the documentation and/or software. Copyright 2000 SCIA Software. All rights reserved.


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TABLE OF CONTENTS The following benchmarks are available (the benchmarks are grouped according to the ESA-Prima Win modules) :

INTRODUCTION 10

1. STEEL CODE CHECK 11

1.1 PST.06.XX – 01 : CALCULATION OF BUCKLING RATIOS 11 1.2 PST.06.XX – 02 : CALCULATION OF BUCKLING RATIOS FOR CROSSING DIAGONALS 14 1.3 PST.06.01 – 01 : EC 3 STEEL CODE CHECK TUTORIAL FRAME 23 1.4 PST.06.01 – 02 : EC 3 STEEL CODE CHECK – WARPING CHECK 45 1.5 PST.06.01 – 03 : EC 3 STEEL CODE CHECK – WARPING CHECK 49 1.6 PST.06.01 – 04 : EC 3 STEEL CODE CHECK – WARPING CHECK 52 1.7 PST.06.01 – 05 : EC 3 STEEL CODE CHECK – WARPING CHECK 56 1.8 PST.06.01 – 06 : EC 3 STEEL CODE CHECK – TORSIONAL BUCKLING CHECK AND SHEAR

BUCKLING CHECK FOR COLD FORMED SECTIONS 60 1.9 PST.06.01 – 07 : EXAMPLE CODE CHECK AND CONNECTIONS ACCORDING TO EC3 : DESIGN OF

AN INDUSTRIAL TYPE BUILDING 68 1.10 PST.06.02 – 01 : DIN 18800 STEEL CODE CHECK (1) 119 1.11 PST.06.02 – 02 : DIN 18800 STEEL CODE CHECK (2) 125 1.12 PST.06.02 – 03 : DIN 18800 STEEL CODE CHECK (3) 131 1.13 PST.06.02 – 04 : DIN 18800 STEEL CODE CHECK (4) 136 1.14 PST.06.02 – 05 : DIN 18800 STEEL CODE CHECK TUTORIAL FRAME 141 1.15 PST.06.03 – 01 : NEN 6770/6771 STEEL CODE CHECK 156 1.16 PST.06.05 – 01 : AISC STEEL CODE CHECK TUTORIAL FRAME 159 1.17 PST.06.06 – 01 : CM 66 STEEL CODE CHECK TUTORIAL FRAME 176 1.18 PST.06.08 - 01 : SIA161 STEEL CODE CHECK TUTORIAL FRAME 197 1.19 PST.06.09 – 01 : BS5950 STEEL CODE CHECK TUTORIAL FRAME 208 1.20 PST.06.09 – 02 : BS5950 STEEL CODE OF PRACTICE FOR DESIGN 225 1.21 PST.06.10 – 01 : GBJ 17-88 STEEL CODE CHECK TUTORIAL FRAME 233 1.22 PST.06.11 – 01 : KOREAN STEEL CODE CHECK TUTORIAL FRAME 250

2. CONNECTIONS 263

2.1 PST.07.01 – 01 : CALCULATION OF A BASE PLATE 263 2.2 PST.07.01 – 02 : CALCULATION OF A BOLTED CONNECTION 272 2.3 PST.07.01 – 03 : CALCULATION OF A BOLTED CONNECTION 299 2.4 PST.07.01 – 04 : CALCULATION OF A BOLTED CONNECTION 305 2.5 PST.07.01 – 05 : CALCULATION OF WELDED CONNECTIONS 323 2.6 PST.07.01 – 06 : CALCULATION OF REQUIRED STIFFNESS 332 2.7 PST.07.01 - 07: BOLTED CONNECTION WITH COLUMN MINOR AXIS 340 2.8 PST.07.01 - 08: WELDED CONNECTION WITH COLUMN MINOR AXIS 349 2.9 PST.07.01 - 09: BOLTED CONNECTION 356 2.10 PST.07.02 – 01 : FRAME PINNED CONNECTION (PLATE WELDED ON THE WEB) 358 2.11 PST.07.02 – 02 : FRAME PINNED CONNECTION (PLATE BOLTED TO THE WEB) 365 2.12 PST.07.02 – 03 : FRAME PINNED CONNECTION (ANGLES) 378 2.13 PST.07.02 – 04 : FRAME PINNED CONNECTIONS (SHORT ENDPLATE) 391 2.14 PST.07.02 - 05 : FRAME PINNED CONNECTION (ANGLES) WITH COLUMN MINOR AXIS 399


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2.15 PST 07 03 01: HOLLOW SECTION JOINT DESIGN ANNEX K 408 2.16 PST 07 03 02: HOLLOW SECTION JOINT DESIGN ANNEX K 413 2.17 PST 07 03 03: HOLLOW SECTION JOINT DESIGN ANNEX K 418 2.18 PST 07 03 04: HOLLOW SECTION JOINT DESIGN ANNEX K 423 2.19 PST.07.03 -5: KLS TRUSS CONNECTION: WELDSIZE CALCULATION 428 2.20 PST.07.04 – 01 : BOLTED DIAGONAL CONNECTIONS 432

3. TIMBER 449

3.1 PTR.06.01 – 01 : EC 5 TIMBER CODE CHECK 449 3.2 PTR.06.01 – 02 : EC 5 TIMBER CODE CHECK 452 3.3 PTR.06.01 – 03 : EC 5 TIMBER CODE CHECK 455


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The ESA-Prima Win modules :

ESA-Prima Win Engineering Structural Analysis for Windows 95/98/NT/2000 - Rel.3.20 FEM = Finite Element Method

RC = Reinforced Concrete

ESA-Prima Win Base PRS.00 Base:

basic module for each ESA-Prima Win installation, including import/export of projects, libraries (profiles, plates, bolts and materials), document generation, gallery of drawings, rendering, manuals, online help and delivery materials

ESA-Prima Win: Basic Structural Analysis PRS.01 2D Frame :

linear static analysis of plane beam structures with loads in their plane

PRE.01 2D Wall (FEM ext.) : linear static analysis of plane wall structures in plane stress (ext. to PRS.01)

PRS.02 2D Grid : linear static analysis of grid structures with loads perpendicular to their plane

PRE.02 2D Plate (FEM ext.) : linear static analysis of plates with loads perpendicular to their plane (ext. to PRS.02)

PRS.11 3D Frame : linear static analysis of spatial beam structures (incl. funct. PRS.01 + PRS.02)

PRE.11 3D Shell (FEM ext.) : linear static analysis of spatial shells (incl. funct. PRE.01 + PRE.02) (ext. to PRS.11)

ESA-Prima Win: Pre-processors PRE.12 Intersec :

intersection of 2D/1D (shell/beam) and 2D/2D (shell/shell) macros

PRS.13 Graphical section : graphical input of cross-sections with arbitrary shape and different materials, thin-walled sections, DXF import of cross-sections

PRE.31 Influence surfaces : calculation of the influence surface of an internal force, deformation or reaction in plate or shell projects/

PRC.70 Beam : pre-processor for fast input of continuous beams, including predefined loadcases and automatic generation of combinations

PST.07.00 Connect : pre-processor for manual input of internal forces on a connection

ESA-Prima Win: Load generators PRS.62 Plane load :

automatic division of a surface load to the beams

PRE.63 Train load : defining of train loads and positioning on plane surfaces

PRS.65.01 Advanced Wind + Snow (EC 1) : advanced automatic generation of wind and snow on complex structures, according to EC 1

PRS.65.02 Wind + Snow (DIN 1055) : automatic generation of wind and snow loads according to DIN 1055

PRS.65.03 Advanced Wind + Snow + Slab (NEN 6702) : advanced automatic generation of wind, snow and slab loads on complex structures, according to NEN


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6702

PRS.65.07 Wind + Snow (CSN 730035) : automatic generation of wind and snow loads according to CSN 730035

PRS.66 Mobile loads Frame : one user defined group of mobile pointloads on frame structures, calculation of the envelope for the whole structure and the local course in a point of the structure

PRE.66 Mobile loads FEM : one user defined group of mobile pointloads on shell structures, calculation of the envelope for the whole structure (ext. to PRS.66)

PRS.67 Advanced mobile loads Frame : several groups of mobile loads with interference, user defined loadgroup of pointloads and uniformly distributed loads, loadgroups according to different codes

PRE.67 Advanced mobile loads FEM : several groups of mobile loads with interference, user defined loadgroup of pointloads and uniformly distributed loads, loadgroups according to different codes (ext. to PRS.67)

ESA-Prima Win: Advanced Structural Analysis PRS.22 2nd order Frame :

geometrical nonlinear analysis incl. modelling of geometric imperfections (initial deformations and member imperfections), prestressed beams

PRE.22 2nd order FEM : geometrical nonlinear analysis of shell structures, membrane effects (ext. to PRS.22)

PRS.25 Stability Frame : determination of the global buckling mode and buckling load, extraction of critical geometric imperfections, results can be used as input for PRS.22

PRE.25 Stability FEM : determination of the global buckling mode and buckling load (ext. to PRS.25)

PRS.28 Dynamics Frame : definition of eigenfrequencies and eigenmodes for frames

PRS.29 Dynamics Frame (ext.) : harmonic, spectral and time history analysis, seismic loads (ext. to PRS.28)

PRE.28 Dynamics FEM : definition of eigenfrequencies and eigenmodes for shells (ext. to PRS.28)

PRE.29 Dynamics FEM (ext.) : harmonic, spectral and time history analysis, seismic loads (ext. to PRE.28)

PRP.01 Dynamics package : PRS.28 + PRE.28 + PRS.29 + PRE.29

PRS.55 Building phases Frame : calculation of Frame structures in different phases : adding or removing supports, members, loadcases, changing cross section properties in different steps ; the history of internal forces is calculated

PRE.55 Building phases FEM : calculation of FEM structures in different phases : adding or removing supports, members, loadcases, changing cross section properties in different steps ; the history of internal forces is calculated (ext. to PRS.55)

PRS.80 Physical nonlinear conditions : analysis of structures with local physical nonlinearities: members with limited tension/compression, elimination of tension springs, gap elements, nonlinear supports

PRS.81 Physical nonlinear Frame (steel) : analysis of steel structures with plastic hinges (for EC, DIN, NEN)

PRS.82 Physical nonlinear Frame (concrete) : analysis of RC structures with physical nonlinearities: bending, creep (for EC, NEN, DIN, ÖNORM, CSN)


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PRE.82 Physical nonlinear FEM (concrete) : analysis of RC structures with physical nonlinearities: bending, creep (for EC, NEN, DIN, ÔNORM, CSN)

ESA-Prima Win: Steel Design PST.06.01 Steel Code Check (EC 3) :

stress and stability verification of steel members according to EC 3, with profile optimization

PST.06.02 Steel Code Check (DIN 18800) : stress and stability verification of steel members according to DIN 18800, with profile optimization

PST.06.03 Steel Code Check (NEN 6770/6771) : stress and stability verification of steel members according to NEN 6770/6771, with profile optimization

PST.06.04 Steel Code Check (Önorm 4300) : stress and stability verification of steel members according to Önorm 4300, with profile optimization

PST.06.05 Steel Code Check (AISC) : stress and stability verification of steel members according to AISC, with profile optimization

PST.06.06 Steel Code Check (CM 66) : stress and stability verification of steel members according to CM 66, with profile optimization

PST.06.07 Steel Code Check (CSN 731401) : stress and stability verification of steel members according to CSN 731401, with profile optimization

PST.06.08 Steel Code Check (SIA 161) : stress and stability verification of steel memebers according to SIA 161, with profile optimization

PST.06.09 Steel Code Check (BS 5950 - Part 1) : stress and stability verification of steel members according to BS 5950 - Part 1, with profile optimization

PST.06.10 Steel Code Check (CHIN GBJ 17-88) : stress and stability verification of steel members according to CHIN GBJ 17-88, with profile optimization

PST.06.11 Steel Code Check (KOR) : stress and stability verification of steel members according to KOR, with profile optimization

PST.07.01 Connect Frame - Rigid (EC 3 Revised annex J) : design, verification and drawing of bolted and welded steel frame connections according to EC 3 Revised annex J

PST.07.02 Connect Frame - Pinned (EC 3) : design, verification and drawing of hinged steel frame connections according to EC 3

PST.07.03 Truss connections : calculation of welded connections in trusses (tubes, rectangular hollow sections and I sections) acc. To EC 3 and CIDECT

PST.07.04 Bolted Diagonals : calculation of bolted diagonals in steel structures according to Eurocode 3 (bolts, net section)

PST.07.10 Expert system Connect Frame : intelligent selection of a steel frame connection from an extended library with DSTV, SPRINT and user defined connections.

PST.11 Project : general overview drawings for steel structures with annotations, detailed bill of material

ESA-Prima Win: Foundations

PRS.14 Foundation block stability : input of foundation blocks under colums, calculation of the resulting rigidity of the support (optionally in combination with Soilin for input of Ground layers), check of: bearing resistance, sliding and overturning.

PRE.32 Soilin : Iterative analysis of soil-structure interaction : calculation of soil parameters for structures on foundation plates


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ESA-Prima Win: Concrete Design

PRC.71.01 RC Beams & Columns Analysis (EC 2) : reinforcement analysis of concrete beams & columns according to EC 2

PRC.71.02 RC Beams & Columns Analysis (DIN 1045-1) : reinforcement analysis of concrete beams & columns according to DIN 1045-1

PRC.71.03 RC Beams & Columns Analysis (NEN 6720) : reinforcement analysis of concrete beams & columns according to NEN 6720

PRC.71.04 RC Beams & Columns Analysis (Önorm) : reinforcement analysis of concrete beams & columns according tot önorm

PRC.71.07 RC Beams & Columns Analysis (CSN) : reinforcement analysis of concrete beams & columns according to CSN

PRC.71.09 RC Beams & Columns Analysis (BS8110) : reinforcement analysis of concrete beams & columns according to British Standard 8110

PRC.71.10 RC Beams & Columns Analysis (GBJ 10-89) : reinforcement analysis of concrete beams & columns according to the Chinese code GBJ 10-89

PRC.72.01 RC Plates & Shells Analysis (EC 2) : reinforcement analysis of plates & shells according to EC 2

PRC.72.02 RC Plates & Shells Analysis (DIN 1045) : reinforcement design of plates & shells according to DIN 1045

PRC.72.03 RC Plates & Shells Analysis (NEN 6720) : reinforcement design of plates & shells according to NEN 6720

PRC.72.04 RC Plates & Shells Analysis (Önorm) : reinforcement design of plates & shells according to Önorm

PRC.72.07 RC Plates & Shells Analysis (CSN) : reinforcement design of plates & shells according to CSN

PRC.72.08 RC Plates & Shells Analysis (SIA) : reinforcement design of plates & shells according to SIA

PRC.72.09 RC Plates & Shells Analysis (BS8110) : reinforcement design of plates & shells according to British Standard 8110

PRC.72.10 RC Plates & Shells Analysis (GBJ 10-89) : reinforcement design of plates & shells according to the Chinese code GBJ 10-89

PRC.73 RC Beams & Columns Design & Drawings : reinforcement design for concrete beams & columns : conversion from theoretical to practical reinforcement, generation of drawings, generation of bill of material

PRC.74 RC Plates Design & Drawings : reinforcement design for concrete plates : conversion from theoretical to practical reinforcement, generation of drawings, generation of bill of material

PRC.75.01 Punching (Eurocode 2) : punching check for plates according to Eurocode 2

PRC.80 Prestress : calculation of the internal force distribution and time dependent deformation of 2D Frame structures with prestressed elements ; prestressing and poststressing ; calculation of losses (immediate and time-dependent)

ESA-Prima Win: Timber Design PTR.06.01 Timber Code Check (EC 5) :

stress and stability verification of timber members according to Eurocode 5, serviceability check including creep


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INTRODUCTION This verification report contains a series of benchmarks for the design modules of ESA-Prima Win. At least one relevant example of each module is checked and verified with results from the literature, with analytical results or with the result of a manual calculation.


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1. STEEL CODE CHECK 1.1 PST.06.xx – 01 : Calculation of buckling ratios Description Calculation of buckling ratios for columns of simple frames. Project data

Section Moment of inertia

[cm4] IPE240 3890 IPE270 5790 IPE360 16270 IPE400 23130 Reference [1] Eurocode 3 : Design of steel structures

Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992 Annex E : Buckling length of compression members

[2] G. Hünersen, E. Fritzsche Stahlbau in Beispielen Berechnungspraxis nach DIN 18 800 Teil 1 bis Teil 3 Werner Verlag GmbH & Co. KG – Dusseldorf 1995


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Calculation of buckling ratio according to EC3 – Annex E Stiffness coefficients Beam

K (I/L) [cm³]

1 40.68 2 40.68 3 46.26 4 7.78 5 12.97 6 9.73 7 7.78 8 12.97 9 9.73 10 9.65 11 6.48 12 9.65 Calculation buckling ratio’s with formula (E.7) Beam

Kc K1 K2 K11 K12 K21 K22 ηηηη1 ηηηη2 l/L

1 40.68 0 0 0 46.26 0 0 0.47 1.00 2.47 4 7.78 12.97 0 0 9.65 0 0 0.68 0.00 1.37 5 12.97 9.73 7.78 0 6.48 0 9.65 0.78 0.68 2.06 6 9.73 0 12.97 0 9.65 0 6.48 0.49 0.78 1.81 Result Beam EPW EC3

Annex E % Diff. Ref.[2] % Diff. Remark

1 2.35 2.47 4.86 % 2.30 2.17 % Example 6.6.1. from Ref.[2] 2 2.35 2.47 4.86 % 2.30 2.17 % Example 6.6.1. from Ref.[2] 4 1.21 1.37 11.68 % 1.15 5.22 % Example 6.6.4. from Ref.[2] 5 1.99 2.06 3.40 % 2.03 1.97 % Example 6.6.4. from Ref.[2] 6 1.79 1.81 1.10 % 2.30 22.17 % Example 6.6.4. from Ref.[2] 13 1.00 Standard Euler case: ratio = 1.00 14 2.02 Standard Euler case: ratio = 2.00 Version ESA-Prima Win 3.20.03 Input file + calculation note PST06xx01.epw Modules 2D Frame (PRS.01) EC 3 Steel code check (PST.06.01) Author


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CVL


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1.2 PST.06.xx – 02 : Calculation of buckling ratios for crossing diagonals Description Calculation of buckling ratios of crossing diagonals according to DIN18800 Teil 2, table 15. The buckling check of member 17 is performed. Project data See Input file.

12

34

56

78

9

10

11

12

13

14

15

16

17

18

19

20

The diagonal crossings are introduced by using the input option <Cross-Links>. The column sections are the cold formed RHS section SC140/140/8. The diagonal sections are the cold formed RHS section AC100/80/6. The weak axis of this section is in the calculation plane. Reference [1] DIN18800 Teil 2

Stahlbauten : Stabilitätsfälle, Knicken von Stäben und Stabwerken

See the chapter "Manual calculation" for the detailed calculation according to this reference. Result


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Type of result Manually ESA-Prima Win % Diff Unity check "Buckling check" - No "crossing diagonals"

1.03 1.03 0 %

Unity check "Buckling check" - With "crossing diagonals"

0.82 0.82 0 %

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file PST06xx02.epw Modules 2D Frame (PRS.01) EC3 Steel code check (PST.06.01)

Author CVL Manual calculation 1 For the section AC100/80/6, the following properties are valid : A 2020 mm² Iy 2800000 mm4 Iz 1960000 mm4 iy 37.23 mm iz 31.15 mm fy 235 N/mm² When the option “Crossing diagonals” is not active, the element 17 is considered as a hinged member. strong axis weak axis system length 3610 mm 3610 mm buckling ratio 1.0 1.0 buckling length 3610 mm 3610 mm slenderness 3610/37.23 = 96.9 3610/31.15 = 115.9 reduced slenderness 96.9/93.9 = 1.03 115.9/93.9 = 1.23 imperfection curve for cold formed section

b b

reduction factor 0.58 0.46 In the element, a normal compressive force NSd = 204.7 kN is acting. The capacity for the compressive force Nb,Rd is given by


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( )

kN5.1981.1

23520200.146.0Rd,Nb

fA46.0,58.0minRd,Nb

1M

yA

=⋅

⋅⋅=

γ

⋅⋅β⋅=

The resulting unity check is 204.7/198.5 = 1.03. See also Calculation note 1. Manual calculation 1 When the option “Crossing diagonals” is active, the element 17 is supported by the tension element nr.13. The buckling length sk around the weak axis is given by :

l5.0s

lI

lI1

lN4

lZ31

ls

k

31

31

1k

⋅≥

⋅

⋅+

⋅⋅⋅⋅

−

=

In this case, we have Z 151.6 kN N 204.7 kN l 3610 mm l1 3610 mm I 1960000 mm4 I1 1960000 mm4 This results in :

l5.0s

47.0l2

7.2044

6.15131

ls

k

k

⋅≥

⋅=⋅⋅

−=

strong axis weak axis system length 3610 mm 3610 mm buckling ratio 1.0 0.5 buckling length 3610 mm 1805 mm slenderness 3610/37.23 = 96.9 1805/31.15 = 57.9 reduced slenderness 96.9/93.9 = 1.03 57.9/93.9 = 0.62 imperfection curve for cold formed section

b b

reduction factor 0.58 0.83 In the element, a normal compressive force NSd = 204.7 kN is acting. The capacity for the compressive force Nb,Rd is given by


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( )

kN2501.1

23520200.158.0Rd,Nb

fA83.0,58.0minRd,Nb

1M

yA

=⋅

⋅⋅=

γ

⋅⋅β⋅=

The resulting unity check is 204.7/250 = 0.82. See also Calculation note 2. Calculation note 1

EC3 Code Check

Macro 11 Member 17 AC100/80/6 Fe 360 Loadcase 1 1.16

Basic data EC3

partial safety factor Gamma M0 for resistance of cross-sections 1.10

partial safety factor Gamma M1 for resistance to buckling 1.10

partial safety factor Gamma M2 for resistance of net sections 1.10

Material data

yield strength fy 235.00 MPa

tension strength fu 360.00 MPa

fabrication cold formed

SECTION CHECK

Width-to-thickness ratio for webs (Tab.5.3.1. a).

ratio 10.33 on position 0.00 m

ratio

maximum ratio 1 33.00



==> Class cross-section 1

Width-to-thickness ratio for internal flanges (Tab.5.3.1. b).


ratio





The critical check is on position 1.80 m

Internal forces

NSd -204.78 kN

Vy.Sd 0.00 kN

Vz.Sd 0.60 kN

Mt.Sd -0.00 kNm

My.Sd 1.07 kNm

Mz.Sd 0.00 kNm

Only elastic check

Compression check

according to article 5.4.4. and formula (5.16)

Section classification is 3.


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Table of values

Nc.Rd 431.55 kN

unity check 0.47

Shear check (Vy)



Table of values

Vpl.Rd 110.73 kN

unity check 0.00

Shear check (Vz)



Table of values

Vpl.Rd 138.42 kN

unity check 0.00

Combined bending, axial force and shear force check

according to article Part 1-3 5.7 and formula (5.11a,5.11b,5.11c)


Table of values

sigma N 101.38 MPa

sigma Myy 19.18 MPa

sigma Mzz 0.03 MPa

Tau z 0.00 MPa

Tau z 0.00 MPa

Tau t -0.00 MPa

ro 0.00 place 8

unity check 0.56

Element satisfies the section check !

STABILITY CHECK

Buckling parameters yy zz

type non-sway non-sway

Slenderness 96.84 115.75

Reduced slenderness 1.03 1.23

Buckling curve b b

Imperfection 0.34 0.34

Reduction factor 0.58 0.46

Length 3.61 3.61 m

Buckling factor 1.00 1.00

Buckling length 3.61 3.61 m

Critical Euler load 446.43 312.50 kN

Buckling check


Table of values

Nb.Rd 198.86 kN

Beta A 1.00

unity check 1.03

Torsional-flexural buckling check

according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)

Table of values

Nb.Rd 198.86 kN

Beta A 1.00


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Table of values

Reduced slenderness 1.23

Reduction factor 0.46

sigma,cr,T 54735.22 MPa

sigma,cr,TF 154.70 MPa

Torsional buckling length 3.61 m

unity check 1.03

LTB check


Table of values

Mb.Rd 11.96 kNm

Beta W 0.82

reduction 1.00

imperfection 0.49

Mcr 385.19 kNm

LTB

LTB length 3.61 m

k 1.00

kw 1.00

C1 1.35

C2 0.55

C3 1.73

load in center of gravity

unity check =0.09

Compression and bending check


Table of values

ky 1.50

kz 1.50

muy -1.44

muz -1.73

BetaMy 1.30

BetaMz 1.30

unity check = 1.03 + 0.13 + 0.00 = 1.16

Compression, bending and LTB check


Table of values

klt 0.92

kz 1.50

mult 0.09

muz -1.73

BetaMlt 1.30

BetaMz 1.30

unity check =1.03 + 0.08 + 0.00 = 1.11

Element does NOT satisfy the stability check !

Calculation note 2 EC3 Code Check

Macro 11 Member 17 AC100/80/6 Fe 360 Loadcase 1 0.96

Basic data EC3




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Material data




SECTION CHECK



ratio





Width-to-thickness ratio for internal flanges (Tab.5.3.1. b).


ratio






Internal forces

NSd -204.78 kN

Vy.Sd 0.00 kN

Vz.Sd 0.60 kN

Mt.Sd -0.00 kNm

My.Sd 1.07 kNm

Mz.Sd 0.00 kNm

Only elastic check

Compression check



Table of values

Nc.Rd 431.55 kN

unity check 0.47

Shear check (Vy)



Table of values

Vpl.Rd 110.73 kN

unity check 0.00

Shear check (Vz)



Table of values

Vpl.Rd 138.42 kN

unity check 0.00



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Table of values

sigma N 101.38 MPa

sigma Myy 19.18 MPa

sigma Mzz 0.03 MPa

Tau z 0.00 MPa

Tau z 0.00 MPa

Tau t -0.00 MPa

ro 0.00 place 8

unity check 0.56


STABILITY CHECK





Buckling curve b b



Length 3.61 3.61 m




Remark : The buckling data around the weak axis are calculated

according to DIN 18800 T2 Tab.15 (case 1)

Table of values

Z 151.61 kN

L 3.61 m

L1 3.61 m

I 1.960000e+006 mm^4

I1 2.800000e+006 mm^4

Buckling check


Table of values

Nb.Rd 249.16 kN

Beta A 1.00

unity check 0.82



Table of values

Nb.Rd 249.16 kN

Beta A 1.00






unity check 0.82

LTB check


Table of values

Mb.Rd 11.96 kNm

Beta W 0.82

reduction 1.00


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Table of values

imperfection 0.49

Mcr 385.19 kNm

LTB

LTB length 3.61 m

k 1.00

kw 1.00

C1 1.35

C2 0.55

C3 1.73


unity check =0.09



Table of values

ky 1.50

kz 1.45

muy -1.44

muz -0.86

BetaMy 1.30

BetaMz 1.30

unity check = 0.82 + 0.13 + 0.00 = 0.96



Table of values

klt 1.00

kz 1.45

mult -0.03

muz -0.86

BetaMlt 1.30

BetaMz 1.30

unity check =0.82 + 0.09 + 0.00 = 0.91

Element satisfies the stability check !


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1.3 PST.06.01 – 01 : EC 3 Steel Code Check Tutorial Frame Description The unity check according to EC3 of members 4, 7 and macro 18 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win EC3 Steel code check. Project data See input file. Reference [1] Eurocode 3

Design of steel structures Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992

[2] Essentials of Eurocode 3 Design manual for Steel Structures in Building First edition 1991

[3] Construction Métallique et mixte acier-béton Volume 1 APK Edition Eyrolle

See the chapter "Manual calculation" for the detailed calculation according to this reference. Result

Type of result Manually ESA-Prima Win % Diff Max. unity check Member 4

0.63 0.63 0 %

Max. unity check Member 7

0.28 0.28 0 %

Max. unity check Macro 18

0.557 0.56 0 %

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060101.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01)


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Author CVL Manual calculation - Member 4 Critical check : Load Combination : 7 Section : x = 2.22 m in member 4 Beam type : HEB160

Steel : σe=235 2mmN

System length L : system length for member 4: Ly=Lz=5m Sway modes : Y-Y non-sway Z-Z non-sway The member is loaded through the shear centre. The effective length factors k and kw for LTB are taken as 1 (No end fixity and no special provision for warping fixity). Section Check Classification of the section (Table 5.3.1 EC3)

a) Width-to-thickness ratio for webs

By using Art. 3.2.2.1 (1)table 3.1. of EC3, we can determine the yield strength fy:

• Normal steel grade: Fe 360 • Nominal thickness of the element t ≤ 40 mm ⇒ Nominal value of yield strength: fy=235 N/mm2

⇒ 1f

235

y

=

=ε (Using Table 5.3.1. EC3)

The web of member is subjected to bending and compression in position x=0m. By using table 5.3.1.a of EC3, we find:

( )68

113

396138

104t

dw

=−α⋅ε⋅

≤== with 52.0ftd

N1

2

1

yw

Sd =

⋅⋅+⋅=α ⇒ WEB is CLASS 1

b) Width-to-thickness ratio for outstand flanges

By using table 5.3.1.c of EC3, we find in position x=0m:

101015.61380

tc

f=ε⋅≤== ⇒ FLANGES are CLASSE 1

The section HEB160 is a CLASS-1 section for the stability check, following the EC3 rules. Normal stress and shear stress (Art. 5.4.3.and 5.4.6. EC3)

The member 4 is subjected to a normal force NSd=-88700 N and a shear force VSd,y=20 N VSd,z=-2130N in the critical section. According to EC3 we can verify:


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N45.11600451.1

2351043.5fAN8870N

3

0M

yRd,cSd =

⋅⋅=

γ

⋅=≤−=

( ) 2ffy,v mm4598tr2t2hAtdAA =⋅⋅−⋅−−=⋅−= (Using Art.5.4.6. (2).d EC3)

( ) 2fwfz,v mm1764tr2ttb2AA =⋅⋅++⋅⋅−= (Using Art.5.4.6. (2).a EC3)

N16.56713131.1

2354598

3

fAV20V

0M

yvRd,ply,Sd =

⋅

⋅=

⋅γ

⋅=≤=

N07.21757731.1

2351764

3

fAV2130V

0M

yvRd,plz,Sd =

⋅

⋅=

⋅γ

⋅=≤−=

Unity Check : 101.0V

V and 101.0

N

N

RdPl,

z&ySd,

Rd,t

Sd ≤=≤= ⇒ Section OK for tension and shear

Combined bending, axial force and shear force

By using Art.5.4.7. (1), 5.4.8.1. (4), 5.4.9. (2) and 5.4.5.2. (1) of EC3 and table 5.17 of Essentials of EC3, we determined: NSd≤0.25Nt,Rd: low level of axial loads (Essentially by using Table 5.17 of Essential of EC3) VSd≤0.5Vpl,Rd: MNvy,Rd=My,Rd and MNVz,Rd=Mz,Rd (Essentially by using Table 5.17 of Essential of EC3)

with Nmm72.756272721.1

2351054.3fWM

5

0M

yRd,plPl,y

y =⋅⋅

=γ

⋅= (Using Art. 5.4.5.2. (1) EC3)

Nmm818.363181811.1

235107.1fWM

5

0M

yRd,plPl,z

z =⋅⋅

=γ

⋅= (Using Art. 5.4.5.2. (1) EC3)

We verify: 129.0M

M

M

M

Rd,NV

Sd,z

Rd,NV

Sd,y

zy

≤=

+

βα

(Using Art.5.4.8.1.(11) formula 5.35 EC3)

with: α=2 and β=1 for I section (Using Art. 5.4.8.1. (11) EC3) My,Sd=40650000 Nmm Mz,Sd=--600000 Nmm Stability Check: Check for bending, compression and LTB Calculation of Reduction factor in buckling mode: χy, χz, kLT

Reduction factors in buckling mode: 733.01

22yy

y

y

=λ−φ+φ

=χ (Using Art.5.5.1.2. Formula 5.46 EC3)

382.01

22zz

z

z

=λ−φ+φ



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with: • 1=ε (Using Art.5.5.1.2. EC3)

• 9.939.93f

E

y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)

• Slenderness: 836.73

AI

L

i

L

yyy ===λ (Using Art.5.5.1.2. (1) EC3)

571.123

AI

L

i

L

zzz ===λ (Using Art.5.5.1.2. (1) EC3)

• Section 1 CLASS 1A =β (Using Art.5.5.1.1. (1) EC3)

• To determine the equivalent uniform moment factor βy, βz and βMLT, we use the figure 5.5.3. in EC3 of EC3and the

moment diagram of member 4 around y and z axis between the relevant braced point. Since de moment diagram is parabolic around y axis and linear around z axis, we have:

Internal forces.Selected members : 4

0.0

Member : 4

5.0

My /kNm/

0.0

10.0

20.0

30.0

40.0

0.0

10.0

20.0

30.0

40.0

40.7

-0.1

βM,ψ=1.8 (ψ=0) βM,Q=1.3 MQmax=27.7 kNm ∆M=40.5 kNm

( ) 46.1M

M,MQ,M

Q,MMLT =β−β⋅

∆+β=β ΨΨ

46.1MLTMy =β=β

8.17.08.1Mz =Ψ⋅−=β


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• Reduced Slenderness: 786.0N

fAA

1

y

cr

yAy =β⋅

λ

λ=

⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)

315.1N

fAA

1

z

cr

yAz =β⋅

λ

λ=

⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)

• ( ) 578.0W

WW42

y,el

y,ely,plMyyy −=

−+−β⋅⋅λ=µ (Using Art.5.5.4. (1) EC3 for Class 1 section)

( ) 006.0W

WW42

z,el

z,elz,plMzzz =


• 14.015.015.0 MLTzLT =−β⋅λ⋅=µ (Using Art.5.5.4. (2) EC3)

• 01.1fA

N1k

yy

Sdy

y=

⋅⋅χ

⋅µ−= (Using Art.5.5.4. (1) EC3 for Class 1 section)

0.1fA

N1k

yz

Sdz

z=

⋅⋅χ⋅µ

−= (Using Art.5.5.4. (1) EC3 for Class 1 section)

• 0.1fA

N1k

yz

SdLTLT =

⋅⋅χ

⋅µ−= (Using Art.5.5.4. (2) EC3)

• Buckling Curve “b” around y axis and “c” around z axis (table 5.5.3. EC3)

• By 5.5.1.2. (2) EC3, we find the imperfections factor: 49.0 34.0 zy =α=α

• ( )( ) 908.02.015.0 2yyyy =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2. (1) EC3)

( )( ) 637.12.015.0 2zzzz =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2. (1) EC3)

Calculation of Reduction factor in lateral-torsional buckling mode: χLT

Reduction factor for lateral torsional buckling: 89.01

2LT

2LTLT

LT =λ−φ+φ

=χ (Art.5.5.2. (2) EC3)

with : ( )( ) 7213.02.015.0 2LTLTLTLT =λ+−λ⋅α+⋅=φ (Art.5.5.2. (2) EC3) In this expression:

Imperfection for lateral –torsional buckling: αLT=0.21 for rolled section (Art.5.5.2.(3) EC3)

245.56

th

iL

20

11C

iL9.0

25.02

f

z1

zLT =

⋅+⋅

⋅=λ (Annexe F.2. (6) Formula F.26)

where: 57.123iL

y=


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3.12th

f= and 59.1C1 = (using Annexe F table F1.2. with k=1)

598.0M

fWw

1

5.0

cr

yy,plwLT

LT =β⋅λ

λ=

⋅⋅β=λ (Using Art.5.5.2.(5) EC3)

where: βw=1 (CLASS_1 Section) (Using Art.5.5.2. (1) EC3)

Buckling Check

The design buckling resistance of member 47, using article 5.5.1.1. (1) Formula 5.45 of EC3, is:

N36.443137fA

N8870N1M

yAminRd,bSd =

γ

⋅⋅β⋅χ=≤=

Unity Check: 102.0N

N

Rd,b

Sd ≤= ⇒Section OK for buckling due to compression

Compression and bending

The design buckling resistance moment of member 47, using article 5.5.2. of EC3, is :

Nmm72.67308272fW

M1M

yy,plwLTRd,b =

γ

⋅⋅β⋅χ=

with 1w =β for class-1 section

Unity Check : 161.0M

M

Rd,b

Sd ≤= ⇒Section OK for lateral-torsional buckling

Combined Compression and bending

The internal forces for the ultimate combination 7 in the critical section x=2.22m of member 4 are: NSd=-8.87 kN Vy,Sd=0.02 kN Vz,Sd=-2.13 kN My,Sd=40.65 kNm Mz,Sd=-0.06 kNm We consider that Vy,Sd 0 precision to be neglected. Normally we should perform a check for bending and axial tension according to article 5.5.3. of EC3 but the program doesn’t take account for the beneficial effect of the tension forces. Using article 5.5.4. and formula 5.52 of EC3, we must verify:

OK 156.00.054.002.0

1f

W

Mk

fW

Mk

fA

N

1M

yz.pl

sd.zz

1M

yy.pl

sd.yy

1M

ymin

sd

⇒≤=++

≤

γ⋅⋅+

γ⋅⋅+

γ⋅⋅χ

(Using Art.5.5.4. (1) EC3)

Combined Compression, bending and LTB


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We can perform exactly the same check than previously but considering lateral-torsional buckling as a potential failure mode by using Art.5.5.4. (2) formula 5.52 of EC3:

OK 163.00.061.002.0

1f

W

Mk

fW

Mk

fA

N

1M

yz.pl

sd.zz

1M

yy.plLT

sd.yLT

1M

yz

sd

⇒≤=++

≤

γ⋅⋅+

γ⋅⋅χ⋅+

γ⋅⋅χ

(Using Art.5.5.4. (2) EC3)

Manual calculation - Member 7 Critical check : Load Combination : 5 Section : x = 3 m Beam type : IPE270


Beam length : 6 m Sway modes : Y-Y non-sway Z-Z non-sway The member is loaded through the shear centre. The effective length factors k and kw for LTB. are taken as 1 (No end fixity and no special provision for warping fixity). Section check Classification of the section (Table 5.3.1 EC3)

a) Width-to-thickness ratio for webs

By using Art. 3.2.2.1. (1) table 3.1. of EC3, we can determine the yield strength fy:

• Normal steel grade: Fe 360 • Nominal thickness of the element t ≤ 40 mm ⇒ Nominal value of yield strength: fy=235 N/mm2

⇒ 1f

235

y

=

=ε (Using Table 5.3.1. EC3)

The web of member 7 is subjected both to bending and tension in section x=0.55 m. By using table 5.3.1.a of EC3, we find:

( )95.71

113

39627.336.6

6.219t

dw

=−α⋅ε⋅

≤== where 5.0ftd

N1

2

1

yw

Sd =

⋅⋅+⋅=α ⇒ WEB is CLASSE 1

b) Width-to-thickness ratio for outstand flanges

By using table 5.3.1.c of EC3, we find for section x=0 m:

1062.62.105.67

tc

f≤== ⇒ FLANGES are CLASSE 1

The IPE 270 section is a CLASS-1 section for the stability check.


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By using Art. 5.4.7. (1), 5.4.8. (4), 5.4.9. (2) and 5.4.5.2. (1) of EC3 and table 5.17 of Essentials of EC3, we determined : NSd≤0.25Nt,Rd: low level of axial load VSd≤0.5Vpl,Rd: MNvy,Rd=My,Rd and MNVz,Rd=Mz,Rd (essentially by using Table 5.17 of Essential of EC3)

with Nmm1034000001.1

2351084.4fWM

5

0M

yRd,plPl,y

y =⋅⋅

=γ

⋅= (Using Art. 5.4.5.2. (1) EC3)

Nmm27.207227271.1

235107.9fWM

4

0M

yRd,plPl,z

z =⋅⋅

=γ

⋅= (Using Art. 5.4.5.2. (1) EC3)

We verify: 102.0M

M

M

M

Rd,NV

Sd,z

Rd,NV

Sd,y

zy

≤=

+

βα

(Using 5.4.8.1. (11) formula 5.35 EC3)

with: α=2 and β=1 for I section (Using Art. 5.4.8.1. (11) EC3) My,Sd=14338660Nmm Mz,Sd≈0 Stability Check: Check for bending, compression and L.T.B. Calculation of Reduction factor in buckling mode: χy, χz, kLT

Reduction factor in buckling mode: 902.01

2y

2yy

y =λ−φ+φ


1903.01

22zz

z

z

=λ−φ+φ

=χ (Using Art.5.5.1.2. Formula5.46 EC3)

with : • 1=ε (Using Art.5.5.1.2. EC3)

• 9.939.93f

E

y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)

• Slenderness : 42.53

AI

L

i

L

yyy ===λ (Using Art.5.5.1.2. (1) EC3)

35.198

AI

L

i

L

zzz ===λ (Using Art.5.5.1.2. (1) EC3)


• To determine the equivalent uniform factors βy, βz and βMLT, we use the figure 5.5.3. of EC3 and the moment

diagram of member 7 around y and z axis between the relevant braced point. Since the moment is have a parabolic shape around y axis and is linear around z axis, we have:


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3.1y =β

8.1z =β

3.1MLT =β (Figure 5.5.3.)

• Reduced slenderness : 568.0N

fAA

1

y

cr

yAy =β⋅

λ

λ=

⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)

11.2N

fAA

1

z

cr

yAz =β⋅

λ

λ=

⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)

• Buckling Curve “a” around y axis and “b” around z axis (Table 5.5.3. EC3)

• ( ) 666.0W

WW42

y,el

y,ely,plMyyy −=


( ) 126.0W

WW42

z,el

z,elz,plMzzz −=


• 2614.015.015.0 MLTzLT =−β⋅λ⋅=µ (Using Art.5.5.4. (1) EC3)

• 99.0fA

N1k

yy

Sdy

y=

⋅⋅χ

⋅µ−= (Using Art.5.5.4. (1) EC3 for Class 1 section)

99.0fA

N1k

yz

Sdz

z=

⋅⋅χ⋅µ

−= (Using Art.5.5.4. (1) EC3 for Class 1 section)

999.0fA

N1k

yz

SdLTLT =

⋅⋅χ

⋅µ−= (Using Art.5.5.4. (2) EC3)

• By using 5.5.1.2. (2) EC3, we find : 34.0 21.0 zy =α=α

• ( )( ) 699.02.015.0 2yyyy =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2. (1) EC3)

( )( ) 05.32.015.0 2zzzz =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2. (1) EC3)


Reduction factor for lateral-torsional buckling: 48.01

2LT

2LTLT

LT =λ−φ+φ

=χ (Art.5.5.2. (2) EC3)

with: ( )( ) 431.12.015.0 2LTLTLTLT =λ+−λ⋅α+⋅=φ (Art.5.5.2. (2) EC3) In this expression:

Imperfection for lateral-torsional buckling:αLT=0.21 for rolled section (Art.5.5.2. (3) EC3)

163.120

th

iL

20

11C

iL9.0

25.02

f

z1

zLT =

⋅+⋅

⋅=λ (Annexe F.2. (6) Formula F.26)


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where: 35.198iL

y=

5.26th

f= and 132.1C1 = (using Annexe F table F1.2. with k=1)

279.1M

fWw

1

5.0

cr

yy,plwLT

LT =β⋅λ

λ=

⋅⋅β=λ (Using Art.5.5.2.(5) EC3)

where: βw=1 (CLASS_1 Section) (Using Art.5.5.2. (1) EC3) Buckling

To improve the security of the stability check, we consider that NSd=0 since the element is in tension and not in compression. The first term of is thus equal to 0. Compression and bending

The design buckling resistance moment of member 47, using article 5.5.2. of EC3, is:

Nmm49632000fW

M1M

yy,plwLTRd,b =

γ

⋅⋅β⋅χ=

with 1w =β for class-1 section


M

Rd,b

Sd ≤= ⇒Section OK for lateral-torsional buckling


The internal forces for the ultimate combination 4 in the critical section x=3 m are: NSd=199.38N Vz,Sd=2250.05N My,Sd=14338660Nmm We consider that Vy,Sd and Mz,Sd approach the 0 precision to be neglected. Normally we should perform a check for bending and axial tension according to article 5.5.3. of EC3 but the program doesn’t take account for the beneficial effect of the tension forces. Using article 5.5.4. and formula 5.52 of EC3, we must verify:

OK 1137.00.0137.00.0

1f

W

Mk

fW

Mk

fA

N

1M

yz.pl

sd.zz

1M

yy.pl

sd.yy

1M

ymin

sd

⇒≤=++

≤

γ⋅⋅+

γ⋅⋅+

γ⋅⋅χ

(Using Art.5.5.4. (1) EC3)

Combined Compression, bending and LTB

We can perform exactly the same check than previously but considering lateral-torsional buckling as a potential failure mode by using Art.5.5.4. (2) formula 5.52 of EC3:


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OK 1286.00.0286.00.0

1f

W

Mk

fW

Mk

fA

N

1M

yz.pl

sd.zz

1M

yy.plLT

sd.yLT

1M

yz

sd

⇒≤=++

≤

γ⋅⋅+

γ⋅⋅χ⋅+

γ⋅⋅χ

(Using Art.5.5.4. (2) EC3)

Manual calculation - Macro 18 Critical check : Load Combination : 6 Section : x = 0 m in member 47 Beam type : T120/120/13


System length L : macro 18 is made of member 41 to 52 System length for member 41 to 52:

• Ly=1 m(member length) • Lz=6 m(Lateral restraint by middle-rafter) • LLTB=6 m(Lateral restraint by middle-rafter)

Sway modes: Y-Y non-sway Z-Z non-sway The macro is loaded through the shear centre. The effective length factors k and kw for LTB are taken as 1 (No end fixity and no special provision for warping fixity). Section check Classification of the section (Table 5.3.1 EC3)

Since EC3 Table 5.3.1 gives no formulas for T-section, we have to classify the T-section as a Class-3 section. This simplification is also done is the program. Normal stress and shear stress (Art. 5.4.3.and 5.4.6. EC3)

The member 47, the critical member of macro 18, is subjected to a normal force NSd=-38333N and shear forces VSd,y=-1.39N (can be neglected) VSd,z=-461.01N in the critical section. According to EC3 we can verify:

N63.6323631.1

2351096.2fAN38333N

3

0M

yRd,cSd =

⋅⋅=

γ

⋅=≤−=

098.19241531.1

23513120

3

fAV0V

0M

yvRd,ply,Sd =

⋅

⋅⋅=

⋅γ

⋅=≤≅

( )N12.17157013

31.1

2351313120

3

fAV01.461V

0M

yvRd,plz,Sd =⋅

⋅

⋅⋅−=

⋅γ

⋅=≤−=

Unity Check : 10.0V

V and 10604.0

N

N

RdPl,

z&ySd,

Rd,t

Sd ≤≅≤= ⇒ Section OK for tension and shear



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By using EC3 Part 1-3 Art. 5.7. we can verify that the Von Mises criteria is respected. To simplify the checking, we’ll consider only stress due to compression and due to bending:

63.213f

238.2628.1395.12

65.851066.3

27.569800

1096.2

72.38265

vI

M

A

N

0M

y

63

max

y

ySdMN y

=γ

≤=+=⋅

+⋅

=+=σ+σ

Stability Check : Check for bending, compression and L.T.B. Calculation of Reduction factor in buckling mode: χy, χz, kLT

To calculate the first and the second term, we have:

Reduction factors in buckling mode: 948.01

22yy

y

y

=λ−φ+φ


123.01

22zz

z

z

=λ−φ+φ


with: • 1=ε (Using Art.5.5.1.2. EC3)

• 9.939.93f

E

y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)


AI

L

i

L

y

y

yy ===λ (Using Article 5.5.1.2. (1) EC3)

673.244

AI

L

i

L

z

z

zz ===λ (Using Article 5.5.1.2. (1) EC3)

• Section 3 CLASS 1A =β (Using Article 5.5.1.1. (1) EC3)

• To determine the equivalent uniform moment factors βy βz and βML, we use the figure 5.5.3. of EC3 and the moment

diagram of member 47 around y and z axis between the relevant braced point. Since the moment diagram is linear, we have:

4.1

8.1M

M7.08.17.08.1

859.13.569800

6.480557.08.1

,M

,M7.08.17.08.1

MLT

47BeginMem,z

47EndMem,zMz

47BeginMemy

47EndMemyMy

=β

=

⋅−=Ψ⋅−=β

=

−⋅−=

⋅−=Ψ⋅−=β

• Reduce Slenderness: 302.0N

fAA

1

y

cr

yAy =β⋅

λ

λ=

⋅⋅β=λ (Using Art. 5.5.1.2. (1) EC3)

605.2N

fAA

1

z

cr

yAz =β⋅

λ

λ=

⋅⋅β=λ (Using Art. 5.5.1.2. (1) EC3)


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• ( ) 0851.042 Myyy −=−β⋅⋅λ=µ (Using Art. 5.5.4. (3) EC3 for Class 3 section)

( ) 042.142 Mzzz −=−β⋅⋅λ=µ (Using Art 5.5.4. (3) EC3 for Class 3 section)

• 397.015.015.0 MLTzLT =−β⋅λ⋅=µ (Using Art 5.5.4. (2) EC3 for Class 3 section)

• 004.1fA

N1k

yy

Sdyy =

⋅⋅χ

⋅µ−= (Using Art. 5.5.4. (1&3) EC3 for Class 3 section)

466.1fA

N1k

yz

Sdzz =

⋅⋅χ

⋅µ−= (Using Art. 5.5.4. (1&3) EC3 for Class 3 section)

• 822.0fA

N1k

yz

SdLTLT =

⋅⋅χ

⋅µ−= (Using Art. 5.5.4. (2) EC3 for Class 3 section)

• Buckling Curve “c” (table 5.5.3. EC3)

• By Article 5.5.1.2. (2) Table 5.5.1. of EC3, we find the imperfections factor: 49.0=α

• ( )( ) 57.02.015.0 2yyy =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2.(1) EC3)

( )( ) 482.42.015.0 2zzz =λ+−λ⋅α+⋅=φ (Using Art. 5.5.1.2.(1) EC3)


Reduction factor for lateral torsional buckling: 923.01

2LT

2LTLT

LT =λ−φ+φ

=χ (Art.5.5.2.(2) EC3)

with : ( )( ) 658.02.015.0 2LTLTLTLT =λ+−λ⋅α+⋅=φ (Art. 5.5.2. (2) EC3) In this expression:

Imperfection for lateral–torsional buckling: αLT=0.21 for rolled section (Art. 5.5.2.(3) EC3)

88.1C1 = (using Annexe F1.2. (6) with k=1 and Table F1.1.)

Iw=0 for T section

Nmm49.38919458IE

IGL

I

I

L

IEM

5.0

z2

t2LTB

z

w2LTB

z2

cr =

⋅⋅π

⋅⋅+⋅

⋅⋅π= (Using Annexe F F1.1.(1) Formula F.1 EC3)

5035.0M

fW5.0

cr

yy,plwLT =

⋅⋅β=λ (Using Art.5.5.2.(5) EC3)

where: βw= 443.0W

W

y,pl

y,el= (CLASS_3 Section) (Art. 5.5.2. (1) EC3)

Buckling Check

The design buckling resistance of member 47, using article 5.5.1.1. of EC3, is:


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N727.77780fA

N72.38265N1M

yAminRd,bSd =

γ

⋅⋅β⋅χ=≤=

Unity Check : 1491.0N

N

Rd,b

Sd ≤= ⇒ Section OK for buckling due to compression

Lateral torsional buckling check

The design buckling resistance moment of member 47, using article 5.5.2. of EC3, is:

Nmm811.8282571fW

M1M

yy,plwLTRd,b =

γ

⋅⋅β⋅χ=

with 443.0W

W

y,pl

y,elw ==β for class-3 section


M

Rd,b

Sd ≤= ⇒ Section OK for lateral torsional buckling


The internal forces for the ultimate combination 6 in the critical section x=0 m of member 47 are: NSd=-38265.72N Vy,Sd=-1.39 Vz,Sd=-461.01N My,Sd=569800.27Nmm Mz,Sd=-9409.25Nmm Normally we should perform a check for bending and axial tension according to article 5.5.3. of EC3 but the program doesn’t take account for the beneficial effect of the tension forces. To perform the combined compression and bending check, we must verify:

OK 1 0.5570.0021 0.063 4919.0

1f

W

Mk

fW

Mk

fA

N

1M

yz.el

sd.zz

1M

yy.el

sd.yy

1M

ymin

sd

⇒≤=++

≤

γ⋅⋅+

γ⋅⋅+

γ⋅⋅χ

(Using Art. 5.5.4. (3) EC3)

Combined compression, bending and LTB

We can perform exactly the same check than previously but considering lateral-torsional buckling as a potential failure mode by using Art. 5.5.4. (4) formula 5.54:

OK 1 0.550.0021 0.056 4919.0

1f

W

Mk

fW

Mk

fA

N

1M

yz.el

sd.zz

1M

yy.elLT

sd.yLT

1M

yz

sd

⇒≤=++

≤

γ⋅⋅+

γ⋅⋅χ⋅+

γ⋅⋅χ

(Using Art. 5.5.4. (4) EC3)


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Calculation note - Member 4

EC3 Code Check

Macro 2 Member 4 HEB160 S 235 Ult. comb 7 0.63

Basic data EC3




Material data



fabrication rolled

SECTION CHECK



ratio





Width-to-thickness ratio for outstand flanges (Tab.5.3.1. c).


ratio






Internal forces

NSd -8.87 kN

Vy.Sd 0.02 kN

Vz.Sd -2.13 kN

Mt.Sd -0.00 kNm

My.Sd 40.65 kNm

Mz.Sd -0.06 kNm

Compression check



Table of values

Nc.Rd 1160.05 kN

unity check 0.01

Shear check (Vy)



Table of values

Vpl.Rd 567.13 kN

unity check 0.00


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Shear check (Vz)



Table of values

Vpl.Rd 217.58 kN

unity check 0.01




Table of values

MNVy.Rd 75.63 kNm

MNVz.Rd 36.32 kNm

alfa 2.00 beta 1.00

unity check 0.29


STABILITY CHECK


type sway non-sway



Buckling curve b c



Length 5.00 5.00 m




Buckling check


Table of values

Nb.Rd 443.38 kN

Beta A 1.00

unity check 0.02



Table of values

Nb.Rd 486.45 kN

Beta A 1.00






unity check 0.02

LTB check


Table of values

Mb.Rd 66.72 kNm

Beta W 1.00

reduction 0.88

imperfection 0.21

Mcr 216.35 kNm


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LTB

LTB length 5.00 m

k 1.00

kw 1.00

C1 1.47

C2 0.25

C3 2.64


unity check =0.61



Table of values

ky 1.01

kz 1.00

muy -0.71

muz 0.01

BetaMy 1.46

BetaMz 1.80

unity check = 0.02 + 0.54 + 0.00 = 0.56



Table of values

klt 1.00

kz 1.00

mult 0.14

muz 0.01

BetaMlt 1.46

BetaMz 1.80

unity check =0.02 + 0.61 + 0.00 = 0.63



Macro 4 Member 7 IPE270 S 235 Ult. comb 5 0.28

Basic data EC3




Material data



fabrication rolled

SECTION CHECK



ratio








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ratio






Internal forces

NSd 0.20 kN

Vy.Sd 0.00 kN

Vz.Sd 2.25 kN

Mt.Sd 0.00 kNm

My.Sd 14.34 kNm

Mz.Sd -0.00 kNm

Normal force check


Table of values

Nt.Rd 980.59 kN

unity check 0.00

Shear check (Vz)



Table of values

Vpl.Rd 272.50 kN

unity check 0.01




Table of values

MNVy.Rd 103.40 kNm

MNVz.Rd 20.72 kNm

alfa 2.00 beta 1.00

unity check 0.02


STABILITY CHECK


type sway non-sway



Buckling curve a b



Length 6.00 6.00 m




LTB check


Table of values

Mb.Rd 51.47 kNm


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Table of values

Beta W 1.00

reduction 0.50

imperfection 0.21

Mcr 72.51 kNm

LTB

LTB length 6.00 m

k 1.00

kw 1.00

C1 1.13

C2 0.45

C3 0.53


unity check =0.28



Table of values

ky 1.00

kz 1.00

muy -0.67

muz -0.29

BetaMy 1.30

BetaMz 1.80

unity check = 0.00 + 0.14 + 0.00 = 0.14



Table of values

klt 1.00

kz 1.00

mult 0.26

muz -0.29

BetaMlt 1.30

BetaMz 1.80

unity check =0.00 + 0.28 + 0.00 = 0.28


Calculation note - Macro 18 EC3 Code Check

Macro 18 Member 47 T120/120/13 S 235 Ult. comb 6 0.56

Basic data EC3




Material data



fabrication rolled

SECTION CHECK




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ratio






Internal forces

NSd -38.33 kN

Vy.Sd -0.00 kN

Vz.Sd -0.46 kN

Mt.Sd -0.00 kNm

My.Sd 0.57 kNm

Mz.Sd 0.01 kNm

Compression check



Table of values

Nc.Rd 632.36 kN

unity check 0.06

Shear check (Vy)



Table of values

Vpl.Rd 192.42 kN

unity check 0.00

Shear check (Vz)



Table of values

Vpl.Rd 171.57 kN

unity check 0.00




Table of values

sigma N 12.95 MPa

sigma Myy 13.28 MPa

sigma Mzz 0.02 MPa

Tau z -0.00 MPa

Tau z 0.00 MPa

Tau t 0.00 MPa

ro 0.00 place 10

unity check 0.12


STABILITY CHECK





Buckling curve c c



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Length 1.00 6.00 m




Buckling check


Table of values

Nb.Rd 77.77 kN

Beta A 1.00

unity check 0.49



Table of values

Nb.Rd 81.43 kN

Beta A 1.00






unity check 0.47

LTB check


Table of values

Mb.Rd 8.28 kNm

Beta W 1.00

reduction 0.92

imperfection 0.21

Mcr 38.92 kNm

LTB

LTB length 6.00 m

k 1.00

kw 1.00

C1 1.88

C2 0.00

C3 0.94


unity check =0.07



Table of values

ky 1.01

kz 1.49

muy -0.09

muz -1.10

BetaMy 1.86

BetaMz 1.79

unity check = 0.49 + 0.06 + 0.00 = 0.56



Table of values


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Table of values

klt 0.82

kz 1.49

mult 0.40

muz -1.10

BetaMlt 1.40

BetaMz 1.79

unity check =0.49 + 0.06 + 0.00 = 0.55



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1.4 PST.06.01 – 02 : EC 3 Steel Code Check – Warping check Description The elastic stresses, inclusive the warping check, is compared with literature results. Project data See input files. Reference [1] Eurocode 3


[2] ENV 1993-1-3:1996 Eurocode 3 : Design of steel structures Part 1-3 : General rules – Supplementary rules for cold formed thin gauge members and sheeting CEN 1996

[3] Schneider Bautabellen mit Berechnungshinweisen und Beispielen 7. Auflage Werner-Verlag, 1986

Result Ref.[3], pp.8.14 EPW % Diff. Mx = 1500 kNcm Mxs = 15 kNm 0 % Mwa = -1.32 105 kNcm Mw = 13.20 kNm 0.08 % σT = 10.4 kN/cm² sigma warping = -104.12 N/mm² 0.12 % max σ =120 N/mm² composed stress = -119.81 N/mm² 0.16 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060102.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL


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Calculation note EC3 Code Check

Macro 1 Member 1 HEM280 Fe 360 Loadcase 1 0.51

Basic data EC3




Material data



fabrication rolled

SECTION CHECK



ratio







ratio






Internal forces

NSd 0.00 kN

Vy.Sd 0.00 kN

Vz.Sd 20.00 kN

Mt.Sd -15.00 kNm

My.Sd -40.00 kNm

Mz.Sd 0.00 kNm

Warning : The unity check for pure torsion is 0.49 for Loadcase 1.

Shear check (Vz)



Table of values

Vpl.Rd 975.04 kN

unity check 0.02

Stress check (incl. warping and torsional moment)

according to article ENV 1993-1-3 : 5.7

Warping fixed at begin beam. 1

Warping free at end beam 1


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x(m) Mxp(kNm) Mxs(kNm) Mw(kNm2)

0.00 0.00 15.00 -13.20

0.20 2.91 12.09 -10.50

0.40 5.22 9.78 -8.32

0.60 7.04 7.96 -6.55

0.80 8.48 6.52 -5.11

1.00 9.58 5.42 -3.92

1.20 10.43 4.57 -2.93

1.40 11.04 3.96 -2.08

1.60 11.46 3.54 -1.33

1.80 11.70 3.30 -0.65

2.00 11.78 3.22 0.00

Table of values

Mxp (St.Venant Torque) 0.00 kNm

Mxs (warping torque) 15.00 kNm

Mw (bimoment) -13.20 kNm2

unity check 0.51

Direct stress check (5.11a)

sigma N 0.00 MPa

sigma Myy -15.69 MPa

sigma Mzz 0.00 MPa

sigma Warping -104.12 MPa

total stress -119.81 MPa

unity check 0.51

Shear stress check (5.11b)

Tau y 0.00 MPa

Tau z 0.00 MPa

Tau t 0.00 MPa

tau Warping 8.52 MPa

total stress 8.52 MPa

unity check 0.06

Composed stress check (5.11c)

sigma N 0.00 MPa


sigma Mzz 0.00 MPa


Tau y 0.00 MPa

Tau z 0.00 MPa

Tau t 0.00 MPa


Composed stress 119.81 MPa

unity check 0.46


STABILITY CHECK


type non-sway sway



Buckling curve b c



Length 2.00 2.00 m




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LTB check


Table of values

Mb.Rd 632.36 kNm

Beta W 1.00

reduction 1.00

imperfection 0.21

Mcr 21788.32 kNm

LTB

LTB length 2.00 m

k 1.00

kw 1.00

C1 1.88

C2 0.00

C3 0.94


unity check =0.06



Table of values

ky 1.00

kz 1.00

muy 0.11

muz 0.30

BetaMy 1.80

BetaMz 1.80

unity check = 0.00 + 0.06 + 0.00 = 0.06



Table of values

klt 1.00

kz 1.00

mult 0.01

muz 0.30

BetaMlt 1.80

BetaMz 1.80

unity check =0.00 + 0.06 + 0.00 = 0.06



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[3] Dietrich von Berg Krane und Kranbahnen – Berechnung Konstruktion Ausführung B.G. Teubner, Stuttgart 1988

Result Ref.[3], pp.130 EPW % Diff. Mxw = 500 kNcm Mxs = 5 kNm 0 % Mw = 6.17 kNm² Mw = 6.19 kNm² 0.32 % σwxx = 12.9 kN/cm² sigma warping = 129.05 N/mm² 0.04 %

τS =0.68 kN/cm² tau warping = 6.78 N/mm² 0.29 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060103.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL Calculation note


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EC3 Code Check

Macro 1 Member 1 HEB260 Fe 360 Loadcase 1 0.55

Basic data EC3




Material data



fabrication rolled

SECTION CHECK


Internal forces

NSd 0.00 kN

Vy.Sd 0.00 kN

Vz.Sd 0.00 kN

Mt.Sd -5.00 kNm

My.Sd 0.00 kNm

Mz.Sd 0.00 kNm




Warping free at begin beam 1


x(m) Mxp(kNm) Mxs(kNm) Mw(kNm2)

0.00 4.09 0.91 0.00

0.60 3.98 1.02 0.57

1.20 3.64 1.36 1.27

1.80 2.98 2.02 2.27

2.40 1.85 3.15 3.79

3.00 0.00 5.00 6.19

3.00 -0.00 -5.00 6.19

3.60 -1.85 -3.15 3.79

4.20 -2.98 -2.02 2.27

4.80 -3.64 -1.36 1.27

5.40 -3.98 -1.02 0.57

6.00 -4.09 -0.91 0.00

Table of values

Mxp (St.Venant Torque) 0.00 kNm

Mxs (warping torque) 5.00 kNm

Mw (bimoment) 6.19 kNm2

unity check 0.55


sigma N 0.00 MPa

sigma Myy 0.00 MPa

sigma Mzz 0.00 MPa




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unity check 0.55


Tau y 0.00 MPa

Tau z 0.00 MPa

Tau t 0.00 MPa



unity check 0.05


sigma N 0.00 MPa

sigma Myy 0.00 MPa

sigma Mzz 0.00 MPa


Tau y 0.00 MPa

Tau z 0.00 MPa

Tau t 0.00 MPa



unity check 0.50



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[3] Kaltprofile 3. Auflage Verlag Stahleisen mbH, Düsseldorf 1982

Result Ref.[3], pp.68 EPW % Diff. MwT = 128.7 kNcm² Mw =130.34 kNcm² 1.27 % σB = 4.40 kN/cm² sigma Myy = 48.32 N/mm² 9.81 %

σw = 4.24 kN/cm² sigma warping = 42.91 N/mm² 1.20 % σ = 8.64 kN/cm² total stress = 91.23 N/mm² 5.59 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060104.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL


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Calculation note

EC3 Code Check

Macro 1 Member 1 CC100/40/3 Fe 360 Loadcase 1 0.43

Basic data EC3




Material data




SECTION CHECK


ratio 32.33 on position 18.00 cm

ratio







ratio





The critical check is on position 90.00 cm

Internal forces

NSd 0.00 kN

Vy.Sd 0.00 kN

Vz.Sd -0.00 kN

Mt.Sd -0.00 kNcm

My.Sd 81.00 kNcm

Mz.Sd 0.00 kNcm




Warping free at begin beam 1


x(cm) Mxp(kNcm) Mxs(kNcm) Mw(kNcm2)

0.00 -2.03 -3.37 0.00

18.00 -1.90 -2.42 -51.74

36.00 -1.58 -1.66 -88.14

54.00 -1.13 -1.03 -112.20

72.00 -0.58 -0.50 -125.89

90.00 -0.00 0.00 -130.34

108.00 0.58 0.50 -125.89

126.00 1.13 1.03 -112.20


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144.00 1.58 1.66 -88.14

162.00 1.90 2.42 -51.74

180.00 2.03 3.37 0.00

Table of values

Mxp (St.Venant Torque) -0.00 kNcm

Mxs (warping torque) 0.00 kNcm

Mw (bimoment) -130.34 kNcm2

unity check 0.43


sigma N 0.00 MPa

sigma Myy 48.32 MPa

sigma Mzz 0.00 MPa

sigma Warping 42.91 MPa


unity check 0.43


Tau y 0.00 MPa

Tau z 0.00 MPa

Tau t 0.00 MPa



unity check 0.00


sigma N 0.00 MPa

sigma Myy 48.32 MPa

sigma Mzz 0.00 MPa

sigma Warping 42.91 MPa

Tau y 0.00 MPa

Tau z 0.00 MPa

Tau t 0.00 MPa



unity check 0.39


STABILITY CHECK


type non-sway sway



Buckling curve b b



Length 180.00 180.00 cm


Buckling length 180.00 180.00 cm


LTB check


Table of values

Mb.Rd 232.11 kNcm


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Table of values

Beta W 1.00

reduction 0.67

imperfection 0.34

Mcr 481.80 kNcm

LTB

LTB length 180.00 cm

k 1.00

kw 1.00

C1 1.13

C2 0.45

C3 0.53


unity check =0.35



Table of values

ky 1.00

kz 1.00

muy -0.70

muz -0.54

BetaMy 1.30

BetaMz 1.80

unity check = 0.00 + 0.23 + 0.00 = 0.23



Table of values

klt 1.00

kz 1.00

mult 0.11

muz -0.54

BetaMlt 1.30

BetaMz 1.80

unity check =0.00 + 0.35 + 0.00 = 0.35



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[3] Stahl im Hochbau 14. Auglage Band I/ Teil 2 Verlag Stahleisen mbH, Düsseldorf 1986

Comparison Ref.[3], pp.713 EPW % Diff. Mxs = 14.5 kNcm² Mxs =14.48 kNcm² 0 % σx = 9.26 kN/cm² sigma Myy = -92.59 N/mm² 0 %

σx’ = 3.03 kN/cm² sigma warping = -26.94 N/mm² 11.08 % σv = 12.30 kN/cm² composed stress = 120.11 N/mm² 2.35 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060105.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL Calculation note


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EC3 Code Check

Macro 1 Member 1 UNP140 Fe 360 Loadcase 1 0.51

Basic data EC3




Material data



fabrication rolled

SECTION CHECK



ratio







ratio






Internal forces

NSd 0.00 kN

Vy.Sd 0.00 kN

Vz.Sd 4.00 kN

Mt.Sd 14.48 kNcm

My.Sd -800.00 kNcm

Mz.Sd 0.00 kNcm


Shear check (Vz)



Table of values

Vpl.Rd 138.28 kN

unity check 0.03



Warping fixed at begin beam. 1




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0.00 0.00 -14.48 448.86

20.00 -6.88 -7.60 235.46

40.00 -10.50 -3.98 123.51

60.00 -12.39 -2.09 64.78

80.00 -13.38 -1.10 33.97

100.00 -13.90 -0.58 17.80

120.00 -14.18 -0.30 9.30

140.00 -14.32 -0.16 4.80

160.00 -14.39 -0.09 2.38

180.00 -14.42 -0.06 0.98

200.00 -14.43 -0.05 0.00

200.00 -14.43 -0.05 0.00

Table of values

Mxp (St.Venant Torque) 0.00 kNcm

Mxs (warping torque) -14.48 kNcm

Mw (bimoment) 448.86 kNcm2

unity check 0.51


sigma N 0.00 MPa


sigma Mzz 0.00 MPa



unity check 0.51


Tau y 0.00 MPa

Tau z 3.68 MPa

Tau t 0.00 MPa



unity check 0.05


sigma N 0.00 MPa


sigma Mzz 0.00 MPa


Tau y 0.00 MPa

Tau z 3.68 MPa

Tau t 0.00 MPa



unity check 0.46


STABILITY CHECK


type non-sway sway



Buckling curve c c



Length 200.00 200.00 cm



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LTB check


Table of values

Mb.Rd 1574.87 kNcm

Beta W 1.00

reduction 0.85

imperfection 0.21

Mcr 4287.03 kNcm

LTB


k 1.00

kw 1.00

C1 1.88

C2 0.00

C3 0.94


unity check =0.51



Table of values

ky 1.00

kz 1.00

muy -0.11

muz -0.99

BetaMy 1.80

BetaMz 1.80

unity check = 0.00 + 0.43 + 0.00 = 0.43



Table of values

klt 1.00

kz 1.00

mult 0.52

muz -0.99

BetaMlt 1.80

BetaMz 1.80

unity check =0.00 + 0.51 + 0.00 = 0.51



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1.8 PST.06.01 – 06 : EC 3 Steel Code Check – Torsional buckling check and Shear buckling check for cold formed sections Description The torsional buckling check and the shear buckling check are manually calculated, according to the regulations given in Ref.[2]. Project data See input files. Reference [1] Eurocode 3



See the chapter "Manual calculation" for a detailed calculation according to this reference. Result

Type of result Manually ESA-Prima Win % Diff Unity check LC 1 0.36 0.36 0 % Unity check LC 2 0.144 0.14 0 %

Version ESA-Prima Win 3.20.03 Input file + calculation note PST060106.epw Modules 3D Frame (PRS.11) EC3 Steel code check (PST.06.01) Author CVL Manual calculation - 1

The section CC120/40/3 is checked. The following properties are used : Ag 620 mm²


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iy 45.0 mm iz 14.0 mm y0 28.3 mm i0 55.0 mm E 210000 N/mm² G 80769 N/mm² It 1962 mm4 Cm 3.98 108 mm6 lT 2000 mm ly 1470 mm sw 117 mm t 3 mm This section is checked with the following geometry :

The section is classified in section class 3. For load case 1, the torsional buckling and torsional flexural buckling is checked (See Ref.[2], part 6.2.3) :


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( ) ( )[ ]

( ) ( )[ ]

116.10.1188

235f

²mm

N188),min(

²mm

N1881941942735.04²19419421941942

735.02

1

4²2

1

735.0²0.55

3.281²

i

y1

²mm

N1942

²45

1470210000²

²i

l

E²

²mm

N194

2000

e98.3210000²196280769

3032620

1

l

EC²GI

iA

1

²mm3032yiii

Acr

yb

TF,crT,crcr

TF,cr

T,cry,crT,cry,crT,cry,crTF,cr

0

0

y

yy,cr

T,cr

2

8

2T

mt2

0gT,cr

20

2z

2y

20

==βσ

=λ

=σσ=σ

=⋅⋅⋅−+−+⋅

=σ

σβσ−σ+σ−σ+σβ

=σ

=

−=

−=β

=

⋅π=

π=σ

=σ

⋅⋅π+⋅

⋅=

π+=σ

=++=

With the reduced slenderness and the buckling curve b, the reduction factor χ=0.53 is found. This results in the design buckling resistance Nb,Rd

kN2.701.1

620235153.0AfRd,Nb

1M

gyA =⋅⋅⋅

=γ

⋅⋅β⋅χ=

The unity check is 25/70.2 =0.36. See also calculation note 1. Manual calculation - 2 For load case 2, the shear buckling is checked according to Ref.[2] part 5.8. The relative web slenderness is

451.0210000

235

3

117346.0

E

f

t

s346.0 ybw

w

_

=⋅=⋅=λ


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The shear buckling strength fbv, is given by

²mm

N249

451.0

23548.0

f48.0f

w

_

ybbv ==

λ=

The shear buckling resistance Vb,Rd is given by

kN73.791.1

2493117ftsV

1M

bvwRd,b =

⋅⋅=

γ

⋅⋅=

The plastic shear resistance Vpl,Rd is given by

kN29.4331.1

2353117

3

ftsV

0M

ywRd,pl =

⋅⋅=

γ

⋅⋅=

The unity check is 6.24/43.29=0.144. See also calculation note 2. Calculation note 1

EC3 Code Check

Macro 1 Member 1 CC120/40/3 S 235 Loadcase 1 0.36

Basic data EC3




Material data




SECTION CHECK



ratio







ratio







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Internal forces

NSd -25.00 kN

Vy.Sd 0.00 kN

Vz.Sd 0.00 kN

Mt.Sd 0.00 kNcm

My.Sd 0.00 kNcm

Mz.Sd 0.00 kNcm

Compression check



Table of values

Nc.Rd 132.45 kN

unity check 0.19




Table of values

sigma N 40.32 MPa

sigma Myy 0.00 MPa

sigma Mzz 0.00 MPa

ro 0.00 place 15

unity check 0.19


STABILITY CHECK





Buckling curve b b



Length 200.00 200.00 cm




Buckling check


Table of values

Nb.Rd 69.87 kN

Beta A 1.00

unity check 0.36



Table of values

Nb.Rd 69.64 kN

Beta A 1.00





Torsional buckling length 200.00 cm

unity check 0.36


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Table of values

ky 1.03

kz 1.14

muy -0.14

muz -0.45

BetaMy 1.80

BetaMz 1.80

unity check = 0.36 + 0.00 + 0.00 = 0.36



Table of values

klt 0.95

kz 1.14

mult 0.15

muz -0.45

BetaMlt 1.80

BetaMz 1.80

unity check =0.36 + 0.00 + 0.00 = 0.36


Calculation note 2

EC3 Code Check

Macro 1 Member 1 CC120/40/3 S 235 Loadcase 2 0.94

Basic data EC3




Material data




SECTION CHECK



ratio







ratio






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Internal forces

NSd 0.00 kN

Vy.Sd 0.00 kN

Vz.Sd -6.24 kN

Mt.Sd 0.00 kNcm

My.Sd -247.80 kNcm

Mz.Sd 0.00 kNcm

Shear check (Vz)

according to article ENV 1993-1-3 : 5.8 and formula (5.13) (5.14)


Table of values

VRd (Sum min(Vpl,Rd,Vb,Rd)) 43.29 kN

unity check 0.14




Table of values

sigma N 0.00 MPa

sigma Myy 115.05 MPa

sigma Mzz 0.00 MPa

ro 0.00 place 13

unity check 0.54


STABILITY CHECK





Buckling curve b b



Length 200.00 200.00 cm




LTB check


Table of values

Mb.Rd 263.94 kNcm

Beta W 1.00

reduction 0.59

imperfection 0.34

Mcr 480.20 kNcm

LTB


k 1.00

kw 1.00

C1 1.58

C2 0.66

C3 2.64


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unity check =0.94



Table of values

ky 1.00

kz 1.00

muy -0.36

muz -0.45

BetaMy 1.48

BetaMz 1.80

unity check = 0.00 + 0.55 + 0.00 = 0.55



Table of values

klt 1.00

kz 1.00

mult 0.10

muz -0.45

BetaMlt 1.48

BetaMz 1.80

unity check =0.00 + 0.94 + 0.00 = 0.94



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1.9 PST.06.01 – 07 : Example Code Check and Connections according to EC3 : Design of an industrial type building Description The example is based on the illustration given in Ref.[1] :

Chapter 12 : Worked Example 3 Design of an industrial type building

The example is calculated using EPW release 3.1. The results from EPW are printed in italics. The member design is based on ref.[2]. The connection design is based on ref.[3]. The following possibilities of EPW are illustrated : • the use of haunched sections in the analysis model • the automatic generation of SLS and ULS combinations according to EC3 • the stability analysis for the determination of the elastic critical load ratio • the implementation of the global frame imperfection • the member design for class 4 sections • the calculation of the moment capacity for the connections based on the component method • the check of the required stiffness for the beam connections

Reference [1] Frame design including joint behaviour

Volume 1 ECSC Contracts n° 7210-SA/212 and 7210-SA/320 January 1997

[2] ENV 1993-1-1:1992 Eurocode 3 Design of steel structures – Part 1-1 General rules and rules for buildings

[3] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames, ENV 1993-1-1/pr A2


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Version ESA-Prima Win 3.20.03 Input file + calculation note PST060107.epw Author CVL Contents 1. Frame geometry 2. Design assumptions 3. Loadings 3.1. Basic loadings 3.2. Load combinations 4. Analysis

4.1. Linear elastic analysis 4.2. Stability calculation 4.3. Elastic analysis with local non-linearties

5. Member check

5.1. SLS check 5.2. ULS check

5.2.1. Column check 5.2.2. Beam check

6. Connection design 6.1. Bolted beam-to-column connection

6.2. Bolted plate-to-plate connection 6.3. Base plate connection


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Worked example 1. Frame geometry A two bay pinned-base pitched portal frame (with haunches) for an industrial building is considered. The dimensions of the building are the following : width (centrellines) 2 x 23.5 m height 10 m length 60.5 m The portal frames, which are at 6 m intervals, have 8 m high columns and have rafters sloped at 7.7° with a centreline ridge height of 9.5 m above ground level. Haunches are used for the joints of the rafters to the columns. Hot-rolled standard sections are used for the members : IPE550 for the columns, IPE400 for the roof beams. For the steel elements (members, haunches, endplates, stiffeners) the steel S275 is used. Material

Name

S 275

Ultimate strength 430.00 MPa

Yield design 275.00 MPa

E modulus 210000.00 MPa

Poisson coeff. 0.30

Specific weight 7850.00 kg/m^3

Extensibility 0.012 mm/m.K

List of material

Group of members :

1/7

num. Name unit weight

kg/m

length

m

weight

kg

1 IPE550 105.50 24.00 2532.10

2 IPE400 66.30 47.38 4716.28

The total weight of the structure: 7248.38 kg

Surface for painting: 117.23 m^2

Nodes

node X

m

Y

m

Z

m

1 0.000 0.000 0.000

2 0.000 0.000 8.000

3 23.500 0.000 0.000

4 23.500 0.000 8.000

5 47.000 0.000 0.000

6 47.000 0.000 8.000

7 11.750 0.000 9.500

8 35.250 0.000 9.500

Members


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macro memb node 1 node 2 length

m

Rx

deg

profile

1 1 1 2 8.00 0.00 1 - IPE550

2 2 3 4 8.00 0.00 1 - IPE550

3 3 5 6 8.00 0.00 1 - IPE550

4 4 2 7 11.85 0.00 2 - IPE400

5 5 4 7 11.85 0.00 2 - IPE400

6 6 4 8 11.85 0.00 2 - IPE400

7 7 6 8 11.85 0.00 2 - IPE400

Profiles

Figure 1: IPE550

Profile num. 1 - IPE550

Material : 47 - S 275

A 1.344000e+004 mm^2

Ay/A 0.477 Az/A 0.435

Iy 6.712000e+008 mm^4 Iz 2.668000e+007 mm^4

Iyz 2.710505e-008 mm^4 It 1.232000e+006 mm^4

Iw 1.921780e+012 mm^6

Wely 2.441000e+006 mm^3 Welz 2.541000e+005 mm^3

Wply 2.780000e+006 mm^3 Wplz 4.000000e+005 mm^3

cy 105.00 mm cz 275.00 mm

iy 223.47 mm iz 44.55 mm

dy -0.00 mm dz 0.00 mm

Type for check: I section

Height 550.00 mm Width 210.00 mm

Thickness of flange 17.20 mm Thickness of web 11.10 mm

Radius 24.00 mm

Figure 2: IPE400


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Profile num. 2 - IPE400

Material : 47 - S 275

A 8.446000e+003 mm^2

Ay/A 0.509 Az/A 0.391

Iy 2.313000e+008 mm^4 Iz 1.318000e+007 mm^4

Iyz 0.000000e+000 mm^4 It 5.108000e+005 mm^4

Iw 4.968547e+011 mm^6

Wely 1.156000e+006 mm^3 Welz 1.464000e+005 mm^3

Wply 1.308000e+006 mm^3 Wplz 2.300000e+005 mm^3

cy 90.00 mm cz 200.00 mm

iy 165.49 mm iz 39.50 mm

dy -0.00 mm dz 0.00 mm

Type for check: I section

Height 400.00 mm Width 180.00 mm

Thickness of flange 13.50 mm Thickness of web 8.60 mm

Radius 21.00 mm

Variable profile

macro cross-section length

m

Parts position alignment size[original/changed]

mm

4 3 - I + I var (IPE400,400) 1.750 5 Begin Align Z+ 400/0




Supports

support boundary node type rot

deg

flexibility

kN/m-kNm/rad

funct

1 1 XZ

2 3 XZ

3 5 XZ


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1 2 3

4 5 6 7

Figure 3: Member numbers

1

2

3

4

5

6

7 8

Figure 4: Node numbers

IPE550

IPE550

IPE550

IPE400 IPE400 IPE400 IPE400

Figure 5: Profile assignment


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Figure 6: Column and haunched beam

2. Design assumptions The structure is unbraced in its plane. In the longitudinal direction of the building, bracing is provided, so that the purlins act as out-of-plane support points to the frame. The position of the purlins will be defined and checked in 0. Several analysis were carried out : a linear elastic analysis for the serviceabililty limit states and to retrieve the critical combinations, a stability calculation for determining the critical load which leads to sway/non-sway classification ,an elastic analysis with local non-linearties for implementing the frame imperfections, used for the ultimate limit states for member check and connection check. The traditional assumption that joints are rigid is adopted. This assumption is verified. 3. Loadings 3.1. Basic loadings While the loads given are typical for a building of this type, the values should be taken as indicative. The values are taken from Ref.[1]. The following load cases are considered : load case 1 and 2 G : Self weight and dead load load case 3 and 4 W : Wind load load case 5,6,7 and 8 S : Snow load

Loadcases

Case Name coeff Description

1 Self weight 1.00 Self weight

2 Self weight (cladding + roof) 1.00 Permanent

3 Wind W1 1.00 Variable - Wind Excl.

4 Wind W2 1.00 Variable - Wind Excl.

5 Snow S1 1.00 Variable - Snow Excl.





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Loadcases num. 2 - distributed loads

memb macro bound type dx

m

exY

m

exZ

m

X beg

end

Y beg

end

Z beg

end

1 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.20

-1.20

3 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.20

-1.20

4 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.60

-1.60

5 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.60

-1.60

6 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.60

-1.60

7 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.60

-1.60

-1.2

-1.2

-1.2

-1.2

-1.6

-1.6

-1.6

-1.6

-1.6

-1.6

-1.6

-1.6

Figure 7: Load case 2



m

exY

m

exZ

m

X beg

end

Y beg

end

Z beg

end

1 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

1.80

2.22

0.00

0.00

0.00

0.00

3 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

3.12

4.15

0.00

0.00

0.00

0.00

4 force

kN/m

0.00 rel

1.00

0.00 0.00 loc

len

0.00

0.00

0.00

0.00

4.44

4.44

5 force

kN/m

0.00 rel

1.00

0.00 0.00 loc

len

0.00

0.00

0.00

0.00

3.47

3.47

6 force

kN/m

0.00 rel

1.00

0.00 0.00 loc

len

0.00

0.00

0.00

0.00

3.96

3.96

7 force

kN/m

0.00 rel

1.00

0.00 0.00 loc

len

0.00

0.00

0.00

0.00

3.86

3.86


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1.8

2.2

3.1

4.2

4.4

4.43.5

3.5

4.0

4.0

3.9

3.9




m

exY

m

exZ

m

X beg

end

Y beg

end

Z beg

end

1 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

4.28

5.70

0.00

0.00

0.00

0.00

3 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.52

0.68

0.00

0.00

0.00

0.00

4 force

kN/m

0.00 rel

1.00

0.00 0.00 loc

len

0.00

0.00

0.00

0.00

0.96

0.96

6 force

kN/m

0.00 rel

1.00

0.00 0.00 loc

len

0.00

0.00

0.00

0.00

-0.48

-0.48

7 force

kN/m

0.00 rel

1.00

0.00 0.00 loc

len

0.00

0.00

0.00

0.00

0.48

0.48

4.3

5.7

0.5

0.7

1.0

1.0

-0.5

-0.5

0.5

0.5



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m

exY

m

exZ

m

X beg

end

Y beg

end

Z beg

end

4 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-2.64

-2.64

5 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-2.64

-2.64

6 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-2.64

-2.64

7 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-2.64

-2.64

-2.6

-2.6

-2.6

-2.6

-2.6

-2.6

-2.6

-2.6




m

exY

m

exZ

m

X beg

end

Y beg

end

Z beg

end

4 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.32

-1.32

5 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-2.64

-2.64

6 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-2.64

-2.64

7 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.32

-1.32


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-1.3

-1.3

-2.6

-2.6

-2.6

-2.6

-1.3

-1.3




m

exY

m

exZ

m

X beg

end

Y beg

end

Z beg

end

4 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.32

-1.32

5 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-5.40

0.00

6 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-5.40

0.00

7 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-1.32

-1.32

-1.3

-1.3

-5.4

0.000

-5.4

0.000

-1.3

-1.3



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m

exY

m

exZ

m

X beg

end

Y beg

end

Z beg

end

4 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-5.40

0.00

5 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-5.40

0.00

6 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-5.40

0.00

7 force

kN/m

0.00 rel

1.00

0.00 0.00 glo

len

0.00

0.00

0.00

0.00

-5.40

0.00

-5.4

0.000

-5.4

0.000

-5.4

0.000

-5.4

0.000


3.2. Load combination The simplified load combination cases of Ref.[2] – Chapter 2 are adopted. For the ultimate load limit state combinations : • 1.35 G + 1.50 W • 1.35 G + 1.50 S • 1.35 G + 1.35 W + 1.35 S For the serviceability limit state combinations : • 1.00 G + 1.00 W • 1.00 G + 1.00 S • 1.00 G + 0.90 W + 0.90 S 4. Analysis 4.1. Linear elastic analysis A linear elastic analysis is performed. This generates 18 possible ULS combinations and 7 possible SLS combinations.


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Combinations

Combi Norma Case coeff

1 EC-ultimate 1 Self weight 1.00

1 EC-ultimate 2 Self weight (cladding + roof) 1.00

1 EC-ultimate 3 Wind W1 1.00

1 EC-ultimate 4 Wind W2 1.00

1 EC-ultimate 5 Snow S1 1.00




2 EC-serviceability 1 Self weight 1.00

2 EC-serviceability 2 Self weight (cladding + roof) 1.00

2 EC-serviceability 3 Wind W1 1.00

2 EC-serviceability 4 Wind W2 1.00

2 EC-serviceability 5 Snow S1 1.00




Basic rules for generation of ultimate load combinations:

1 : 1.35*LC1 / 1.35*LC2

2 : 1.35*LC1 / 1.35*LC2 / 1.50*LC3 / 1.50*LC4

3 : 1.00*LC1 / 1.00*LC2 / 1.50*LC3 / 1.50*LC4

4 : 1.35*LC1 / 1.35*LC2 / 1.50*LC5 / 1.50*LC6 / 1.50*LC7 / 1.50*LC8

5 : 1.00*LC1 / 1.00*LC2 / 1.50*LC5 / 1.50*LC6 / 1.50*LC7 / 1.50*LC8

6 : 1.35*LC1 / 1.35*LC2 / 1.35*LC3 / 1.35*LC4 / 1.35*LC5 / 1.35*LC6 / 1.35*LC7

/ 1.35*LC8

7 : 1.00*LC1 / 1.00*LC2 / 1.35*LC3 / 1.35*LC4 / 1.35*LC5 / 1.35*LC6 / 1.35*LC7

/ 1.35*LC8

Basic rules for generation of serviceability load combinations:

1 : 1.00*LC1 / 1.00*LC2

2 : 1.00*LC1 / 1.00*LC2 / 1.00*LC3 / 1.00*LC4

3 : 1.00*LC1 / 1.00*LC2 / 1.00*LC5 / 1.00*LC6 / 1.00*LC7 / 1.00*LC8

4 : 1.00*LC1 / 1.00*LC2 / 0.90*LC3 / 0.90*LC4 / 0.90*LC5 / 0.90*LC6 / 0.90*LC7

/ 0.90*LC8

List of extremal ultimate load combinations

1/ 3 : +1.00*LC1+1.00*LC2+1.50*LC3

2/ 5 : +1.00*LC1+1.00*LC2+1.50*LC8

3/ 4 : +1.35*LC1+1.35*LC2+1.50*LC5

4/ 4 : +1.35*LC1+1.35*LC2+1.50*LC6

5/ 4 : +1.35*LC1+1.35*LC2+1.50*LC7

6/ 4 : +1.35*LC1+1.35*LC2+1.50*LC8

7/ 7 : +1.00*LC1+1.00*LC2+1.35*LC3+1.35*LC6

8/ 7 : +1.00*LC1+1.00*LC2+1.35*LC4+1.35*LC6

9/ 7 : +1.00*LC1+1.00*LC2+1.35*LC3+1.35*LC8

10/ 7 : +1.00*LC1+1.00*LC2+1.35*LC4+1.35*LC8

11/ 6 : +1.35*LC1+1.35*LC2+1.35*LC3+1.35*LC5

12/ 6 : +1.35*LC1+1.35*LC2+1.35*LC4+1.35*LC5

13/ 6 : +1.35*LC1+1.35*LC2+1.35*LC3+1.35*LC6

14/ 6 : +1.35*LC1+1.35*LC2+1.35*LC3+1.35*LC7

15/ 6 : +1.35*LC1+1.35*LC2+1.35*LC4+1.35*LC6

16/ 6 : +1.35*LC1+1.35*LC2+1.35*LC3+1.35*LC8

17/ 6 : +1.35*LC1+1.35*LC2+1.35*LC4+1.35*LC7

18/ 6 : +1.35*LC1+1.35*LC2+1.35*LC4+1.35*LC8


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List of extremal serviceability load combinations

1/ 2 : +1.00*LC1+1.00*LC2+1.00*LC3

2/ 2 : +1.00*LC1+1.00*LC2+1.00*LC4

3/ 3 : +1.00*LC1+1.00*LC2+1.00*LC5

4/ 3 : +1.00*LC1+1.00*LC2+1.00*LC6

5/ 3 : +1.00*LC1+1.00*LC2+1.00*LC8

6/ 4 : +1.00*LC1+1.00*LC2+0.90*LC4+0.90*LC5

7/ 4 : +1.00*LC1+1.00*LC2+0.90*LC4+0.90*LC8

Deformations in nodes. Global extreme

Linear static - dangerous or all combinations

Group of nodes :1/8

Group of serviceability combi :1/7

node combi Ux

[mm]

Uz

[mm]

Fiy

[mrad]

6 6 44.62 -0.18 1.10

2 3 -14.86 -0.19 2.06

7 1 32.83 19.17 -1.02

8 3 7.42 -59.93 0.63

5 6 0.00 -0.00 7.76

1 3 -0.00 -0.00 -3.73

Figure 14: Deformation SLS combination 3


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Figure 15: Deformation SLS combination 6

Internal forces on members. Member extreme

Linear static - dangerous or all combinations

Group of members :1/7

Group of ultimate combi :1/18

memb cr.nr combi dx

[m]

N

[kN]

Vz

[kN]

My

[kNm]

1 1 1 8.000 51.76 15.45 223.47

1 1 6 0.000 -107.44 -31.36 0.00

1 1 1 0.000 33.72 39.57 -0.00

1 1 12 8.000 -59.84 -48.67 -163.54

1 1 3 8.000 -81.91 -36.48 -291.84

2 1 1 8.000 80.81 14.35 114.78

2 1 6 0.000 -185.01 -0.00 0.00

2 1 1 0.000 72.37 14.35 0.00

2 1 6 8.000 -173.61 -0.00 -0.00

3 1 1 8.000 35.12 -32.21 -74.96

3 1 6 0.000 -107.44 31.36 -0.00

3 1 12 0.000 -102.60 44.25 -0.00

3 1 12 8.000 -78.25 37.82 329.42

4 2 1 11.845 25.35 2.34 -58.16

4 2 12 0.000 -55.85 53.20 -163.54

4 2 6 0.000 -41.63 78.45 -250.88

4 2 1 0.000 21.88 -49.39 223.47

4 2 3 0.000 -46.56 76.63 -291.84

5 2 1 11.845 25.13 4.11 -58.16

5 2 12 0.000 -56.88 76.65 -349.88

5 2 5 0.000 -37.14 82.24 -292.87

5 2 1 0.000 21.66 -30.38 100.44

5 2 3 11.845 -36.44 -2.67 119.09

6 2 1 11.845 41.26 -0.30 -47.11

6 2 3 0.000 -47.06 80.54 -338.10

6 2 5 0.000 -37.14 82.24 -292.87

6 2 1 0.000 37.80 -43.49 215.22

7 2 1 11.845 39.87 10.65 -47.11


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memb cr.nr combi dx

[m]

N

[kN]

Vz

[kN]

My

[kNm]

7 2 12 0.000 -47.42 72.83 -329.42

7 2 6 0.000 -41.63 78.45 -250.88

7 2 1 0.000 36.40 -30.76 74.96

7 2 3 10.836 -36.83 0.45 122.18

-291.8

223.5 114.8

-75.0

329.4

-291.8

223.5

-349.9

119.1

-338.1

215.2

-329.4

122.2

Figure 16: Extremes for My (ULS combinations)

4.2. Stability calculation For the stability check, the 5 critical combinations are used. The stability analysis determines the sway classification of the frame. With this calculation, the value of Vcr is obtained for the relevant load combination. This value can be used to evaluate the sensitivity of the structure to second-order effects. The critical (smallest and positive) load coefficient is found for combination 3 : 13.30. This value is compared with the results of Ref.[1] Method Critical load coefficient EPW 13.71 Ref.[1] 12.5 a) 1/0.073=13.69 Ref.[1] 12.5 b) 1/0.07=14.30 Ref.[1] 12.5 c) 13.20 Ref.[1] 12.5 d) 11.06 There 13.71 > 10.0, we can define the frame as non-sway. A second-order elastic analysis is not necessary. Stability combination

Combi Case coeff

1 1 Self weight 1.00

1 2 Self weight (cladding + roof) 1.00

1 3 Wind W1 1.50



2 5 Snow S1 1.50



3 7 Snow S3 1.50



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Combi Case coeff


4 8 Snow S4 1.50



5 4 Wind W2 1.35

5 5 Snow S1 1.35

Stability combination:

SC2, 1. critical load coefficient : 13.30

node Ux []

Uy []

Uz []

Fix []

Fiy []

Fiz []

1 0.00 0.00 -0.00 0.00 -267.37 0.00 2 -1947.34 0.00 -0.58 0.00 -194.97 0.00 3 -0.00 0.00 0.00 0.00 -297.78 0.00 4 -1986.87 0.00 0.00 0.00 -151.13 0.00 5 0.00 0.00 0.00 0.00 -267.36 0.00 6 -1947.29 0.00 0.58 0.00 -194.98 0.00 7 -1967.31 0.00 154.57 0.00 114.31 0.00 8 -1967.28 0.00 -154.78 0.00 114.32 0.00 9 -1955.89 0.00 66.36 0.00 -190.99 0.00 10 -1964.24 0.00 131.72 0.00 -185.92 0.00 11 -1972.33 0.00 195.05 0.00 -179.39 0.00 12 -1980.08 0.00 255.75 0.00 -170.90 0.00 13 -1987.40 0.00 313.04 0.00 -159.87 0.00 14 -1993.48 0.00 -51.72 0.00 -147.28 0.00 15 -1999.89 0.00 -101.92 0.00 -142.41 0.00 16 -2006.05 0.00 -150.17 0.00 -136.16 0.00 17 -2011.89 0.00 -195.91 0.00 -128.06 0.00 18 -2017.32 0.00 -238.40 0.00 -117.61 0.00 19 -1993.48 0.00 51.72 0.00 -147.28 0.00 20 -1999.89 0.00 101.92 0.00 -142.41 0.00 21 -2006.05 0.00 150.17 0.00 -136.16 0.00 22 -2011.89 0.00 195.91 0.00 -128.06 0.00 23 -2017.32 0.00 238.39 0.00 -117.60 0.00 24 -1955.84 0.00 -66.36 0.00 -190.99 0.00 25 -1964.19 0.00 -131.72 0.00 -185.93 0.00 26 -1972.28 0.00 -195.06 0.00 -179.40 0.00 27 -1980.03 0.00 -255.76 0.00 -170.91 0.00 28 -1987.35 0.00 -313.06 0.00 -159.88 0.00


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Figure 17: Stability deformation for combination 2

4.3. Elastic analysis with local non-linearties The 5 critical combinations are used. The sway imperfections are derived from the following formula :

1n

12.0k

1n

15.0k

kk

cs

cc

0sc

≤+=

≤+=

φ=φ

For the actual structure we have nc=3 (number of columns per plane) and ns=1 (number of story in the frame). nc 3 ns 1 kc 0.913 ks 1.000 φ0 1/200

φ 1/219 The initial deformation at the eaves is 8000/219=36,5 mm, at the ridge 9500/219=43,4 mm. These are introduced as initial deformation in the local non-linearities. Therefore non-linear combinations are defined.


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Figure 18: Global frame imperfections

Initial deformation num. 1

node X

mm

Y

mm

2 36.50 0.00

4 36.50 0.00

6 36.50 0.00

7 43.40 0.00

8 43.40 0.00

Nonlinear combination

Combi Group of

init. deformations

Group of

init. curvatures

Case coeff

C 1 1 0 1 Self weight 1.00

C 1 1 0 2 Self weight (cladding + roof) 1.00

C 1 1 0 3 Wind W1 1.50



C 2 1 0 5 Snow S1 1.50



C 3 1 0 7 Snow S3 1.50



C 4 1 0 8 Snow S4 1.50



C 5 1 0 4 Wind W2 1.35

C 5 1 0 5 Snow S1 1.35

Internal forces on members. Member extreme

Nonlinear calculation, local nonlinearities Group of members :1/7

Group of nonlinear combinations :1/5


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memb cr.nr non. c. dx

[m]

N

[kN]

Vz

[kN]

My

[kNm]

1 1 1 8.000 51.71 15.23 222.04

1 1 4 0.000 -107.28 -30.86 -0.00

1 1 1 0.000 33.78 39.44 0.00

1 1 5 8.000 -59.79 -48.32 -160.34

1 1 2 8.000 -81.77 -36.09 -288.27

2 1 1 8.000 80.84 14.01 112.24

2 1 4 0.000 -184.96 0.84 -0.00

2 1 1 0.000 72.40 14.05 0.00

3 1 1 8.000 35.07 -32.41 -76.20

3 1 4 0.000 -107.56 31.84 0.00

3 1 5 0.000 -102.64 44.68 0.00

3 1 5 8.000 -78.31 38.14 332.46

4 2 1 11.845 25.35 2.45 -58.13

4 2 5 0.000 -55.74 52.94 -160.34

4 2 4 0.000 -41.57 78.15 -247.29

4 2 1 0.000 21.88 -49.26 222.04

4 2 2 0.000 -46.50 76.34 -288.27

5 2 1 11.845 25.15 3.99 -58.13

5 2 5 0.000 -56.84 76.89 -352.73

5 2 3 0.000 -37.12 82.46 -295.61

5 2 1 0.000 21.68 -30.48 101.60

5 2 2 11.845 -36.46 -2.36 119.09

6 2 1 11.845 41.28 -0.18 -46.99

6 2 2 0.000 -47.00 80.24 -334.76

6 2 3 0.000 -37.14 81.97 -289.91

6 2 1 0.000 37.82 -43.36 213.84

7 2 1 11.845 39.92 10.54 -46.99

7 2 5 0.000 -47.42 73.07 -332.46

7 2 4 0.000 -41.66 78.71 -254.27

7 2 1 0.000 36.45 -30.85 76.20

7 2 2 10.836 -36.85 0.72 121.66

-288.3

222.0 112.2

-76.2

332.5

-288.3

222.0

-352.7

119.1

-334.8

213.8

-332.5

121.7

Figure 19 : Extremes for my (for non-linear ULS combinations)


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5. Member check 5.1. SLS check We use the SLS results from 0. The limit for the maximum vertical deflection of the roof under SLS is :

mm5.117200

23500

200

Lmax ==≤δ

Since the vertical deflection of 59.93 < 117.5 mm, the condition is satisfied. The limit for the horizontal displacement (SLS) of a portal frame without gantry crane is :

mm3.53150

8000

150

hhoriz ==≤δ

Since the maximum lateral displacement is 44.62 mm < 53.3 mm, the condition is satisfied. 5.2. ULS check The results of the unity checks are as follows :

0.81 0.46 0.91

0.71

0.95 0.85 0.88

Figure 20 : Steel code unity checks

5.2.1. Column check

Macro Member Section Position

m

Combi sect. chk. stab chk.

1 1 IPE550 8.00 2 0.17 0.81

2 2 IPE550 8.00 5 0.05 0.46

3 3 IPE550 8.00 5 0.23 0.91

The critical column is member 3.


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Given the results in 0, we can define the frame as non-sway in the plane. Outside the plane we use a buckling factor of 1.0. At the support, the IPE550 is only charged by pure compression. This results in a class 4 classification. The detailed results are as follows : EC3 Code Check

Macro 1 Member 1 IPE550 S 275 Combi 2 0.81

Basic data EC3




Material data



fabrication rolled

SECTION CHECK Width-to-thickness ratio for webs (Tab.5.3.1. a).


ratio







ratio






Internal forces

NSd -81.77 kN

Vy.Sd 0.00 kN

Vz.Sd -36.09 kN

Mt.Sd 0.00 kNm

My.Sd -288.27 kNm

Mz.Sd 0.00 kNm


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Compression check



Table of values

Nc.Rd 3360.00 kN

unity check 0.02

Shear check (Vz)



Table of values

Vpl.Rd 1043.92 kN

unity check 0.03

Combined bending, axial force and shear force check according to article 5.4.9. and formula (5.35)


Table of values

MNVy.Rd 695.00 kNm

MNVz.Rd 100.00 kNm

alfa 2.00 beta 1.00

unity check 0.17


STABILITY CHECK

Calculation effective area properties with direct method.

Properties

sectional area A eff 11919.4 mm^2 mm^2

Shear area Vy eff 7224.0 mm^2 Vz eff 4695.4 mm^2

radius of gyration iy eff 231.7 mm iz eff 47.2 mm

moment of inertia Iy eff 639646575.6 mm^4 Iz eff 26606961.0 mm^4

elastic section modulus Wy eff 2325987.5 mm^3 Wz eff 253399.6 mm^3

Eccentricity eny -0.0 mm enz 0.0 mm





Buckling curve a b



Length 8.00 8.00 m




Buckling check


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Table of values

Nb.Rd 654.18 kN

Beta A 0.89

unity check 0.13

Torsional-flexural buckling check according to article ENV 1993-1-3 : 6.2.3 and formula (6.1) (6.4a-b)(6.5a-b)(6.6)

Table of values

Nb.Rd 654.18 kN

Beta A 0.89






unity check 0.13

LTB check according to article 5.5.2. and formula (5.48)

Table of values

Mb.Rd 405.59 kNm

Beta W 0.84

reduction 0.70

imperfection 0.21

Mcr 702.71 kNm

LTB

LTB length 8.00 m

k 1.00

kw 1.00

C1 1.88

C2 0.00

C3 0.94


unity check =0.71

Compression and bending check according to article 5.5.4. and formula (5.56)

Table of values

ky 1.00

kz 1.09

muy -0.12

muz -0.78

BetaMy 1.80

BetaMz 1.80


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unity check = 0.03 + 0.50 + 0.00 = 0.53



Table of values

klt 0.96

kz 1.09

mult 0.38

muz -0.78

BetaMlt 1.80

BetaMz 1.80

unity check =0.13 + 0.68 + 0.00 = 0.81


5.2.2. Beam check To prevent the LTB, the purlins in the beam have to be positioned as follows :

ab

cd

e

f

g

Figure 21 : Position of purlins

The top flange of the beam is held by purlins at the points a, b, c, d and e. At the points f and g, the lower flange of the beam is held by LTB bracings. EC3 Code Check

Macro Member Section Position

m

Loadcase sect. chk. stab chk.

4 4 IPE400 1.75 2 0.26 0.71

5 5 IPE400 1.75 5 0.49 0.95

6 6 IPE400 1.75 2 0.40 0.85

7 7 IPE400 1.75 5 0.43 0.88


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The detailed results from critical beam nr 5 are as follows :

EC3 Code Check

Macro 5 Member 5 IPE400 S 275 Loadcase 5 0.95

Basic data EC3




Material data



fabrication rolled

SECTION CHECK Width-to-thickness ratio for webs (Tab.5.3.1. a).


ratio







ratio






Internal forces

NSd -55.27 kN

Vy.Sd 0.00 kN

Vz.Sd 64.62 kN

Mt.Sd 0.00 kNm

My.Sd -229.07 kNm

Mz.Sd 0.00 kNm


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Section properties

A 8.446000e+003 mm^2

Ay/A 0.509 Az/A 0.391

Iy 2.313000e+008 mm^4 Iz 1.318000e+007 mm^4

Iyz 0.000000e+000 mm^4 It 5.108000e+005 mm^4

Iw 4.968547e+011 mm^6

Wely 1.156000e+006 mm^3 Welz 1.464000e+005 mm^3

Wply 1.308000e+006 mm^3 Wplz 2.300000e+005 mm^3

cy 200.00 mm cz 90.00 mm

dy -0.00 mm dz 0.00 mm

Compression check



Table of values

Nc.Rd 2111.50 kN

unity check 0.03

Shear check (Vz) according to article 5.4.6. and formula (5.20)


Table of values

Vpl.Rd 616.19 kN

unity check 0.10

Combined bending, axial force and shear force check according to article 5.4.9. and formula (5.35)


Table of values

MNVy.Rd 327.00 kNm

MNVz.Rd 57.50 kNm

alfa 2.00 beta 1.00

unity check 0.49


STABILITY CHECK


type non-sway sway



Buckling curve a b



Length 11.85 11.85 m





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Warning: slenderness 299.86 is larger then 200.00 !

Buckling check


Table of values

Nb.Rd 160.84 kN

Beta A 1.00

unity check 0.34



Table of values

Nb.Rd 160.84 kN

Beta A 1.00






unity check 0.34

LTB check according to article 5.5.2. and formula (5.48)

Table of values

Mb.Rd 311.08 kNm

Beta W 1.00

reduction 0.95

imperfection 0.21

Mcr 2186.57 kNm

LTB

LTB length 1.75 m

k 1.00

kw 1.00

C1 1.20

C2 0.00

C3 1.00

negative influence of load position

unity check =0.74

Compression and bending check according to article 5.5.4. and formula (5.51)

Table of values

ky 1.00

kz 1.25

muy -0.06

muz -0.81


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Table of values

BetaMy 1.80

BetaMz 1.80

unity check = 0.03 + 0.70 + 0.00 = 0.73



Table of values

klt 0.83

kz 1.25

mult 0.55

muz -0.81

BetaMlt 1.35

BetaMz 1.80

unity check =0.34 + 0.61 + 0.00 = 0.95


6. Connection design 6.1. Bolted beam-to-column connection

CD

IPE40010

10

7

Section CD

IPE550

13

13

7

11

1111

10

10

Figure 22: Beam-to-column connection


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End plate

180

779

2D Plate 20

40 100

65

590

60

6 x M-20 (DIN6914)

Figure 23: Endplate dimensions

Haunch

1426

523

30

311

IPE400

1519

Figure 24: Haunch dimensions

Stiffener

514

98

24 466

23

23

2D Plate 15

Figure 25: Stiffener dimensions


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The detailed calculation note for tension on the top side is as follows : Node 6 : bolted beam-to-column connection side AB

According to EC3, Revised Annex J

1. Input data

Column IPE550

h 550.00 mm

b 210.00 mm

tf 17.20 mm

tw 11.10 mm

r 24.00 mm

fy 275.00 MPa

fu 430.00 MPa

Connected beam IPE400

h 400.00 mm

b 180.00 mm

tf 13.50 mm

tw 8.60 mm

r 21.00 mm

fy 275.00 MPa

fu 430.00 MPa

Haunch under IPE400

hc 355.52 mm

lc 1498.30 mm

b 180.00 mm

tf 13.50 mm

tw 8.60 mm

weld ab 13.00 mm

weld ac 8.00 mm

Partial safety factors

Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.10

Gamma Mw 1.25

Stiffener

Stiffener in tension zone

No. pos.[mm] fy[MPa]

1 744.08 275.00

End plate

h 779.00 mm

b 180.00 mm

t 20.00 mm

fy 275.00 MPa

fu 430.00 MPa

Bolts M-20 (DIN6914)


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type prestressed

grade 10.9

fu 1000.00 MPa

As 245.00 mm^2

do 22.00 mm

S 32.00 mm

e 35.00 mm

h head 13.00 mm

h nut 16.00 mm

Bolt position

row y[mm] spacing[mm]

1 715.00 100.00

2 655.00 100.00

3 65.00 100.00

Internal forces

Combination number 5

N -47.17 kN

Vz 71.26 kN

My -312.53 kNm

Tension top

2. Design moment resistance MRd

2.1. Design resistance of basic components

2.1.1. Column web panel in shear (J.3.5.2.)

Vwp,Rd data

Vwp,Rd 939.53 kN

Beta 1.00

Avc 7232.52 mm^2

2.1.2. Column web in compression (J.3.5.3.)

Fc,wc,Rd data

Fc,wc,Rd 495.28 kN

beff 263.87 mm

twc 11.10 mm

ro1 0.91

ro2 0.73

ro 0.91

kwc 1.00

lambda_rel 1.07

dc 467.60 mm

2.1.3. Haunch in compression


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Fc,h,Rd data

Fc,h,Rd 570.50 kN

bhf 180.00 mm

bhi 524.14 mm

alfa 20.15 deg

2.1.4. Design tension resistance of bolt row

(effective lengths in mm, resistance in kN)

Bt,Rd = 176.40 kN

2.1.4.1. Column flange

kfc = 1.00

row p (p1+p2) alfa e m n e1

1 0.0+30.0 8.00 55.00 25.25 31.56 64.00

2 30.0+295.0 - 55.00 25.25 31.56 -

3 295.0+ 0.0 - 55.00 25.25 31.56 -

row leff,cp,i leff,nc,i

1 158.65 202.00

2 158.65 169.75

3 158.65 169.75

row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2 leff,nc,ge2

1 - - - - 139.33 147.12

2 650.00 325.00 139.33 114.87 669.33 379.87

3 - - 669.33 379.87 - -

For individual bolt row:

row leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro

1 158.65 202.00 202.00 327.48 570.50 1.00

2 158.65 169.75 169.75 306.49 570.50 1.00

3 158.65 169.75 169.75 306.49 570.50 1.00

For bolt group:

group leff,1 leff,2 leff Ft,fc,Rd Ft,wc,Rd ro

1- 1 158.65 202.00 202.00 327.48 570.50 1.00

1- 2 262.00 262.00 262.00 562.54 570.50 1.00

1- 3 852.00 852.00 852.00 1058.40 570.50 1.00

2.1.4.2. Endplate

row p (p1+p2) alfa e m n

1 0.0+30.0 6.31 40.00 37.78 40.00

2 30.0+295.0 5.42 40.00 37.78 40.00

3 295.0+ 0.0 6.31 40.00 37.78 40.00


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1 237.38 238.28

2 237.38 204.76

3 237.38 238.28


1 - - - - 178.69 167.72

2 - - 178.69 134.20 - -

3 - - 708.69 432.72 - -


row leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd

1 237.38 238.28 238.28 334.61 512.31

2 204.76 204.76 204.76 313.06 440.24

3 237.38 238.28 238.28 334.61 512.31

For bolt group:

group leff,1 leff,2 leff Ft,ep,Rd Ft,wb,Rd

1- 1 237.38 238.28 238.28 334.61 512.31

1- 2 301.92 301.92 301.92 556.95 649.13

3- 3 237.38 238.28 238.28 334.61 512.31

2.2. Determination of Mj,Rd

row h[mm] Ft[kN]

1 697.58 327.48

2 637.58 167.79

3 47.58 0.00

Mj,Rd = 335.43 kNm

Mj,Rd = 335.43 kNm (inclusive normal force)

2.3.Determination of Mj,Rd for compressed haunch at beam

data

alfa 12.87 deg

Af 2430.00 mm^2

Ad 1599.60 mm^2

Me 289.00 kNm

Mj,Rd 289.00 kNm

MSd -217.03 kNm

3. Design shear resistance VRd

VRd data

VRd 290.93 kN

ks 1.00

n 1.00

slip factor 0.30


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VRd data

Fp,Cd 171.50 kN

Ft,Sd -7.86 kN

Fs,Rd 48.49 kN

VRd beam 1336.90 kN

4. Stiffness calculation

4.1. Design rotational stiffness

row k3[mm] k4[mm] k5[mm] k7[mm] keff[mm]

1 37.43 2.44 21.15 7.58 1.63

2 30.86 2.82 16.92 7.58 1.73

Sj data

Sj 49308.21 kNm/rad

Sj,ini 121752.72 kNm/rad

z 667.99 mm

mu 2.47

k1 4.11 mm

k2 4.38 mm

keq 3.35 mm

4.2. Stiffness classification

Stiffness data

E 210000.00 MPa

Ib 231300000.45 mm^4

Lb 23710.00 mm

frame type unbraced

S1 51215.73 kNm/rad

S2 1024.31 kNm/rad

System RIGID

4.3 Check of stiffness requirement

Stiffness data

Fi y infinity kNm/rad

Stiffness modification coef. 2.00

Sj,app infinity kNm/rad

Sj,lower boundary 49167.10 kNm/rad

Sj,upper boundary infinity kNm/rad

Sj,ini is inside the boundaries.

The actual joint stiffness is conform with the joint stiffness of the analysis model.

4.4 Ductility classification

The failure mode is not situated in the column shear zone.

In the endplate we have the following :

0.36 sqrt(fub/fy) d < t <= 0.53 sqrt(fub/fy) d

This results in an intermediate classification for ductility : class 2.

5. Unity checks


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Unity checks

MSd/MjRd 0.93

VSd/VRd 0.24

The connection satisfies.

6. Design calculations

6.1. Calculation weldsize af / Minimum thickness th for stiffener in column

data

MRd 335.43 kNm

Gamma 1.70

h 744.83 mm

FRd 765.58 kN

NT,Rd 607.50 kN

N 607.50 kN

fu 430.00 MPa

BetaW 0.85

minimum af 5.90 mm

af 10.00 mm

Minimum th 13.50 mm

6.2. Calculation aw

data

Ft 531.89 kN

Fv 25.17 kN

lw 301.92 mm

fu 430.00 MPa

BetaW 0.85

minimum aw (a2) 4.00 mm

aw 7.00 mm

Sj,ini = 121752.72 kNm/radSj,MRd = 40741.06 kNm/rad

4.12 8.23 12.35 16.47

mrad

100.0

200.0

300.0

kNm

Figure 26: Moment-rotation diagramma


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In the present case, the length Lb for the stiffness classification is taken as the developed length of the rafter, i.e. 23.71 m. As shown in the previous output, the connection stiffness is conform with the analysis model.

Sj,ini

Sj,ini = 121752.72 kNm/rad

Sj,low

Sj,low = 49167.10 kNm/rad

Sj,upper

Sj,upper = infinity kNm/rad

1.38 2.75 4.13 5.51

mrad

100.0

200.0

300.0

kNm

Figure 27: Stiffness boundaries

The normal output for tension on the bottom side is as follows :

Node 2 : bolted beam-to-column connection side CD


1. Input data

Column IPE550


Haunch under IPE400

hc 355.52 mm

lc 1498.30 mm

b 180.00 mm

tf 13.50 mm

tw 8.60 mm

weld ab 13.00 mm

weld ac 8.00 mm


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.10

Gamma Mw 1.25

Stiffener




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1 744.08 275.00

End plate

h 779.00 mm

b 180.00 mm

t 20.00 mm

fy 275.00 MPa

fu 430.00 MPa


type prestressed

grade 10.9

fu 1000.00 MPa

As 245.00 mm^2

do 22.00 mm

S 32.00 mm

e 35.00 mm

h head 13.00 mm

h nut 16.00 mm

Bolt position


1 715.00 100.00

2 655.00 100.00

3 65.00 100.00

Internal forces


N 21.98 kN

Vz -48.16 kN

My 208.57 kNm

Tension bottom




Bt,Rd = 176.40 kN

row Ft,fc,Rd Ft,ep,Rd

3 306.49 313.06

2 306.49 313.06

1 327.48 334.61

data

Vwp,Rd 939.53 kN

Fc,wc,Rd 838.38 kN

Fc,fb,Rd 838.38 kN


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row h[mm] Ft[kN]

3 697.20 306.49

2 107.20 306.49

1 47.20 225.39

Mj,Rd = 257.18 kNm



VRd =275.84 kN



Sj data

Sj 69046.60 kNm/rad


z 587.47 mm

mu 1.70

k1 4.68 mm

k2 -

keq 2.47 mm


Stiffness data

E 210000.00 MPa

Ib 231300000.45 mm^4

Lb 23710.00 mm

frame type unbraced

S1 51215.73 kNm/rad

S2 1024.31 kNm/rad

System RIGID


Stiffness data











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5. Unity checks

Unity checks

MSd/MjRd 0.81

VSd/VRd 0.17



data

af 10.00 mm

aw 7.00 mm

Minimum th 13.50 mm

The configuration at the middle column is :

Figure 28: Bolted beam-to-column at middle column

6.2. Bolted plate-to-plate connection


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AB

IPE400

7

7

5

Section AB CD

IPE400

7

7

5

Section CD

87

10

87

10

Figure 29: plate-to-plate connection

End plate

180

500

2D Plate 20

40 100

46

95

295

6 x M-20 (DIN6914)

Figure 30: Endplate dimensions

Node 7 : bolted plate-to-plate connection


1. Input data

Right side


h 400.00 mm

b 180.00 mm

tf 13.50 mm

tw 8.60 mm

r 21.00 mm

fy 275.00 MPa

fu 430.00 MPa

End plate

h 500.00 mm


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End plate

b 180.00 mm

t 20.00 mm

fy 275.00 MPa

fu 430.00 MPa


type prestressed

grade 10.9

fu 1000.00 MPa

As 245.00 mm^2

do 22.00 mm

S 32.00 mm

e 35.00 mm

h head 13.00 mm

h nut 16.00 mm

Bolt position

row y[mm]

1 436.00 100.00

2 141.00 100.00

3 46.00 100.00

Left side


h 400.00 mm

b 180.00 mm

tf 13.50 mm

tw 8.60 mm

r 21.00 mm

fy 275.00 MPa

fu 430.00 MPa

End plate

h 500.00 mm

b 180.00 mm

t 20.00 mm

fy 275.00 MPa

fu 430.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.10

Gamma Mw 1.25

Internal forces


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N -36.46 kN

Vz 2.36 kN

My 119.09 kNm

Tension bottom



2.1.1.Beam flange and web in compression (J.3.5.4.) - Right side

Fc,fb,Rd data

Fc,fb,Rd 846.05 kN

section class 1

Mc,Rd 327.00 kNm

hb-tfb 386.50 mm

2.1.2. Beam flange and web in compression (J.3.5.4.) - Left side

Fc,fb,Rd data

Fc,fb,Rd 846.05 kN

section class 1

Mc,Rd 327.00 kNm

hb-tfb 386.50 mm



Bt,Rd = 176.40 kN

2.1.3.1. Endplate - right side

row p (p1+p2) alfa e m

3 0.0+47.5 - 46.00 32.83 41.04

2 47.5+147.5 5.83 40.00 40.04 40.00

1 147.5+ 0.0 5.83 40.00 40.04 40.00

row leff,cp,i

3 90.00 90.00

2 251.60 233.40

1 251.60 233.40

row leff,cp,g leff,nc,g leff,cp,ge1 leff,nc,ge1 leff,cp,ge2

3 90.00 90.00 - - - -

2 - - - - 420.80 275.81

1 - - 420.80 275.81 - -


row leff,1 leff,2 leff Ft,ep,Rd

3 90.00 90.00 90.00 256.91 -

2 233.40 233.40 233.40 322.10 501.81

1 233.40 233.40 233.40 322.10 501.81


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For bolt group:

group leff,1 leff,2 leff Ft,ep,Rd

3- 3 90.00 90.00 90.00 256.91 -

2- 2 233.40 233.40 233.40 322.10 501.81

2- 1 551.63 551.63 551.63 697.19 1186.00

2.1.3.2. Endplate - left side


3 0.0+47.5 - 46.00 32.83 41.04

2 47.5+147.5 5.83 40.00 40.04 40.00

1 147.5+ 0.0 5.83 40.00 40.04 40.00

row leff,cp,i

3 90.00 90.00

2 251.60 233.40

1 251.60 233.40


3 90.00 90.00 - - - -

2 - - - - 420.80 275.81

1 - - 420.80 275.81 - -



3 90.00 90.00 90.00 256.91 -

2 233.40 233.40 233.40 322.10 501.81

1 233.40 233.40 233.40 322.10 501.81

For bolt group:


3- 3 90.00 90.00 90.00 256.91 -

2- 2 233.40 233.40 233.40 322.10 501.81

2- 1 551.63 551.63 551.63 697.19 1186.00


row h[mm] Ft[kN]

3 437.20 256.91

2 342.20 322.10

1 47.20 267.04

Mj,Rd = 235.15 kNm




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VRd data

VRd 288.59 kN

ks 1.00

n 1.00

slip factor 0.30

Fp,Cd 171.50 kN

Ft,Sd -6.08 kN

Fs,Rd 48.10 kN



row k5[mm] k5[mm] k7[mm]

3 17.29 17.29 7.19 3.93

2 24.72 24.72 7.19 4.55

1 24.72 24.72 7.19 4.55

Sj data

Sj 271519.93 kNm/rad


z 370.81 mm

mu 1.00

keq 9.40 mm


Right side

Stiffness data

E 210000.00 MPa

Ib 231300000.45 mm^4

Lb 23710.00 mm

frame type unbraced

S1 51215.73 kNm/rad

S2 1024.31 kNm/rad

System RIGID

Left side

Stiffness data

E 210000.00 MPa

Ib 231300000.45 mm^4

Lb 23710.00 mm

frame type unbraced

S1 51215.73 kNm/rad

S2 1024.31 kNm/rad

System RIGID


Right side


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Stiffness data








Left side

Stiffness data












5. Unity checks

Unity checks

MSd/MjRd 0.51

VSd/VRd 0.01



6.1. Calculation af - Right side

data

MRd 235.15 kNm

Gamma 1.70

h 389.69 mm

FRd 1025.80 kN

NT,Rd 607.50 kN

N 607.50 kN

fu 430.00 MPa

BetaW 0.85

minimum af 5.90 mm

af 7.00 mm

6.2. Calculation aw - Right side


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data

Ft 322.10 kN

Fv 1.33 kN

lw 233.40 mm

fu 430.00 MPa

BetaW 0.85


aw 5.00 mm

6.3. Calculation af - Left side

data

MRd 235.15 kNm

Gamma 1.70

h 389.69 mm

FRd 1025.80 kN

NT,Rd 607.50 kN

N 607.50 kN

fu 430.00 MPa

BetaW 0.85

minimum af 5.90 mm

af 7.00 mm

6.4. Calculation aw - Left side

data

Ft 322.10 kN

Fv 1.33 kN

lw 233.40 mm

fu 430.00 MPa

BetaW 0.85


aw 5.00 mm


1.29 2.59 3.88 5.18

mrad

50.0

100.0

150.0

200.0

kNm

Figure 31: Moment-rotation diagramma


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6.3. Base plate connection

CD

IPE550

13 138

Section CD

1010

Figure 32: Baseplate connection

Baseplate

210

570

2D Plate 30

42 126

286

2 x M-24 (DIN601)

Figure 33: Baseplate dimensions


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102

448

Anchor:M-24 (DIN601)

Figure 34: Anchor dimensions

Node 3 : bolted baseplate connection

According to EC3, Annex L & Revised Annex J

1. Input data

Column IPE550


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Mw 1.25

Gamma c 1.10

Gamma fr 1.10

Concrete block

fck_c 25.00 MPa

bond condition poor

Beta_j 0.66

kj 2.00

kfr 0.25

Baseplate

h 570.00 mm

b 210.00 mm

t 30.00 mm

fy 275.00 MPa

fu 430.00 MPa

Anchors M-24 (DIN601)

type straight

bar type high bond

grade 4.6

fu 400.00 MPa

As 353.00 mm^2

do 26.00 mm


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S 36.00 mm

e 39.60 mm

h head 15.00 mm

h nut 19.00 mm

Anchor position


1 285.50 125.60

Internal forces


N 72.40 kN

Vz 14.05 kN

My 0.00 kNm

Tension on right side.

Projected forces (Reactions)

N' = 72.40 kN

T' = 14.05 kN

2. Design compression resistance NRd,c

According to EC3, Annex L

NRd,c data

NRd,c 2357.91 kN



3.1 Design resistance of basic components

For individual anchor row:

Bt,Rd = 101.66 kN

row

1 203.33

data

Fc,base,Rd 486.36 kN

Fc,fb,Rd 1304.43 kN

3.2 Determination of Mj,Rd

row h[mm] Ft[kN]

1 265.90 203.33

Mj,Rd = 54.06 kNm



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4. Design tension resistance NRd,t


NRd,t = 203.33 kN


VRd (friction included) 48.72 kN

6. Unity checks

Unity checks

NSd/NRd,t 0.36

MSd/MjRd 0.00

VSd/VRd 0.29


7. Design Calculations.

7.1 Anchorage length.

Designed for Combination number 1

Anchorage data

l,anchor 448.11 mm

7.2. Calculation weldsize

data

af 13.00 mm

aw 8.00 mm


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1.10 PST.06.02 – 01 : DIN 18800 Steel code check (1) Description Stress and stability check of a member with normal force and bending moments and of a member in a simple frame. Project data The following examples of Ref.[1] are calculated : - 9.5.1. Träger mit konstanter Normalkraft - 9.5.3. Rahmenstiel mit Biege-und Normalkraftbeanspruchung Reference [1] G. Hünersen, E. Fritzsche

Stahlbau in Beispielen Berechnungspraxis nach DIN 18 800 Teil 1 bis Teil 3 Werner Verlag GmbH & Co. KG – Dusseldorf 1995

Result Member Example Type Ref[1] EPW % Diff. Remark 4 9.5.1.

Bending+Compression 0.51

0.52

0 %

4 9.5.1. Bending+LTB+Compression

0.99 0.97 3.00 % Difference due to different fabrication conditions for LTB check

2 9.5.3. Bending+LTB+Compression

0.97 0.98 1.03 % Some differences in internal forces for Second Order calculation with global imperfection.

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060201.epw Modules 2nd order Frame (PRS.22) DIN 18800 Steel code check (PST.06.02) Author CVL Calculation note

Macro 2 Member 2 IPE360 Steel 37 Comb 1 0.99


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Basic data DIN18800

partial safety factor Gamma M =1.10

Material data

Yield strenght fy,k 235.00 MPa

Tensile strength fu,k 360.00 MPa

fabrication rolled

SECTION CHECK - DIN18800 Teil 1.

Width-to-thickness ratio for webs


ratio

maximum ratio PL-PL 32.34 (Tab. 18)

maximum ratio EL-PL 37.39 (Tab. 15)

maximum ratio EL-EL 66.00 (Tab. 12,13,14)

==> Class cross-section : plastic.

Width-to-thickness ratio for flanges


ratio






Internal forces

N -521.36 kN

Vy 0.00 kN

Vz 16.92 kN

Mt 0.00 kNm

My 78.49 kNm

Mz 0.00 kNm

Only elastic check

Normal force check

according to article (756) and formula (Bild 18)

Section classification isplastic.

Table of values

Npl.d 1553.78 kN

unity check 0.34

Shear check (Vz)



Table of values

Vpl.d 342.70 kN

unity check 0.05

Plastic check around strong axis.


according to article (757) and formula (Tab.16)


Table of values

alfa.pl.y 1.13

alfa.pl.z 1.25


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Table of values

unity check 0.66


STABILITY CHECK - DIN18800 Teil 2.


type non-sway sway



Buckling curve a b



Length 4.00 4.00 m




Buckling check

according to article T2 (304) and formula (3)

Table of values

Kappa*Npl.d 807.42 kN

unity check 0.65

LTB check


unity check = 0.38

Table of values

KappaM*Mpl.d 208.13 kNm

KappaM 0.95

LambdaM_r 0.66

n 2.50

kn 1.00

Mkiy =548.06 kNm according to DIN18800 T.2 form.(19)

LTB

LTB length 4.00 m

Betaz 1.00

Beta0 1.00

Ksi 1.77




Table of values

Beta_m 1.00

delta_n 0.01

unity check =0.34 + 0.33 + 0.01 = 0.68



Table of values

ky 0.90

kz 0.93

ay 0.15

az 0.10


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Table of values

BetaMy 1.80

BetaMz 1.80

unity check =0.65 + 0.34 = 0.99

LTB parameters

Table of values

KappaM 0.95

LambdaM_r 0.66

n 2.50

kn 1.00

Lambda_v 105.78

Lambda_vr 1.13

KappaM_v 0.47

ip 0.15 m

c 0.23 m



Macro 4 Member 4 IPE360 Steel 37 Comb 1 0.97

Basic data DIN18800


Material data



fabrication rolled




ratio







ratio






Internal forces

N -150.00 kN

Vy 0.00 kN

Vz 26.00 kN

Mt 0.00 kNm

My 89.00 kNm

Mz 0.00 kNm

Only elastic check


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Normal force check



Table of values

Npl.d 1553.78 kN

unity check 0.10

Shear check (Vz)



Table of values

Vpl.d 342.70 kN

unity check 0.08





Table of values

alfa.pl.y 1.13

alfa.pl.z 1.25

unity check 0.41




type non-sway sway



Buckling curve a b



Length 6.00 6.00 m




Buckling check


Table of values


unity check 0.34

LTB check


unity check = 0.67

Table of values


KappaM 0.61

LambdaM_r 1.19

n 2.50

kn 1.00


LTB


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LTB

LTB length 6.00 m

Betaz 1.00

Beta0 1.00

Ksi 1.35




Table of values

Beta_m 1.00

delta_n 0.01

unity check =0.10 + 0.41 + 0.01 = 0.52



Table of values

ky 0.94

kz 1.04

ay 0.18

az -0.12

BetaMy 1.30

BetaMz 1.80

unity check =0.34 + 0.63 = 0.97

LTB parameters

Table of values

KappaM 0.61

LambdaM_r 1.19

n 2.50

kn 1.00

Lambda_v 158.67

Lambda_vr 1.69

KappaM_v 0.26

ip 0.15 m

c 0.28 m




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1.11 PST.06.02 – 02 : DIN 18800 Steel Code Check (2) Description Stress and stability check of a simple beam. Project data The following example of Ref.[1] is calculated : - 10.6 Beispiel für Träger mit Druck und zweiachsiger Biegebeanspruchung Reference [1] G. Hünersen, E. Fritzsche


Result Member Example Type Ref[1] EPW % Diff. Remark 1 10.6.

Bending+Compression Method 1

0.76

0.77

0 %

1 10.6. Bending++Compression Method 2

0.66 0.71 6.06 %

1 10.6. Bending+LTB+Compression 0.99 0.99 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060202.epw Modules 2D Frame (PRS.11) DIN 18800 Steel code check (PST.06.02) Author CVL Calculation note

Method 1

Macro 1 Member 1 IPE300 Fe 360 Loadcase 1 1.00


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Basic data DIN18800


Material data



fabrication rolled




ratio







ratio






Internal forces

N -100.00 kN

Vy 0.00 kN

Vz 0.00 kN

Mt 0.00 kNm

My 40.63 kNm

Mz -3.13 kNm

Normal force check



Table of values

Npl.d 1149.36 kN

unity check 0.09

Plastic check around both axis.


according to article (757) and formula (40)(41)(42)


Table of values

alfa.pl.y 1.13

alfa.pl.z 1.25

unity check 0.21




type non-sway sway


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Buckling curve a b



Length 5.00 5.00 m




Buckling check


Table of values


unity check 0.28

LTB check


unity check = 0.53

Table of values


KappaM 0.57

LambdaM_r 1.25

n 2.50

kn 1.00


LTB

LTB length 5.00 m

Betaz 1.00

Beta0 1.00

Ksi 1.12




Table of values

ky 1.04

kz 1.47

ay -0.47

az -1.67

BetaMy 1.30

BetaMz 1.30

unity check =0.28 + 0.32 + 0.17 = 0.77



Table of values

ky 0.96

kz 1.47

ay 0.16

az -1.67

BetaMy 1.30

BetaMz 1.30

unity check =0.28 + 0.51 + 0.21= 1.00

LTB parameters


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Table of values

KappaM 0.57

LambdaM_r 1.25

n 2.50

kn 1.00

Lambda_v 149.23

Lambda_vr 1.59

KappaM_v 0.29

ip 0.13 m

c 0.23 m



Method 2


Basic data DIN18800


Material data



fabrication rolled




ratio







ratio






Internal forces

N -100.00 kN

Vy 0.00 kN

Vz 0.00 kN

Mt 0.00 kNm

My 40.63 kNm

Mz -3.13 kNm


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Normal force check



Table of values

Npl.d 1149.36 kN

unity check 0.09





Table of values

alfa.pl.y 1.13

alfa.pl.z 1.25

unity check 0.21




type non-sway sway



Buckling curve a b



Length 5.00 5.00 m




Buckling check


Table of values


unity check 0.28

LTB check


unity check = 0.53

Table of values


KappaM 0.57

LambdaM_r 1.25

n 2.50

kn 1.00


LTB

LTB length 5.00 m

Betaz 1.00

Beta0 1.00

Ksi 1.12



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Table of values

ky 0.79

kz 1.00

cy 0.79

cz 1.26

BetaMy 1.00

BetaMz 1.00

delta_n 0.05

unity check =0.28 + 0.24 + 0.15 + 0.05 = 0.71

Table of values

My 40.63 kNm

Mz 3.13 kNm



Table of values

ky 0.96

kz 1.47

ay 0.16

az -1.67

BetaMy 1.30

BetaMz 1.30

unity check =0.28 + 0.51 + 0.21= 1.00

LTB parameters

Table of values

KappaM 0.57

LambdaM_r 1.25

n 2.50

kn 1.00

Lambda_v 149.23

Lambda_vr 1.59

KappaM_v 0.29

ip 0.13 m

c 0.23 m




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1.12 PST.06.02 – 03 : DIN 18800 Steel Code Check (3) Description Stress and stability check of two simple beams. Project data The following example of Ref.[1] is calculated : - A) Dachtragwerk mit zwei Trägerlagen 1/ Pfette (pp.50-51) - B) Dachtragwerk mit einer Trägerlage / Dachträger (pp.54-56) Reference [1] G. Kahlmeyer

Stahlbau nach DIN18800 (11.90) Bemessung und Konstruktion Träger – Stützen – Verbindungen Werner Verlag GmbH & Co. KG – Dusseldorf 1996

Result Member Example Type Ref[1] EPW % Diff. Remark 2 A)Pfette erf cθ,k

[kNm/m] 0.605

0.58

4.3 %

2 A)Pfette vorh cθ,k [kNm/m]

3.78 3.77 0.26 %

4 B)Träger cθM,k [kNm/m]

318 317.9 0 %

4 B)Träger cθA,k reduced [kNm/m]

3.1 3.1 0 %

4 B)Träger cθA,k [kNm/m]

8.72 5.81 33.37 % Error in Ref[1]

4 B)Träger erf cθ,k [kNm/m]

71.8 68.7 4.5 %

4 B)Träger It.id [cm4]

80.3 62.3 22.42 %

4 B)Träger unity check 0.99 1.072 8.28 % See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060203.epw Modules 2D Frame (PRS.01) DIN 18800 Steel code check (PST.06.02)


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Author CVL Calculation note Macro 1 Member 2 IPE180 Fe 360 Loadcase 1 0.18

Basic data DIN18800


Material data



fabrication rolled




ratio







ratio






Internal forces

N 0.00 kN

Vy 0.00 kN

Vz 0.00 kN

Mt 0.00 kNm

My 5.74 kNm

Mz 0.00 kNm

Only elastic check

Normal stress check

according to article (747) and formula (33)

Section classification is elastic.

Table of values

Sigma 39.17 MPa

unity check 0.18



LTB check


unity check = 0.15


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S =28768.70

S > 10327.04 kN ==> fixed rotation axis

Table of values

k0 0.23

kv 0.35

c0Mk 93.07 kNm/m (form. 10)

c0Pk 45.44 kNm/m

c0Ak 4.31 kNm/m (form. 11a / 11b)

c0Ak 5.20 kNm/m ( Tab. 7 )

vorh ck 3.77 kNm/m

erf ck 0.58 kNm/m

LTB

LTB length 6.00 m

Betaz 1.00

Beta0 1.00

Ksi 1.29


direction : downward

Diaphragm data : 40/183/0.88

Table of values

I 277000.00 mm^4

K1 0.20 m/kN

K2 6.71 m^2/kN

Length 10.00 m

frame dist 2.50 m

k 4.00

assembling: positive

bolt position : underside

bolt pitch : br



Basic data DIN18800


Material data



fabrication rolled




ratio








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ratio






Internal forces

N 0.00 kN

Vy 0.00 kN

Vz 3.96 kN

Mt 0.00 kNm

My 86.48 kNm

Mz 0.00 kNm

Shear check (Vz)



Table of values

Vpl.d 253.35 kN

unity check 0.02





Table of values

alfa.pl.y 1.13

alfa.pl.z 1.25

unity check 0.64



LTB check


unity check = 1.08

S =24945.59

0.2 S < 19316.22 kN ==> free rotation axis

Table of values

k0 4.00

kv 1.00

c0Mk 317.89 kNm/m (form. 10)

c0Pk 64.95 kNm/m

c0Ak 5.81 kNm/m (form. 11a / 11b)

c0Ak 3.10 kNm/m ( Tab. 7 )

vorh ck 5.25 kNm/m

erf ck 68.68 kNm/m

Table of values


KappaM 0.60

LambdaM_r 1.21

n 2.50

kn 1.00


It,id =202000.00 + 421255.62 =623255.61 mm^4


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LTB

LTB length 8.00 m

Betaz 1.00

Beta0 1.00

Ksi 1.12


direction : downward

Diaphragm data : 100/275/0.88

Table of values

I 1703000.00 mm^4

K1 0.22 m/kN

K2 21.41 m^2/kN

Length 13.50 m

frame dist 4.50 m

k 4.00

assembling: positive

bolt position : underside

bolt pitch : 2br



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1.13 PST.06.02 – 04 : DIN 18800 Steel Code Check (4) Description Stress and stability check of a slender section. Project data The example of Ref.[1] pp.B-Knick01-12. Reference [1] H. Owczarzak, M. Stracke

DIN188000 in Beispielen Seminarunterlagen zum Dortmunder Praxisseminar L S+S Februar 1997

Result Member Example Type Ref[1] EPW Remark 1 BKNICK Biegeknicken

without slender section option (only elastic check)

0.79

0.79

0 %

1 BKNICK Biegeknicken with slender section influence

0.98 0.99 1.00 %

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060204.epw Modules 2D Frame (PRS.01) DIN 18800 Steel code check (PST.06.02) Author CVL Calculation note

Macro 1 Member 1 SC450/450/8 St 37 Loadcase 1 0.79

Basic data DIN18800


Material data



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Material data






ratio




==> Class cross-section : slender section


Internal forces

N -1100.00 kN

Vy 0.00 kN

Vz 0.00 kN

Mt 0.00 kNm

My 156.25 kNm

Mz 0.00 kNm

Only elastic check

Normal stress check



Table of values

Sigma 154.08 MPa

unity check 0.71







Buckling curve b b



Length 10.00 10.00 m




Buckling check


Table of values


unity check 0.42



Table of values

Beta_m 1.00


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Table of values

delta_n 0.06

unity check =0.42 + 0.31 + 0.06 = 0.79


Macro 1 Member 1 SC450/450/8 St 37 Loadcase 1 1.31

Basic data DIN18800


Material data







ratio




==> Class cross-section : slender section


Internal forces

N -1100.00 kN

Vy 0.00 kN

Vz 0.00 kN

Mt 0.00 kNm

My 156.25 kNm

Mz 0.00 kNm

Normal stress check

according to article DIN18800 T2 (707) and formula DIN18800 T1 (38)

Section classification is slender section

Table of values

A eff 13229.70 mm^2

Wy eff 1777830.58 mm^3

Wz eff 2004388.63 mm^3

ey 15.27 mm

ez -0.00 mm

Table of values

Sigma 180.48 MPa

unity check 0.83




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Buckling curve b b



Length 10.00 10.00 m




Slender section check according to DIN18800 T2 / 7.

Calculation effective area properties for El-El (Art.7.3)

with direct method (sigmaD=fy,d) (position = 2.00 m

Table of values

sectional area A' 13229.7 mm^2

Shear area Vy' 6285.7 mm^2 Vz' 6944.0 mm^2

radius of gyration iy' 176.7 mm iz' 184.6 mm

moment of inertia Iy' 412942505.0 mm^4 Iz' 450987429.7 mm^4

elastic section modulus Wy' 1718637.0 mm^3 Wz' 2004388.6 mm^3

Eccentricity eny' 15.3 mm enz' -0.0 mm

Increasing bow imperf woy' 15.3 mm woz' 0.0 mm

Buckling factor k 4.0

Critical ratio b/t 54.2

Buckling check


Table of values


unity check 0.52



Table of values

Beta_m 1.00

delta_n 0.05

unity check =0.52 + 0.42 + 0.05 = 0.99

Shear buckling check

in buckling field 5


Table of values

N -1100.00 kN

My 156.25 kNm

Mz 0.00 kNm

Vy 0.00 kN

Vz 0.00 kN

unity check =1.31 + 0.00 + 0.00 + 0.00 = 1.31

Table of values

a 1.11 m

b 0.43 m

t 8.00 mm

alfa 2.56

sigma_e 64.49 MPa


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Table of values

Psi 1.00

sigma_x 154.08 MPa

tau 0.00 MPa

k_sigma_x 4.00

k_tau 5.95

sigma_x_pi 257.96 MPa

tau_pi 383.74 MPa

lambda_p_sig 0.96

lambda_p_t 0.60

ro -24.22

kappa_x 0.80

kappa_tau 1.00

kappa_k 0.73

sigma_xPRd 127.51 MPa

tau_PRd 125.97 MPa

e1 1.41

e3 1.80



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1.14 PST.06.02 – 05 : DIN 18800 Steel Code Check Tutorial Frame Description Three members (beam, column and a truss beam) of the tutorial project of ESA-Prima win are calculated manually and compared with the results of EPW. Project data See input file. Reference [1] Din 18800 : 1990.11 (neu)

Stahlbauten [2] G. Hünersen, E. Fritzsche


See the chapter "Manual calculation" for the manual calculation according to this reference. Result Member/Macro Manual EPW member 7 0.24 0.24 0 % macro 11 0.31

0.71 0.31 0.75 (0.73)

0 % 1.41 %

macro 18 0.44 0.44 (0.49) 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060205.epw Modules 3D Frame (PRS.11) DIN 18800 Steel code check (PST.06.02) Author CVL Manual calculation

1.14.1 Check of member 7.


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1.14.1.1 Buckling data First we will discuss the buckling data of this member.

1. System length L : since there are no intermediate restraints on this member the system length L = the full

member length for all buckling modes (L = 6m).

2. The member is loaded through the shear centre.

3. Sway modes: Y-Y: non-sway Z-Z: non-sway.

4. The effective length factors k and kw for L.T.B. are taken as 1 (No end-fixity and no special provision for warping fixity).

1.14.1.2 Check of IPE 270 section.

Now, we will discuss the different steps of a section check.

A. Classification of the section a) Width-to-thickness ratio for webs (using Tab. 18) : b/tw = 219.6 / 6.6 = 33.27 Actually, the web is subjected to bending and tension. But because of the small value of this tensile force (0.20 kN), we consider bending only. For this case, the maximal ratio for a class-1 (PL-PL) member is 64 Since 33.27 < 64 , the web is a class-1 element. b) Width-to-thickness ratio for outstand flanges (using Tab. 18) : b/tf = (64.2-15)/10.2 = 4.82 Max. ratio for a class-1 section flange subject to compression is 9. Since 6.62 < 9 , the flanges are a class 1 element. � Section IPE270 is a class-1 (PL-PL) section for the stability check. B. Stability check : Check for L.T.B. Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 6 on position x=3m. Combination 4, member 7 on x =3.0 m : X = 0.20 kN (tension) My = 14.34 kNm Z = 2.25 kN (Shear) Normally, we should perform a check for bending and axial tension, according to Art. 5.5.3 but the program doesn’t take account for the beneficial effect of the tension force. Using Article T2 (311) and Formula 16 :


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M

k M

y

M pl y d. .

≤ 1

Substitution of values : • My = 14.34 kNm

• Determination of Mpl.y.d

• Mpl.y = 240 N/mm² x 484 cm³ = 116.16 kNm • γM1 = 1.1

� Mpl.y.d = 116.16 / 1.1 = 105.6

• Determination of κM :

Determination of λM,red = M

M

pl y

Ki y

.

.

• Mpl.y = 116.16 kNm • Determination of Mki.y :

h < 60 cm => Formula 20

� Mki.y = 50.53 kNm Or by using formula 19:

� Mki.y = 71.88 kNm (assumption: zp = 0, load in center of gravity)

Note 1: ζ = 1.12

Note 2: c² is calculated according to reference (2) :

cI

ll

l I

I

zz t

z

²

( )²( )² . ( )²

=+ω

ββ β

0 00 039

where: β0 = warping factor (default-value = 1), analogue to kw in EC3 βz = LTB factor (default-value = 1), analogue to k in EC3

� λM,red = 1.27 ( > 0.4 => Formula 18)

� Formula 18 => κM = 0.56 Unity check: = 0.24 � Section is o.k.

1.14.2 Check of macro 11

1.14.2.1 Buckling data First we will discuss the buckling data of this macro.

1. System length L : the beams on a height of 3m provide restraint to the column :

the system lengths for member 18: Ly = Lz = 3 m. the system lengths for member 19: Ly = Lz = 5 m.


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3. Sway modes: Y-Y: non-sway (bracing in roof-plane) Z-Z: non-sway

4. The effective length factors k and kw for L.T.B. are taken as 1 (No end-fixity and no special provision for warping fixity).

1.14.2.2 2.2. Check of HEB 160 section A. Classification of the section a) Width-to-thickness ratio for webs (using Tab. 18) : b/tw = 104 / 8 = 13 On position 0 m. of the beam, the web is subjected to compression only. For this case, the maximal ratio for a class-1 (PL-PL) member is 32. Since 13 < 32 , the web is a class-1 element. b) Width-to-thickness ratio for outstand flanges (using Tab. 18) : b/tf = (76-15)/13 = 4.69 Max ratio for a class-1 section flange subject to compression is 9. Since 4.69 < 9 , the flanges are a class 1 element. � Section HEB 160 is a class-1 (Pl. - Pl.) section for the stability check. B. Section check This check is executed at member 19 on position x = 0 m (start of member 19). Combination 6 : X =-69.74 kN (compression) My = 44.37 kNm Mz = -0.67 kNm => Can be neglected. Z = -8.87 kN (Shear) Y = 0.13 kN => Can be neglected. B.1. Normal force check Using article 756, Bild 18 : • NSd = 69.74 kN • Npl.d = A x fy / γM

= 5430 mm² x 240/1.1 N/mm² = 1184.73 kN

�Unity check: 69.74 / 1185 = 0.059 : Section is o.k. for Compression. B.2. Shear check


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Using article 756, Bild 18 : • Vz.Sd = 8.87 kN

• V

Af

pl z d

vy

M. . =

30γ

Av = h x s Av = 147 x 8 = 1176 mm² � Vpl.z.d = 148.14 kN � Unity check : 8.87/148.14 =0.06 : section is o.k. for shear. B.3. Combined bending, axial force and shear force check Using article 757. Since the small value of Mz , it is o.k. to neglect Mz => only major axis bending. Using Table 16 : Vz.sd / Vpl.z.d < 0.33 & N/Npl.d < 0.1

� So, the only condition to check is M/Mpl.d ≤ 1 • My.Sd = 44.4 kNm • Mpl.y.d = 240 N/mm² x 354 cm³ / 1.1 = 77.2 kNm Unity check: = 0.58 OR, by using Formula 40 • My

* = 74.61 kNm • My < My

* => Formula 41 • c1 = 0.637 x 10-3 • c2 = 1.011 • Mz / Mpl.zd

= 0.0189 Formula 41: = 0.308

�Section is o.k.

B.4. Stability check for Bending + Compression + L.T.B. Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 6 on position x=0m of member 19. Combination 6, member 19 on x =0.0 m : X =-69.74 kN (compression) My = 44.4 kNm Mz = -0.67 kNm => Can be neglected. Using article Teil 2, 323 and formula 30 :

N

N

M

Mk

M

Mk

z pl d

y

M pl y d

yz

pl z d

zκ κ. . . . .

+ + ≤ 1


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Substitution of values: 1. First term:

• N = 69.74 kN • Npl.d = 1184.73 kN • Determination of κz (Formula 4)

• Determination of λκ,red: λKz = lz/iz

lz = Lz x k’z (k’z = buckling factor, calculated by the program)

k’z = 0.90 Lz = 500 cm � lz = 450 cm � λΚz = 261/4.05 = 111.11

� λ Kz= 111.11 / 92.9 = 1.19 > 0.2 => Formula 4b

κz = 1

2k k K+ −² λ

• Determination of k : • α = 0.34

� k = 1.45 � κz = 0.44 � First term = 0.134 2. Second term (L.T.B):

• My = 44.4 kNm • Mpl.y.d = 77.2 kNm • Calculation of ky : according to Article 320.

kN

Nay

z pl d

y= −1κ .

but ky ≤ 1

ay Kz M y= −015 015. ..λ β (but ≤0.9)

λ Kz = 1.19

Calculation of β M y. :

Using Table 11: with ψ = 0

� β M y. = 1.8 − 0.7ψ = 1.8

� ay = 0.171

� ky = 0.98 • Determination of κM :

Determination of λM,red = M

M

pl y

Ki y

.

.

• Mpl.y = 84.9 kNm • Determination of Mki.y :

Or by using formula 19:

� Mki.y = 260.39 kNm (Assumption: zp = 0, Load in center of gravity)

Note : c² is calculated according to reference (2)


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cI

ll

l I

I

zz t

z

²

( )²( )² . ( )²

=+ω

ββ β

0 00 039

where: β0 = warping factor (default-value = 1), analogue to kw in EC3 βz = LTB factor (default-value = 1), analogue to k in EC3

� λM,red = 0.57 ( > 0.4 => Formula 18)

� Formula 18 => κM = 0.98

� Second term = 0.575

3. Third term:

• Mz = 0.70 ≈ 0 � Third term is neglected since the small value of Mz

4. Unity check:

0.134 + 0.575 = 0.709 < 1 � Section HEB 160 is o.k.

1.14.3 Check of macro 18.

1.14.3.1 Buckling data First we will discuss the buckling data of this macro.

1. System length L : for each member :

Ly = member length = 1m. Lz = macrolength / 2 = 6 m. (Lateral restraint by middle-rafter) Lltb = macrolength / 2 = 6 m. (Lateral restraint by middle-rafter)

2. The member is loaded through the shear center.

3. Sway modes: Y-Y: non-sway Z-Z: non-sway (bracing in roof-plane)

4. The effective length factors k and kw for L.T.B. are taken as 1 (No end fixity and no special provision for warping fixity).

1.14.3.2 Check of T120/120/13 section A. Cassification of the section a) Width-to-thickness ratio for outstand flanges 1 (using table 5.3.1c of the code) : c/tf = 60/13 = 4.62


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Max ratio for a class-1 section for a rolled flange subject to compression is 10 ε = 10. Since 4.62 < 10, this flange is a class 1 element. b) Width-to-thickness ratio for outstand flanges 2 (using table 5.3.1c of the code) : c/tf =120/13 = 9.23 Max ratio for a class-1 section for a rolled flange subject to compression is 10 ε = 10. Since 9.23 < 10, this flange is a class 1 element. � Section T120/120/13 is a class-1 section . � Note : Since DIN 18800 gives no formulas for T-sections, we have to classify all T-sections as a Class-3 section. (This is also done by the program) B. Stability check : Compression critical buckling check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 1 on position x=0m. of member 46. Combination 5, member 47 on x =0.0 m : X = -38.23 kN (compression) My = 0.59 kNm => Can be neglected (only induced by the self-weight) Z = 0.49 kN (Shear) LTB is neglected, because of the small value of My = 0.59 kNm, induced by the self-weight. Using Article Teil2, 304 and Formula 3:

N

Nz pl dκ .

≤ 1

Substitution of values : • N = 38.23 kN • A = 2960 mm² • fy = 240 N/mm² • γM = 1.1 • => Npl.d = 645.8 kN • Determination of κz (Formula 4)

• Determination of λκ,red: λKz = lz/iz

lz = Lz x k’z (k’z = buckling factor, calculated by the program)

k’z = 0.94 Lz = 600 cm � lz = 564 cm � λΚz = 564/245 = 230.2

� λ Kz= 230.2 / 92.9 = 2.48 > 0.2 => Formula 4b

κz = 1

2k k K+ −² λ

• Determination of k : • α = 0.49

� k = 4.13 � κz = 0.135 Unity check :


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= 0.44

� Section is o.k.

Calculation note

Macro 4 Member 7 IPE270 Fe 360 Ult. comb 5 0.25

Basic data DIN18800


Material data



fabrication rolled




ratio







ratio






Internal forces

N 0.20 kN

Vy 0.00 kN

Vz 2.25 kN

Mt 0.00 kNm

My 14.34 kNm

Mz -0.00 kNm

Normal force check



Table of values

Npl.d 980.59 kN

unity check 0.00

Shear check (Vz)



Table of values


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Table of values

Vpl.d 211.49 kN

unity check 0.01





Table of values

alfa.pl.y 1.13

alfa.pl.z 1.25

unity check 0.14



LTB check


unity check = 0.25

Table of values


KappaM 0.57

LambdaM_r 1.26

n 2.50

kn 1.00


LTB

LTB length 6.00 m

Betaz 1.00

Beta0 1.00

Ksi 1.12



Macro 11 Member 19 HEB160 Fe 360 Ult. comb 7 0.75

Basic data DIN18800


Material data



fabrication rolled




ratio





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ratio






Internal forces

N -69.74 kN

Vy 0.13 kN

Vz -8.86 kN

Mt -0.00 kNm

My 44.29 kNm

Mz -0.67 kNm

Normal force check



Table of values

Npl.d 1160.05 kN

unity check 0.06

Shear check (Vy)



Table of values

Vpl.d 513.11 kN

unity check 0.00

Shear check (Vz)



Table of values

Vpl.d 145.05 kN

unity check 0.06





Table of values

alfa.pl.y 1.14

alfa.pl.z 1.25

unity check 0.32






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Buckling curve b c



Length 5.00 5.00 m




Buckling check


Table of values


unity check 0.14

LTB check


unity check = 0.60

Table of values


KappaM 0.98

LambdaM_r 0.57

n 2.50

kn 1.00


LTB

LTB length 5.00 m

Betaz 1.00

Beta0 1.00

Ksi 1.77




Table of values

ky 1.01

kz 0.99

ay -0.13

az 0.05

BetaMy 1.80

BetaMz 1.80

unity check =0.14 + 0.59 + 0.02 = 0.75



Table of values

ky 0.98

kz 0.99

ay 0.17

az 0.05

BetaMy 1.80

BetaMz 1.80

unity check =0.14 + 0.58 + 0.02= 0.75


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LTB parameters

Table of values

KappaM 0.98

LambdaM_r 0.57

n 2.50

kn 1.00

Lambda_v 73.84

Lambda_vr 0.79

KappaM_v 0.67

ip 0.08 m

c 0.12 m



Macro 18 Member 47 T120/120/13 Fe 360 Ult. comb 6 0.49

Basic data DIN18800


Material data



fabrication rolled




ratio






Internal forces

N -38.33 kN

Vy -0.00 kN

Vz -0.46 kN

Mt -0.00 kNm

My 0.57 kNm

Mz 0.01 kNm

Normal stress check



Table of values

Sigma 26.25 MPa

unity check 0.12

Shear stress check



Table of values


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Table of values

tau 0.76 MPa

unity check 0.01







Buckling curve c c



Length 1.00 6.00 m





Buckling check


Table of values


unity check 0.44

LTB check


unity check = 0.05

Table of values


KappaM 0.98

LambdaM_r 0.56

n 2.50

kn 1.00

Mkiy =39.35 kNm

LTB

LTB length 6.00 m



Table of values

ky 0.95

kz 1.14

ay 0.80

az -0.32

BetaMy 1.86

BetaMz 1.79

unity check =0.44 + 0.05 + 0.00 = 0.49



Table of values


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Table of values

ky 0.84

kz 1.14

ay 0.36

az -0.32

BetaMy 1.40

BetaMz 1.79

unity check =0.44 + 0.04 + 0.00= 0.49

LTB parameters

Table of values

KappaM 0.98

LambdaM_r 0.56

n 2.50

kn 1.00

Lambda_v 43.46

Lambda_vr 0.46

KappaM_v 0.86

ip 0.04 m

c 0.08 m

Mkiy =39.35 kNm



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1.15 PST.06.03 – 01 : NEN 6770/6771 Steel Code Check Description The stability results for beam 5 of EPW are compared with the results given in Ref.[3], 1.5, pp.1.91-1.97 Project data See the input file. Reference [1] Staalconstructies TGB 1990

Basiseisen en basisrekenregels voor overwegend statisch belaste constructies NEN 6770, december 1991

[2] Staalconstructies TGB 1990 Stabiliteit NEN 6771, december 1991

[3] SG Cursus Rekenen met nieuwe normen januari 1992

Result EPW Ref.[3] Diff. l eff [m] 14.8 11.3 23.6 % ω kip 0.75 0.75 0 % unity check 0.47 0.46 2.12 % The difference in leff is due to the fact that for the calculation of the buckling ratio, EPW does not consider the occasional restraint in the hinged column foot. See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060301.epw Modules 2D Frame (PRS.01) NEN 6770/6771 Steel code check (PST.06.03) Author CVL


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Calculation note

NEN CHECK 6770/6771


Basic data NEN6770/6771

partial safety factor Gamma M0 for resistance of cross-sections = 1.00

Material data

Yield strenght fy;rep 235.00 MPa

Tensile strength ft;rep 360.00 MPa

fabrication rolled

SECTION CHECK

Width-to-thickness ratio for webs (NEN 6771 Tab.1.a)


ratio





Width-to-thickness ratio for outstand flanges (NEN 6771 Tab.1.c)


ratio






Internal forces

Ns;d -94.21 kN

Vy;s;d 0.00 kN

Vz;s;d 13.08 kN

Mx;s;d 0.00 kNm

My;s;d 0.00 kNm

Mz;s;d 0.00 kNm

Compression check

according to article NEN6770 11.2.2. and formula (11.2-5)


Table of values

Nc;u;d 1713.05 kN

unity check 0.05

Shear check (Vz)

according to article NEN6770 11.2.4. and formula (11.2-10) (11.2-14)


Table of values

Vu;d 557.36 kN

unity check 0.02


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STABILITY CHECK


type sway non-sway



Buckling curve a b



Length 5.80 5.80 m




Buckling check

according to article NEN6771 12.1.1.1. and formula (12.1-1a) (12.1-1b)

Table of values

Nc;u;d 1713.05 kN

unity check 0.18


according to article NEN6771 12.3.1.2.1. and formula (12.3-1) (12.3-2)

Table of values

ny 16.32

nz 6.83

chi y 1.00

chi z 1.00

ey* 25.18 mm

ez* 12.78 mm

My2;s;d 75.86 kNm

Mz2;s;d 0.00 kNm

My1;s;d 0.00 kNm

Mz1;s;d 0.00 kNm

My;mid;s;d 37.93 kNm

Mz;mid;s;d 0.00 kNm

My;equ;s;d 64.48 kNm

Mz;equ;s;d 0.00 kNm

My;u;d 240.13 kNm

Mz;u;d 44.95 kNm

Fy;tot;s;d 94.21 kN

Fz;tot;s;d 94.21 kN

Nc;u;d 1713.05 kN

wkip 0.75

unity check = 0.05+0.39+0.00=0.45 (12.3-1)

unity check = 0.05+0.38+0.03=0.47 (12.3-2)

Torsional buckling check for bending and compression

according to article NEN6771 12.3.3. and formula

Table of values

wkip 0.75

unity check 0.05



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1.16 PST.06.05 – 01 : AISC Steel code Check Tutorial Frame Description The unity check according to AISC-LRFD of members 4, 7 and macro 18 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win LRFD Steel code check. Project data See input file. Reference Manual of Steel Construction Load & Resistance Factor Design Part 6, Specifications and Codes AISC, Volume I, Second Edition, 1995 See the chapter "Manual calculation" for the manual calculation according to this reference. Result


0.479 0.48 0 %


0.22 0.22 0 %


0.52 0.52 0 %

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060501.epw Modules 3D Frame (PRS.11) AISC-LRFD Steel code check (PST.06.05) Author NEM/CVL Manual calculation

1.16.1 Member 4 Critical check : Load Combination : 5 Section : x = 2.22 m in member 4


SCIA Software

160

Beam type : HEB160


Beam length : 5 m Sway modes : Y-Y non-sway Z-Z non-sway

The member is loaded through the shear center. The effective length factors k and kw for LTB. are taken as 1 (No end fixity and no special provision for warping fixity).

1.16.1.1 Classification of the section (Table B5.1) a) Widh-to-thickness ratio for webs The web of member 7 is subjected to flexural compression in section x=3 m. By using table B.5.1, we find :

0.208160

td

w==

Maximum ratio for compact section : 625.109ksi083.34

640

F

640

w,y

== ⇒ WEB is COMPACT SECTION

b) With-to-thickness ratio for outstand flanges By using table B.5.1., we find for section x=0 m:

15.62.102

160

tb

f==

Maximum ratio for compact section : 13.11ksi083.34

65

F

65

w,y

== ⇒ ⇒ FLANGES are COMPACT SECTION

The HEB 160 section is a COMPACT SECTION section.

1.16.1.2 Buckling parameters (Art. E.2.) The formulas used to calculate the slenderness and reduced slenderness in LRFD are the same as in Eurocode 3.


AI

L

i

L

yyy ===λ (Using Art.5.5.1.2. (1) EC3)

571.123

AI

L

i

L

zzz ===λ (Using Art.5.5.1.2. (1) EC3)

• 9.939.93f

E

y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)



fAA

1

y

cr

yAy =β⋅

λ

λ=

⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)


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161

315.1N

fAA

1

z

cr

yAz =β⋅

λ

λ=

⋅⋅β=λ (Using Art.5.5.1.2. (1) EC3)

1.16.1.3 Normal force (Art. E.1) The design strength for flexural buckling of compression in member 4 is calculated as following : we have: 85.0c =φ

N95.113F658.0F ycr

2c =⋅

= λ

N5.6187481043.595.113AFP 3gcrn =⋅⋅=⋅=

Unity Check : 11062.15.61874885.0

41.8560

P

P 2

nc

u ≤⋅=⋅

=⋅φ

− ⇒ Section OK for tension

1.16.1.4 Torsional buckling (Art.Appendix E.3.) The checking of member 4 of macro 2 for lateral torsional-buckling and flexural-torsional buckling is made in the following way: • 85.0c =φ

• 610ESA,ww mm10807236.4IC ⋅==

• 47ESA,yx mm1049.2II ⋅== 46

ESA,zy mm1089.8II ⋅==

• 45ESA,t mm1014.3IJ ⋅==

• ( )

N33.868II

1JG

lK

CEF

yx2

z

w2

e =+

⋅

⋅+

⋅⋅π=

• Equivalent slenderness: 52.0F

F

e

ye ==λ

• Nominal critical stress: 2yQ

cr mmN85.209F658.0QF

2e =⋅

⋅= λ⋅ with 1Q = and 5.1Qe ≤⋅λ

• Nominal resistance in compression: N31.1139504FAP crgn =⋅=

Unity Check : 11083.8P

P 3

nc

u ≤⋅=⋅φ

− ⇒ Section OK for LTB

1.16.1.5 Strong axis bending (Art.F1)

Using Article F1.2a Design for Flexure : DETERMINATION OF LB:

The laterally unsupported length of the compression flange: Lb = 5 m DETERMINATION OF LP (Formula F1-4):


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162

mm23.2079in593.1F

r300L

yf

yp ==

⋅=

with mm 40.46 in593.1A

I r ESA,z

y ===

ksi 34.08 Fyf =

Since Lb> Lp we can use Article F1.2. of LRFD code. Using Lateral-torsional buckling rules, we see that we have to determine the flexural design strength φbMn where: Reduction factor φb = 0.90 Mn = nominal strength

DETERMINATION OF LR : (Formula F1-6) mm16.13382in85.526FX11F

XrL 2

L2L

1yr ==++= with:

• FL = 24.08 ksi

• Determination of X1:(Formula F1-8): 2x

1 mmN43.38412329.5571

2

EGJA

SX ==

π=

• Sx :35

ESAy, mm1011.3 ³ni978.18 W ⋅==

• J : 445ESAt, in 0.7543 mm1014.3I =⋅=

• E : modulus of elasticity of steel = 2mmN210000ksi 30457.92 =

• G : Shear modulus of elasticity = 2mmN80769.2ksi 11200 =

• A : in² 8.416 mm² 105.43 3 =⋅ • Determination of X2: (Formula F1-9):

2

4642

x

y

w2 N

mm10247.310546.1GJ

S

I

C4X −− ⋅=⋅=

=

• 446ESAz,y in 21.35 mm108.89 I I =⋅==

• Cw = Warping constant = 6610w in 179.016 mm10.84 I =⋅=

Since Lb < Lr, we use Article F1.2b. to determine the critical value of the moment: Mn = Mcr ≤ Mp

DETERMINATION OF MN :(Formula F1-3) ( ) Nmm24.84048021LL

LLMMMC

pr

pbrppb =

−

−⋅−−⋅

where Nmm831900001054.3235WFZFM 5yESA,plyyp =⋅⋅=⋅=⋅=

( ) Nmm5.516618851011.3115.166WF,10FminSFM 5yESA,elywyfxLr =⋅⋅=⋅−=⋅=

Determination of Cb: Modification factor for non-uniform moment diagram (Formula F1-3):

12.1M3M4M3M5.2

M5.12C

CBAmax

maxb =

+++= with

• Nm32.35115 M max =


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163

• Nm58.32819 M A =

Nm93.22816 MC = (Absolute value of moment at ¼ and ¾ of the unbraced segment)

• Nmm3.34077 M B = (Absolute value at centreline of the unbraced segment)

The nominal flexural strength MN is the lowest value obtained according to the limit state of yielding, lateral torsional buckling and flange local buckling. In the present situation, MN=Mp.

Unity check : 1469.09.083190

11.35189

M

M

nb

ux ≤=⋅

=⋅φ

⇒ SECTION IS OK

1.16.1.6 Weak axis bending (Art.F1) The introduction of LRFD Chapter F specifies that lateral-torsional buckling limit state is not applicable to members subjected to bending about the minor axis. We just have to perform yielding control following Art. F1.1.

where Nmm39950000107.1235WFZFM 5zESA,plyyp =⋅⋅=⋅=⋅=

Unity check : 11061.19.039950

97.57

M

M 3

nb

uy ≤⋅=⋅

=⋅φ

− ⇒ SECTION IS OK

1.16.1.7 Shear stress (Art. A-F2.2. and F2.)

Web Area: 2www mm8328104thA =⋅=⋅=

Ratio: 260138104

th

w≤== and 27.27F

k187th

yw

v

w=⋅≤ with 5kv =

We find: N117312235000000000832.06.0FA6.0V ywwn =⋅⋅=⋅⋅=

9.0v =φ

Unity Check : 11073.1V

V 2

nv

u ≤⋅=⋅φ

− ⇒ Section OK for Shear Stress

1.16.1.8 Shear Stress Check (Art. H2.) For member under combined torsion, flexure, shear, and axial force, we have:

Shear stress given by ESA-Prima Win : 2uv mN29.1678698f =

Unity Check: 11032.1F6.0

f 2

y

uv ≤⋅=⋅φ⋅

− with 9.0=φ

1.16.1.9 Combined stresses (Art.H1.1.) Following Art. H1.1. of LRFD, we have, for a symmetric member in flexure and tension, the following check to perform:

N20.618232)LTBP;bucklingPmin(P nnn ==


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164


M

M

M

P2

P 2.0

P

P

nyb

y,u

nxb

x,u

n

u

nn

u =

⋅φ+

φ+

⋅φ⋅⇒≤

⋅φ⇒ Section OK

1.16.2 Member 7 Critical check : Load Combination : 6 Section : x = 3 m Beam type : IPE270


Beam length : 6 m Sway modes : Y-Y non-sway Z-Z non-sway The member is loaded through the shear centre. The effective length factors k and kw for L.T.B. are taken as 1 (No end fixity and no special provision for warping fixity).

1.16.2.1 Classification of the section (Table B5.1) a) Width-to-thickness ratio for webs The web of member 7 is subjected to flexural compression in section x=3 m. By using table B.5.1, we find:

909.406.6270

td

w==

Maximum ratio for compact section: 625.109ksi083.34

640

F

640

w,y

== ⇒ WEB is COMPACT SECTION

b) With-to-thickness ratio for outstand flanges By using table B.5.1., we find for section x=0 m:

61.62.102

135

tb

f==


65

F

65

w,y

== ⇒ ⇒ FLANGES are COMPACT SECTION

The IPE 270 section is a COMPACT SECTION.

1.16.2.2 Normal force (Art. D.1) The design strength of tension in member 7 is calculated as following : For yielding in gross section : 9.0t =φ

10786501059.4235AFP 3gyn =⋅⋅=⋅=

Unity Check : 11082.110786509.0

28.177

P

P 4

nt

u ≤⋅=⋅

=⋅φ

− ⇒ Section OK for tension

1.16.2.3 Strong axis bending (Art.F1)


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Using Article F1.2a Design for Flexure : DETERMINATION OF LB:

The laterally unsupported length of the compression flange: Lb = 6 m DETERMINATION OF LP (Formula F1-4):

mm39.1554in19.61F

r300L

yf

yp ==

⋅=

with in 1.19 cm 30.2 ry ==

ksi 34.08 N/mm² 235 Fy ==

Since Lb> Lp we can use Article F1.2. of LRFD code. Using Lateral-torsional buckling rules, we see that we have to determine the flexural design strength φbMn where: Reduction factor φb = 0.90 Mn = nominal strength

DETERMINATION OF LR : (Formula F1-6) mm05.5521in36.217FX11F

XrL 2

L2L

1yr ==⋅++⋅

⋅= with:

• FL = 24.08 ksi

• Determination of X1:(Formula F1-8): 2x

1 mmN80.1827568.2650

2

AJGE

SX ==

⋅⋅⋅⋅

π=

• Sx :35

ESAy, mm104.29 ³ni179.26 W ⋅==

• J : in4 0.383 mm101.6 I 45ESAt, =⋅=

• E : modulus of elasticity of steel = 2mmN210000ksi 30457.92 =

• G : Shear modulus of elasticity = 2mmN23.80769ksi 11200 =

• A : in² 7.12 mm²104.59 3 =⋅

• Determination of X2: (Formula F1-9):

2

4532

x

y

w2 N

mm1048.710556.3JG

S

I

C4X −− ⋅=⋅=

⋅⋅⋅=

• 446ESAz,y in 10.09 mm104.2 I I =⋅==

• Cw = Warping constant = 6610w in 265.42 mm10.1277 I =⋅=

Since Lb > Lr, we use Article F1.2b. to determine the critical value of the moment: Mn = Mcr ≤ Mp

DETERMINATION OF MCR :(Formula F1-13) Nmm30.73427747

rL2

XX1

rL

2XSCMM

2

y

b

221

y

b

1xbncr =

⋅+

⋅⋅⋅==


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166

• Determination of Cb: Modification factor for non-uniform moment diagram(Formula F1-3):

1467.1M3M4M3M5.2

M5.12C

CBAmax

maxb =

⋅+⋅+⋅+⋅

⋅= with

• Nmm1015.1 M 7max ⋅=

• Nmm101.1 M M 7CA ⋅== (Absolute value of moment at ¼ and ¾ of the unbraced segment)

• Nmm105.1 M 7B ⋅= (Absolute value at centreline of the unbraced segment)

Unity check : 12255.09.030.73427747

76.14905676

M

M

nb

u ≤=⋅

=⋅φ

⇒ SECTION IS O.K.

1.16.2.4 Shear stress (Art.F2. and A-F2.2.)

Web Area: 2ww mm17826.6270tdA =⋅=⋅=

Ratio: 26027.336.66.219

th

w≤== and 11.34

F523

th26.27

F418

ywwyw

=≤≤=

We find: N57.205911

th

F418FA6.0

V

w

ywyww

n =

⋅⋅⋅

=

9.0v =φ

Unity Check : 10129.060.185335

05.2400

V

V

nv

u ≤==⋅φ

⇒ Section OK for Shear Stress

1.16.2.5 Shear stress (Art. H2.) For member under combined torsion, flexure, shear, and axial force, we have:

Shear stress given by ESA-PRIMAWIN: 2uv mmN52.1f =

Unity Check : 11018.7F

f 3

y

uv ≤⋅=⋅φ

− with 9.0=φ

1.16.2.6 Combined stresses (Art.H1.1.) Following Art. H1.1. of LRFD, we have, for a symmetric member in flexure and tension, the following check to perform :

Unity Check : 22.0M

M

M

M

P2

P 2.0

P

P

nyb

y,u

nxb

x,u

n

u

nn

u =

⋅φ+

φ+

⋅φ⋅⇒≤

⋅φ⇒ Section OK


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167

1.16.3 Macro 18 Critical check : Load Combination : 1 Section : x=0 m in member 47 Beam type : T120/120/13


Beam lengths : Ly = member length = 1 m Lz = macro length divided by 2 = 6m(Lateral restraint by middle-rafter) LLTB = macro length divided by 2 = 6m(Lateral restraint by middle-rafter) Sway mode : Y-Y non-sway Z-Z non-sway The member is loaded through the shear centre. The effective length factors k and kw for LTB. are taken as 1 (No end fixity and no special provision for warping fixity).

1.16.3.1 Classification of the section (Table B5.1) a) Width-to-thickness ratio for Legs The web of member 47 is subjected to flexural compression in section x=0 m. By using table B.5.1, we find:

61.4132

120

tb

w==


76

F

76

w,y

== ⇒ LEG is NON-COMPACT SECTION

The T120/120/13 section is a NON-COMPACT SECTION.

1.16.3.2 Buckling parameter (Art. E.2.) The formulas used to calculate the slenderness and reduced slenderness in LRFD are the same as in Eurocode 3.

• 9.939.93f

E

y1 =ε⋅=⋅π=λ (Using Art.5.5.1.2. EC3)


AI

L

i

L

y

y

yy ===λ (Using Article 5.5.1.2. (1) EC3)

673.244

AI

L

i

L

z

z

zz ===λ (Using Article 5.5.1.2. (1) EC3)

• Section 3 CLASS 1A =β (Using Article 5.5.1.1. (1) EC3)


fAA

1

y

cr

yAy =β⋅

λ

λ=

⋅⋅β=λ (Using Art. 5.5.1.2. (1) EC3)

605.2N

fAA

1

z

cr

yAz =β⋅

λ

λ=

⋅⋅β=λ (Using Art. 5.5.1.2. (1) EC3)


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168

1.16.3.3 Normal force (Art. D.1) The design strength for flexural buckling of compression in member 47 is calculated as follows : we have : 85.0c =φ

N37.30F877.0

F y2c

cr =⋅

λ=

N69.898961096.237.30AFP 3gcrn =⋅⋅=⋅=

Unity Check : 1463.069.8989685.0

69.35437

P

P

nc

u ≤=⋅

=⋅φ

⇒ Section OK for tension

1.16.3.4 Torsional buckling (Art.Appendix E.3.) The checking of member 47 of macro 18 for lateral torsional-buckling and flexural-torsional buckling is made in the following way: • 85.0c =φ

• 6ESA,ww mm0IC ==

• 46ESA,yx mm1066.3II ⋅== 46

ESA,zy mm1078.1II ⋅==

• 45ESA,t mm10834.1IJ ⋅==

• Co-ordinate of shear centre with respect to centroid: 0x0 = and mm59.27y0 =

• 98.50A

IIyxr yx2

020

20 =

+++=

• 707.0r

yx1H

20

20

20 =

+−=

• 762.2562

rLk

EF

2

x

xx

2

ex =

⋅

⋅π=

• 43.34

rLk

EF

2

y

yy

2

ey =

⋅

⋅π=

• ( )

283.1921rA

1JG

lk

CEF

20

2LTBz

w2

ez =⋅

⋅

⋅+

⋅

⋅⋅π=

• Equivalent slenderness: 349.0F

F

ez

ye ==λ

• Nominal critical stress: 2yQ

cr mmN27.223F658.0QF

2e =⋅

⋅= λ⋅ with 1Q = and 5.1Qe ≤⋅λ

• Nominal resistance in compression: N21.660885FAP crgn =⋅=

Unity Check : 110308.6P

P 2

nc

u ≤⋅=⋅φ

− ⇒ Section OK for LTB

1.16.3.5 Strong axis bending check (Art.F1.2c)

Using Article F1.2c Design for Flexure :


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DETERMINATION OF LB:

The laterally unsupported length of the compression flange: Lb = 6 m DETERMINATION OF MN :(Formula F1-13)

Nm62.9905

WFSFM,Nm62.9905B1BL

JGIEminMM elESA,yyxyr

2

b

ycrn

=

⋅=⋅==

++⋅

⋅⋅⋅⋅π==

with 120mm4.72ind with 143.0J

I

L

d3.2B

y

b

==−=⋅

⋅−=

Unity check : 10622.09.062.9905

24.553

M

M

nb

ux ≤=⋅

=⋅φ

⇒ SECTION is O.K.

1.16.3.6 Weak axis bending (Art.F1.1.) The introduction of LRFD Chapter F specifies that lateral-torsional buckling limit state is not applicable to members subjected to bending about the minor axis. We just have to perform yielding control following Art. F1.1. We remark that, for non-compact section, it’s more useful to calculate Mp with Wz,elESA. where Nm69.7004WFZFMM zESA,elyypn =⋅=⋅==

Unity check : 11041.39.069.7004

5.21

M

M 3

nb

uy ≤⋅=⋅

=⋅φ

− ⇒ SECTION IS OK

1.16.3.7 Shear Stress (Art. H2.) For member under combined torsion, flexure, shear, and axial force, we have:

Shear stress given by ESA-Prima Win : 2uv mmN83.0f =

Unity Check : 11092.3F

f 3

y

uv ≤⋅=⋅φ

− with 9.0=φ

1.16.3.8 Combined Stresses (Art.H1.1.) Following Art. H1.1. of LRFD, we have, for a symmetric member in flexure and tension, the following check to perform :

( ) N43.89874P,PminP LTB,nbuckling,nn ==


M

M

M

9

8

P2

P 2.0

P

P

nyb

y,u

nxb

x,u

n

u

nn

u =

⋅φ+

φ⋅+

⋅φ⋅⇒≥

⋅φ⇒ Section OK


AISC - LRFD Check


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170

Macro 2 Member 4 HEB160 Fe 360 Ult. comb 6 0.48

Material data

Yield stress Fy 235.00 MPa

Tensile stress Fu 360.00 MPa

fabrication rolled

Cfr. Table B5.1. ratio Compact Non-compact

Webs 20.00 107.08 166.15

Outstanding flanges 6.15 11.13 28.73

Section is classified as compact section.

Section is checked as compact section.


Axis definition :

- local x- axis in this code check is referring to the local y axis in EPW

- local y- axis in this code check is referring to the local z axis in EPW

Internal forces

Pu -8.55 kN

Vux 0.02 kN

Vuy -1.85 kN

Mut -0.00 kNm

Mux 35.23 kNm

Muy -0.06 kNm

Buckling parameters xx yy




Length 5.00 5.00 m



Buckling check

according to article E2 and formula (E2-1)

Table of values

Pn 618.23 kN

Pu 8.55 kN

Fcr 113.85 MPa

Resistance factor 0.85

unity check 0.02

Torsional buckling check

according to article A-E3. and formula (A-E3-1)

Table of values

Pn 1139.42 kN

Pu 8.55 kN

Fe 868.53 MPa

Equiv.slenderness 0.52


unity check 0.01


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LTB data

Lb 5.00 m

Cb 1.12

Strong axis bending check

according to article F1.2a and formula (F1-2)

Table of values

Lr 13.38 m

Lp 2.08 m

Mp 83.19 kNm

Mr 51.83 kNm

Mcr 165.19 kNm

Mn 83.19 kNm

Mu 35.23 kNm


unity check 0.47

Weak axis bending check

according to article F1. and formula -

Table of values

Mn 39.27 kNm

Mu 0.06 kNm


unity check 0.00

Shear stress check

according to article A-F2.2. and formula (A-F2-1)

in buckling field 1

Table of values

a 5.00 m

h 0.10 m

tw 8.00 mm

kv 5.00

Vn 117.31 kN

Vu -1.85 kN


unity check 0.02

Shear stress check

according to article H2.(b) and formula (H2-2)

Table of values

fuv 1.70 MPa


unity check 0.01

Combined stresses check

according to article H1.2. and formula (H1-1b)

Table of values

Pn 618.23 kN

Mnx 83.19 kNm

Mny 39.27 kNm

Pu 8.55 kN

Mux 35.23 kNm

Muy 0.06 kNm

Res. factor compression 0.85

Res. factor flexure 0.90


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unity check = 0.01+0.47+0.00=0.48 (H1-1b)




Material data



fabrication rolled


Webs 40.91 109.62 166.15

Outstanding flanges 6.62 11.13 28.73

Section is classified as compact section.

Section is checked as compact section.


Axis definition :



Internal forces

Pu 0.18 kN

Vux 0.00 kN

Vuy 2.40 kN

Mut 0.00 kNm

Mux 14.91 kNm

Muy -0.00 kNm

Normal force check

according to article D1 and formula (D1-1)

Table of values

Pn 1078.65 kN

Pu 0.18 kN


unity check 0.00

LTB data

Lb 6.00 m

Cb 1.15


according to article F1.2b and formula (F1-12)

Table of values

Lr 5.52 m

Lp 1.55 m

Mp 113.74 kNm

Mr 71.49 kNm

Mcr 74.23 kNm


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Table of values

Mn 74.23 kNm

Mu 14.91 kNm


unity check 0.22

Shear stress check

according to article A-F2.2. and formula (A-F2-1)

in buckling field 1

Table of values

a 6.00 m

h 0.22 m

tw 6.60 mm

kv 5.00

Vn 204.36 kN

Vu 2.40 kN


unity check 0.01

Shear stress check


Table of values

fuv 1.52 MPa


unity check 0.01


according to article H1.1. and formula (H1-1b)

Table of values

Pn 1078.65 kN

Mnx 74.23 kNm

Mny 22.00 kNm

Pu 0.18 kN

Mux 14.91 kNm

Muy 0.00 kNm

Res. factor tension 0.90


unity check = 0.00+0.22+0.00=0.22 (H1-1b)


Calculation note - Macro 18


Material data



fabrication rolled


Outstanding flanges 4.62 - 13.02

Section is classified as non-compact section.


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Section is checked as non-compact section.


Axis definition :



Internal forces

Pu -35.48 kN

Vux -0.00 kN

Vuy -0.44 kN

Mut -0.01 kNm

Mux 0.55 kNm

Muy 0.02 kNm





Length 1.00 6.00 m




Buckling check

according to article E2 and formula (E2-1)

Table of values

Pn 89.87 kN

Pu 35.48 kN

Fcr 30.36 MPa


unity check 0.46

Torsional buckling check

according to article A-E3. and formula (A-E3-1)

Table of values

Pn 89.61 kN

Pu 35.48 kN

Fe 34.52 MPa

Equiv.slenderness 2.61


unity check 0.47

LTB data

Lb 6.00 m

Cb 4.04


according to article F1.2c and formula (F1-15)

Table of values

Mcr 9.91 kNm

Mn 9.91 kNm

Mu 0.55 kNm



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Table of values

unity check 0.06

Weak axis bending check

according to article F1. and formula -

Table of values

Mn 7.00 kNm

Mu -0.02 kNm


unity check 0.00

Shear stress check


Table of values

fuv 0.82 MPa


unity check 0.01


according to article H1.2. and formula (H1-1a)

Table of values

Pn 89.61 kN

Mnx 9.91 kNm

Mny 7.00 kNm

Pu 35.48 kN

Mux 0.55 kNm

Muy -0.02 kNm

Res. factor compression 0.85


unity check = 0.47+8/9(0.06+0.00) =0.52 (H1-1a)



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1.17 PST.06.06 – 01 : CM 66 Steel Code Check Tutorial Frame Description The unity check according to CM 66 of members 3, 7 and 46 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win CM66 Steel code check. Project data See input file. Reference Règles de calcul des constructions en acier ITBTP / CTICM Règles CM Décembre 1966 Editions Eyrolles 1982 See the chapter "Manual calculation" for the manual calculation according to this reference. Result


0.392 0.4 0 %


0.379 0.38 0 %


0.426 0.43 0 %

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060601.epw Modules 3D Frame (PRS.11) CM66 Steel code check (PST.06.06) Author NEM/CVL Manual calculation

1.17.1 Member 3 Critical check : Load Combination : 9


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Section : x=0 m Beam Type : HEA180


Beam Length : 3 m Sway modes : Y-Y non-sway Z-Z non-sway

The member is loaded through the shear centre. We choose the ultimate loading case to compute and to verify the tutorial TUTCM66.epw. We must note capital letters are used to indicate ESA-Prima Win axis and small letter CM 66 axis.

1.17.1.1 Section Check A. Calculation of the plastic factor (Art.3,212-13,212) Using the table and figure 13,212 for H profile and Art.3,212 we have the following plastic factor :

ψx=1.06 (figure)

ψy=1.185 (table) B. Normal Stress (Art.1,3-3,3) The member is subjected to the following internal forces

X=-4861.09 N MX=-0.92Nm Y=-17.9 N MY=0 Nm Z=24198.37N MT=-1.2Nm

An= 0.00453 m2

By converting these internal forces according to the CM66 axis, we have N=-4861.09 N Mx=-0.92 Nm Ty=-17.9 N My=0 Nm Tz=24198.37 N Mt=-1.2 Nm

• Normal Stress (Art.1,312) : 2

net

N/m 3.107308800453.0

09.4861

A

N===σ

Unity Check : 11056.4235000000

3.1073088 3

e

≤⋅==σσ − ⇒ Section OK for Normal force

• Simple Bending (Art.3,2) The stresses due to the simple bending in the critical section x=0 in x&y direction are :

2y

y

yy

y

2x

x

xx

x

mN0

W

M

mN81.3147

000294.0

925.0

W

M

=ψ

=σ

−=−

=ψ

=σ


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Unity Check : 11057.4235000000

11.1076236 3

e

fyfx ≤⋅==σ

σ+σ+σ − ⇒ Section OK

B. Shear Stress (Art.1,3-3,3) The shear stress due to Y=-37.82N,Z=31960.09N and Mt=-0.002Nm is calculate by (Art.3,31) :

2tCenterShear,zCenter Shear,yCenter Shear

27wt

tt

253

4

xa

xxzCenterShear,z

Center Shear,y

mN27.26078441

mN14.48322

1049.1

006.02.1t

I

M

mN 12.26030119

1051.2106

1062.137.24198

Ie

ST

0

=τ+τ+τ=τ

−=⋅

⋅−=⋅=τ

=⋅⋅⋅

⋅⋅=

⋅

⋅=τ

=τ

−

−−

−

Unity Check: 117.054.1

e

≤=σ

τ⋅⇒ Section OK for shear stress

1.17.1.2 Stability Check A. Buckling Data (Art.3,401) The buckling parameters for members 3 subjected to compression are described in Art.3,401 and Art.3,411: • Bulking length: Lx= 1.8 m kxx=0.6 Ly= 2.1 m kyy=0.7 • Slenderness parameters:

48.46i

L 19.24

i

L

y

yy

x

xx ==λ==λ

• Euler critical loads and stresses:

m

N 079.959674558A

N

mN63.3544455672

A

N

N 748.4347325L

IEN N 19.16056384

L

IEN

2n

cryky2

n

crxkx

2

y2

cry2x

2

crxyx

==σ==σ

=⋅⋅π

==⋅⋅π

=

• Coefficients for Critical State:

13.1

1k 1

3.1

1k

31.894 04.3303

y

y1y

x

xx1

kyy

kxx

=−µ

−µ==

−µ

−µ=

=σ

σ=µ=

σ

σ=µ

• Buckling coefficients:


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b

ea

ef

Fig. 2

b

e

ef

Fig. 1

0946.165.05.065.05.0k

0212.165.05.065.05.0k

ky

e

2

ky

e

ky

ey

kx

e2

kx

e

kx

ex

=σ

σ−

σ

σ⋅++

σ

σ⋅+=

=σ

σ−

σ

σ⋅++

σ

σ⋅+=

B. Buckling Check (Art.3,411-3,441) B.1. Compression of full section beam (Art.3,44)

The method used in Art.3,411 to control the bucking phenomena is applicable to slender section only if the ratio width-to-thickness respected the rules presented in Art.3,441. We hall verify this rules both for the flanges and the web of the concerned section. Slenderness 75401.66 and 753.40 yx ≤=λ≤=λ (Art.3,441)

Flange: Outstand Element (Fig. 1): b = 0.087 m

ef = 0.0095 m

We verify 1587.15240

151578.9e

b

e

=σ

⋅≤=

Web: Internal Element (Fig.2): b = 0.152 ea=0.006

We verify 47.45240

4533.25e

b

e

=σ

⋅≤=

As we can see, we can apply the buckling check for this slender section as a full section. The unity check for compression is:

Unity Check : ( )

11099.4k,kmax 3

e

yx ≤⋅=σ

⋅σ − ⇒ Buckling Check OK in compression

B.2. Section subjected to compression and bending in the bucking direction (Art.3,5) The member 3 is subjected to several loads in the same direction. So, we apply the Art.3,516 to calculate the amplification coefficient of the stress flexion. We note that AM and Mmed are respectively the surface under the moment distribution and the moment in the middle of the buckling length.

0017.13.1

lM

A172.125.0

kx

2

medx

Mxx

fx =−µ

⋅−⋅−+µ

= with AMx=61794.45m2 and Mmedx=24291.99 Nm

994.03.1

lM

A172.125.0

ky

2

medy

Myy

fy =−µ

⋅−⋅−+µ

= with AMy=80.56m2 and Mmedy=26.85 Nm

We consider that σfx&y, described in Art.3,730, design the greater value of all the sections in the member submitted to a simple bending around x&y axis.


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24fy

y

maxyy

fy

2fx

x

maxxx

fx

mN58.438198

1003.119.1

71.53

W

M

mN 72.90680780

000294.007.1

36.28526

W

M

=⋅

=ψ

=σ

==ψ

=σ

−

C. LTB Check (Art.3,6) First, we have to calculate the LTB data described in Art.3,611 and Art.3,641-642-643. The coefficients B, C, D included in the kd and σd expressions are calculated in the following way: • The B coefficient (Art.3,643) is function of the load applied to the member. As we can see, the moment distribution in member 3 corresponds to the moment appearing in the case of uniform loads. On one side of this member, the moment equals 0. Using the table presented in Art. 3,643-21, we have, for loads applied to the shear center: B=1 • The C coefficient (Art.3,642-21) depends on the repartition of the loads on the member. In this case, we consider a uniform load:1.132 ≤C=1.7439≤1.88 • The D coefficient is calculate with the following expression:

33147.1h

l

I

J

E

G41D

2

2

y2

=⋅⋅⋅π

+=

with ( ) 2m

N2.9807692307612

EG =

ν+⋅= J=1.49 10-7 m4 h=0.171m

The member 3 is not subjected to loads between the supports, so that we use Art.3,611:

( ) e22

2

x

y2

d mN499.275892423CB1D

l

h

I

I

2.5

Eσ≥=⋅⋅−⋅⋅⋅

⋅π=σ ⇔ LTB Check is not necessary

D. Shear Buckling Check (Art.5,212) To prevent any risk of shear buckling, we have to control the relation Art.5,212-3 where h’a represents the free height of the web between the flanges, ea the width of the web, σ the normal stress in the critical section, d the distance between the stiffeners (here the length of the beam) and ra the rounding between web and flange. In this case, we have:

N37.24198T

m006.0e

m122.0r2t2hh

y

a

af'a

=

=

=⋅−⋅−=

The distance from the shear center to the two extreme fibers is:

'yfy v061.0rt

2

hv −==−−=

The normal stress taking as the maximum of two following values and the shear stress are:


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( )

2'aa

yy

221

25z

zz'z

y

yy'y0x,2

25z

zzz

y

yyy0x,1

mN51.33057882

he

Tm

N15.1075324,max

mN44.10708520.0

1051.2

92.0061.0

00391.0

09.4861

I

Mv

I

Mv

A

N

mN15.10753240.0

1051.2

92.0061.0

00453.0

09.4861

I

Mv

I

Mv

A

N

=⋅

=τ

=σσ

=+⋅

⋅−=⋅+⋅+=σ

=+⋅

⋅+=⋅+⋅+=σ

−=

−=

Considering that the beam is equipped with web stiffeners to improve the security, we have the following unity check to control:

Unity Check : 11024.110

h

e1000015.0

d4

h31

7

3144

'a

a

2

2

2'a

y2

≤⋅=⋅

⋅⋅

⋅

⋅+

τ+

σ

−− ⇒ Shear bucking check OK

E. Combined Moment & Normal Forces (Art.3,731) Following the Art.3,731, we calculate the unity check for combined moment and normal forces, taking into account that σfx&y design the greater stresses due to simple flexion (Art.3,730). Buckling in the x direction:

Unity Check : 1392.0kkkk

e

fxdfxfyfyy1 ≤=σ

⋅⋅σ+⋅σ+⋅σ⇒ OK

Buckling in the y direction:


e

fxdfxfyfyx1 ≤=σ

⋅⋅σ+⋅σ+⋅σ ⇒ OK


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1.17.2 Member 7 Critical check : Load Combination : 8 Section : x = 0 m Beam Type : IPE 240


Beam length : 6 m Sway modes : Y-Y sway Z-Z non-sway The member is loaded through the shear centre. We must note capital letters are used to indicate ESA-Prima Win axis and small letter CM 66 axis.

1.17.2.1 Section Check A. Calculation of the plastic factor (Art.3,212-13,212) Using the table and the figure 13,212 for I profile and Art.3,212 we have the following plastic factor :

ψx=1.06 (figure)

ψy=1.185 (table) B. Normal Stress (Art.1,3-3,3) The member is subjected to a normal force X=-2527,4939 N and a shear force Z=8615.80 N in the X=0 m section, considering that the moment approaches 0 precision.

X=-2527.5 N Z=8615.80 N

An= 0.00391 m2

• Normal Stress (Art.1,312): 2

net

N/m 43.64641900391.0

5.2527

A

N−=

−==σ

Unity Check : 11075.2235000000

34.646437 3

e


• Simple Bending (Art.3,2) The stress due to the simple bending in the critical section x=0 equal zero, therefor:

Unity Check : 10.0e

y

fy

e

x

fx

≤=σ

ψσ

=σ

ψσ

⇒ Section OK for simple bending

C. Shear Stress (Art.1,3-3,3) The shear stress due to Y=8615.80 N is calculate by (Art.3,31):

253

4

xa

xz m

N 26.65867251089.3102.6

1083.180.8615

Ie

ST=

⋅⋅⋅

⋅⋅=

⋅

⋅=τ

−−

−


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Unity Check : 11031.454.1 2

e

z ≤⋅=σ

τ⋅ − ⇒ Section OK for shear stress

1.17.2.2 Stability Check A. Bucking Data (Art.3,401) We consider that σfx&y, described in Art.3,730, design the greater value of all the sections in the member submitted to a simple bending around x&y axis. Moreover, we get the normal tension X to 0, the program doesn’t taking account for the beneficial effect of tension forces.

0W

M

mN 8.44389482

1024.30591.1

18.15232

W

M

fy

y

maxyy

fy

24fx

x

maxxx

fx

≅ψ

=σ

=⋅

=ψ

=σ−

The buckling parameters for members subjected to compression are described in Art.3,401: • Bulking length (calculate by EC3): Lx= 6 m kxx=1

Ly= 6 m kyy=1

• Slenderness parameters: 6345.222i

L 1564.60

i

L

y

yy

x

xx ==λ==λ


m

N 43.41817505A

N

mN 64.572782028

A

N

N 44.163506L

IEN N 73.2239577

L

IEN

2n

cryky2

n

crxkx

2y

2

cry2x

2

crx

==σ==σ

=⋅⋅π

==⋅⋅π

=


6891.64 05.886ky

ykx

x =σ

σ=µ=

σ

σ=µ (due to N=0)

0047.13.1

1k 0003.1

3.1

1k

y

y1y

x

xx1 =

−µ

−µ==

−µ

−µ=


5624.765.05.065.05.0k

188.165.05.065.05.0k

ky

e

2

ky

e

ky

ey

kx

e2

kx

e

kx

ex

=σ

σ−

σ

σ⋅++

σ

σ⋅+=

=σ

σ−

σ

σ⋅++

σ

σ⋅+=

B. Buckling Check (Art.3,411-3,441) B.1. Compression of full section beam (Art.3,44)


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The method used in Art.3,411 to control the bucking phenomena is applicable to slender section only if the ratio width-to-thickness respected the rules presented in Art.3,441. We shall verify this rules both for the flange and the web of the concerned section.

• Slenderness 751564.60x ≤=λ (Art.3,441)

Flange: Outstand Element (Fig. 1): b = 0.0569 m ef = 0.0098 m


15806.5e

b

e

=σ

⋅≤=

Web: Internal Element (Fig.2): b = 0.2204 ea=0.00619

We verify 47.45240

456058.35e

b

e

=σ

⋅≤=

• Slenderness λy=222.62 ≥ 75 (Art.3,442):

Flange: Outstand Element (Fig. 1): b = 0.0569 m

ef = 0.0098 m

We verify 995.44240

7515806.5

e

b

e

=σ

⋅λ

⋅≤=

Web: Internal Element (Fig.2): b = 0.2204

ea=0.00619


75456058.35

e

b

e

=σ

⋅λ

⋅≤=

As we can see, we can apply the buckling check for this section as a full section. The unity check for compression is:

Unity Check : ( )

11008.2k,kmax 2

e

yx ≤⋅=σ

⋅σ − ⇔ Buckling Check OK in compression


=−µ

⋅−⋅−+µ

=3.1

lM

A172.125.0

kx

2

medx

Mxx

fx 1.0014 with AMx=58073.37m2 and Mmedx=15232.18 Nm

b

ea

ef

Fig. 2

b ea

ef

Fig. 1


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0244.13.1

25.0k

y

yfy =

−µ

+µ=

To improve the security of the program, we’ve performed the calculation of AM. The program integrates the surface under the moment distribution by applying Simpson Method. We have verified this integration by applying this method manually.

C. LTB Check (Art.3,6) First, we have to calculate the LTB data described in Art.3,611 and Art.3,641-642-643. The coefficient B, C, D include in the kd expression are calculated in the following way: • The B coefficient (Art.3,643) is function of the load applied to the member. As we can see, the moment distribution in member 7 corresponds to the moment appearing in the case of a uniform loads. Using the table presented in Art. 3,643-

21, we have, for loads applied to the shear center: B=1 • The C coefficient (Art.3,642) depends on the repartition of the loads on the member. In this case, we consider a uniform load: C=1.13 • The D coefficient is calculate with the following expression:

329.2h

l

I

J

E

G41D

2

2

y2

=⋅⋅⋅π

+=

with ( ) 2m

N231.9807692307612

EG =

ν+⋅= J=1.29e-7 m4 Iy=2.84 10-6 m4 and h=0.24m

The member is symmetrically loaded and supported so that we use the expression Art.3,611 to calculate the LTB stress:

( ) e22

2

x

y2

d mN955.70843063CB1D

l

h

I

I

2.5

Eσ≤=⋅⋅−⋅⋅⋅

⋅π=σ

Total Surface

5110Nm 10117.89Nm

11923.53N

15232.4Nm

13626.89N

1533 m2

34733.79m2

29036.6m2

58073.3m2

6101.3m2

12713.8m2

20378.9m2 N

m

Simpson Method


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This relation implicated that a LTB check is necessary. The other LTB data are:

( )9677.1

1k1

kk

378.365.05.065.05.0k

mN41.99186648

E

55.1441I

I

CB

4

h

l

0e

d

0d

k

e2

k

e

k

e0

22

2

k

e

d

y

x0

0

=−⋅

σ

σ+

=

=σ

σ−

σ

σ⋅++

σ

σ⋅+=

=λ

⋅π=σ

=

σ

σ−⋅⋅

⋅⋅=λ

The unity check for LTB is given by (Art.3,611):

Unity Check : 10W

Mkk

fxe

y

m0x,xxd

e

dfx ≤=⋅σ

ψ⋅

=σ

⋅σ=

⇒ LTB check OK

D. Shear Buckling Check (Art.5,212) To prevent any risk of shear buckling, we have to control the relation Art.5,212-3 where h’a represents the free height of the web between the flanges, ea the width of the web, σ the normal stress in the critical section, d the distance between the stiffeners (here the length of the beam) and ra the rounding between web and flange. In this case, we have:

N80.8615T

m0062.0e

m1904.0r2t2hh

y

a

af'a

=

=

=⋅−⋅−=

The distance from the shear center to the two extreme fibers is:

'yfy v0952.0rt

2

hv −==−−=

The normal stress taking as the maximum of two following values and the shear stress are:

( )

2'aa

yy

221

2z

zz'z

y

yy'y0x,2

2z

zzz

y

yyy0x,1

mN51.7298556

he

Tm

N34.646437,max

mN34.646437

00391.0

57.2527

I

Mv

I

Mv

A

N

mN34.646437

00391.0

57.2527

I

Mv

I

Mv

A

N

=⋅

=τ

−=σσ

−=−

=⋅+⋅+=σ

−=−

=⋅+⋅+=σ

=

=

Considering that the beam is equipped with web stiffeners to improve the security, we have the following unity check to control :


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Unity Check : 11015.310

h

e1000015.0

d4

h31

7

5144

'a

a

2

2

2'a

y2

≤⋅=⋅

⋅⋅

⋅

⋅+

τ+

σ

−− ⇒ Shear bucking check OK

E. Combined Moment & Normal Forces (Art.3,731) Following the Art.3,731, we calculate the unity check for combined moment and normal forces (N=0 in this case), taking into account that σfx&y design the greater stresses due to simple flexion (Art.3,730). Buckling in the x direction:


e

fxdfxfyfyy1 ≤=σ

⋅⋅σ+⋅σ+⋅σ⇒ OK



e

fxdfxfyfyx1 ≤=σ

⋅⋅σ+⋅σ+⋅σ ⇒ OK

1.17.3 Member 46 Critical check : Load Combination : 10 Section : x = 0 m Beam type : T120/120/13


Beam length : 1 m Sway modes : Y-Y non-sway Z-Z non-sway

The member is loaded through the shear centre. We must note capital letters are used to indicate ESA-Prima Win axis and small letter CM 66 axis.

1.17.3.1 Section Check A. Calculation of the plastic factor (Art.3,212-13,212) Using the table and the figure 13,212 for H profile and Art.3,212 we have the following plastic factor :

ψx=1.23 (figure)

ψy=1.20 (table)

B. Normal Stress (Art.1,3-3,3) The member is subjected to the following internal forces :

X=36858.06N MX=-46.07Nm Y=1.34 N MY=8.26Nm Z=748.86 N MT=7.06-6.74Nm


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An= 0.00453 m2

By converting these internal forces according to the CM66 axis, we have N=-36858.06 N Mx=-46.07Nm Tx=1.34 N My=8.26Nm Ty=748.86 N Mt=6.74Nm

• Normal Stress (Art.1,312) : 2

net

N/m 29.1245204700296.0

06.36858

A

N===σ

Unity Check : 11029.5235000000

29.12452047 2

e


• Simple Bending (Art.3,2) The stress due to the simple bending in the critical section x=0 in x&y direction are :

y

y

yy

y

x

x

xx

x

W

M

W

M

ψ=σ

ψ=σ

Unity Check : 11054.5235000000

49.13035581 2

e

fyfx ≤⋅==σ

σ+σ+σ − ⇒ Section OK

C. Check Shear Stress (Art.1,3-3,3) The shear stress due to Tx=1.34N, Ty=748.86N and Mt=-46.07Nm is calculate by (Art.3,31):

2tzy mN05.1197693=τ+τ+τ=τ

Unity Check : 11084.754.1 3

e

≤⋅=σ

τ⋅ − ⇒ Section OK for shear stress

1.17.3.2 Stability Check A. Bucking Data (Art.3,401) The buckling parameters for members 3 subjected to compression are described in Art.3,401 and Art.3,411: • Buckling length: Lx= 1 m kxx=1

Ly= 5.64 m kyy=0.94 • Slenderness parameters:

204.230i

L 49.28

i

L

y

yy

x

xx ==λ==λ



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b

ea

ef

Fig. 2

b

e

ef

Fig. 1

m

N 63.39182227A

N

mN47.2562762818

A

N

N 39.115979L

IEN N 94.7585777

L

IEN

2n

cryky2

n

crxkx

2

y2

cry2x

2

crxyx

==σ==σ

=⋅⋅π

==⋅⋅π

=


16.13.1

1k 1

3.1

1k

146.3 81.05212.11023673

47.2562762818

y

y1y

x

xx1

kyy

kxx

=−µ

−µ==

−µ

−µ=

=σ

σ=µ==

σ

σ=µ


052.865.05.065.05.0k

03.165.05.065.05.0k

ky

e

2

ky

e

ky

ey

kx

e2

kx

e

kx

ex

=σ

σ−

σ

σ⋅++

σ

σ⋅+=

=σ

σ−

σ

σ⋅++

σ

σ⋅+=

B. Buckling Check (Art.3,411-3,441) B.1. Compression of full section beam (Art.3,44) The method used in Art.3,411 to control the bucking phenomena is applicable to slender section only if the ratio width-to-thickness respected the rules presented in Art.3,441. We shall verify this rules both for the flanges and the web of the concerned section. Slenderness 7549.28x ≤=λ (Art.3,441)

Flange: Outstand Element (Fig. 1): b=0.01135 m

ef=0.013 m


1573.8e

b

e

=σ

⋅≤=

Web: Internal Element (Fig.2): b=0.05349

ea=0.013

We verify 15.15240

1511.4e

b

e

=σ

⋅≤=

Slenderness 75204.230y ≥=λ (Art.3,441)

Flange: Outstand Element (Fig. 1): b=0.0107 m ef=0.013 m

We verify 52.46240

751523.8

e

b

e

y =σ

⋅λ

⋅≤=


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Web: Internal Element (Fig.2): b=0.05349

ea=0.013

We verify 52.46240

751511.4

e

b

e

y =σ

⋅λ

⋅≤=

As we can see, we can apply the buckling check for this slender section as a full section. The unity check for compression is:

Unity Check : ( )

1426.0k,kmax

e

yx ≤=σ

⋅σ ⇒ Buckling Check OK in compression


01.13.1

lM

A172.125.0

kx

2

medx

Mxx

fx =−µ

⋅−⋅−+µ

= with AMx=251.07m2 and Mmedx=251.07 Nm

84.13.1

lM

A172.125.0

ky

2

medy

Myy

fy =−µ

⋅−⋅−+µ

= with AMx=8.93 m2 and Mmedx=8.93 Nm

B.3. Combined Moment & Normal Forces (Art.3,731) Following the Art.3,731, we calculate the unity check for combined moment and normal forces, taking into account that σfx&y design the greater stresses due to simple flexion (Art.3,730). Buckling in the x direction :


e

fxdfxfyfyy1 ≤=σ

⋅⋅σ+⋅σ+⋅σ⇒ OK



e

fxdfxfyfyx1 ≤=σ

⋅⋅σ+⋅σ+⋅σ ⇒ OK


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Calculation note - Member 3 CM66 Check

Macro 2 Member 3 HEA180 Fe 360 Ult. comb 10 0.40

Material data

Yield strength 235.00 MPa

Tensile strength 360.00 MPa

fabrication rolled

Section Check CM66


Axis definition :



Internal forces

N -4.85 kN

Tx -0.02 kN

Ty 24.24 kN

Mt -0.00 kNm

Mx -0.00 kNm

My 0.00 kNm

Normal stress check

according to article (3,1) (3,2)

Table of values

sigma 1.07 MPa

Psix 1.07

Psiy 1.19

unity check 0.00

Shear stress check

according to article (3,3)

Table of values

tau 26.15 MPa

unity check 0.17


Stability check CM66



Length 3.00 3.00 m





Critical Euler stress 3544.46 959.67 MPa

mu 3312.21 896.79

Amplification factor k1 1.00 1.00

Buckling coefficient k 1.02 1.09


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Buckling check

according to article 3,411

Table of values

sigma 1.07 MPa

k 1.09

unity check 0.00

LTB parameters

LTB length l0 3.00 m

k 1.00

LTB length l 3.00 m

C 1.65

Beta 3.00

B 1.00

D 1.33


LTB check


Table of values

Sigma f 0.00 MPa

LTB factor kd 1.00

Sigma d 261.54 MPa

unity check 0.00



Table of values

sigma 1.07 MPa

Sigma fx 91.41 MPa

Sigma fy 0.45 MPa

LTB factor kd 1.00

Amplification factor kfx 1.00

Amplification factor kfy 1.00

AMx 62110500.09 kN mm^2

AMy 81800.44 kN mm^2

Mmed x 24.81 kNm

Mmed y 0.03 kNm

My max 28.62 kNm

Mz max 0.05 kNm

unity check 0.40

1.07+91.45+0.45=92.97 MPa

1.07+91.45+0.45=92.97 MPa


in buckling field 1

according to article 5,212-3

Table of values

sigma 0.11 daN/mm^2

tau 3.31 daN/mm^2

h'a 122.00 mm

ea 6.00 mm

d 3000.00 mm

unity check 0.00



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Material data



fabrication rolled

Section Check CM66


Axis definition :



Internal forces

N -2.58 kN

Tx 0.00 kN

Ty 8.62 kN

Mt 0.00 kNm

Mx -0.00 kNm

My -0.00 kNm

Normal stress check


Table of values

sigma 0.66 MPa

Psix 1.06

Psiy 1.19

unity check 0.00

Shear stress check


Table of values

tau 6.54 MPa

unity check 0.04





Length 6.00 6.00 m






mu 869.62 63.49




Buckling check


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Table of values

sigma 0.66 MPa

k 7.56

unity check 0.02

LTB parameters

LTB length l0 6.00 m

k 1.00

LTB length l 6.00 m

C 1.13

Beta 1.00

B 1.00

D 2.33




Table of values

sigma 0.66 MPa

Sigma fx 44.37 MPa

Sigma fy 0.00 MPa

LTB factor kd 1.99



AMx 58040926.24 kN mm^2

AMy 0.00 kN mm^2

Mmed x 15.23 kNm

Mmed y 0.00 kNm

My max 15.23 kNm

Mz max -0.00 kNm

unity check 0.38

0.66+88.50+0.00=89.16 MPa

0.66+88.50+0.00=89.16 MPa


in buckling field 1

according to article 5,212-3

Table of values

sigma 0.07 daN/mm^2

tau 0.73 daN/mm^2

h'a 190.40 mm

ea 6.20 mm

d 6000.00 mm

unity check 0.00



Material data



fabrication rolled

Section Check CM66


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Axis definition :



Internal forces

N -36.87 kN

Tx 0.00 kN

Ty 0.75 kN

Mt 0.01 kNm

Mx -0.04 kNm

My 0.01 kNm

Normal stress check


Table of values

sigma 13.03 MPa

Psix 1.23

Psiy 1.20

unity check 0.06

Shear stress check


Table of values

tau 1.19 MPa

unity check 0.01





Length 1.00 6.00 m






mu 205.73 3.15




Buckling check


Table of values

sigma 12.46 MPa

k 8.05

unity check 0.43



Table of values

sigma 12.46 MPa


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Table of values

Sigma fx 10.39 MPa

Sigma fy 0.27 MPa

LTB factor kd 1.00



AMx 270071.33 kN mm^2

AMy 8945.17 kN mm^2

Mmed x 0.29 kNm

Mmed y 0.01 kNm

My max 0.55 kNm

Mz max -0.01 kNm

unity check 0.11

14.48+10.47+0.50=25.45 MPa

12.48+10.47+0.50=23.44 MPa


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1.18 PST.06.08 - 01 : SIA161 Steel Code Check Tutorial Frame Description The unity check according to SIA161 of members 7, 4 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win SIA161 Steel code check. Project data See input file. Reference SIA 161 Norme Edition 1990 Constructions métalliques Editeur: Société suisse des ingénieurs et des architectes Eurocode 3: Calcul des structures en acier Edition 1992 Essentials of Eurocode 3:Design Manual for Steel Structures in Building First Edition 1991 See the chapter "Manual calculation" for the manual calculation according to this reference. Result Member EPW Manually 4 section check 0.253 0.253 LTB 0.559 0.558 Flexion+normal force 0.48 0.48 7 section check 0.023 0.0234 LTB 0.33 0.3316 Flexion + normal force 0.37 0.37 See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST060801.epw Modules 3D Frame (PRS.11) SIA161 Steel code check (PST.06.08) Author NEM/CVL


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Manual calculation

1.18.1 Member 7

1.18.1.1 Classification of the section (Table 3. SIA161) A. Width-to-thickness ratio for webs By using Table 16a of SIA161, we can determine the yield strength fy:

• Normal steel grade: S275 • Nominal thickness of the element t ≤ 40 mm

⇒ Nominal value of yield strength: fy=275 N/mm2

The web of member 7 is subjected both to bending and tension in section x=0.55 m. By using Table 3. of SIA161, we find:

NAfN ypl 1075250=⋅= and 00.N

Nn

R

pl=

γ

=

( ) ( ) 326641142093700620

230 .f

En....

.t

tht

dyw

f

w=⋅⋅−⋅≤==−= ⇒ WEB is CLASSE 1 (PP Method)

B. Width-to-thickness ratio for flanges By using table 3. for outstand element, we find for section x=0 m

491038012600980

120.

f

E..

.

.

T

b

y

=⋅≤== ⇒ FLANGES are CLASSE 1 (Method PP)

The section IPE 240 is a plastic section for the stability check, following SIA 161 rules.

1.18.1.2 Check Normal Stress and shear stress (Art. 3.2.11.1 and Art. 4.13.6) The member 7 is subjected to a normal tension N=262.81N and a small shear forces Fvy=2250.05N in the critical section. According to SIA 161, we can verify: Unity Check:

Normal check: 110442

11003910275000000

81262 4 ≤⋅=⋅

=

γ⋅

−.

..

.fAF

R

y

Shear area: ( ) 2001427024000620 m...tbtA fwwz =⋅=−⋅=

Shear check: 110091

1178226604

052250

3

2 ≤⋅==

γ⋅

⋅=

γ

−.

...

fAV

VV

R

ywz

dz

R

zRd

dz

⇒ Section OK for tension and shear


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1.18.1.3 Combined bending, axial force (Art. 4.13.4.) By using Art. 4.13.4 (42), we can determine:

N.AfN ypl 1075250003910275000000 =⋅=⋅=

Nm.ZfM yyply 1006500003660275000000 =⋅=⋅= and Nm.ZfM zyplz 203501047275000000 5 =⋅⋅=⋅= −

5741

1

11 .

A

A w=

−=ξ and 212231

21

122 . .

A

A w=ξ⇒=

⋅−

=ξ

NmMM plzN,plz 20350==

( ) Nm.;minN

NM;MminM

R

pl

dplyplyN,ply 1006504712081210065012 ==

γ

−⋅ξ⋅=

115

11 .N

N;.max

R

pl

d =

γ

⋅=α

Unity check: 110342 2

2

≤⋅=

γ

+

γ

−

α

.M

MM

M

R

N,plz

dz

R

N,ply

dy

1.18.1.4 Stability Check: Check for bending, compression and L.T.B.

A. Calculation of Lateral Torsional Buckling (Art. 3.254)

Table 3 of SIA161 proposes the calculation of the critical LTB length to check if a LTB is necessary. In this case, we have:

ml.f

Eil D

yzcr 6531

3

212 =<=⋅

ψ−⋅⋅= where 0.1

M

M

max,d

min,d ==ψ ⇒ LTB check necessary

Before the calculation of the LTB resistant moment, we must determinate irc. irc is defined as the radius gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web. Before the calculation of the compression area and the compression inertia, we must calculate distribution and the height of compression stress due to the moment My: Level arm: m.a 11020=

Stress: 23139702047m

N.bottop =σ−=σ

Height in compression: m.h

bottop

wtop11020=

σ+σ

⋅σ

Reduced area: 2310403713

m.tb

tbA wcwcffr

−⋅=⋅

+⋅=

Reduced area: 4633

1041113612

m.tbbt

I wcwcffrc

−⋅=⋅

+⋅

=

Reduced radius giration: m.A

Ii

rc

rcrc 03170==


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0440.M

M

max,d

min,d −==ψ 13130051751 2 .... =ψ⋅+ψ⋅−=η

m.l

l DK 645=

η= 83177.

i

l

rc

KK ==λ

22

2

2965537559m

N.E

KDw =

λ

⋅π=σ 2923143952330

mN.IEKG

Wl zyD

Dv =⋅⋅⋅⋅⋅

π⋅η=σ

222 131158169049

mN.DwDvcrD =σ+σ=σ

4011.W

Zf

ycrD

yyD =

⋅σ

⋅=λ 4610

1

1450

54.

.

.D

=

λ+=ζ 295127005186

mN.f yD =⋅ζ=σ

Nm.ZM yDD 8946483=⋅σ=

Unity check : 133160 ≤=

γ

.M

M

R

D

dy => OK LTB check

B. Tension members with moments (Art. 4.142.(48)) The internal forces for the ultimate combination 4 in the critical section x=3 m are N=262.81 N (tension) and My=14014.607 Nm. As we don’t take into account the beneficial effect of tension force (N=0), we find:

N.l

IEN

Ky

ycry 732239577

2

2

=⋅⋅π

= and N.l

IEN

Kz

zcrz 44163506

2

2

=⋅⋅π

=

0.1y =ω and 14060 =⋅+=ωmax,dz

min,dzz M

M..

12

40 =⋅

+

γ

+=βb

cN

N.

R

pl

d

( ) kNm7.46MkNm89.41MM DyDN,Ry =η⋅ω<== NmMM plzN,Rz 20350==

Unity check: 137.0M

MM

M

R

N,Rz

dzz

R

N,Ry

dyy ≤=

γ

⋅ω+

γ

⋅ω

ββ

=> Stability check OK

1.18.2 Member 4

1.18.2.1 Classification of the section (Table 3. BS5950) A. Width-to-thickness ratio for webs By using Table 16a of SIA161, we can determine the yield strength fy:

• Normal steel grade: S275 • Nominal thickness of the element t ≤ 40 mm


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⇒ Nominal value of yield strength: fy=275 N/mm2

The web of member 4 is subjected both to bending and tension in section x=0 m. By using Table 3. of SIA161, we find:

NAfN ypl 1245750=⋅= and 00.N

Nn

R

pl=

γ

=

( ) ( ) 32664114291260060

16150 .f

En....

.t

tht

dyw

f

w=⋅⋅−⋅≤==−= ⇒ WEB is CLASSE 1 (PP Method)

B. Width-to-thickness ratio for outstand flanges By using table 3. for outstand element, we find for section x=0 m

491038047900950

090.

f

E..

.

.

T

b

y

=⋅≤== ⇒ FLANGES are CLASSE 1 (Method PP)

The section HEA 180 is a plastic section for the stability check, following SIA 161 rules.

1.18.2.2 Check Normal Stress and shear stress (Art. 3.2.11.1 Art. 4.13.6) The member 4 is subjected to a normal tension N=2276.208N and shear forces Vvy=18.6 N Vzz=-2151.64 N in the critical section. According to SIA 161, we can verify: Unity Check:

Normal check: 1102

11004530275000000

22276 3 ≤⋅=⋅

=

γ⋅

−

...

fAF

R

y

Shear area: ( ) 20034202 m.tbA fwy =⋅⋅=

( ) 20009690 m.tbtA fwwz =−⋅=

Shear check: 11083

1192542997

7618

3

5 ≤⋅==

γ⋅

⋅=

γ

−.

..

.fA

V

V

V

R

ywy

dy

R

yRd

dy

1105381

1141153849

752150

3

2 ≤⋅==

γ⋅

⋅=

γ

−.

...

fAV

VV

R

ywz

dz

R

zRd

dz


1.18.2.3 Combined bending, axial force (Art. 4.13.4.) By using Art. 4.13.4 (42), we can determine:

N.AfN ypl 1245750004530275000000 =⋅=⋅=

Nm.ZfM yyply 891000003240275000000 =⋅=⋅= and Nm.ZfM zyplz 429000001560275000000 =⋅=⋅=

271

1

11 .

A

Aw=

−=ξ and 21121

21

122 . .

A

A w=ξ⇒=

⋅−

=ξ


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NmMM plzN,plz 42900==

NmMN

NM;MminM ply

R

pl

dplyplyN,ply 8910012 ==

γ

−⋅ξ⋅=

115

11 .N

N;.max

R

pl

d =

γ

⋅=α

Unity check: 12530

2

≤=

γ

+

γ

α

.M

MM

M

R

N,plz

dz

R

N,ply

dy

1.18.2.4 Stability Check: Check for bending, compression and L.T.B. A. Calculation of Lateral torsional Buckling (Art. 3.254)

Table 3 of SIA161 proposes the calculation of the critical LTB length to check if a LTB is necessary. In this case, we have:

ml.f

Eil D

yzcr 5492

3

212 =<=⋅

ψ−⋅⋅= where 0==ψ

max,d

min,d

M

M⇒ LTB check necessary

Before the calculation of the LTB resistant moment, we must determinate irc. irc is defined as the radius gyration of a section comprising the compression flange plus 1/3 of the compression web area, taken about an axis in the plane of the web. Before the calculation of the compression area and the compression inertia, we must calculate distribution and the height of compression stress due to the moment My: Height in compression: m.bwc 0760=

Reduced area: 200186203

m.tb

tbA wcwcffr =

⋅+⋅=

Reduced area: 4633

1061743612

m.tbbt

I wcwcffrc

−⋅=⋅

+⋅

=

Reduced radius gyration: m.A

Ii

rc

rrc 049790==

0==ψmax,d

min,d

M

M 411.=η

m.l

l DK 24=

η= 049790.

i

l

rc

KK ==λ

22

2

85290404639m

N.E

KDw =

λ

⋅π=σ 216461562551

mN.IEKG

Wl zyD

Dv =⋅⋅⋅⋅⋅

π⋅η=σ

222 87545320862

mN.DwDvcrD =σ+σ=σ

7450.W

Zf

ycrD

yyD =

⋅σ

⋅=λ 90

1

1450

54.

.

.D

=

λ+=ζ 273247248657

mN.f yD =⋅ζ=σ


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Nm.ZM yDD 5680108=⋅σ=

Unity check : 15580 ≤=

γ

.M

M

R

D

dy => OK LTB check

B. Tension members with moments (Art. 4.142. (48))

The internal forces for the ultimate combination 3 in the critical section x=2.22 m are N=2276.208 N (tension) and My=40699.02Nm Mz=52.11Nm. As we don’t take into account the beneficial effect of tension force (N=0), we find:

N.l

IEN

Ky

ycry 47812854

2

2

=⋅⋅π

= and N.l

IEN

Kz

zcrz 93299557

2

2

=⋅⋅π

=

0.1y =ω (transversal loading is present) and 14060 =⋅+=ωmax,dz

min,dzz M

M..

5112

40 .b

cN

N.

R

pl

d =⋅

+

γ

+=β

( ) kNm1.80MkNm52.72MM DyDN,Ry =η⋅ω<== NmMM plzN,Rz 42900==

Unity check: 10.048.0M

MM

M

R

N,Rz

dzz

R

N,Ry

dyy ≤+=

γ

⋅ω+

γ

⋅ω

ββ


Calculation note SIA161 check

Macro 2 Member 4 HEA180 S 275 Ult. comb 4 0.56

Material data

Gamma_r 1.10

Design strength 275.00 MPa

fabrication rolled

SECTION CHECK

Width to thickness ratio for webs


ratio

Maximum ratio 1 66.32



==>Class cross-section 1 (PP Method)

Width to thickness ratio for outstand flanges



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ratio






Internal forces

Nd 2.28 kN

Vdy 0.02 kN

Vdz -2.15 kN

Mt -0.00 kNm

Mdy 40.70 kNm

Mdz -0.05 kNm

Normal force check

according to 3.2.11.1 and formula (1) && Table 4

Table of values

Nt_Rd 1245.75 kN

Unity check 0.00

Shear check (Vy)

according to 4.13.6 and formula (46)

Table of values

Avy 3420.00 mm^2

Vy_Rd 543.00 kN

Unity check 0.00

Shear check (Vz)


Table of values

Avz 969.00 mm^2

Vz_Rd 153.85 kN

Unity check 0.02

Combined bending and normal force


Table of values

xi_1 1.27

xi_2 1.12

Npl 1245.75 kN

alfa 1.10

MplyN 89.10 kNm

MplzN 42.90 kNm

Unity check 0.25


STABILITY CHECK


LTB

L ltb 5.00 m

eta 1.41

Lcr 2.50 m

k 1.00

kw 1.00


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LTB check

according to 3.254 and formula (19) & 3.254.1

Table of values

psi -0.00

eta 1.41

l_K 4.21 m

A reduced 1862.00 mm^2

I reduced 4617456.40 mm^4

i reduced 49.80 mm

LTB slender. 84.54

sigma_Dw 290.01 MPa

sigma_Dv 460.94 MPa

sigma_crD 544.59 MPa

lamda_D 0.75

zeta 0.90

sigma_D 247.18 MPa

M_D 80.09 kNm

Unity check 0.56



Table of values

My max 40.70 kNm

Mz max 0.09 kNm

N_cry 812.85 kN

N_crz 299.56 kN

N_Kz 236.35 kN

M_D(eta=1) 72.52 kNm

M_D(eta) 80.09 kNm

omega_y 1.00

omega_z 1.00

beta 1.51

M_Ry,N 72.52 kNm

M_Rz,N 42.90 kNm

Unity check 0.48

0.48 +0.00=0.48

No shear buckling check


SIA161 check

Macro 4 Member 7 IPE240 S 275 Ult. comb 5 0.37

Material data

Gamma_r 1.10


fabrication rolled

SECTION CHECK



ratio



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ratio






ratio






Internal forces

Nd 0.26 kN

Vdy 0.00 kN

Vdz 2.25 kN

Mt 0.00 kNm

Mdy 14.01 kNm

Mdz -0.00 kNm

Normal force check

according to 3.2.11.1 and formula (1) && Table 4

Table of values

Nt_Rd 1075.25 kN

Unity check 0.00

Shear check (Vz)


Table of values

Avz 1427.24 mm^2

Vz_Rd 226.60 kN

Unity check 0.01

Combined bending and normal force


Table of values

xi_1 1.57

xi_2 1.20

Npl 1075.25 kN

alfa 1.10

MplyN 100.65 kNm

MplzN 20.35 kNm

Unity check 0.02


STABILITY CHECK


LTB

L ltb 6.00 m

eta 1.13

Lcr 1.01 m

k 1.00

kw 1.00


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LTB check

according to 3.254 and formula (19) & 3.254.1

Table of values

psi 1.00

eta 1.13

l_K 5.64 m

A reduced 1403.75 mm^2

I reduced 1411929.47 mm^4

i reduced 31.71 mm

LTB slender. 177.97

sigma_Dw 65.44 MPa

sigma_Dv 143.95 MPa

sigma_crD 158.13 MPa

lamda_D 1.40

zeta 0.46

sigma_D 126.98 MPa

M_D 46.47 kNm

Unity check 0.33



Table of values

My max 14.01 kNm

Mz max 0.00 kNm

N_cry 2239.58 kN

N_crz 163.51 kN

N_Kz 143.30 kN

M_D(eta=1) 41.89 kNm

M_D(eta) 46.47 kNm

omega_y 1.00

omega_z 1.00

beta 1.00

M_Ry,N 41.89 kNm

M_Rz,N 20.35 kNm

Unity check 0.37

0.37 +0.00=0.37

No shear buckling check



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1.19 PST.06.09 – 01 : BS5950 Steel Code Check Tutorial Frame Description The unity check according to BS5950 of members 7, 4 and 46 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win BS5950 Steel code check. Project data See input file. Reference British Standard BS5950 Part 1.: 1990 + Revised text 1992 Structural use of steelwork in building Part 1. Code of practice for design in simple and continuous construction: hot rolled sections Steelwork Design Guide to BS5950: Part 1: 1990 Volume 2 Worked examples (Revised edition) Eurocode 3: Calcul des structures en acier Edition 1992 Essentials of Eurocode 3:Design Manual for Steel Structures in Building First Edition 1991 See the chapter "Manual calculation" for the manual calculation according to this reference. Result


0.4298 0.43 0 %


0.67 0.67 0 %


0.429 0.43 0 %

Version ESA-Prima Win 3.20.03 Input file + calculation note PST060901.epw Modules 3D Frame (PRS.11) BS5950 Steel code check (PST.06.09) Author


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NEM/CVL Manual calculation

1.19.1 Member 7

1.19.1.1 Classification of the section (Table 7. BS5950) A. Width-to-thickness ratio for webs

By using Table 7 of BS5950, we can determine the yield strength fy:

• Normal steel grade: S275 • Nominal thickness of the element t ≤ 40 mm ⇒ Nominal value of yield strength: py=275 N/mm2

⇒ 1235

=

=ε

yf (Using Note 3. Table 7.)

The web of member 7 is subjected both to bending and tension in section x=0.55 m. By using Table 7. of BS5950, we find:

( )9678

6040

79730

26194 .

....t

dw

=α⋅+

ε⋅≤== with 000811 .

ftd

N

yw

Sd =

⋅⋅+=α ⇒ WEB is CLASSE 1

B. Width-to-thickness ratio for flanges By using table 7. for outstand element, we find for section x=0 m

575712600980

120...

.

.

T

b=ε⋅≤== ⇒ FLANGES are CLASSE 1

The section IPE 240 is a plastic section for the stability check, following BS5950 rules.

1.19.1.2 Check Normal Stress and shear stress (Art. 4.6.1. Art. 4.2.3) The member 7 is subjected to a normal tension F=262.81N and a small shear forces Fvy=2250.05N in the critical section. According to BS5950, we can verify: Unity Check:

Normal check: 110442003910275000000

81262 4 ≤⋅=⋅

=⋅

−..

.

pyA

F

Shear area: 2001488024000620 m...DtA wvy =⋅=⋅=

Shear check: 110169245520

052250

60

3 ≤⋅==⋅⋅

= −..

pA.

F

P

F

yvy

vy

vy

vy


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1.19.1.3 Combined bending, axial force (Art. 4.8.2.) By using Art. 4.8.2. (1), we can determine: Fvy≤0.6Pvy (LOW SHEAR): ( ) ( ) Nm ;minpZ.;pSminM yxxyxxcx 10065010688710065021 ==⋅⋅⋅=

( ) ( ) Nm ;minpZ.;pSminM yyyyyycy 15609156092035021 ==⋅⋅⋅=

We verify: 1139480

21

≤=

+

.

M

M

M

Mz

cy

yz

cx

x using 4.8.2.

with z1=2.0 z2=1.0 Mx=14014.38 Nm My=0 Nm


A. Calculation of Lateral Torsional Buckling (Art. 4.3.7. Appendix B)

To determined LTB parameters, the rules prescribed by BS5950 are different for section with flange symmetrical about major or minor axis. As we’ll see, for a double symmetrical section as member 7, this distinction leads to the same results.

Slenderness: 0422302690

6.

.A

I

L

i

L

yyy ====λ

N=0.5 (symmetrical section)

Limiting equivalent slenderness: 7234402

12

.p

E.

yLO =

⋅π⋅=λ

92699010893

1086211

5

6

..

.

I

I

x

y =⋅

⋅−=−=γ

−

−

Torsional index: 682210291

00391202302056605660

71 ..

...

J

Ah.x s =

⋅⋅⋅=⋅⋅=

−

73221029110842

107763003912013211321

76

8

2 ...

...

JI

HA.x

y

=⋅⋅⋅

⋅⋅⋅=

⋅⋅

⋅=−−

−

Buckling parameter: 88404 4

1

22

2

1 .hA

Su

s

x =

⋅

γ⋅⋅=

88301077530039120

926990000366010842 41

82

2641

2

2

2 ...

...

HA

SIu

xy =

⋅⋅

⋅⋅⋅=

⋅

γ⋅⋅=

−

−

Slenderness factor: ( ) 6433020

114

21

21

22

1 .x

NNv =

ψ+

ψ+

λ⋅+−⋅⋅=

−

( ) 6439020

114

21

21

22

2 .x

NNv =

ψ+

ψ+

λ⋅+−⋅⋅=

−


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Equivalent slenderness: 85126111 .vun y,LTB =λ⋅⋅⋅=λ

81126222 .vun y,LTB =λ⋅⋅⋅=λ

Perry coefficient: ( ) 644900070 11 .. LO,LT,LT =λ−λ⋅=η

( ) 644600070 22 .. LO,LT,LT =λ−λ⋅=η

Plastic moment: Nm SpM xxyp 100650=⋅=

Elastic critical moment: Nm .ES

p

EMM

,LT

xx

y,LT

p,E 2147143

21

2

21

2

1 =λ

⋅π⋅=

⋅λ

⋅π⋅=

Nm .ES

p

EMM

,LT

yy

y,LT

p,E 9547172

22

2

22

2

2 =λ

⋅π⋅=

⋅λ

⋅π⋅=

Reduced LTB factor: ( )

93890972

1 111 .

MM ,E,LTP,b =

⋅+η+=φ

( )3289115

2

1 112 .

MM ,E,LTP,b =

⋅+η+=φ

Equivalent uniform moment: 60714014.MmM A =⋅=

Buckling resistance moment: ( )

Nm .MM

MMM

,p,E,b,b

P,E,b 0632587

21

112

11

11 =

⋅−φ+φ

⋅=

( )Nm .

MM

MMM

,p,E,b,b

P,E,b 5232603

21

222

21

22 =

⋅−φ+φ

⋅=

Unity check : 1429805232603

60714014

21

≤== ..

.

M

M

),min(,b

=> OK LTB check

B. Tension members with moments (Art. 4.8.3.3.2.) The internal forces for the ultimate combination 4 in the critical section x=3 m are: F=262.81 N (tension) Mx=14014.607 Nm Using the more precise approach described in article 4.8.3.3.2., we find: Maximum buckling moment around major axis:

Nm .P

F.M;

P

F.P

F

MminMcy

b

cx

cxcxax 7832585

501

501

1

=

⋅−⋅

⋅+

−

⋅=

Maximum buckling moment around minor axis:

Nm M

P

F.

P

F

MM cy

cy

cxcyay 20350

501

1

==

⋅+

−

⋅=


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Unity check: 1430 ≤=⋅

+⋅

.M

Mm

M

Mm

ay

y

ax

x => Stability check OK

1.19.2 Member 4

1.19.2.1 Classification of the section (Table 7. BS5950) A. Width-to-thickness ratio for webs

By using Table 7 of BS5950, we can determine the yield strength fy:


⇒ 1235

=

=ε


The web of member 7 is subjected both to bending and tension in section x=0.55 m. By using Table 7 of BS5950 and Art. 3.5.4., we find:

( )05477

611

1203320

00601220 .

R...

.t

dw

=⋅+ε⋅

≤==

where 5010877 3 ..p

Ry

web,m ≤⋅=σ

= − ⇒ WEB is plastic

B. Width-to-thickness ratio for outstand flanges

By using Table 7 of BS5950, we find for section x=0 m:

5959473900950

090 .....

Tb =ε⋅≤== ⇒ FLANGES are compact

The section HEA180 is a compact section for stabilty check, following BS5950 rules.

1.19.2.2 Check Normal Stress and shear stress (Art. 4.6.1. Art. 4.2.3) The member 7 is subjected to a normal compression F=7404.15 N and a shear force Fvy=2145.32 N in the critical section. According to BS5950, we can verify: Unity Check:

Normal check: 1109550045250275000000

157404 3 ≤⋅=⋅

=⋅

−..

.

pyA

F

Shear area: 2001026017100060 m...DtA wvy =⋅=⋅=

Shear check: 110261169290

322145

60

2 ≤⋅==⋅⋅

= −..

pA.

F

P

F

yvy

vy

vy

vy


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1.19.2.3 Combined bending, axial force (Art. 4.8.3.2.) By using Art. 4.8.2. (1), we can determine: Fvy≤0.6Pvy (LOW SHEAR): ( ) ( ) Nm ;minpZ.;pSminM yxxyxxcx 89100970208910021 ==⋅⋅⋅=

( ) ( ) Nm ;minpZ.;pSminM yyyyyycy 33990339904290021 ==⋅⋅⋅=

We verify: 146610 ≤=

+

+

⋅.

M

M

M

M

pA

F

cy

z

cx

y

y

(Using 4.8.3.2.)

with: z1=2.0 z2=1.0 Mx=14014.38 Nm My=0 Nm

1.19.2.4 Stability Check: Check for bending, compression and L.T.B. A. Calculation of Buckling (Art. 4.7.5. Appendix C)

• Slenderness: 47.1070744.0

8

AI

L

i

L

xxx ====λ

3817704510

8.

.A

I

L

i

L

yyy ====λ

• Limiting slenderness: 3617202

12

.p

E.

yO =

⋅π⋅=λ

• Robertson constant: 55.a x = 8=ya

• Perry coefficient: ( ) 495800010 .a. Oxxx =λ−λ⋅⋅=η

( ) 2801610010 .a. LOyyy =λ−λ⋅⋅=η

• Euler strength: N/m² .E

px

Ex 341792835852

2

=λ

⋅π=

N/m² .E

py

Ey 31658733482

2

=λ

⋅π=

• Reduced buckling factor: ( )

822715933642

1.

pp Exxyx =

⋅+η+=φ

( )9421200886

2

1.

pp Eyyyy =

⋅+η+=φ

• Compressive strength: ( )

Nm .pp

ppp

yExxx

yExcx 307115196530

21

2

=⋅−φ+φ

⋅=

( )Nm .

pp

ppp

yEyyy

yEycy 5748028816

21

2

=⋅−φ+φ

⋅=

Unity Check: 1104339217330

157404 2 ≤⋅==⋅

−..

.

pA

N

minc

=> Section OK for buckling


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B. Calculation of Lateral Torsional Buckling (Art. 4.3.7. Appendix B)

To determined LTB parameters, the rules prescribed by BS5950 are different for section with flange symmetrical about major or minor axis. As we’ve seen in the benchmark concerning member 7 of TutBS5950.epw, this distinction gives the same results for double symmetrical section.

• Slenderness: 8611004510

5.

.A

I

L

i

L

yyy ====λ

• N=0.5 (symmetrical section)

• Limiting equivalent slenderness: 7234402

12

.p

E.

yLO =

⋅π⋅=λ

• 6314010512

1025911

5

6

..

.

I

I

x

y =⋅

⋅−=−=γ

−

−

• Torsional index: 9291510491

00452501615056605660

7.

.

...

J

Ah.x s =

⋅⋅⋅=⋅⋅=

−

• Buckling parameter: 83940

41

2

2

.HA

SIu

xy =

⋅

γ⋅⋅=

• Slenderness factor: ( ) 7356020

114

21

21

22

.x

NNv =

ψ+

ψ+

λ⋅+−⋅⋅=

−

• Equivalent slenderness: 34468.vun yLTB =λ⋅⋅⋅=λ

• Perry coefficient: ( ) 235300070 .. LOLTLT =λ−λ⋅=η

• Elastic critical moment: Nm .ES

p

EMM

,LT

yy

yLT

pE 41143767

22

2

2

2

=λ

⋅π⋅=

⋅λ

⋅π⋅=

• Reduced LTB factor: ( )

981333492

1.

MM ELTPb =

⋅+η+=φ

• Equivalent uniform moment: 60714014.MmM A =⋅=

• Buckling resistance moment: ( )

Nm .MM

MMM

pEbb

PEb 7362833

21

2

=⋅−φ+φ

⋅=

Unity check : 16507362833

9540683≤== .

.

.

M

M

b

=> OK LTB check

1.19.2.5 Tension members with moments (Art. 4.8.3.3.2.)


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The internal forces for the ultimate combination 6 in the critical section x=2.22 m are: F=7404.15 N (tension) Mx=14014.607 Nm Using the more precise approach described in article 4.8.3.3.2., we find: Maximum buckling moment around major axis:

( ) Nm 60702.29.;.minP

F.M;

P

F.P

F

MminMcy

b

cx

cxcxax ==

⋅−⋅

⋅+

−

⋅= 2960702188724850

150

1

1

Maximum buckling moment around minor axis: Nm .

P

F.

P

F

MM

cy

cxcyay 53640753

501

1

=

⋅+

−

⋅=

Unity check: 167320 ≤=⋅

+⋅

.M

Mm

M

Mm

ay

y

ax

x => Stability check OK

1.19.3 Member 47

1.19.3.1 Classification of the section (Table 7. BS5950):Stem of T-section By using Table 7 of BS5950, we can determine the yield strength fy:


⇒ 1235

=

=ε


The section of member 47 is subjected both to bending and tension in section x=0 m. By using Table 7. of BS5950, we find:

59592390130

120 .....

td

w=ε⋅≤== ⇒ Section is compact

1.19.3.2 Check Normal Stress and shear stress (Art. 4.6.1. Art. 4.2.3) The member 47 is subjected to a normal tension F=37369.5N and a small shear force Fvy=441.92N in the critical section. According to BS5950, we can verify:

Unity Check: Normal check: 110594002960275000000

537369 2 ≤⋅=⋅

=⋅

−..

.

pyA

F


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Shear area: 2001560 m.AA vyvx ==

Shear Check: 31071125740

92441

60

−⋅==⋅⋅

= ..

pA.

F

P

F

yvy

vy

vy

vy


1.19.3.3 Combined bending, axial force (Art. 4.8.2.) By using Art. 4.8.2. (1), we can determine: Fvy≤0.6Pvy (LOW SHEAR): Nm pZM yxxcx 11550=⋅=

Nm .pZM yyycy 58167=⋅=

A elastic check of the stress in the critical section gives:

110299275000000

4525562183

275000000

2319532831295688285912624832 2 ≤⋅==−+

=σ+σ+σ −.

....

p y

mymxn

=> Section check OK for combined bending and normal force


A. Calculation of Buckling (Art. 4.7.5. Appendix C)

• Slenderness: 492803510

1.

.A

I

L

i

L

xxx ====λ

897924402450

1.

.A

I

L

i

L

yyy ====λ

• Limiting slenderness: 3617202

12

.p

E.

yO =

⋅π⋅=λ

• Robertson constant: 55.a x = 55.a y =

• Perry coefficient: ( ) 061200010 .a. Oxxx =λ−λ⋅⋅=η

( ) 251410010 .a. LOyyy =λ−λ⋅⋅=η

• Euler strength: N/m² .E

px

Ex 8225534898832

2

=λ

⋅π=

N/m² .E

py

Ey 28345580252

2

=λ

⋅π=

• Reduced buckling factor: ( )

3614923817322

1.

pp Exxyx =

⋅+η+=φ

( )058176401969

2

1.

pp Eyyyy =

⋅+η+=φ

• Compressive strength: ( )

Nm .pp

ppp

yExxx

yExcx 717257475453

21

2

=⋅−φ+φ

⋅=

( )Nm .

pp

ppp

yEyyy

yEycy 74829384290

21

2

=⋅−φ+φ

⋅=


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Unity Check: 14290586977

537369≤==

⋅.

.

.

pA

F

minc

=> Section OK for buckling

B. Calculation of Lateral Torsional Buckling (Art. 4.3.7. Appendix B) Using the formula of section with flange symmetrical about the minor axis, we find:

• Slenderness: 8141.

AI

L

i

L

yyy ===λ

• N=1

• Limiting equivalent slenderness: 7234402

12

.p

E.

yLO =

⋅π⋅=λ

• 51301 .I

I

x

y =−=γ

• Torsional index: 17810831

0029601135056605660

7.

.

...

J

Ah.x s =

⋅⋅⋅=⋅⋅=

−

• Buckling parameter: 635704 4

1

22

2

.hA

Su

s

x =

⋅

γ⋅⋅=

• Slenderness factor: ( ) 678020

114

21

21

22

.x

NNv =

ψ+

ψ+

λ⋅+−⋅⋅=

−

• Equivalent slenderness: 5917.vun yLTB =λ⋅⋅⋅=λ

• Perry coefficient: ( ) 000070 =η⇒≤λ−λ⋅=η LTLOLTLT .

• Elastic critical moment: Nm .ES

p

EMM

LT

xx

yLT

pE 75634678

2

2

2

2

=λ

⋅π⋅=

⋅λ

⋅π⋅=

• Reduced LTB factor: ( )

3753303742

1.

MM ELTPb =

⋅+η+=φ

• Equivalent uniform moment: 68553.MmM A =⋅=

• Buckling resistance moment: ( )

Nm MM

MMM

pEbb

PEb 26070

21

2

=⋅−φ+φ

⋅=

Unity check : 110122 2 ≤⋅= −.M

M

b

=> OK LTB check

1.19.3.5 Tension members with moments (Art. 4.8.3.3.2.) The internal forces for the ultimate combination 5 in the critical section x=0 m are: F=37369.5 N (tension) Mx=553.58 Nm Using the more precise approach described in article 4.8.3.3.2., we find: Maximum buckling moment around major axis:

( ) Nm 10721.08.;.minP

F.M;

P

F.P

F

MminMcy

b

cx

cxcxax ==

⋅−⋅

⋅+

−

⋅= 8314887081072150

150

1

1


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Maximum buckling moment around minor axis: Nm .

P

F.

P

F

MM

cy

cxcyay 563840

501

1

=

⋅+

−

⋅=

Unity check: 110425 2 ≤⋅=⋅

+⋅

−.ayM

yMm

axMxMm


Calculation note - Member 4 BS 5950 Check

Macro 2 Member 4 HEA180 Grade 43 Ult. comb 7 0.67

Material data


fabrication rolled

SECTION CHECK



ratio




==> Class cross-section Plastic



ratio




==> Class cross-section Compact


Axis definition :



Internal forces

F -7.40 kN

Fvx 0.04 kN

Fvy -2.15 kN

Mt -0.00 kNm

Mx 40.68 kNm

My -0.12 kNm

Compression check

according to article 4.7.4.

Table of values


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Table of values

Pc 1245.75 kN

Unity check 0.01

Shear check (Fvx)


Table of values

Avx 3420.00 mm^2

Pvx 564.30 kN

Unity check 0.00

Shear check (Fvy)


Table of values

Avy 1026.00 mm^2

Pvy 169.29 kN

Unity check 0.01


according to article 4.8.3.2.(a)

Table of values

Mcx 89.10 kNm

Mcy 33.99 kNm

Unity check 0.47


STABILITY CHECK




Length 8.00 8.00 m



Euler strength pE 179.44 66.13 MPa

Robertson Constant 5.50 8.00

Perry factor a 0.50 1.28

Reduced buckling factor 271.68 212.80 MPa

Compressive strength pc 115.27 48.18 MPa

Buckling check

according to article 4.7.5. & Appendix C

Table of values

Pc 218.27 kN

Unity check 0.03

LTB

L ltb 5.00 m

k 1.00

m 1.00

n 1.00

Stabilizing load according to Art. 4.3.4. and Table 13.

LTB check

according to article 4.3.7. & Appendix B

Table of values


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Table of values

N factor 0.50

Slenderness 110.65

Torsional index x 15.94

Buckling parameter u 0.84

Slender. factor v 0.74

Equivalent slender. 68.31

Limiting equiv. slender. 34.73

Perry factor 0.24

Mcr elastic 143.90 kNm

Red. LTB factor 133.41 kNm

Mb 62.86 kNm

Max. MA 40.68 kNm

Equiv. uniform M 40.68 kNm

Unity check 0.65


according to article 4.8.3.3.2.

Table of values

Max 60.73 kNm

May 40.75 kNm

Unity check 0.67

0.67 +0.00=0.67

NO shear buckling check



Macro 4 Member 7 IPE240 Grade 43 Ult. comb 5 0.43

Material data


fabrication rolled

SECTION CHECK



ratio







ratio






Axis definition :


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Internal forces

F 0.26 kN

Fvx 0.00 kN

Fvy -2.25 kN

Mt 0.00 kNm

Mx 14.01 kNm

My -0.00 kNm

Normal force check


Table of values

Pt 1075.25 kN

Unity check 0.00

Shear check (Fvy)


Table of values

Avy 1488.00 mm^2

Pvy 245.52 kN

Unity check 0.01



Table of values

Mcx 100.65 kNm

Mcy 15.61 kNm

Unity check 0.14


STABILITY CHECK

LTB

L ltb 6.00 m

k 1.00

m 1.00

n 1.00


LTB check


Table of values

N factor 0.50

Slenderness 222.63






Perry factor 0.64



Mb 32.59 kNm

Max. MA 14.01 kNm


Unity check 0.43


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according to article 4.8.3.2.

Table of values

Max 32.59 kNm

May 20.35 kNm

Unity check 0.43

0.43 +0.00=0.43




Macro 18 Member 47 T120/120/13 Grade 43 Ult. comb 6 0.43

Material data


fabrication rolled

SECTION CHECK



ratio




==> Class cross-section Compact


Axis definition :



Internal forces

F -37.37 kN

Fvx -0.00 kN

Fvy -0.44 kN

Mt -0.01 kNm

Mx 0.55 kNm

My 0.01 kNm

Compression check


Table of values

Pc 814.00 kN

Unity check 0.05

Shear check (Fvx)


Table of values


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Table of values

Avx 1560.00 mm^2

Pvx 257.40 kN

Unity check 0.00

Shear check (Fvy)


Table of values

Avy 1391.00 mm^2

Pvy 229.51 kN

Unity check 0.00


according to article 4.8.3.2.(a)

Table of values

sigma n 12.62 MPa

sigma Mx 12.96 MPa

sigma My 0.02 MPa

Unity check 0.09


STABILITY CHECK




Length 1.00 6.00 m



Euler strength pE 2562.76 34.62 MPa

Robertson Constant 5.50 5.50

Perry factor a 0.06 1.25

Reduced buckling factor 1496.94 176.45 MPa

Compressive strength pc 257.56 29.43 MPa


Buckling check

according to article 4.7.5. & Appendix C

Table of values

Pc 87.12 kN

Unity check 0.43

LTB

L ltb 1.00 m

k 1.00

m 1.00

n 1.00


LTB check


Table of values

N factor 1.00

Slenderness 40.78





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Table of values



Perry factor 0.00



Mb 22.90 kNm

Max. MA 0.55 kNm


Unity check 0.02


according to article 4.8.3.3.2.

Table of values

Max 10.72 kNm

May 3.84 kNm

Unity check 0.05

0.05 +0.00=0.05




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1.20 PST.06.09 – 02 : BS5950 Steel Code of practice for design Description Calculation of m and n factor of BS5950. Project data See input file. Reference [1] British Standard BS5950 Part 1.: 1990 + Revised text 1992

Structural use of steelwork in building Part 1. Code of practice for design in simple and continuous construction: hot rolled sections

[2] Steelwork Design

Guide to BS5950: Part 1: 1990 Volume 2 Worked examples (Revised edition)

[3] Eurocode 3: Calcul des structures en acier

Edition 1992 [4] Essentials of Eurocode 3:Design Manual for Steel Structures in Building

First Edition 1991 See the chapter "Manual calculation" for the manual calculation according to this reference. Result Example in Ref[2]. Ref.[2] EPW % Diff. Example 2 Mb 397 kNm 397 kNm 0 % M reduced 381 kNm 379 kNm 0.50 % m 0.91 0.91 0 % n 1.00 1.00 0 % Example 3 Mb 450 kNM 451 kNm 0.20 % M reduced 419 kNm 418 kNm 0.20 % m 1.00 1.00 0 % n 0.94 0.94 0 % Example 4 Mb 184 kNm 185 kNm 0.50 % M reduced 126 124 kNm 1.60 % m 0.80 0.81 1.25 % n 1.00 1.00 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file example 2 : PST060902a.epw example 3 : PST060902b.epw example 4 : PST060902c.epw


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Modules 3D Frame (PRS.11) BS5950 Steel code check (PST.06.10) Author NEM/CVL Manual calculation The next 3 examples treat the specific calculation of the equivalent uniform factor m and the equivalent slenderness factor n. BS5950 makes using of those values in LTB check to determine the LTB design moment resistance. For other controls following BS5950, we refer to the corresponding benchmarks. Each beam checked is not laterally fully restrained so that a lateral torsional buckling control must be performed. The condition to be satisfied in all the cases is that:

bxbA pSMMmM ⋅=≤⋅=

where pb is the bending strength and is related to the equivalent slenderness given by

λ⋅⋅⋅=λ vunLT in which n is the equivalent slenderness

For beam without loading between points of lateral restraint, n=1 and m depends on the ratio of the end moments at the point of restraint. Similarly, for beam loaded between points of lateral restraint, m=1 and n depend both on the ratio of the end moment at the point of restraint and on the ratio of the larger moment to the mid-span free moment. There are thus two method to work with lateral buckling: - ‘m approach’ with m calculated and n=1

- ‘n approach’ with m=1 and n calculated Both method are used in the following examples and compare with result found in the second reference Steelwork Design Guide to BS5950: Part 1: 1990 Volume 2 Worked examples (Revised edition). In any given situation, only one method is admissible and it’s always conservative to use m=n=1. Steelwork Design Guide to BS5950: Part 1: 1990 Volume 2 Worked examples (Revised edition) gives two notes appield in EPW: 1. if the loading is destabilising both m and n factors must be taken as unity 2. Since the publication of BS5950 Part 1:1990, doubt has been cast on the correctness of using n-factors less than 1

in combination with an effective length LE less than L in the calculation of λ=λ nuvLT . In the future it may be

possible, some correction may occur. However, as a interim measure, pending clarification from BS, it is recommended that λLT is taken as the smaller of λLT1 and λLT2:

y

E1LT r

Lvu ⋅⋅=λ and

y2LT r

Lvun ⋅⋅⋅=λ

Calculation note - Example 2 : PST060902a.epw BS 5950 Check

Macro 1 Member 2 UB457/191/82 Grade 43 Loadcase 1 0.95


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Material data


fabrication rolled

SECTION CHECK



ratio







ratio






Axis definition :



Internal forces

F 0.00 kN

Fvx 0.00 kN

Fvy -19.03 kN

Mt 0.00 kNm

Mx 417.80 kNm

My 0.00 kNm

Shear check (Fvy)


Table of values

Avy 4554.00 mm^2

Pvy 751.41 kN

Unity check 0.03



Table of values

Mcx 504.35 kNm

Mcy 64.68 kNm

Unity check 0.83


STABILITY CHECK

LTB

L ltb 3.00 m

k 1.00


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LTB

m 0.91

n 1.00


LTB check


Table of values

N factor 0.50

Slenderness 71.09






Perry factor 0.17



Mb 396.96 kNm

Max. MA 417.80 kNm


Unity check 0.95



Table of values

Max 396.96 kNm

May 83.32 kNm

Unity check 0.95

0.95 +0.00=0.95



Calculation note - Example 3 - PST060902b.epw

BS 5950 Check


Material data


fabrication rolled

SECTION CHECK



ratio








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ratio






Axis definition :



Internal forces

F 0.00 kN

Fvx 0.00 kN

Fvy -19.03 kN

Mt 0.00 kNm

Mx 417.80 kNm

My 0.00 kNm

Shear check (Fvy)


Table of values

Avy 8085.32 mm^2

Pvy 1285.57 kN

Unity check 0.01



Table of values

Mcx 1097.65 kNm

Mcy 124.34 kNm

Unity check 0.38


STABILITY CHECK

LTB

L ltb 7.65 m

k 1.00

m 1.00

n 0.94


LTB check


Table of values

N factor 0.50

Slenderness 152.06






Perry factor 0.52




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Table of values

Mb 451.67 kNm

Max. MA 417.80 kNm


Unity check 0.93



Table of values

Max 451.67 kNm

May 162.03 kNm

Unity check 0.93

0.93 +0.00=0.93



Calculation note - Example 4 : PST060902c.epw BS 5950 Check


Material data


fabrication rolled

SECTION CHECK



ratio







ratio






Axis definition :



Internal forces

F 0.00 kN

Fvx 0.00 kN


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Internal forces

Fvy -13.37 kN

Mt 0.00 kNm

Mx 152.80 kNm

My 0.00 kNm

Shear check (Fvy)


Table of values

Avy 3420.00 mm^2

Pvy 564.30 kN

Unity check 0.02



Table of values

Mcx 301.40 kNm

Mcy 27.92 kNm

Unity check 0.51


STABILITY CHECK

LTB

L ltb 3.00 m

k 1.00

m 0.81

n 1.00


LTB check


Table of values

N factor 0.50

Slenderness 96.47






Perry factor 0.31



Mb 184.46 kNm

Max. MA 152.80 kNm


Unity check 0.67



Table of values

Max 184.46 kNm

May 36.48 kNm

Unity check 0.67

0.67 +0.00=0.67



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1.21 PST.06.10 – 01 : GBJ 17-88 Steel Code Check Tutorial Frame Description The unity check according to GBJ 17-88 of members 4, 7 and macro 18 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win. Project data See input file. Reference Ref.[1] National standard of the People’s Republic of China

Code for design of steel structures GBJ 17-88 Beijing 1995

See the chapter "Manual calculation" for the manual calculation according to this reference. Result Member/Macro EPW Manually % Diff. member 7 0.12

0.72 0.12 0.72

0 % 0 %

member 19 0.66 0.06 0.47 0.68

0.66 0.06 0.47 0.68

0 % 0 % 0 % 0 %

macro 18 0.09 0.44 0.04

0.09 0.44 0.04

0 % 0 % 0 %

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST061001.epw Modules 3D Frame (PRS.11) GBJ-17 Code Check (PST.06.10) Author CVL Manual calculation - Member 7.


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Buckling data First we will discuss the buckling data of this member.

5. System length L: Since there are no intermediate restraints on this member the system length L = the full

member length for all buckling modes. (L=6m)


7. Sway modes: Y-Y: non-sway Z-Z: non-sway. Buckling factor kx=ky=1.0.

8. The load application is on the top flange.

Check of IPE270 section. Section data E 210000 N/mm² A 4590 mm² fy 235 N/mm² Wx 429000 mm³ Wy 62200 mm³ ix 112 mm iy 30.2 mm Sx 242000 mm³ height h 270 mm width b 135 mm flange tf 10.2 mm web tw 6.6 mm radius r 15 mm

Now, we will discuss the different steps :

Classification of the section c) Width-to-thickness ratio for webs. (Using art.5.4.2.) b/tw = 219.6 / 6.6 = 33.27 The web is subjected to compression at 0.0 m. The slenderness λ in the web plane = 53.4. The maximal ratio for a slender section is 25 + 0.5 λ = 51.70

Since 33.27 < 51.7, the web is no slender element. d) Width-to-thickness ratio for outstand flanges (Using art.5.4.1.)


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b/tf = 67.5/10.2 = 6.61

Max. ratio for flange subject to compression is 20. Since 6.62 < 15 , the flanges are no slender elements. � Section IPE270 is no slender section. Since 6.61 < 13 (art.4.1.1.) we can use the plasticity factors : γx =1.05 γy =1.20

Stability check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 7 on position x=3m. Combination 7, member 7 on x =3.0 m: X = 1.57 kN Mx = 11.58 kNm Z = 1.79 kN (Shear) Stability check for Bending + Compression Using article 5.2.5., and formula (5.2.5.-1) and (5.2.5.-2) :

fW

M

N

N8.01W

M

A

N

yby

yty

EXxx

xmx

x

≤ϕ

β+

−γ

β+

ϕ

f

N

N8.01W

M

W

M

A

N

EYyy

ymy

xbx

xtx

y

≤

−γ

β+

ϕ

β+

ϕ

E 210000 N/mm² A 4590 mm² f 215 N/mm² N 1.57 kN Mx 11.58 kNm Wx 429000 mm³ γx 1.05 γy 1.20 βtx No end moments

� 1.0


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βmx Sway system � 1.0

ϕx b/h < 0.8 � buckling curve a λx=6000/112 slenderness λx = 53.40 using Table A3.1 � 0.906

ϕy buckling curve b λy = 6000/30.2 slenderness λy = 198 using Table A3.2 � 0.19

ϕbx Appendix A1.5, formula A1.3 =1.07 - λy²/44000 λy= 6000 / 30.2 = 198 � 0.18

NEX = π²EA/λx² � 3333 kN

NEY = π²EA/λy² � 242 kN

formula 5.2.5-1 : 0.4 + 25.7 + 0.0 = 26.1 N/mm² unity check = 26.1 / 215 = 0.12 formula 5.2.5-2 : 1.8 + 153.5 + 0.0 = 155.3 N/mm² unity check = 155.3 / 215 = 0.72 Manual calculation - Member 19 Buckling data

First we will discuss the buckling data of this macro.

5. System length L: The beams on a height of 3m provide restraint to the column. Therefore the system lengths for member 19: Ly = Lz = 5 m.



8. K factors : Kx = 0.85 / Ky = 0.90

Check of HEB160 section The critical check is performed on section 0.0 m for combination number 6. The internal forces are : N 63.31 kN


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Vy 8.276 kN Mx 41.33 kNm My 0.61 kNm Section data E 210000 N/mm² A 5430 mm² fy 235 N/mm² Wx 311000 mm³ Wy 111000 mm³ ix 67.8 mm iy 40.5 mm Sx 177000 mm³ height h 160 mm width b 160 mm flange tf 13 mm web tw 8 mm radius r 15 mm Classification of the section a) Width-to-thickness ratio for webs. (Using Art.5.4.2)

b/tw = 104 / 8 = 13 For this case, we calculate α0.

max

maxmax0 σ

σ−σ=α

σN = N/A = 63310/5425 = 11.6 N/mm² σM = Mx h / Ix = 41320000 52 /24920000 = 86.22 N/mm² σmax = 11.67 + 86.22 = 98 N/mm² σmin = 11.6 – 86.22 = -74 N/mm² α0 = (98+74)/98 = 1.76 The slenderness λ in the web plane = 62.8. The maximal ratio for a slender section is 48 α0 + 0.5 λ - 26.2 = 89.44

Since 13 < 89.4 , the web is no slender section element.

c) Width-to-thickness ratio for outstand flanges (Using Art.5.4.1.) b/tf = (80-4)/13 = 5.85

Max. ratio for flange subject to compression/bending is 15. Since 5.85 < 15 , the flanges are no slender elements.


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� Section HEB160 is no slender section. Since 5.85 < 13 (art.4.1.1.) we can use the plasticity factors : γx =1.05 γy =1.20

Section check This check is executed at member 19 on position x = 0 m. (start of member 19) Combination 6 : Normal stress check

Using article 5.2.1., formula 5.2.1.

fW

M

W

M

A

N

yy

y

xx

x <γ

+γ

+

N 63.31 kN A 5425 mm² Mx 41.3 kNm γx 1.05 Wx 311500 mm³ My 0.61 kNm γy 1.20 Wy 111200 mm³ f 215 N/mm² 11.67 + 126 + 4.6 = 142 N/mm² < 215 N/mm² Unity check = 142/215 = 0.66 Shear check

Using article 4.1.2., formula 4.1.2.

vw

fIt

VS<=τ

V 8.27 kN S 177000 mm³ I 24920000 mm4 tw 8 mm fv 125 N/mm² τ = 7.4 N/mm² < 125 N/mm² Unity check = 7.4/125 = 0.06 Stability check for Bending + Compression Since this check is the most critical check, we will only perform this check.


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Critical check = Ultimate combination 6 on position x=0m of member 19. Combination 6, member 19 on x =0.0 m: Using article 5.2.5., and formula (5.2.5.-1) and (5.2.5.-2) :

fW

M

N

N8.01W

M

A

N

yby

yty

EXxx

xmx

x

≤ϕ

β+

−γ

β+

ϕ

f

N

N8.01W

M

W

M

A

N

EYyy

ymy

xbx

xtx

y

≤

−γ

β+

ϕ

β+

ϕ

N 63.31 kN Mx 41.33 kNm My 0.61 kNm Wx 311500 mm³ Wy 111200 mm³ γx 1.05 γy 1.20 βty

βtx Non sway system, no transverse loading, = 0.65 + 0.35 M2/M1 ; M2 = 0.0 � 0.65

βmy

βmx Non sway system, no transverse loading, = 0.65 + 0.35 M2/M1 ; M2 = 0.0 � 0.65

ϕx b/h > 0.8 � buckling curve b λx = 4260/67.8 λx = 62.86 slenderness λx = 62.86 using Table A3.2 � 0.795

ϕy buckling curve b slenderness λy = 4510/40.5 slenderness λy = 111 using Table A3.2 � 0..487

ϕby 1.0 ϕbx Appendix A1.5, formula A1.3

=1.07 - λy²/44000 λy= 5000 / 40.5 = 123,46 � 0.72


NEY = π²EA/λy²


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� 902 kN

formula 5.2.5-1 : 14.6 + 84 + 3.5 = 102 N/mm² unity check = 102 / 215 = 0.47 formula 5.2.5-2 : 24 + 120 + 3.1 = 147 N/mm² unity check = 147 / 215 = 0.68 Manual calculation - Macro 18 Buckling data


5. System length L: 6. For each member: Ly = memberlength = 1m. Lz = Macrolength / 2 = 6 m. (Lateral restraint by middle-rafter) Lltb = Macrolength / 2 = 6 m. (Lateral restraint by middle-rafter)



9. K factors : Kx=1.00; Ky=0.94

Check of T120/120/13 section Section data E 210000 N/mm² A 2960 mm² fy 235 N/mm² Wx 42000 mm³ Wy 29700 mm³ ix 35.1 mm iy 24.5 mm Ix 3660000 mm4 Iy 1780000 mm4 ex 32.8 mm height h 120 mm width b 120 mm flange tf 13 mm web tw 13 mm radius r 13 mm


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Classification of the section

Width-to-thickness ratio for outstand flanges (Using Art.5.4.1.) b/tf = (60-13/2)/13 = 4.12

Max. ratio for flange subject to compression/bending is 15. Since 4.12 < 15 , the flanges are no slender elements. � Section is no slender section. Since 4.12 < 13 (art.4.1.1.) we can use the plasticity factors : γx1 =1.05 γx2 =1.20 γy =1.20

Stability check: Compression critical buckling check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 1 on position x=0m. of member 47. Combination 5, member 47 on x =0.0 m: N = -34.26 kN (compression) Mx = 0.51 kNm My = 0.00941 kNm Using article 5.2.5., and formula (5.2.5.-1) and (5.2.5.-2) :

fW

M

N

N8.01W

M

A

N

yby

yty

EXxx

xmx

x

≤ϕ

β+

−γ

β+

ϕ

f

N

N8.01W

M

W

M

A

N

EYyy

ymy

xbx

xtx

y

≤

−γ

β+

ϕ

β+

ϕ

N 34.27 kN Mx 0.51 kNm My 0.00941 kNm Ix 3660000 mm4 Wx1 at top , at compression side

= Ix/hx = 3660000/87.2 = 41972 mm³


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Wy 29700 mm³ At top side (compression side) the influence of the moment My is 0.0.

γx 1.20 (top side) γy 1.20 βtx No linear moment distribution along the LTB part (6 m) of

this element. � 1.0

βmx Non sway system, no transverse loading, = 0.65 + 0.35 M2/M1 ; M2 = -0.05 kNm M1 = 0.57 kNm � 0.62

ϕx � buckling curve b λx = 1000/35.1 slenderness λx = 28.44 using Table A3.2 � 0.94

ϕy buckling curve c λy = 5640/24.5 slenderness λy = 230 using Table A3.3 � 0.138

ϕby 1.0 ϕbx Appendix A1.5, formula A1.7

Flange in tension � 1.00



formula 5.2.5-1 : 12.3 + 6.1 + 0.0 = 18.4 N/mm² unity check = 18.4 / 215 = 0.09 formula 5.2.5-2 : 83.7 + 11.8 + 0.0 = 95.5 N/mm² unity check = 95.5 / 215 = 0.44 Stability check: Tension critical buckling check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 1 on position x=0m. of member 47. Combination 5, member 47 on x =0.0 m: N = -34.27 kN (compression) Mx = 0.51 kNm My = 0.01 kNm Using article 5.2.2., and (extended) formula (5.2.2.-2)


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f

N

N25.11W

M

N

N25.11W

M

A

N

EYyy

ymy

EXxx

xmx ≤

−γ

β+

−γ

β−

N 34.26 kN Mx 0.41 kNm My 0.01 kNm Ix 3660000 mm4 Wx1 at bottom , at tension side

= Ix/hx = 3660000/32.8 = 111585 mm³ Wy 29700 mm³

γx 1.05 (bottom side) γy 1.20 βmx Non sway system, no transverse loading,

= 0.65 + 0.35 M2/M1 ; M2 = -0.05 kNm M1 = 0.57 kNm � 0.62

βmy Non sway system, no transverse loading, = 0.65 + 0.35 M2/M1 ; M2 = 0.0 kNm � 0.65



formula 5.2.2-2 : 11.6 – 2.8 – 0.2 = 8.6 N/mm² unity check = 8.6 / 215 = 0.04 Calculation note - Member 7 GBJ-17 Code Check

Macro 4 Member 7 IPE270 Grade3 Ult. comb 8 0.72

Material data


f 215.00 MPa

fv 125.00 MPa

fabrication rolled

SECTION CHECK


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Section classification

Cfr. Chapter 5.4. ratio limit ratio Position

Webs 33.27 51.71 0.00 m

Outstanding flanges 6.29 20.00 0.00 m


Axis definition :



Internal forces

N -1.57 kN

Vx 0.00 kN

Vy 1.79 kN

Mt 0.00 kNm

Mx 11.58 kNm

My -0.00 kNm

Normal stress check

according to article 4.1.1./5.2.1. and formula (4.1.1.)(5.2.1.)

Table of values

normal stress 26.07 MPa

f 215.00 MPa

Gamma x 1.05

Gamma y 1.20

unity check 0.12

Shear stress check

according to article 4.1.2. and formula (4.1.2.)

Table of values

shear stress 1.13 MPa

fv 125.00 MPa

unity check 0.01


STABILITY CHECK


type sway non-sway



Buckling curve a b

Alfa 1 0.41 0.65

Alfa 2 0.99 0.96

Alfa 3 0.15 0.30

Fi 0.91 0.19

Length 6.00 6.00 m




LTB

l1 6.00 m



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Distributed loading

No lateral support

Buckling check


Table of values

Fi 0.19

unity check 0.01

1.82 < 215.00 MPa


according to article 5.2.5 and formula (5.2.5-1)

Table of values

Fi x 0.91

Gamma x 1.05

Beta m x 1.00

Beta t y 1.00

Fi b y 1.00

unity check 0.12

0.38 +25.73 +0.00=26.11 < 215.00 MPa



Table of values

Fi y 0.19

Beta t x 1.00

Fi b x 0.18

Beta m y 1.00

Gamma y 1.20

unity check 0.72

1.82 +153.61 +0.00=155.42 < 215.00 MPa


in buckling field 1

according to article A2.1 and formula (A2.1)

Table of values

a 6000.00 mm

ho 219.60 mm

tw 6.60 mm

C1 166.00

l1 6000.00 mm

l2 219.60 mm

Sigma cr 6458.46 MPa

Sigma c cr 1499.45 MPa

Tau cr 1112.16 MPa

Sigma 22.31 MPa

Sigma c 0.00 MPa

Tau 1.23 MPa

unity check 0.00


Macro 11 Member 19 HEB160 Grade3 Ult. comb 7 0.69

Material data


f 215.00 MPa


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Material data

fv 125.00 MPa

fabrication rolled

SECTION CHECK Section classification


Webs 13.00 89.67 0.00 m



Axis definition :



Internal forces

N -63.31 kN

Vx 0.12 kN

Vy -8.27 kN

Mt -0.00 kNm

Mx 41.33 kNm

My -0.61 kNm

Normal stress check


Table of values


f 215.00 MPa

Gamma x 1.05

Gamma y 1.20

unity check 0.66

Shear stress check


Table of values


fv 125.00 MPa

unity check 0.06


STABILITY CHECK





Buckling curve b b

Alfa 1 0.65 0.65

Alfa 2 0.96 0.96

Alfa 3 0.30 0.30

Fi 0.79 0.46

Length 5.00 5.00 m





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LTB

l1 5.00 m


Linear moment distribution

No lateral support

Buckling check


Table of values

Fi 0.46

unity check 0.12

25.42 < 215.00 MPa



Table of values

Fi x 0.79

Gamma x 1.05

Beta m x 0.65

Beta t y 0.65

Fi b y 1.00

unity check 0.47

14.69 +83.70 +3.55=101.95 < 215.00 MPa



Table of values

Fi y 0.46

Beta t x 0.65

Fi b x 0.72

Beta m y 0.65

Gamma y 1.20

unity check 0.69

25.42 +119.39 +3.15=147.96 < 215.00 MPa


in buckling field 1

according to article A2.1 and formula (A2.1)

Table of values

a 5000.00 mm

ho 104.00 mm

tw 8.00 mm

C1 166.00

l1 5000.00 mm

l2 104.00 mm

Sigma cr 42307.70 MPa

Sigma c cr 9822.49 MPa

Tau cr 7280.49 MPa

Sigma 97.97 MPa

Sigma c 0.00 MPa

Tau 9.93 MPa

unity check 0.00


GBJ-17 Code Check


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Macro 18 Member 47 T120/120/13 Grade3 Ult. comb 6 0.44

Material data


f 215.00 MPa

fv 125.00 MPa

fabrication rolled

SECTION CHECK Section classification




Axis definition :



Internal forces

N -34.26 kN

Vx -0.00 kN

Vy -0.41 kN

Mt -0.00 kNm

Mx 0.51 kNm

My 0.01 kNm

Normal stress check


Table of values


f 215.00 MPa

Gamma x 1.20

Gamma y 1.20

unity check 0.10

Shear stress check


Table of values


fv 125.00 MPa

unity check 0.01


STABILITY CHECK





Buckling curve b c

Alfa 1 0.65 0.73

Alfa 2 0.96 1.22

Alfa 3 0.30 0.30


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Fi 0.94 0.14

Length 1.00 6.00 m





LTB

l1 6.00 m


Linear moment distribution

No lateral support

Buckling check


Table of values

Fi 0.14

unity check 0.39

83.69 < 215.00 MPa



Table of values

Fi x 0.94

Gamma x 1.20

Beta m x 0.85

Beta t y 0.65

Fi b y 1.00

unity check 0.10

12.29 +8.42 +0.01=20.72 < 215.00 MPa

Compression and bending (tension side)


Table of values

Gamma x 1.05

Beta m x 0.85

Gamma y 1.20

Beta m y 0.65

unity check 0.03

11.57 +-3.87 +-0.23=7.48 < 215.00 MPa



Table of values

Fi y 0.14

Beta t x 0.85

Fi b x 1.00

Beta m y 0.65

Gamma y 1.20

unity check 0.44

83.69 +10.07 +0.01=93.77 < 215.00 MPa


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1.22 PST.06.11 – 01 : Korean Steel Code Check Tutorial Frame Description The unity check according to KS of members 4, 7 and macro 18 of the Tutorial Frame project are calculated manually. The result is compared with the result of ESA-Prima Win. Project data See input file. Reference Ref.[1] Korean Standard

See the chapter "Manual calculation" for the manual calculation according to this reference. Result Member/Macro EPW Manually % Diff. member 7 0.30

0.14 0.30 0.14

0 % 0 %

member 19 0.50 0.38

0.50 0.38

0 % 0 %

macro 18 0.53 0.53 0 % See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST061101.epw Modules 3D Frame (PRS.11) Korean Steel Code Check (PST.06.11) Author CVL Manual calculation - Member 7 Buckling data First we will discuss the buckling data of this member.


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9. System length L: Since there are no intermediate restraints on this member the system length L = the full member length for all buckling modes. (L=6m)


11. Sway modes: Y-Y: non-sway Z-Z: non-sway. Buckling factor kx=ky=1.0.

12. The load application is on the top flange.

Check of IPE270 section. Section data E 210000 N/mm² A 4590 mm² fy 240 N/mm² Fy 2.4 t/cm² Wx 429000 mm³ Wy 62200 mm³ ix 112 mm iy 30.2 mm Sx 242000 mm³ height h 270 mm width b 135 mm flange tf 10.2 mm web tw 6.6 mm radius r 15 mm

Now, we will discuss the different steps :

Classification of the section e) Width-to-thickness ratio for webs. (Using art.4.1.) b/tw = 219.6 / 6.6 = 33.27 Actually, the web is subjected to bending and tension. But because of the small value of this tensile force (0.15 kN), we consider bending only. For this case, the maximal ratio for a non-slender section is 110/√Fy = 71.0

Since 33.27 < 71 , the web is no slender element. f) Width-to-thickness ratio for outstand flanges (Using art.4.1.) b/tf = 67.5/10.2 = 6.61

Max. ratio for outstanding element is 24/√Fy = 15.5.


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Since 6.62 < 15.5 , the flanges are no slender elements. � Section IPE270 is no slender section.

Stability check Since this check is the most critical check, we will only perform this check. Critical check = Ultimate combination 6 on position x=3m. Combination 6, member 7 on x =3.0 m: X = 0.15 kN (tension) Mx = 9.72 kNm Stability check for Bending + Tension Using article 3.3.2. and formula (3.3.) and (3.4.) :

1f

tt

1f

c

f

c

f

t

bybxt

by

by

bx

bx

bx

t

≤σ+σ+σ

≤σ

+σ

+σ

−

E 210000 N/mm² A 4590 mm² N 0.15 kN Mx 9.72 kNm ft 160 N/mm² fby 160 N/mm² fbx lb = 6000 mm

Cm = 1.0 Af = 270 x 10.2 = 1377 mm² h = 270 mm 1/6 of beam heigth = (270-10.2)/6 = 43.3 mm Ar = 270 x 10.2 + 43.3 x 6.6 = 1663 mm² Ir = 10.2 135³ / 12 + 43.3 6.6³ / 12 = 2092355 mm4 ib = sqrt(Ir/Ar) = 35.5 mm λp = 120 formula (2.7) fbx = 33 N/mm² formula (2.8) fbx = 77 N/mm² � 77 N/mm²

σt 150/4590 = 0.03 N/mm² cσbx 9720000/429000 = 22.66 N/mm² tσbx 9720000/429000 = 22.66 N/mm² cσby 0 N/mm² tσby 0 N/mm²


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formula (3.4) compression side : -0.03/77 + 22.6/77 = 0.29 formula (3.3) tension side : +0.03/160 + 22.6/160 = 0.14 Manual calculation - Member 19 Buckling data


9. System length L: The beams on a height of 3m provide restraint to the column. Therefore the system lengths for member 19: Ly = Lz = 5 m.



12. K factors : Kx = 0.85 / Ky = 0.90

Check of HEB160 section The critial check is performed on section 0.0 m for combination number 3. The internal forces are : N -33.14 kN Vy 3.96 kN Mx 19.79 kNm My 0.32 kNm Section data E 210000 N/mm² A 5430 mm² fy 240 N/mm² Fy 2.4 t/cm² Wx 311000 mm³ Wy 111000 mm³ ix 67.8 mm iy 40.5 mm Sx 177000 mm³ height h 160 mm width b 160 mm flange tf 13 mm web tw 8 mm radius r 15 mm


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Classification of the section a) Width-to-thickness ratio for webs. (Using Art.4.1)

b/tw = 104 / 8 = 13 For this case, the limit is

fyP

P100

F

110−

P = 33.14 kN Pf = 240 N/mm² x A = 1303 kN � limit = 68.46.

Since 13 < 68.46, the web is no slender section element.

d) Width-to-thickness ratio for outstand flanges (Using Art.4.1.) b/tf = 80/13 = 6.15

Max. ratio for flange subject to compression/bending is 15.5. Since 6.15 < 15.5 , the flanges are no slender elements. � Section HEB160 is no slender section.

Section check This check is executed at member 19 on position x = 0 m. (start of member 19) Combination 3 :

sw

fIt

VS<=τ

V 3.96 kN S 177000 mm³ I 24920000 mm4 tw 8 mm fs 92.4 N/mm² τ = 3.54 N/mm² < 92.4 N/mm² Unity check = 3.54/92.4 = 0.04 Stability check for Bending + Compression Critical check = Ultimate combination 3 on position x=0m of member 19. Combination 3, member 19 on x =0.0 m:


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Using article 3.3.1.., and formula (E3.2) and (E3.3.) :

1f

tt

1f

c

f

c

f

t

cbybx

by

by

bx

bx

c

c

≤σ−σ+σ

≤σ

+σ

+σ

N 33.14 kN Mx 19.779 kNm My 0.32 kNm Wx 311500 mm³ Wy 111200 mm³ fc slenderness λx = 4260/67.8

slenderness λx = 62.86 using Table pp.270 � fcx = 127 N/mm² slenderness λy = 4510/40.5 slenderness λy = 111 using Table pp.270 � fcy = 76 N/mm² � fc = 76 N/mm²

ft 160 N/mm² fby 160 N/mm² fbx lb = 5000 mm

M1=0.0 � Cm = 1.75 Af = 160 x 13 = 2080 mm² h = 160 mm 1/6 of beam heigth = (160-13)/6 = 24.5 mm Ar = 160 x 13 + 24.5 x 8 = 2276 mm² Ir = 13 160³ / 12 + 24.5 8³ / 12 = 4438379 mm4 ib = sqrt(Ir/Ar) = 44.16 mm λp = 120 formula (2.7) fbx = 127.44 N/mm² formula (2.8) fbx = 234 N/mm² � 160 N/mm²

σc 33140/5430 = 6.10 N/mm² cσbx 19790000/311000 = 63.6 N/mm² tσbx 19790000/311000 = 63.6 N/mm² cσby 320000/111000 = 2.8 N/mm² tσby 320000/111000 = 2.8 N/mm²

formula (E3.2.): 6.1/76.00 + 63.6/160 + 2.8/160 = 0.08 + 0.40 + 0.02 = 0.50 > 1


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formula (E3.3.): -6.1/160.00 + 63.6/160 + 2.8/160 = -0.04 + 0.40 + 0.02 = 0.38 > 1 Manual calculation - Macro 18 Buckling data


10. System length L: For each member: Ly = memberlength = 1m. Lz = Macrolength / 2 = 6 m. (Lateral restraint by middle-rafter) Lltb = Macrolength / 2 = 6 m. (Lateral restraint by middle-rafter)



13. K factors : Kx =1.0 ; Ky = 0.94

Check of T120/120/13 section Section data E 210000 N/mm² A 2960 mm² fy 240 N/mm² Fy 2.4 t/cm² Wx 42000 mm³ Wy 29700 mm³ ix 35.1 mm iy 24.5 mm Ix 3660000 mm4 Iy 1780000 mm4 ex 32.8 mm height h 120 mm width b 120 mm flange tf 13 mm web tw 13 mm radius r 13 mm Classification of the section a) Width-to-thickness ratio for webs of T section. (Using Art.4.1)

b/tw = (120-13) / 13 = 8.23


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Since 8.23 < 15.5 , the web is no slender section element. b) Width-to-thickness ratio for outstand flanges (Using Art.4.1.) b/tf = 60/13 = 4.62

Max. ratio for flange subject to compression/bending is 15.5. Since 4.62 < 15.5 , the flanges are no slender elements. � Section is no slender section.

Stability check Since this check is the most critical check, we will only perform this check. Combination 6, member 47 on x =0.0 m: Using article 3.3.1.., and formula (E3.2) and (E3.3.) :

1f

tt

1f

c

f

c

f

t

cbybx

by

by

bx

bx

c

c

≤σ−σ+σ

≤σ

+σ

+σ

N 25.35 kN Mx 0.39 kNm My 0.02 kNm fc slenderness λx = 1000/35.1

slenderness λx = 28.44 using Table pp.270 � fcx = 153 N/mm² slenderness λy = 5640/24.5 slenderness λy = 230 using Table pp.270 � fcy = 18.1 N/mm² � fc = 18.1 N/mm²

ft 160 N/mm² fby 160 N/mm² fbx The flange is in tension

� 160 N/mm² σc 25350/2960 = 8.56 N/mm² cσbx 390000/42000 = 9.3 N/mm² tσbx 390000*32.8/3660000 = 3.5 N/mm² cσby 0.00 N/mm² tσby 20000/29700 = 0.67 N/mm²


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formula (E3.2.): 8.56/18.10 + 9.3/160 + 0 = 0.47 + 0.06 + 0 = 0.53 < 1 formula (E3.3.): -8.56/160.00 + 3.5/160 + 0.67/160 = -0.05 + 0.02 + 0 = 0.03 < 1 Calculation note - Member 7 KS Check

Macro 4 Member 7 IPE270 SS41 Ult. comb 7 0.30

Material data


fabrication rolled


Cfr. Chapter 4. ratio limit ratio

Webs 33.27 71.00

Outstanding flanges 6.62 15.49


Axis definition :



Internal forces

N 0.15 kN

Vx 0.00 kN

Vy 1.50 kN

Mt 0.00 kNm

Mx 9.72 kNm

My -0.00 kNm

LTB data

Unsupported length lb 6.00 m

cm 1.00

Shear check


Table of values

tau 0.95 MPa

Allow. shear stress fs 92.38 MPa

unity check 0.01

Combined stresses (tension and bending)

Compression side: according to article 3.3.2. and formula (3.4)


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Tension side: according to article 3.3.2. and formula (3.3)

Table of values Article Formula

ft 2.1.1. (2.1)

fbx 2.1.4.a (2.7 / 2.8)

fby 2.1.4.b (2.1)

Table of values

sigma t 0.03 MPa

t sigma b x -22.67 MPa

t sigma b y -0.00 MPa

c sigma b x 22.67 MPa

c sigma b y 0.00 MPa

ft 160.00 MPa

fbx 76.50 MPa

fby 160.00 MPa

Af 1377.00 mm^2

lb/ib 169.14

-0.00+0.30+0.00=0.30 < 1 ((3.4))

0.00+0.14+0.00=0.14 < 1 ((3.3))



Table of values

a 6.00 m

d 0.22 m

t 6.60 mm

alfa 2.00

k1 32.00

C1 0.27

sigma 0 160.00 MPa

sigma 18.47 MPa

k2 5.35

C2 0.67

v0 92.38 MPa

v 1.03 MPa

0.01+0.00=0.01 < 1 ((7.3))



Macro 11 Member 19 HEB160 SS41 Ult. comb 4 0.50

Material data


fabrication rolled



Webs 13.00 68.46



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Axis definition :



Internal forces

N -33.14 kN

Vx 0.06 kN

Vy -3.96 kN

Mt -0.00 kNm

Mx 19.79 kNm

My -0.32 kNm




Length 5.00 5.00 m



Euler stress fe 529.23 154.12 MPa

Allow. compr. stress fc 127.22 70.82 MPa

LTB data


cm 1.75

Shear check


Table of values

tau 3.53 MPa


unity check 0.04

Combined stresses (compression and bending)

Compression side: according to article 3.3.1. and formula (3.1) (E3.2.)

Tension side: according to article 3.3.1. and formula (3.2) (E3.3.)


fc 2.1.3. (2.3)(2.4)

ft 2.1.1. (2.1)

fbx 2.1.4.a (2.7 / 2.8)

fby 2.1.4.b (2.1)

Table of values

sigma c 6.10 MPa




c sigma b y 2.85 MPa

fc 70.82 MPa

ft 160.00 MPa

fbx 160.00 MPa

fby 160.00 MPa

Af 2080.00 mm^2

lb/ib 113.23


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0.09+0.40+0.02=0.50 < 1 ((3.1) (E3.2.))

-0.04+0.40+0.02=0.38 < 1 ((3.2) (E3.3.))



Table of values

a 5.00 m

d 0.10 m

t 8.00 mm

alfa 1.74

k1 23.75

C1 0.32

sigma 0 160.00 MPa

sigma 47.42 MPa

k2 5.34

C2 0.67

v0 92.38 MPa

v 4.76 MPa

0.09+0.00=0.09 < 1 ((7.3))



KS Check

Macro 18 Member 47 T120/120/13 SS41 Ult. comb 7 0.53

Material data


fabrication rolled





Axis definition :



Internal forces

N -25.35 kN

Vx -0.00 kN

Vy -0.31 kN

Mt -0.00 kNm

Mx 0.39 kNm

My 0.02 kNm




Length 1.00 6.00 m


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Euler stress fe 2562.76 39.18 MPa

Allow. compr. stress fc 152.60 18.09 MPa


LTB data


Shear check


Table of values

tau 0.59 MPa


unity check 0.01

Combined stresses (compression and bending)

Compression side: according to article 3.3.1. and formula (3.1) (E3.2.)

Tension side: according to article 3.3.1. and formula (3.2) (E3.3.)


fc 2.1.3. (2.3)(2.4)

ft 2.1.1. (2.1)

fbx 2.1.4.a (2.7 / 2.8)

fby 2.1.4.b (2.1)

Table of values

sigma c 8.56 MPa




c sigma b y -0.03 MPa

fc 18.09 MPa

ft 160.00 MPa

fbx 160.00 MPa

fby 160.00 MPa

0.47+0.06+0.00=0.53 < 1 ((3.1) (E3.2.))

-0.05+0.02+0.00=-0.03 < 1 ((3.2) (E3.3.))



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2. CONNECTIONS 2.1 PST.07.01 – 01 : Calculation of a base plate Description Calculation of a bolted base plate connection. The moment resistance MRd, the normal force resistance NRd and the shear resistance VRd are calculated manually for node 10 and compared with the result from ESA-Prima Win. Project data See input file. Reference [2] Eurocode 3

Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992

[3] Eurocode 3 : Part 1.1. Revised annex J : Joints in building frames ENV 1993-1-1/pr A2

See the chapter "Manual calculation" for the manual calculation of the connection according to Eurocode 3. Result Manual calculation EPW % Diff. MRd 44.99 kNm 44.76 kNm 0.51 % NRd,t 406 kN 406 kN 0 % NRd,c 1633 kN 1644 kN 0.67 % VRd 64.5 kN 64.5 kN 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070101.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL


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Manual calculation

CD

HEB280

Section CD

15

15

2.1.1 The design compression resistance NRd,c (Ref.[2]-Annex L)

jc,Rd AfN =

with A the resulting bearing area (The area in compression

under the base plate) fj the bearing strength of the joint cdjjj fkf ⋅⋅β= = 22 N/mm²

βj 0.66 kj 2.00 fcd 25 N/mm² For the determination of the resulting bearing area the additional bearing width c is introduced.

0Mj

y

γf3

ftc

⋅⋅⋅=

with t the thickness of the steel base plate

= 40 mm fy the yield strength of the steel base plate material

= 235 N/mm²

In this case we have :

mm9.711.1223

23540c =

⋅⋅⋅=

For the resulting bearing area we have :


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= 74233 mm² NRd,c = 74233 x 22 = 1633 kN

2.1.2 The design moment resistance The design compression resistance for concrete under the flange.

jflRd,base,c fAF ⋅=

with fj the bearing strength of the joint Afl the bearing area under the compression flange.

= 29392

kN6472229392F Rd,base,c =⋅=

Column flange in compression Fc,fb,Rd (Ref.[3]-J.3.5.4) The plastic moment of HEB280 = 360 kNm.

Mc,Rd = 360/1.1 = 327 kN Fc,fb,Rd = Mc,Rd/h = 1249 kN

( ) ( ) ( )297.712182805.1097.712280297.711815A ⋅−⋅−⋅+⋅+⋅⋅++=

( ) 28097.711815Afl ⋅++=


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Design tension resistance of anchor row

e 60 mm m 79.85-10.5/2-0.8x6x√2 = 67.8 mm m2 277-228-0.8x9x√2=38.8 mm λ1 67.8/(67.8+60)= 0.531 λ2 38.8/(67.8+60)= 0.304

α 6.00 p 144 mm leff,cp,i 2πm = 426 mm leff,nc,i αm = 406 mm leff,cp,g πm+p = 357 mm leff,nc,g 0.5p+αm-(2m+0.625e) = 305 mm For individual bolt row : leff,1 406 mm leff,2 406 mm Mpl,1,Rd (elastic moment is taken Mpl = lefft²fy/ 6)

23129696 Nmm

Mpl,2,Rd 23129696 Nmm

Ft,Rd,1 1364 kN Ft,Rd,2 457 kN Ft,Rd,3 203 kN For bolt group : leff,1 610 mm leff,2 610 mm Mpl,1,Rd (elastic moment is taken Mpl = lefft²fy/ 6)

34466666 Nmm

Mpl,2,Rd 34466666 Nmm

Ft,Rd,1 2033 kN Ft,Rd,2 729 kN Ft,Rd,3 406 kN

kN6.10125.1

4003539.0

γ

fA9.0Rd,Bt

mb

ubs =⋅⋅

==


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At the first anchor row, we have Ft,1=203 kN (<327<647 kN). Since 203 kN > 1.9 Bt,Rd , the following bolt row is linear determined in relation to the compression point. Ft,2=60x203/204=59 kN

MRd = 203 x 0.204 + 59 x 0.06 = 44.99 kN

2.1.3 The design tension resistance NRd,t It is the design tension resistance for the group of all bolt-rows (no compression limits). NRd,t is the resistance against tension due to uplift. NRd,t = 406 kN

2.1.4 The design shear resistance VRd.

For anchors, this value need to be corrected with 0.85 (Ref.[3] – 6.5.5.(6)) Since all bolts are under tension, the VRd is given by VRd = 0.28 x 67.7 x 0.85 x 4 = 64.5 kN

kN7.6725.1

4003536.0

γ

fA6.0F

Mb

ubsRd,v =

⋅⋅==


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Calculation note

Node 10 : bolted baseplate connection

According to EC3, Annex L & Revised Annex J

1. Input data

Column HEB280

h 280.00 mm

b 280.00 mm

tf 18.00 mm

tw 10.50 mm

r 24.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Mw 1.25

Gamma c 1.50

Gamma fr 2.00

Concrete block

fck_c 25.00 MPa

bond condition poor

Beta_j 0.66

kj 2.00

kfr 0.25

Baseplate

h 311.00 mm

b 281.00 mm

t 40.00 mm

fy 235.00 MPa

fu 360.00 MPa


type straight

bar type high bond

grade 4.6

fu 400.00 MPa

As 353.00 mm^2

do 26.00 mm

S 36.00 mm

e 39.60 mm

h head 15.00 mm

h nut 19.00 mm

Anchor position


1 228.00 159.70

2 84.00 159.70

Internal forces

Loadcase number 1


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Loadcase number 1

N -293.31 kN

Vz 1.90 kN

My -3.71 kNm

Tension on left side.

WARNING: NSd > 0.1*Npl,Rd,Column

Projected forces (Reactions)

N' = -293.31 kN

T' = 1.90 kN

2. Design compression resistance NRd,c

According to EC3, Annex L

NRd,c data

fcd 16.67 MPa

fj 22.00 MPa

c 71.97 mm

Resulting bearing area 74725.46 mm^2

NRd,c 1643.96 kN



3.1 Design resistance of basic components

3.1.1. Concrete in compression.

Fc,base,Rd data

Fc,base,Rd 655.08 kN

Area under compression flange. 29776.36 mm^2

h eq 193.48 mm

3.1.2 Column flange and web in compression (J.3.5.4)

Fc,fb,Rd data

Fc,fb,Rd 1250.83 kN

section class 1

Mc,Rd 327.72 kNm

hb-tfb 262.00 mm

3.1.3. Design tension resistance of anchor row


Bt,Rd = 101.66 kN


1 0.0+72.0 5.99 60.65 67.81 60.65

2 72.0+ 0.0 5.99 60.65 67.81 60.65


1 426.07 406.52

2 426.07 406.52


1 - - - - 357.04 305.00

2 - - 357.04 305.00 - -

For individual anchor row:


1 406.52 406.52 406.52 203.33 911.91


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2 406.52 406.52 406.52 203.33 911.91

For anchor group:


1- 1 406.52 406.52 406.52 203.33 911.91

1- 2 609.99 609.99 609.99 406.66 1368.32

3.2 Determination of Mj,Rd

row h[mm] Ft[kN]

1 203.00 203.33

2 59.00 59.10

Mj,Rd = 44.76 kNm Mj,Rd = 44.76 kNm(inclusive normal force)

4. Design tension resistance NRd,t


NRd,t = 406.66 kN


VRd data

VRd 64.52 kN

Fv,Rd 57.61 kN

e1,ep 83.00 mm

p1 144.00 mm

alfa,ep 1.00

Fb,ep,Rd 691.20 kN

6. Stiffness calculation 6.1 Design rotational stiffness

row k5[mm] k7[mm] keff[mm]

1 53.21 2.29 2.19

2 53.21 2.29 2.19

Sj data

Sj 17.88 MNm/rad

Sj,ini 17.88 MNm/rad

z 170.57 mm

mu 1.00

kc 22.33 mm

keq 3.37 mm

6.2 Stiffness classification

Not applicable.


Not applicable.



t > 0.53 sqrt(fub/fy) d

This results in a non-ductile classification for ductility : class 3.

7. Unity checks

Unity checks

NSd/NRd,c 0.18

MSd/MjRd 0.08

VSd/VRd 0.03


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8. Design Calculations.

8.1 Anchorage length.

Designed for Loadcase number 1

Anchorage data

Ft,anchor,max 101.66 kN

As,req 353.00 mm^2

As,prov 353.00 mm^2

lb 916.59 mm

a 1.00

lb,net 916.59 mm

lb,min 274.98 mm

l,anchor 916.59 mm

8.2. Calculation weldsize

8.2.1. Calculation af

data

MRd 44.76 kNm

Gamma 1.40

h 262.00 mm

FRd 239.19 kN

NT,Rd 1076.73 kN

N 821.98 kN

fu 360.00 MPa

BetaW 0.80

minimum af 5.77 mm

af 9.00 mm

8.2.2. Calculation aw

data

Ft 203.33 kN

Fv 0.95 kN

lw 406.52 mm

fu 360.00 MPa

BetaW 0.80


aw 6.00 mm


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2.2 PST.07.01 – 02 : Calculation of a bolted connection Description Five bolted connections are calculated with ESA-Prima Win. The moment resistance MRd and the stiffness Sj of node 3, 5, 6, 10 and 9 are compared with results from the literature. Project data See input file. Reference [2] Eurocode 3



[4] Frame Design Including Joint Behaviour Volume 2 ECSC Contracts n° 7210-SA/212 and 7210-SA/320 january 1997

Result Results for MRd (kNm) Description Node

number Source result Ref[4]

ESA-Prima Win results

% Diff.

Worked example Chapter 2 3 30.60 32.75 6.6 % Worked example Chapter 3a 5 20.25 21.37 5.53 % Worked example Chapter 3b 6 20.25 21.37 5.53 % Worked example Chapter 4a 10 24.10 29.52 22.49 % Worked example Chapter 4b 9 24.10 29.52 22.49 % Result for Sj,ini (kNm) Description Node

number Source result Ref[4]

ESA-Prima Win results

% Diff.

Worked example Chapter 2 3 10617 11103 4.58 % Worked example Chapter 3a 5 5906 5220 11.62 % Worked example Chapter 3b 6 5977 5313 11.11 % Worked example Chapter 4a 10 15433 15040 2.55 % Worked example Chapter 4b 9 15433 15040 2.55 % Remark : The source results are calculated with a simplified version of the revised ANNEX J. See the chapter "Calculation note" for the detailed output of ESA-Prima Win.


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Version ESA-Prima Win 3.20.03 Input file + calculation note PST070102.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL Calculation note

CD

IPE220

Section CD

HEB140

10

75

15 15

Figure 35 : node 3



1. Input data

Column HEB140

h 140.00 mm

b 140.00 mm

tf 12.00 mm

tw 7.00 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa



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h 220.00 mm

b 110.00 mm

tf 9.20 mm

tw 5.90 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

End plate

h 305.00 mm

b 140.00 mm

t 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolts M-16 (DIN960)

type normal

grade 8.8

fu 800.00 MPa

As 157.00 mm^2

do 18.00 mm

S 24.00 mm

e 26.75 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position


1 271.00 89.50

2 180.00 89.50

3 60.00 89.50

Internal forces

Loadcase number 1

N 1.12 kN

Vz 12.15 kN

My -7.51 kNm

Tension top


2.1. Design resistance of basic components 2.1.1. Column web panel in shear (J.3.5.2.)

Vwp,Rd data

Vwp,Rd 145.64 kN

Beta 1.00

Avc 1312.00 mm^2


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Fc,wc,Rd data

Fc,wc,Rd 172.16 kN

beff 161.27 mm

twc 7.00 mm

ro1 0.71

ro2 0.45

ro 0.71

kwc 1.00

lambda_rel 0.54

dc 92.00 mm

2.1.3. Beam flange and web in compression (J.3.5.4.)

Fc,fb,Rd data

Fc,fb,Rd 289.85 kN

section class 1

Mc,Rd 61.10 kNm

hb-tfb 210.80 mm



Bt,Rd = 90.43 kN


kfc = 1.00


1 0.0+45.5 - 25.25 31.65 25.25 -

2 45.5+60.0 - 25.25 31.65 25.25 -

3 60.0+ 0.0 - 25.25 31.65 25.25 -


1 198.86 158.16

2 198.86 158.16

3 198.86 158.16


1 - - - - 190.43 124.58

2 211.00 105.50 190.43 124.58 219.43 139.08

3 - - 219.43 139.08 - -



1 158.16 158.16 158.16 123.02 170.44 0.72

2 158.16 158.16 158.16 123.02 170.44 0.72

3 158.16 158.16 158.16 123.02 170.44 0.72

For bolt group:


1- 1 158.16 158.16 158.16 123.02 170.44 0.72

1- 2 249.16 249.16 249.16 227.88 205.20 0.55

1- 3 369.16 369.16 369.16 340.58 224.57 0.41

2.1.4.2. Endplate


1 0.0+45.5 - 34.00 35.34 34.00

2 45.5+60.0 5.11 25.25 38.41 25.25


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3 60.0+ 0.0 5.11 25.25 38.41 25.25


1 161.53 70.00

2 241.31 196.28

3 241.31 196.28


1 161.53 70.00 - - - -

2 - - - - 240.66 163.69

3 - - 240.66 163.69 - -



1 70.00 70.00 70.00 95.20 -

2 196.28 196.28 196.28 145.85 247.40

3 196.28 196.28 196.28 145.85 247.40

For bolt group:


1- 1 70.00 70.00 70.00 95.20 -

2- 2 196.28 196.28 196.28 145.85 247.40

2- 3 327.37 327.37 327.37 267.09 412.64


row h[mm] Ft[kN]

1 256.40 95.20

2 165.40 50.44

3 45.40 0.00



VRd data

VRd 188.10 kN

Fv,Rd 60.29 kN

e1,ep 34.00 mm

p1 91.00 mm

alfa,ep 0.63

alfa,fc 1.00

Fb,ep,Rd 108.80 kN

VRd beam 138.24 kN

VRd beam 196.25 kN




1 5.77 6.64 4.55 6.52 1.43

2 4.89 5.62 8.29 6.52 1.52

Sj data

Sj 11.10 MNm/rad


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Sj data


z 219.41 mm

mu 1.00

k1 2.27 mm

k2 8.59 mm

keq 2.82 mm


Stiffness data

E 210000.00 MPa

Ib 27699999.92 mm^4

Lb 2500.00 mm

frame type braced

S1 18.61 MNm/rad

S2 1.16 MNm/rad

System SEMI RIGID


Stiffness data

Fi y infinity MNm/rad


Sj,app infinity MNm/rad

Sj,lower boundary 18.61 MNm/rad

Sj,upper boundary infinity MNm/rad

Sj,ini is not inside the boundaries.

The actual joint stiffness is not conform with the joint stiffness of the analysis model.


The failure mode is situated in the column shear zone.

This results in a ductile classification for ductility : class 1.

5. Unity checks

Unity checks

MSd/MjRd 0.23

VSd/VRd 0.06


6. Design calculations 6.1. Calculation weldsize af / Minimum thickness th for stiffener in column

data

MRd 32.75 kNm

Gamma 1.40

h 210.80 mm

FRd 217.52 kN

NT,Rd 216.20 kN

N 216.20 kN

fu 360.00 MPa

BetaW 0.80

minimum af 3.86 mm

af 5.00 mm

Minimum th 9.20 mm

6.2. Calculation aw

data

Ft 50.44 kN

Fv 4.05 kN


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data

lw 196.28 mm

fu 360.00 MPa

BetaW 0.80


aw 3.00 mm

CD

IPE220

Section CD

HEB140

77

15 15

Figure 36 : node 5

Node 5 : bolted beam-to-column connection side CD According to EC3, Revised Annex J

1. Input data

Column HEB140

h 140.00 mm

b 140.00 mm

tf 12.00 mm

tw 7.00 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 220.00 mm

b 110.00 mm

tf 9.20 mm

tw 5.90 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25


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End plate

h 206.00 mm

b 140.00 mm

t 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolts M-16 (DIN960)

type normal

grade 8.8

fu 800.00 MPa

As 157.00 mm^2

do 18.00 mm

S 24.00 mm

e 26.75 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position


1 163.00 89.50

2 43.00 89.50

Internal forces

Loadcase number 1

N 1.12 kN

Vz 12.15 kN

My -8.27 kNm

Tension top



Vwp,Rd data

Vwp,Rd 145.64 kN

Beta 1.00

Avc 1312.00 mm^2


Fc,wc,Rd data

Fc,wc,Rd 162.16 kN

beff 144.27 mm

twc 7.00 mm

ro1 0.75

ro2 0.50

ro 0.75

kwc 1.00

lambda_rel 0.51

dc 92.00 mm


Fc,fb,Rd data

Fc,fb,Rd 289.85 kN

section class 1


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Fc,fb,Rd data

Mc,Rd 61.10 kNm

hb-tfb 210.80 mm



Bt,Rd = 90.43 kN


kfc = 1.00


1 0.0+60.0 - 25.25 31.65 25.25 -

2 60.0+ 0.0 - 25.25 31.65 25.25 -


1 198.86 158.16

2 198.86 158.16


1 - - - - 219.43 139.08

2 - - 219.43 139.08 - -



1 158.16 158.16 158.16 123.02 170.44 0.72

2 158.16 158.16 158.16 123.02 170.44 0.72

For bolt group:


1- 1 158.16 158.16 158.16 123.02 170.44 0.72

1- 2 278.16 278.16 278.16 235.72 211.64 0.51

2.1.4.2. Endplate


1 0.0+60.0 5.11 25.25 38.41 25.25

2 60.0+ 0.0 5.11 25.25 38.41 25.25


1 241.31 196.28

2 241.31 196.28


1 - - - - 240.66 163.69

2 - - 240.66 163.69 - -



1 196.28 196.28 196.28 145.85 247.40

2 196.28 196.28 196.28 145.85 247.40

For bolt group:


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1- 1 196.28 196.28 196.28 145.85 247.40

1- 2 327.37 327.37 327.37 267.09 412.64


row h[mm] Ft[kN]

1 165.40 123.02

2 45.40 22.63



VRd data

VRd 67.52 kN

Fv,Rd 60.29 kN

e1,ep 43.00 mm

p1 120.00 mm

alfa,ep 0.80

alfa,fc 1.00

Fb,ep,Rd 137.60 kN

VRd beam 138.24 kN

VRd beam 196.25 kN




1 6.44 7.41 8.29 6.52 1.77

2 6.44 7.41 8.29 6.52 1.77

Sj data

Sj 5.22 MNm/rad

Sj,ini 5.22 MNm/rad

z 139.56 mm

mu 1.00

k1 3.57 mm

k2 7.68 mm

keq 2.68 mm


Stiffness data

E 210000.00 MPa

Ib 27699999.92 mm^4

Lb 2500.00 mm

frame type braced

S1 18.61 MNm/rad

S2 1.16 MNm/rad

System SEMI RIGID


Stiffness data







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5. Unity checks

Unity checks

MSd/MjRd 0.39

VSd/VRd 0.18



data

MRd 21.37 kNm

Gamma 1.40

h 210.80 mm

FRd 141.95 kN

NT,Rd 216.20 kN

N 141.95 kN

fu 360.00 MPa

BetaW 0.80

minimum af 2.53 mm

af 5.00 mm

Minimum th 6.04 mm

6.2. Calculation aw

data

Ft 123.02 kN

Fv 6.08 kN

lw 196.28 mm

fu 360.00 MPa

BetaW 0.80


aw 3.00 mm


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AB

IPE220

Section AB

HEB140

10

10

15 15

Figure 37 : node 6

Node 6 : bolted beam-to-column connection side AB According to EC3, Revised Annex J

1. Input data

Column HEB140

h 140.00 mm

b 140.00 mm

tf 12.00 mm

tw 7.00 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 220.00 mm

b 110.00 mm

tf 9.20 mm

tw 5.90 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

End plate

h 240.00 mm

b 140.00 mm

t 15.00 mm


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End plate

fy 235.00 MPa

fu 360.00 MPa

Bolts M-16 (DIN960)

type normal

grade 8.8

fu 800.00 MPa

As 157.00 mm^2

do 18.00 mm

S 24.00 mm

e 26.75 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position


1 180.00 89.50

2 60.00 89.50

Internal forces

Loadcase number 1

N 1.12 kN

Vz 12.15 kN

My -8.27 kNm

Tension top

2. Design moment resistance MRd 2.1. Design resistance of basic components


Vwp,Rd data

Vwp,Rd 145.64 kN

Beta 1.00

Avc 1312.00 mm^2


Fc,wc,Rd data

Fc,wc,Rd 172.16 kN

beff 161.27 mm

twc 7.00 mm

ro1 0.71

ro2 0.45

ro 0.71

kwc 1.00

lambda_rel 0.54

dc 92.00 mm


Fc,fb,Rd data

Fc,fb,Rd 289.85 kN

section class 1

Mc,Rd 61.10 kNm

hb-tfb 210.80 mm




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Bt,Rd = 90.43 kN


kfc = 1.00


1 0.0+60.0 - 25.25 31.65 25.25 -

2 60.0+ 0.0 - 25.25 31.65 25.25 -


1 198.86 158.16

2 198.86 158.16


1 - - - - 219.43 139.08

2 - - 219.43 139.08 - -



1 158.16 158.16 158.16 123.02 170.44 0.72

2 158.16 158.16 158.16 123.02 170.44 0.72

For bolt group:


1- 1 158.16 158.16 158.16 123.02 170.44 0.72

1- 2 278.16 278.16 278.16 235.72 211.64 0.51

2.1.4.2. Endplate


1 0.0+60.0 5.11 25.25 38.41 25.25

2 60.0+ 0.0 5.11 25.25 38.41 25.25


1 241.31 196.28

2 241.31 196.28


1 - - - - 240.66 163.69

2 - - 240.66 163.69 - -



1 196.28 196.28 196.28 145.85 247.40

2 196.28 196.28 196.28 145.85 247.40

For bolt group:


1- 1 196.28 196.28 196.28 145.85 247.40

1- 2 327.37 327.37 327.37 267.09 412.64



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row h[mm] Ft[kN]

1 165.40 123.02

2 45.40 22.63



VRd data

VRd 67.52 kN

Fv,Rd 60.29 kN

e1,ep 60.00 mm

p1 120.00 mm

alfa,ep 1.00

alfa,fc 1.00

Fb,ep,Rd 172.80 kN

VRd beam 138.24 kN

VRd beam 196.25 kN




1 6.44 7.41 8.29 6.52 1.77

2 6.44 7.41 8.29 6.52 1.77

Sj data

Sj 5.31 MNm/rad

Sj,ini 5.31 MNm/rad

z 139.56 mm

mu 1.00

k1 3.57 mm

k2 8.59 mm

keq 2.68 mm


Stiffness data

E 210000.00 MPa

Ib 27699999.92 mm^4

Lb 2500.00 mm

frame type braced

S1 18.61 MNm/rad

S2 1.16 MNm/rad

System SEMI RIGID


Stiffness data












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5. Unity checks

Unity checks

MSd/MjRd 0.39

VSd/VRd 0.18



6.1. Calculation weldsize af / Minimum thickness th for stiffener in column

data

MRd 21.37 kNm

Gamma 1.40

h 210.80 mm

FRd 141.95 kN

NT,Rd 216.20 kN

N 141.95 kN

fu 360.00 MPa

BetaW 0.80

minimum af 2.53 mm

af 5.00 mm

Minimum th 6.04 mm

6.2. Calculation aw

data

Ft 123.02 kN

Fv 6.07 kN

lw 196.28 mm

fu 360.00 MPa

BetaW 0.80


aw 3.00 mm

AB

IPE220

Section AB CD

IPE220

Section CD

77

15 15

77

15 15

Figure 38 : node 10

Node 10 : bolted plate-to-plate connection



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1. Input data

Right side


h 220.00 mm

b 110.00 mm

tf 9.20 mm

tw 5.90 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa

End plate

h 206.00 mm

b 140.00 mm

t 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolts M-16 (DIN960)

type normal

grade 8.8

fu 800.00 MPa

As 157.00 mm^2

do 18.00 mm

S 24.00 mm

e 26.75 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position

row y[mm]

1 163.00 90.00

2 43.00 90.00

Left side


h 220.00 mm

b 110.00 mm

tf 9.20 mm

tw 5.90 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa

End plate

h 206.00 mm

b 140.00 mm

t 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25


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Gamma Ms 1.25

Gamma Mw 1.25

Internal forces

Loadcase number 1

N 1.12 kN

Vz -0.00 kN

My 6.53 kNm

Tension bottom


2.1. Design resistance of basic components 2.1.1.Beam flange and web in compression (J.3.5.4.) - Right side

Fc,fb,Rd data

Fc,fb,Rd 289.85 kN

section class 1

Mc,Rd 61.10 kNm

hb-tfb 210.80 mm


Fc,fb,Rd data

Fc,fb,Rd 289.85 kN

section class 1

Mc,Rd 61.10 kNm

hb-tfb 210.80 mm



Bt,Rd = 90.43 kN



2 0.0+60.0 5.09 25.00 38.66 25.00

1 60.0+ 0.0 5.09 25.00 38.66 25.00

row leff,cp,i

2 242.88 196.94

1 242.88 196.94


2 - - - - 241.44 164.01

1 - - 241.44 164.01 - -



2 196.94 196.94 196.94 145.39 248.24

1 196.94 196.94 196.94 145.39 248.24

For bolt group:


2- 2 196.94 196.94 196.94 145.39 248.24

2- 1 328.01 328.01 328.01 265.91 413.44


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2 0.0+60.0 5.09 25.00 38.66 25.00

1 60.0+ 0.0 5.09 25.00 38.66 25.00

row leff,cp,i

2 242.88 196.94

1 242.88 196.94


2 - - - - 241.44 164.01

1 - - 241.44 164.01 - -



2 196.94 196.94 196.94 145.39 248.24

1 196.94 196.94 196.94 145.39 248.24

For bolt group:


2- 2 196.94 196.94 196.94 145.39 248.24

2- 1 328.01 328.01 328.01 265.91 413.44


row h[mm] Ft[kN]

2 165.40 145.39

1 45.40 120.52



VRd data

VRd 67.52 kN

Fv,Rd 60.29 kN

data right

e1 43.00 mm

p1 120.00 mm

alfa,ep 0.80

Fb,ep,Rd 137.60 kN

data left

e1 43.00 mm

p1 120.00 mm

alfa,ep 0.80

Fb,ep,Rd 137.60 kN

4. Stiffness calculation 4.1. Design rotational stiffness


2 8.15 8.15 6.05 2.43

1 8.15 8.15 6.05 2.43


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Sj data

Sj 15.04 MNm/rad


z 139.56 mm

mu 1.00

keq 3.68 mm

4.2. Stiffness classification Right side

Stiffness data

E 210000.00 MPa

Ib 27699999.92 mm^4

Lb 2500.00 mm

frame type braced

S1 18.61 MNm/rad

S2 1.16 MNm/rad

System SEMI RIGID

Left side

Stiffness data

E 210000.00 MPa

Ib 27699999.92 mm^4

Lb 2500.00 mm

frame type braced

S1 18.61 MNm/rad

S2 1.16 MNm/rad

System SEMI RIGID

4.3 Check of stiffness requirement Right side

Stiffness data








Left side

Stiffness data






Sj is not inside the boundaries.






5. Unity checks

Unity checks


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Unity checks

MSd/MjRd 0.22

VSd/VRd 0.00


6. Design calculations 6.1. Calculation af - Right side

data

MRd 29.52 kNm

Gamma 1.40

h 210.80 mm

FRd 196.05 kN

NT,Rd 216.20 kN

N 196.05 kN

fu 360.00 MPa

BetaW 0.80

minimum af 3.50 mm

af 5.00 mm


data

Ft 265.91 kN

Fv 0.00 kN

lw 328.01 mm

fu 360.00 MPa

BetaW 0.80


aw 3.00 mm


data

MRd 29.52 kNm

Gamma 1.40

h 210.80 mm

FRd 196.05 kN

NT,Rd 216.20 kN

N 196.05 kN

fu 360.00 MPa

BetaW 0.80

minimum af 3.50 mm

af 5.00 mm


data

Ft 265.91 kN

Fv 0.00 kN

lw 328.01 mm

fu 360.00 MPa

BetaW 0.80


aw 3.00 mm


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AB

IPE220

Section AB CD

IPE220

Section CD

10

10

15 15

10

10

15 15

Figure 39 : node 9

Node 9 : bolted plate-to-plate connection According to EC3, Revised Annex J

1. Input data

Right side


h 220.00 mm

b 110.00 mm

tf 9.20 mm

tw 5.90 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa

End plate

h 240.00 mm

b 140.00 mm

t 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolts M-16 (DIN960)

type normal

grade 8.8

fu 800.00 MPa

As 157.00 mm^2

do 18.00 mm

S 24.00 mm

e 26.75 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position

row y[mm]

1 180.00 90.00


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row y[mm]

2 60.00 90.00

Left side


h 220.00 mm

b 110.00 mm

tf 9.20 mm

tw 5.90 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa

End plate

h 240.00 mm

b 140.00 mm

t 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Internal forces

Loadcase number 1

N -4.03 kN

Vz 0.00 kN

My 8.63 kNm

Tension bottom



2.1.1.Beam flange and web in compression (J.3.5.4.) - Right side

Fc,fb,Rd data

Fc,fb,Rd 289.85 kN

section class 1

Mc,Rd 61.10 kNm

hb-tfb 210.80 mm


Fc,fb,Rd data

Fc,fb,Rd 289.85 kN

section class 1

Mc,Rd 61.10 kNm

hb-tfb 210.80 mm



Bt,Rd = 90.43 kN



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2 0.0+60.0 5.09 25.00 38.66 25.00

1 60.0+ 0.0 5.09 25.00 38.66 25.00

row leff,cp,i

2 242.88 196.94

1 242.88 196.94


2 - - - - 241.44 164.01

1 - - 241.44 164.01 - -



2 196.94 196.94 196.94 145.39 248.24

1 196.94 196.94 196.94 145.39 248.24

For bolt group:


2- 2 196.94 196.94 196.94 145.39 248.24

2- 1 328.01 328.01 328.01 265.91 413.44



2 0.0+60.0 5.09 25.00 38.66 25.00

1 60.0+ 0.0 5.09 25.00 38.66 25.00

row leff,cp,i

2 242.88 196.94

1 242.88 196.94


2 - - - - 241.44 164.01

1 - - 241.44 164.01 - -



2 196.94 196.94 196.94 145.39 248.24

1 196.94 196.94 196.94 145.39 248.24

For bolt group:


2- 2 196.94 196.94 196.94 145.39 248.24

2- 1 328.01 328.01 328.01 265.91 413.44


row h[mm] Ft[kN]

2 165.40 145.39

1 45.40 120.52


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Mj,Rd = 29.52 kNm

Mj,Rd = 29.52 kNm(inclusive normal force)


VRd data

VRd 67.52 kN

Fv,Rd 60.29 kN

data right

e1 60.00 mm

p1 120.00 mm

alfa,ep 1.00

Fb,ep,Rd 172.80 kN

data left

e1 60.00 mm

p1 120.00 mm

alfa,ep 1.00

Fb,ep,Rd 172.80 kN




2 8.15 8.15 6.05 2.43

1 8.15 8.15 6.05 2.43

Sj data

Sj 15.04 MNm/rad


z 139.56 mm

mu 1.00

keq 3.68 mm

4.2. Stiffness classification Right side

Stiffness data

E 210000.00 MPa

Ib 27699999.92 mm^4

Lb 2500.00 mm

frame type braced

S1 18.61 MNm/rad

S2 1.16 MNm/rad

System SEMI RIGID

Left side

Stiffness data

E 210000.00 MPa

Ib 27699999.92 mm^4

Lb 2500.00 mm

frame type braced

S1 18.61 MNm/rad

S2 1.16 MNm/rad

System SEMI RIGID

4.3 Check of stiffness requirement Right side

Stiffness data




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Stiffness data






Left side

Stiffness data






Sj is not inside the boundaries.






5. Unity checks

Unity checks

MSd/MjRd 0.29

VSd/VRd 0.00


6. Design calculations 6.1. Calculation af - Right side

data

MRd 29.52 kNm

Gamma 1.40

h 210.80 mm

FRd 196.05 kN

NT,Rd 216.20 kN

N 196.05 kN

fu 360.00 MPa

BetaW 0.80

minimum af 3.50 mm

af 5.00 mm


data

Ft 265.91 kN

Fv 0.00 kN

lw 328.01 mm

fu 360.00 MPa

BetaW 0.80


aw 3.00 mm


data

MRd 29.52 kNm

Gamma 1.40

h 210.80 mm

FRd 196.05 kN


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data

NT,Rd 216.20 kN

N 196.05 kN

fu 360.00 MPa

BetaW 0.80

minimum af 3.50 mm

af 5.00 mm


data

Ft 265.91 kN

Fv 0.00 kN

lw 328.01 mm

fu 360.00 MPa

BetaW 0.80


aw 3.00 mm


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2.3 PST.07.01 – 03 : Calculation of a bolted connection Description Calculation of a bolted connection : the moment resistance MRd and the stiffness Sj of node 1 are calculated with ESA-Prima Win and compared with results from the literature. Project data See input file. Reference [2] Eurocode 3



[4] Joints in Building Frames (Revised Annex J) CEN / TC250/SC3-PT9 September 1993

Result Source

result Ref.[4]

ESA-Prima Win result

% Diff.

MRd 31.75 31.78 0 % Sj,ini 11760 11592 1.43 % See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070103.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL


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Calculation note

CD

IPE220

Section CD

HEB140

15

70

15 15



1. Input data

Column HEB140

h 140.00 mm

b 140.00 mm

tf 12.00 mm

tw 7.00 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 220.00 mm

b 110.00 mm

tf 9.20 mm

tw 5.90 mm

r 12.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

End plate

h 305.00 mm


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End plate

b 140.00 mm

t 12.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolts M-16 (DIN960)

type normal

grade 8.8

fu 800.00 MPa

As 157.00 mm^2

do 18.00 mm

S 24.00 mm

e 26.75 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position


1 265.00 80.00

2 195.00 80.00

3 55.00 80.00

Internal forces

Loadcase number 1

N 0.00 kN

Vz 9.65 kN

My -9.34 kNm

Tension top

2. Design moment resistance MRd 2.1. Design resistance of basic components


Vwp,Rd data

Vwp,Rd 145.64 kN

Beta 1.00

Avc 1312.00 mm^2


Fc,wc,Rd data

Fc,wc,Rd 173.24 kN

beff 163.27 mm

twc 7.00 mm

ro1 0.71

ro2 0.45

ro 0.71

kwc 1.00

lambda_rel 0.54

dc 92.00 mm


Fc,fb,Rd data

Fc,fb,Rd 289.85 kN

section class 1

Mc,Rd 61.10 kNm

hb-tfb 210.80 mm


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Bt,Rd = 90.43 kN


kfc = 1.00


1 0.0+35.0 - 30.00 26.90 30.00 -

2 35.0+70.0 - 30.00 26.90 30.00 -

3 70.0+ 0.0 - 30.00 26.90 30.00 -


1 169.02 145.10

2 169.02 145.10

3 169.02 145.10


1 - - - - 154.51 107.55

2 210.00 105.00 154.51 107.55 224.51 142.55

3 - - 224.51 142.55 - -



1 145.10 145.10 145.10 134.58 162.68 0.75

2 145.10 145.10 145.10 134.58 162.68 0.75

3 145.10 145.10 145.10 134.58 162.68 0.75

For bolt group:


1- 1 145.10 145.10 145.10 134.58 162.68 0.75

1- 2 215.10 215.10 215.10 245.99 195.32 0.61

1- 3 355.10 355.10 355.10 382.07 223.09 0.42

2.1.4.2. Endplate


1 0.0+35.0 - 40.00 24.34 30.43

2 35.0+70.0 5.99 30.00 33.66 30.00

3 70.0+ 0.0 5.99 30.00 33.66 30.00


1 136.48 70.00

2 211.47 201.57

3 211.47 201.57


1 136.48 70.00 - - - -

2 - - - - 245.73 185.51

3 - - 245.73 185.51 - -



1 70.00 70.00 70.00 88.46 -


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2 201.57 201.57 201.57 133.95 254.07

3 201.57 201.57 201.57 133.95 254.07

For bolt group:


1- 1 70.00 70.00 70.00 88.46 -

2- 2 201.57 201.57 201.57 133.95 254.07

2- 3 371.01 371.01 371.01 260.13 467.64


row h[mm] Ft[kN]

1 245.40 88.46

2 175.40 57.18

3 35.40 0.00

Mj,Rd = 31.74 kNm



VRd data

VRd 188.10 kN

Fv,Rd 60.29 kN

e1,ep 40.00 mm

p1 70.00 mm

alfa,ep 0.74

alfa,fc 1.00

Fb,ep,Rd 102.40 kN

VRd beam 138.24 kN

VRd beam 196.25 kN



1 8.12 5.73 7.13 7.08 1.73

2 7.92 5.59 7.15 7.08 1.71

Sj data

Sj 11.59 MNm/rad


z 216.42 mm

mu 1.00

k1 2.30 mm

k2 8.70 mm

keq 3.34 mm


Stiffness data

E 210000.00 MPa

Ib 27699999.92 mm^4

Lb 2000.00 mm

frame type braced

S1 23.27 MNm/rad

S2 1.45 MNm/rad

System SEMI RIGID


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Stiffness data











5. Unity checks

Unity checks

MSd/MjRd 0.29

VSd/VRd 0.05



data

MRd 31.74 kNm

Gamma 1.40

h 210.80 mm

FRd 210.79 kN

NT,Rd 216.20 kN

N 210.79 kN

fu 360.00 MPa

BetaW 0.80

minimum af 3.76 mm

af 5.00 mm

Minimum th 8.97 mm

6.2. Calculation aw

data

Ft 57.18 kN

Fv 3.22 kN

lw 201.57 mm

fu 360.00 MPa

BetaW 0.80


aw 3.00 mm


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2.4 PST.07.01 – 04 : Calculation of a bolted connection Description Calculation of a bolted connection : a manual calculation for the moment resistance MRd and the stiffness Sj are performed for node 3 and compared with the EPW results. Project data See input file. Reference [2] Eurocode 3

Design of steel structures Part 1 – 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992


See the chapter "Manual calculation" for the manual calculation according to this reference. Result Manual calc. ESA-Prima

Win result % Diff.

MRd 30.9 30.2 2.27 % VRd 231 231 0 % Sj,ini 7882 7795 1.10 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070104.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL Manual calculation • Beam to column.


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• Bolted flush end-plate. The references are default made to Ref[3], if not the reference is mentioned. 1. Input data. Beam & Column : Column HEA 160 Beam IPE 270 For the properties of the beam and the column, see input file. Bolts: M-16, grade 10.9 For the position of the bolts, see the chapter Calculation note. End-plate: Flush end-plate with a thickness of 12.0 mm.

CD

IPE270

Section CD

HEA160

15

5

2. Design moment resistance MRd. 2.1 Design resistance of the basic components. 2.1.1 Column web panel in shear. (J.3.5.2) Vwp,Rd Formula (J.16)

• Avc (Ref[2], 5.4.6) = 1324 mm² � Vwp,Rd = 146.98 kN • Transformation parameter β: Ref[3].Table J.4 β = 1


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2.1.2 Column web in compression. (J.3.5.3) Fc,wc,Rd Formula (J.18) + Annexed page J39’ • beff,c : The effective width of the column web in compression Formula (J.19) = 166.08 • ρ : Reduction factor for possible effects of shear in the column web panel. Table J.5 = ρ1 = 0.76

• λ : Relative slenderness of the column web. • dc = the clear depth of the column web.

dc = 152 - 2(9 + 15) = 104 mm

⇒ λ = 0.68 > 0.67, so reduction factor for local buckling is necessary. Reduction factor: = 0.995 • kwc : Reduction factor for longitudinal compressive stress in the column. σcom,Ed = 42.4 N/mm² < 0.5fy,wc kwc = 1.0 � Fc,wc,Rd = 160.54 kN 2.1.3. Beam flange and part of web in compression. (J.3.5.4) Fc,fb,Rd Formula (J.23)

• Mc,Rd The design moment resistance of the beam cross-section (EC3 5.4.5 & 5.4.7)

The beam is a class-1 section (Wpl is used) ⇒ Mc,Rd= 103.4 kNm • hb - tfb = 259.8 mm � Fc,fb,Rd = 398.0 kN 2.1.4 Design tension resistance of the bolt rows. Bt,Rd The design tension resistance of a bolt assembly. = Ft,,Rd (Ref[3] J.3.2 (6) & Ref[2] Table 6.5.3) � Bt,Rd = 113.04 kN 2.1.4.1 The column flange in bending. (J.3.5.5) The column flange is stiffened. (J.3.5.5.3) Method of the equivalent T-stub flange. (J.3.2) Dimensions: (Figure J.25) • m = 30 mm • e = 35 mm • emin = 22 mm 2.1.4.1.1. Determination of Fti,fc,Rd : Fti,fc,Rd =The design resistance of the column flange in bending for the individual bolt-row i. Determination of Ft1,fc,Rd: Determination of leff: effective lengths for a stiffened column flange Using Table J.7.


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Bolt row 1 is adjacent to a stiffener. (use of α) leff,cp1 = 2 π m = 188.5 mm leff,nc1 = α m = 182.64 mm Determination of α : figure J.27 e = 35 mm m = (bcol - tweb,col)/2 - e - 0.8rcol = 30 mm m2 = (distance from centre-line of bolt-row 1 till edge stiffener) - 0.8 √2aweld Note: The top of the stiffener == top of the beam ⇒ m2 = (45+5-12) - 0.8 √2x6 = 31.21 mm λ1 = 0.4615 λ2 = 0.4802

• α = 6.09

leff for failure mode 1 = leff,1 = leff,nc but ≤ leff,cp • leff,1 = 182.64 mm

leff for failure mode 2 = leff,2 = leff,nc • leff,2 = 182.64 mm Ft1,fc,Rd,1 : The design tension resistance of the column flange for bolt-row 1 individually, for mode 1: Complete yielding of the flange. Formula (J.4)

• Mpl1,Rd = 790 kNmm Formula ( J.7a) ⇒ Ft1,fc,Rd,1 = 105.35 kN Ft1,fc,Rd,2 : The design tension resistance of the column flange for bolt-row 1 individually, for mode 2: Bolt failure + yielding of the flange. Formula (J.5) • Mpl,2,Rd = 790 kNmm Formula ( J.7b) • n = 22 mm Formula (J.8) ⇒ Ft1,fc,Rd,2 = 126.04 kN Ft1,fc,Rd,3 : The design tension resistance of the column flange for bolt-row 1 individually, for mode 3: Bolt Failure. Formula (J.6)

• ∑ Bt,Rd = 226.08 kN (2 bolts in bolt-row 1)

⇒ Ft1,fc,Rd,3 = 226.08 kN Ft1,fc,Rd = Minimum of ( Ft1,fc,Rd,1 , Ft1,fc,Rd,2 , Ft1,fc,Rd,3 ) � Ft1,fc,Rd = 105.35 kN � Failure mode is mode 1: Complete yielding of the flange. Determination of Ft2,fc,Rd:

Determination of leff: Using Table J.7. Bolt row 2 is NOT adjacent to a stiffener. leff,1 = 163.75 mm leff,2 = 163.75 mm

The determination of the other Fti,fc,Rd is analogue to that of Ft1,fc,Rd , so we’ll just mention the results: • Mpl,1,Rd = 708 kNmm • Ft2,fc,Rd,1 = 94.45 kN


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• Mpl,2,Rd = 708 kNmm • Ft2,fc,Rd,2 = 122.90 kNmm • Ft2,fc,Rd,3 = 226.08 kN � Ft2,fc,Rd = 94.45 kN � Failure mode is mode 1: Complete yielding of the flange. Determination of Ft3,fc,Rd: • Mpl,1,Rd = 708 kNmm • Ft3,fc,Rd,1 = 94.45 kN • Mpl,2,Rd = 708 kNmm • Ft3,fc,Rd,2 = 122.9 kNmm • Ft3,fc,Rd,3 = 226.08 kN � Ft3,fc,Rd = 94.45 kN � Failure mode is mode 1: Complete yielding of the flange. Determination of Ft4,fc,Rd: • Mpl,1,Rd = 708 kNmm • Ft4,fc,Rd,1 = 94.45 kN • Mpl,2,Rd = 708 kNmm • Ft4,fc,Rd,2 = 122.9 kNmm • Ft4,fc,Rd,3 = 226.08 kN � Ft4,fc,Rd = 94.45 kN � Failure mode is mode 1: Complete yielding of the flange. 2.1.4.1.2. Determination of Ft(i+j+…),fc,Rd : F(ti+j+…),fc,Rd = The design resistance of the column flange in bending for the group of bolts (i + j + …) Determination of Ft(1+2),fc,Rd: Determination of leff: effective lengths for a stiffened column flange Using Table J.7. Bolt-row 1 is adjacent to a stiffener. leff1,cp,ge = π m + p = 144.25 mm leff1,nc,ge = 0.5p + α m - (2m + 0.625e) = 125.76 mm Bolt-row 2 is an end bolt-row for the group (1+2) leff2,cp,ge = π m + p = 144.25 mm leff2,nc,ge = 2m + 0.625e + 0.5 p = 106.88 mm

Note: p is taken as the pitch for the concerned bolt group, therefore in the output tables the distinction between leff,..,ge1

& leff,..,ge2 is made.

E.g. for the bolt-group (1+2), the pitch for bolt row 2 is taken as p1, the pitch between bolt-row 1 and bolt-row 2; this

results in the use of leff,..,ge1.

(Analogue: for the group of bolt-rows (2+3), leff,..,ge2 is used for bolt-row 2, and leff,..,ge1 for bolt-row 3)

Mode 1:


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leff(1+2),1 = ∑ leff,nc,g but ≤ ∑ leff,cp

• leff(1+2),1 = 125.76 + 106.88 = 232.64 mm • Mpl,Rd,1 = 1006 kNmm => Ft(1+2),fc,Rd,1 = 134.19 kN Mode 2:

leff(1+2),2 = ∑ leff,nc,g

• leff(1+2),2 = 232.64 • Mpl,Rd,2 = 1006 kNmm => Ft(1+2),fc,Rd,2 = 230.0 kN Mode 3:

=> Ft(1+2),fc,Rd,3 = 452.2 kN Result: �Ft(1+2),fc,Rd = 134.19 kN �Failure mode is mode 1 The determination of Ft(i+j+…),fc,Rd for the other bolt groups is completely analogue to that of Ft(1+2),fc,Rd. Determination of Ft(1+2+3),fc,Rd : Bolt-row 1 is adjacent to a stiffner. Bolt-row 2 is an inner bolt-row for this group. Bolt-row 3 is an end bolt-row for this group. Result: �Ft(1+2+3),fc,Rd = 163.03 kN Determination of Ft(1+2+3+4),fc,Rd : Bolt-row 1 is adjacent to a stiffner. Bolt-row 2 is an inner bolt-row for this group. Bolt-row 3 is an inner bolt-row for this group. Bolt-row 4 is an end bolt-row for this group. Result: �Ft(1+2+3+4),fc,Rd = 217.83 kN According to Annex J of EC3, we also have to consider extra groups of bolt-rows. A group of bolt-rows is an extra group within a bolt-group.

Determination of Ft(2+3): Bolt-row 2 is an end bolt-row for this group. Bolt-row 3 is an end bolt-row for this group. Result: �Ft(2+3),fc,Rd = 123.3 kN Other Results: �Ft(3+4),fc,Rd = 149.25 kN �Ft(2+3+4),fc,Rd = 178.1 kN 2.1.4.2 The column web in tension. (J.3.5.6) Ft,wc,Rd Formula (J.26)


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• beff : For a bolted connection, the effective width beff of the column web, is always taken as the non-circular effective length of the equivalent T-stub, representing the column flange.

• ρ : Reduction factor for the possible effects of shear in the column web-panel is determined from Table J.5.

But, in this particular case, none of the above is used, because the column web is stiffened.

• For stiffened column webs:

Ft,wc,Rd is taken as equal to Fc,fb,Rd : the design resistance of the beam flange in compression. � Ft,wc,Rd = 398.0 kN

This is only allowed, if the stiffeners are designed to resist the applied forces: Annex J, J.3.3(2) gives us an easy and quick check for this requirement:

1. The steel grade of the stiffeners is not lower than the that of the beam flanges. => O.K.

2. The thickness of the stiffeners is not smaller than the flange thickness of the beam. => O.K.

3. The outstand of the stiffeners is not less than (bb - twc) / 2 where: bb = the breadth of the beam flange. twc = the thickness of the column web => O.K.

Note: These 3 checks are executed by the program at the moment of input of the stiffeners.

2.1.4.3 Endplate in bending: (J.3.5.7) Analogue to the analysis of the column flange, we get the following results: Note: The flanges of the beam act as stiffeners to the endplate. Effective lengths: According to Table J.8.

Results: Ft1,ep,Rd = 132.49 kN Ft2,ep,Rd = 129.85 kN Ft3,ep,Rd = 129.85 kN Ft4,ep,Rd = 136.15 kN Ft(1+2),ep,Rd = 195.58 kN Ft(1+2+3),ep,Rd = 236.96 kN Ft(1+2+3+4),ep,Rd = 335.61 kN Ft(2+3),ep,Rd = 187.2 kN Ft(3+4),ep,Rd = 244.47 kN Ft(2+3+4),ep,Rd = 285.84kN 2.1.4.4 The beam web in tension. (J.3.5.8) Ft,wb,Rd Formula (J.31) • beff : The effective width beff of the beam web, is always taken as the non-circular effective length of the equivalent T-

stub, representing the end-plate. (= leff in the output tables) Results: Ft1,wb,Rd = 262.7 kN Ft2,wb,Rd = 248.4 kN Ft3,wb,Rd = 248.4 kN Ft4,wb,Rd = 282.6 kN Ft(1+2),wb,Rd = 333.2 kN


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Ft(1+2+3),wb,Rd = 403.7 kN Ft(1+2+3+4),wb,Rd = 571.8 kN Ft(2+3),wb,Rd = 318.9 kN / beff(2+3) = leff(2+3),nc = 113.1 + 113.1 = 226.2 mm Ft(3+4),wb,Rd = 416.5 kN / beff(3+4) = leff(3+4),nc = 135.6 + 159.8 = 295.4 mm Ft(2+3+4),wb,Rd = 487.0 kN / beff(2+3+4) = leff(2+3+4),nc = 113.1 + 72.5 + 159.8 = 345.4 mm 2.1.4.5 Determination of the effective design tension resistance Ftr,Rd for each bolt-row r : According to the procedure of J.3.6.2 Ft1,Rd is the smallest value of: • Vwp,Rd/ β = 147.0 kN • Fc,wc,Rd = 160.5 kN • Fc,fb,Rd = 398.0 kN • Ft1,fc,Rd = 105.4 kN • Ft1,wc,Rd = 398.0 kN • Ft1,ep,Rd = 132.5 kN • Ft1,wb,Rd = 262.7 kN � Ft1,Rd = 105.4 kN Ft2,Rd is the smallest value of: • Vwp,Rd/ β - Ft1,Rd = 41.6 kN • Fc,wc,Rd - Ft1,Rd = 55.1 kN • Fc,fb,Rd - Ft1,Rd = 292.6 kN • Ft2,fc,Rd = 94.5 kN • Ft2,wc,Rd = 398.0 kN • Ft2,ep,Rd = 129.9 kN • Ft2,wb,Rd = 248.4 kN • Ft(1+2),fc,Rd - Ft1,Rd = 134.19 - 105.4 = 28.8 kN • Ft(1+2),wc,Rd - Ft1,Rd = 398.0 - 105.4 = 292.6 kN • Ft(1+2),ep,Rd - Ft1,Rd = 195.6 - 105.4 = 90.2 kN • Ft(1+2),wb,Rd - Ft1,Rd = 333.2 - 105.4 = 227.8 kN � Ft2,Rd = 28.8 kN Ft3,Rd is the smallest value of: • Vwp,Rd/ β - Ft1,Rd - Ft2,Rd = 12.8 kN • Fc,wc,Rd - Ft1,Rd - Ft2,Rd = 26.3 kN • Fc,fb,Rd - Ft1,Rd - Ft2,Rd = 263.8 kN • Ft3,fc,Rd = 94.5 kN • Ft3,wc,Rd = 398.0 kN • Ft3,ep,Rd = 129.9 kN • Ft3,wb,Rd = 248.4 kN • Ft(1+2+3),fc,Rd - Ft1,Rd - Ft2,Rd = 163.03 - 105.4 - 28.8 = 28.8 kN • Ft(1+2+3),wc,Rd - Ft1,Rd - Ft2,Rd = 398.0 - 105.4 - 28.8 = 263.8 kN • Ft(1+2+3),ep,Rd - Ft1,Rd - Ft2,Rd = 237.0 - 105.4 - 28.8 = 102.8 kN • Ft(1+2+3),wb,Rd - Ft1,Rd - Ft2,Rd = 335.61 - 105.4 - 28.8 = 201.4 kN • Ft(2+3),fc,Rd - Ft2,Rd = 123.3 - 28.8 = 94.5 kN • Ft(2+3),wc,Rd - Ft2,Rd = 398.0 - 28.8 = 369.2 kN • Ft(2+3),ep,Rd - Ft2,Rd = 187.2 - 28.8 = 158.4 kN • Ft(2+3),wb,Rd -Ft2,Rd = 318.9 - 28.8 = 290.1 kN


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� Ft3,Rd = 12.8 kN Ft4,Rd is the smallest value of: • Vwp,Rd/ β - Ft1,Rd - Ft2,Rd -Ft3,Rd = 0.0 KN �Bolt-row 4 is in the compression zone! � Ft4,Rd = 0.0 kN For the sake of completeness, the other possible limitations are mentioned: • Fc,wc,Rd - Ft1,Rd - Ft2,Rd -Ft3,Rd • Fc,fb,Rd - Ft1,Rd - Ft2,Rd -Ft3,Rd • Ft4,fc,Rd • Ft4,wc,Rd • Ft4,ep,Rd • Ft4,wb,Rd • Ft(1+2+3+4),fc,Rd - Ft1,Rd - Ft2,Rd - Ft3,Rd • Ft(1+2+3+4),wc,Rd - Ft1,Rd - Ft2,Rd - Ft3,Rd • Ft(1+2+3+4),ep,Rd - Ft1,Rd - Ft2,Rd - Ft3,Rd • Ft(1+2+3+4),wb,Rd - Ft1,Rd - Ft2,Rd - Ft3,Rd • Ft(3+4),fc,Rd - Ft3,Rd • Ft(2+3+4),fc,Rd - Ft2,Rd - Ft3,Rd • Ft(3+4),wc,Rd - Ft3,Rd • Ft(2+3+4),wc,Rd - Ft2,Rd - Ft3,Rd • Ft(3+4),ep,Rd - Ft3,Rd • Ft(2+3+4),ep,Rd - Ft2,Rd - Ft3,Rd • Ft(3+4),wb,Rd -Ft3,Rd • Ft(2+3+4),wb,Rd - Ft2,Rd - Ft3,Rd

2.2 Determination of Mj,Rd. (J.3.6.2) Mj,Rd : The design moment resistance of the joint: Formula (J.32)

None of the bolt-rows has an effective design tension resistance greater than 1.9Bt,Rd, so there is no need to reduce any of the bolt-row effective tension resistance’s. (J.3.6.2 (8)) � Mj,Rd = 30.97 kNm We can also make allowance for the normal force acting in the beam. This is done as follows: N = 13.15 kN (compression) MjRd = 30.97 kNm –13.15/2 x (lever-arm = (hb-tfb) = 0.2598 m) �Mj,Rd(N) = 29.22 kNm

Check: Msd = 13.7 kNm => Joint is O.K. for Moment & Normal force. 3. Determination of the design shear resistance of the joint. According to EC3 6.5.5 & J.3.1.2

Fv,Rd : The design shear resistance of 1 bolt. (EC3 Table 6.5.3) • grade: 10.9 • fub = 1000 N/mm²


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• As = 157 mm² • γMb = 1.25 (Most negative case is considered: shear plane passes through the threaded portion of the bolt.) �Fv,Rd = 62.8 kN Bearing resistance for the column-flange: Fb,fc,Rd • αfc is the smallest of: • e1,fc / 3d0 = 38/17x3 = 0.745

e1 = end-distance between the first bolt-row and the top of the column. • p1/ 3d0 -0.25 = 50/17x3 -0.25 = 0.73

p1 = pitch between first bolt-rows = 50 mm • fub/fu = 1000/360 = 2.78 • 1.0 ⇒ αfc = 0.73 �Fb,fc,Rd = 75.73 kN Bearing resistance for the end-plate: Fb,ep,Rd Analogue to Fb,fc,Rd

⇒ αep =0.73 �Fb,ep,Rd = 100.97 kN

Vrd: The design shear resistance of the joint. • For bolts who are already subject to tension, the shear design resistance is reduced to 0.286 Fv,Rd . (J.3.1.2 (2b)) ⇒ Vrd1 = 62.8(2+6x0.28) = 231.1 kN ⇒ Vrd2 = 8 x 75.73 = 605.84 kN ⇒ Vrd3 = 8 x 100.97 = 807.76 kN � Vrd = min(Vrd1, Vrd2, Vrd3) = 231.1 kN

Check: Vsd = 8.65 kN => Joint is O.K. for shear.

4. Stiffness calculation.

4.1 Design rotational stiffness. (J.4.1) Since, the joint exists of an end-plate connection with more than one bolt row in tension , the general method of J.4.2.2 is used. Determination of keq: Formula (J.36) Since this example is a beam-to-column joint with an end-plate connection, keq should be based upon the following stiffness coefficients: • k3: The column flange in bending. • k4: The column web in tension. • k5: The end-plate in bending. • k7: The bolts in tension.

I. Determination of keff,r: the effective stiffness coefficient for bolt row r: Formula (J.37) 1. keff,r for bolt-row 1: (keff,1) A. Determination of ki1: ki1: The stiffness coefficient representing component i, relative to bolt row 1

• k31: Formula (J.41)

• leff,1: The smallest of the effective lengths given for bolt-row 1. (considered as an individual bolt-group, or as part of a bolt group.)


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� leff,1 = 117.48 mm � k31 = 2.70 mm

• k41: Formula (J.42) • beff,1 is taken as the smallest non-circular effective length for bolt-row 1. (considered as an individual bolt-group, or as part of a group of bolt rows.)

� beff,1 = 117.48 mm

• dc = the clear depth of the column web. � dc = 152 - 2(9 + 15) = 104 mm � k41 = 4.74 mm

• k51: Formula (J.43) • leff,1: The smallest of the effective lengths given for bolt-row 1 for the endplate.

(considered as an individual bolt-group, or as part of a group of bolt-rows.) � leff,1 = 123.24 mm

• tp = the thickness of the end-plate. � tp = 12.0 mm

• m = 37.17 mm �k51 = 3.52 mm

• k71: Formula (J.45) • As = 157 mm² • Lb: The elongation length of the bolt. Lb = tfc + tep + 0.5(hbolt,head + hbolt,nut)

� Lb = 32.5 mm �k71 = 7.73 mm

B. Determination of keff,1: keff,1: The effective stiffness coefficient for bolt-row 1.

Formula (J.37) �keff,1 = 1.01 mm

2. keff,r for the other Bolt-rows:

This is analogue to the determination of keff,1 keff,2 = 0.46 keff,3 = 0.64 Bolt-row 4 is not in tension. II. Determination of z: the lever arm. (J.4.3) Formula (J.38)

�z = 197.86 mm According to Formula (J.36): �keq = 2.01 mm Determination of k1: For an unstiffened column web-panel in shear. Formula (J.39):

• Avc = 1324 mm² • z = 197.86 mm • β = 1.0

� k1 = 2.54 mm Determination of k2: For an Unstiffened column web in compression. Formula (J.40):

• beff,c = 166.1 mm (See 2.1.2 or J.3.5.3) � k2 = 6.71 mm


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Determination of Sj,ini: The initial rotational stiffness of the joint. Sj,ini = Sj x µ (Formula (J.34)) �Sj,ini = 7882 x 106 Nmm/rad Determination of µµµµ: The stiffness ratio. Formula (J.35)

• Mj,Rd = 32.26 kNm (inclusive normal force N = 13.15 kN (compression)) • Msd = 13.7 kNm (Tension in the top of the joint) • ψ = 2.7

� µ = 1.0 Determination of Sj: The rotational stiffness of the joint. Formula (J.34)

� Sj = 7882 x 106 Nmm/rad 4.2. Stiffness classification. (J.2.5.1) Figure J.8

• Frame type: braced. • Lb = 6325 mm • Ib =5790 cm4 Determination of the classification boundaries: • Rigid: Sj,ini ≥ 8EIb/Lb = 15380 x 106 Nmm/rad • Semi-rigid • Nominally pinned: Sj,ini ≤ 0.5EIb/Lb = 961 x 106 Nmm/rad

�Joint-system is SEMI-RIGID Calculation note


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5.786e-003 1.157e-002 1.736e-002 2.314e-002

rad

10.0

20.0

30.0 kNm

Figure 40 : Moment-rotation diagram



1. Input data

Column HEA160

h 152.00 mm

b 160.00 mm

tf 9.00 mm

tw 6.00 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 270.00 mm

b 135.00 mm

tf 10.20 mm

tw 6.60 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Stiffener



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1 276.23 235.00

End plate

h 295.00 mm

b 135.00 mm

t 12.00 mm

fy 235.00 MPa

fu 360.00 MPa


type normal

grade 10.9

fu 1000.00 MPa

As 157.00 mm^2

do 18.00 mm

S 27.00 mm

e 29.60 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position


1 250.00 90.00

2 200.00 90.00

3 150.00 90.00

4 55.00 90.00

Internal forces

ULS Combination number 6

N -13.76 kN

Vz 8.42 kN

My -14.24 kNm

Tension top



Vwp,Rd data

Vwp,Rd 146.98 kN

Beta 1.00

Avc 1324.00 mm^2


Fc,wc,Rd data

Fc,wc,Rd 160.66 kN

beff 166.48 mm

twc 6.00 mm

ro1 0.76

ro2 0.50

ro 0.76

kwc 1.00

lambda_rel 0.68

dc 104.00 mm


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Fc,fb,Rd data

Fc,fb,Rd 398.00 kN

section class 1

Mc,Rd 103.40 kNm

hb-tfb 259.80 mm



Bt,Rd = 113.04 kN


kfc = 1.00


1 0.0+25.0 5.67 35.00 30.00 22.50 44.40

2 25.0+25.0 - 35.00 30.00 22.50 -

3 25.0+47.5 - 35.00 30.00 22.50 -

4 47.5+ 0.0 - 35.00 30.00 22.50 -


1 188.50 169.97

2 188.50 163.75

3 188.50 163.75

4 188.50 163.75


1 - - - - 144.25 113.10

2 100.00 50.00 144.25 106.87 144.25 106.87

3 145.00 72.50 144.25 106.87 189.25 129.37

4 - - 189.25 129.37 - -



1 169.97 169.97 169.97 98.04 398.00 1.00

2 163.75 163.75 163.75 94.45 398.00 1.00

3 163.75 163.75 163.75 94.45 398.00 1.00

4 163.75 163.75 163.75 94.45 398.00 1.00

For bolt group:


1- 1 169.97 169.97 169.97 98.04 398.00 1.00

1- 2 219.97 219.97 219.97 126.88 398.00 1.00

1- 3 269.97 269.97 269.97 155.72 398.00 1.00

1- 4 364.97 364.97 364.97 210.52 398.00 1.00

2.1.4.2. Endplate


1 0.0+25.0 5.03 22.50 37.17 22.50

2 25.0+25.0 - 22.50 37.17 22.50

3 25.0+47.5 - 22.50 37.17 22.50

4 47.5+ 0.0 5.42 22.50 37.17 22.50


1 233.57 187.09

2 233.57 176.82

3 233.57 176.82


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4 233.57 201.44


1 - - - - 166.79 123.68

2 100.00 50.00 166.79 113.41 166.79 113.41

3 145.00 72.50 166.79 113.41 211.79 135.91

4 - - 211.79 160.53 - -



1 187.09 187.09 187.09 133.47 263.80

2 176.82 176.82 176.82 130.82 249.32

3 176.82 176.82 176.82 130.82 249.32

4 201.44 201.44 201.44 137.17 284.04

For bolt group:


1- 1 187.09 187.09 187.09 133.47 263.80

1- 2 237.09 237.09 237.09 196.20 334.30

1- 3 287.09 287.09 287.09 237.58 404.80

1- 4 406.71 406.71 406.71 336.57 573.46


row h[mm] Ft[kN]

1 228.83 98.04

2 178.83 28.84

3 128.83 20.09

4 33.83 0.00

Mj,Rd = 30.18 kNm



VRd data

VRd 231.10 kN

Fv,Rd 62.80 kN

e1,ep 45.00 mm

e1,cf 44.40 mm

p1 50.00 mm

alfa,ep 0.68

alfa,fc 0.68

Fb,ep,Rd 93.44 kN

VRd beam 70.08 kN

VRd beam 272.50 kN




1 2.60 4.57 3.54 7.73 0.98

2 1.15 2.02 1.43 7.73 0.46

3 1.66 2.93 2.07 7.73 0.64

Sj data

Sj 7.79 MNm/rad

Sj,ini 7.79 MNm/rad


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Sj data

z 197.09 mm

mu 1.00

k1 2.55 mm

k2 6.72 mm

keq 1.98 mm


Stiffness data

E 210000.00 MPa

Ib 57900000.68 mm^4

Lb 6324.56 mm

frame type braced

S1 15.38 MNm/rad

S2 0.96 MNm/rad

System SEMI RIGID


Stiffness data











5. Unity checks

Unity checks

MSd/MjRd 0.47

VSd/VRd 0.04



data

MRd 30.18 kNm

Gamma 1.40

h 274.13 mm

FRd 154.14 kN

NT,Rd 294.18 kN

N 154.14 kN

fu 360.00 MPa

BetaW 0.80

minimum af 2.24 mm

af 6.00 mm

Minimum th 5.34 mm

6.2. Calculation aw

data

Ft 126.88 kN

Fv 2.11 kN

lw 237.09 mm


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data

fu 360.00 MPa

BetaW 0.80


aw 4.00 mm


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2.5 PST.07.01 – 05 : Calculation of welded connections Description Calculation of welded simple T connection : the moment resistance MRd and its components, and the weld sizes are calculated for node 10. Project data See input file. Reference [2] Eurocode 3 : Part 1.1.

Revised annex J : Joints in building frames ENV 1993-1-1/pr A2

[3] Eurocode 3 Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992

See the chapter "Manual calculation" for the manual calculation according to Eurocode 3. Result Manual

calculation EPW % Diff.

Vwp,Rd 652 kN 652 kN 0 % Fc,wc,Rd 668 kN (*) 643 kN 3.74 % Fc,fb,Rd 1116 kN 1114 kN 0 % Ft,fc,Rd 677 kN 677 kN 0 % Ft,wc,Rd 635 kN (*) 614 kN 3.31 % Mj,Rd 338 kN 327 kNm 3.25 % af 7.2 mm 7.2 mm 0 % aw 3 mm 3 mm 0 % (*) Remark : the differences between the EPW and the hand calculation, are due to the fact the program starts its calculation with the minimal weld size. The calculation of af and aw is performed after the calculation of the moment resistance. It means that the values of EPW are on the safe side. The program can use some default values for the weld sizes (see Ref.1). In this case, the program starts its calculation with these default values for the weld sizes. See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070105.epw Modules


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2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL Manual calculation

CD

IPE550

8

8

3

Section CD

HEB280

9

1. Calculation Vwp,Rd : Column web panel in shear (Ref.[2] – J.3.5.2)

When a web doubler is used :

2. Calculation Fc,wc,Rd : Column web in compression (Ref.[2] – J.3.5.3)

0M

vcyRd,wp

γ3

'Af9.0V =

kN6521.13

58792350.9RdVwp,

²mm58795.101724073'A

²mm4073A

18)2425.10(18280213100A

t)r2t(bt2AA

tbA'A

vc

vc

vc

fwfvc

ssvcvc

=⋅

⋅⋅=

=⋅+=

=

⋅++⋅⋅−=

++−=

+=


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3. Calculation Fc,fb,Rd : Beam flange in compression (Ref.[2] – J.3.5.4)

4. Calculation Ft,fc,Rd : Column flange in bending (Ref.[2] – J.3.5.5.1)

Ft fc, Bd,

twc

2 rc

7 ktfc

twc

fy

γM0

.

k =

tfc

tfb

fy fc,

fy fb,

1

Ft fc, Rd,

10.5 2 24. 7 1. 18.( )17.20 235.

1.1. 677 kN.

5. Calculation Ft,wc,Rd : Column web in tension (Ref.[2] – J.3.5.6)

( )

kN6681.1

23575.1525079.0F

79.0

'A

tb3.11

1ρ

ρρ

(*)mm250)2418(58222.17b

rt5a22tb

mm75.155.105.1t5.1t

γ

ftbρF

Rd,wc,c

2

vc

wceff

1

1

eff

fcfbeff

wwc

0M

ywceffRd,wc,c

=⋅⋅⋅

=

=

+

=

=

=++⋅+=

+++=

=⋅==

=

kN11162.17550

595F

kNm5951.1

655

γ

MM

th

MF

Rd,fb,c

0M

Rd,plRd,c

fbb

Rd,cRd,fb,c

=−

=

===

−=


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6. Calculation MRd : Design moment resistance

7. Calculation af The weld size af is designed according to the resistance of the joint. The design force in the beam flange can be estimated as:

kN635532.0

338F

h

MF

Rd

RdRd

==

=

The design resistance of the weld Fw shall be greater than the flange force FRd, multiplied by a factor γ. The value of the factor γ is (ref[2], J.3.1.3.) :

γ = 1.7 for sway frames γ = 1.4 for non sway frames

However, in no case shall the weld design resistance be required to exceed the design plastic resistance of the beam flange Nt.Rd :

kN7711.1

2352.17210N

γ

ftbN

Rd,t

M

ybfbfRd,t

0

=⋅⋅

=

⋅⋅=

kNm338635532.0M

FzM

Rd

RdRd

=⋅=

⋅=

Ft wc, Rd,

ρbeff twc

fy

γM0

twc

1.4 tw

1.4 10.5. 14.7 mm

beff

tfb

2 2 a. 5 tfc

r

beff

17.2 2 2 8. 5 18 24( ) 250 mm

ρ ρ1

ρ1

1

1 1.3beff

twc

Avc

2

0.81

Ft wc, Rd,

0.81 250. 14.7. 235.

1.1635 kN


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Fw = min ( Nt.Rd, γ FRd) = min (771, 1.4 x 635)= 771 kN

The weld size design for af, using Annex M of EC3 (Ref.[3])

mm23.72210360

8.025.1771000a

2bf

βγFa

f

fu

WMwwf

=⋅⋅

⋅⋅≥

⋅⋅

⋅⋅≥

We take af=8 mm.

Calculation of aw

The section is sollicitated by the moment M, the normal force N and the shear force D.

The moment M is defined by the critical design moment resistance of the connection. The normal force

N is taken as the maximum internal normal force on the node, the shear force D is taken as the

maximum internal shear force on the node.

M = 338 kNm

N = 148 kN

D = 84 kN

To determine the weldsize a2 in a connection, we use a iterative process with a2 as parameter until the Von Mises rules is respected (Ref[3],Annex M/EC3). We start with the minimal weld size a2=3 mm.

We can define the following properties :

a1 = 8 mm

a3 = 8 mm

a2 = 3 mm

l1 = 210 mm

l2 = h –3 tfb –2r = 550 – 3*17.2-2*24= 450 mm

l3 = (bf – twb – 2r) /2.0 = (210-11.1-2*24)/2.0=75.45 mm

43

fb33

32211

mm08e601.4)²2.17.2550(45.7586

4503

2

²5502108I

)²t.2h(la6

la

2

²hlaI

+=−⋅+⋅

+⋅⋅

=

−⋅+⋅

+⋅⋅

=


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²mm/N1292

1

08e601.42

450338000000

8474

148000τσ

2

1

I2

lM

A

Nτσ

21

221

=

⋅

⋅+==

⋅

⋅+==

²mm/N3.3145032

84000τ

la2

Dτ

1

221

=⋅⋅

=

⋅⋅=

( ) ( )

²mm/N28825.1

360

γ

f129σ

N/mm² 360 25.18.0

360

γβ

f²mm/N263²1293.313129ττ3σ

w

w

211

M

u1

Mw

u22222

==≤=

=⋅

=⋅

≤=+⋅+=+⋅+

Calculation note


3.239e-003 6.477e-003 9.716e-003 1.295e-002

rad

100.0

200.0

300.0

kNm

Node 3 : welded beam-to-column connection side CD


1. Input data

Column HEB280

h 280.00 mm

b 280.00 mm

tf 18.00 mm

tw 10.50 mm

r 24.00 mm

fy 235.00 MPa

fu 360.00 MPa


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h 550.00 mm

b 210.00 mm

tf 17.20 mm

tw 11.10 mm

r 24.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Webdoubler

ls 768.49 mm

bs 172.00 mm

ts 12.00 mm

as 9.00 mm

fy 235.00 MPa

Internal forces

Loadcase number 1

N 142.93 kN

Vz 79.99 kN

My -104.61 kNm

Tension top



Vwp,Rd data

Vwp,Rd 652.62 kN

Beta 1.00

Avc 5879.00 mm^2


Fc,wc,Rd data

Fc,wc,Rd 643.59 kN

beff 235.69 mm

twc 15.75 mm

ro1 0.81

ro2 0.57

ro 0.81

kwc 1.00

lambda_rel 0.42

dc 196.00 mm


Fc,fb,Rd data

Fc,fb,Rd 1114.69 kN

section class 1

Mc,Rd 593.91 kNm


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Fc,fb,Rd data

hb-tfb 532.80 mm

2.1.4. Column flange in bending (J.3.5.5.)

Ft,fc,Rd data

Ft,fc,Rd 677.95 kN

k 1.00

2.1.5. Column web in tension (J.3.5.6.)

Ft,wc,Rd data

Ft,wc,Rd 614.36 kN

beff 235.69 mm

twc 14.70 mm

ro1 0.83

ro2 0.60

ro 0.83


Mj,Rd data

F 614.36 kN

h 532.80 mm

Mj,Rd 327.33 kNm

Mj,Rd 327.33 kNm

(inclusive normal force)


VRd =887.15 kN



Sj data

Sj 151.02 MNm/rad


z 532.80 mm

mu 1.00

k1 4.19 mm

k2 13.26 mm

k4 12.37 mm


Stiffness data

E 210000.00 MPa

Ib 670999987.05 mm^4

Lb 6000.00 mm

frame type braced

S1 187.88 MNm/rad

S2 11.74 MNm/rad

System SEMI RIGID


Stiffness data







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5. Unity checks

Unity checks

MSd/MjRd 0.32

VSd/VRd 0.09



data

MRd 327.33 kNm

Gamma 1.40

h 532.80 mm

FRd 860.10 kN

NT,Rd 771.65 kN

N 771.65 kN

fu 360.00 MPa

BetaW 0.80

minimum af 7.22 mm

af 8.00 mm

Minimum th 17.20 mm

6.2. Calculation aw

data

M 327.33 kNm

N 142.93 kN

V 79.99 kN

fu 360.00 MPa

BetaW 0.80

a1 8.00 mm

a3 8.00 mm

l1 210.00 mm

l2 450.40 mm

l3 75.45 mm

A 6675.20 mm^2

I 429791090.71 mm^4


aw 3.00 mm


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2.6 PST.07.01 – 06 : Calculation of required stiffness Description Calculation of a bolted knee connection : the moment resistance MRd, the rotational stiffness and the stiffness boundaries are calculated and compared with literature results. Project data See input file. Reference [1] Eurocode 3 : Part 1.1.

Revised annex J : Joints in building frames ENV 1993-1-1/pr A2

[2] Eurocode 3 Design of steel structures Part 1 - 1 : General rules and rules for buildings ENV 1993-1-1:1992, 1992

[3] Frame Design Including Joint Behaviour Volume 1 ECSC Contracts n° 7210-SA/212 and 7210-SA/320 January 1997

Result The comparison is performed for node nr.7. The approximate joint stiffness is introduced in the model as Sj,app/2 = 13000 kNm/rad. Ref.[3],

Chapter 10 Worked example 1

EPW % Diff.

Mj,Rd 128 kNm 129 kNm 0.78 % Sj,ini 58000 kNm/rad 60369 kNm/rad 4.08 % Sj,upper 68000 kNm/rad 62786 kNm/rad 7.67 % S,app 26000 kNm/rad 26000 kNm/rad 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070106.epw Modules 2D Frame (PRS.01)


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Connect Frame - Rigid (PST.07.01) Author CVL Calculation note

1 2 3

4 5 6

7 8 9

IPE500 IPE500

IPE400 IPE400

HEA200

HEA200

HEA300

HEA300

HEA200

HEA200

Figure 41 : Frame geometry

CD

IPE400

7

7

5

Section CD

HEA200

11

14

5

15

15

Figure 42 : Connection geometry


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Sj,ini

Sj,ini = 60369.63 kNm/rad

Sj,low

Sj,low = 15008.30 kNm/rad

Sj,upper

Sj,upper = 62786.74 kNm/rad

1.070e-003 2.141e-003 3.211e-003 4.282e-003

rad

50.0

100.0

kNm

Figure 43 : Check required stiffness


3.199e-003 6.398e-003 9.597e-003 1.280e-002

rad

50.0

100.0

kNm

Figure 44 : Moment rotation diagramma



1. Input data

Column HEA200

h 190.00 mm

b 200.00 mm

tf 10.00 mm

tw 6.50 mm

r 18.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 400.00 mm

b 180.00 mm

tf 13.50 mm

tw 8.60 mm

r 21.00 mm


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fy 235.00 MPa

fu 360.00 MPa

Haunch under IPE400

hc 360.00 mm

lc 623.25 mm

b 180.00 mm

tf 13.50 mm

tw 8.60 mm

weld ab 14.00 mm

weld ac 11.00 mm


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

End plate

h 790.00 mm

b 180.00 mm

t 20.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolts M-20 (DIN960)

type normal

grade 8.8

fu 800.00 MPa

As 245.00 mm^2

do 22.00 mm

S 30.00 mm

e 33.53 mm

h head 13.00 mm

h nut 16.00 mm

Bolt position


1 721.00 90.00

2 640.00 90.00

3 429.00 90.00

4 71.00 90.00

Internal forces


N -22.53 kN

Vz 151.08 kN

My -31.72 kNm

Tension top




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Vwp,Rd data

Vwp,Rd 200.37 kN

Beta 1.00

Avc 1805.00 mm^2


Fc,wc,Rd data

Fc,wc,Rd 196.55 kN

beff 198.40 mm

twc 6.50 mm

ro1 0.78

ro2 0.52

ro 0.78

kwc 1.00

lambda_rel 0.78

dc 134.00 mm


Fc,fb,Rd data

Fc,fb,Rd 722.99 kN

section class 1

Mc,Rd 279.44 kNm

hb-tfb 386.50 mm



Bt,Rd = 141.12 kN


kfc = 1.00


1 0.0+40.5 - 55.00 27.35 34.19 69.00

2 40.5+105.5 - 55.00 27.35 34.19 -

3 105.5+179.0 - 55.00 27.35 34.19 -

4 179.0+ 0.0 - 55.00 27.35 34.19 -


1 171.85 158.08

2 171.85 178.15

3 171.85 178.15

4 171.85 178.15


1 - - - - 166.92 129.58

2 292.00 146.00 166.92 129.58 296.92 194.58

3 569.00 284.50 296.92 194.58 443.92 268.08

4 - - 443.92 268.08 - -



1 158.08 158.08 158.08 123.48 184.13 0.84

2 171.85 178.15 178.15 134.23 199.67 0.81

3 171.85 178.15 178.15 134.23 199.67 0.81

4 171.85 178.15 178.15 134.23 199.67 0.81

For bolt group:


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1- 1 158.08 158.08 158.08 123.48 184.13 0.84

1- 2 239.08 239.08 239.08 186.75 236.92 0.71

1- 3 450.08 450.08 450.08 351.56 297.45 0.48

1- 4 808.08 808.08 808.08 631.20 323.82 0.29

2.1.4.2. Endplate


1 0.0+40.5 6.26 45.00 35.04 43.80

2 40.5+105.5 - 45.00 35.04 43.80

3 105.5+179.0 6.26 45.00 35.04 43.80

4 179.0+ 0.0 6.26 45.00 35.04 43.80


1 220.18 219.51

2 220.18 196.42

3 220.18 219.51

4 220.18 219.51


1 - - - - 191.09 161.80

2 292.00 146.00 191.09 138.71 321.09 203.71

3 - - 321.09 226.80 - -

4 - - 468.09 300.30 - -



1 219.51 219.51 219.51 275.75 403.30

2 196.42 196.42 196.42 263.24 360.88

3 219.51 219.51 219.51 275.75 403.30

4 219.51 219.51 219.51 275.75 403.30

For bolt group:


1- 1 219.51 219.51 219.51 275.75 403.30

1- 2 300.51 300.51 300.51 476.45 552.12

1- 3 534.60 534.60 534.60 760.10 982.21

4- 4 219.51 219.51 219.51 275.75 403.30


row h[mm] Ft[kN]

1 698.20 123.48

2 617.20 63.27

3 406.20 9.80

4 48.20 0.00

Mj,Rd = 129.24 kNm



VRd data

VRd 346.21 kN

Fv,Rd 94.08 kN

e1,ep 69.00 mm

e1,cf 69.00 mm


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VRd data

p1 81.00 mm

alfa,ep 0.98

alfa,fc 0.98

Fb,ep,Rd 281.45 kN

VRd beam 140.73 kN

VRd beam 1147.19 kN




1 4.55 3.72 25.57 8.81 1.56

2 5.38 4.96 21.92 8.81 1.83

3 7.14 6.05 34.69 8.81 2.23

Sj data

Sj 60.37 MNm/rad


z 584.16 mm

mu 1.00

k1 1.17 mm

k2 6.74 mm

keq 5.35 mm


Stiffness data

E 210000.00 MPa

Ib 230999998.17 mm^4

Lb 7200.00 mm

frame type braced

S1 53.90 MNm/rad

S2 3.37 MNm/rad

System RIGID


Stiffness data

Fi y 13.00 MNm/rad


Sj,app 26.00 MNm/rad


Sj,upper boundary 62.79 MNm/rad





In the column flange we have the following :

t <= 0.36 sqrt(fub/fy) d


5. Unity checks

Unity checks

MSd/MjRd 0.25

VSd/VRd 0.44



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data

MRd 129.24 kNm

Gamma 1.40

h 745.45 mm

FRd 242.73 kN

NT,Rd 519.14 kN

N 242.73 kN

fu 360.00 MPa

BetaW 0.80

minimum af 2.65 mm

af 7.00 mm

Minimum th 6.31 mm

6.2. Calculation aw

data

Ft 186.75 kN

Fv 37.77 kN

lw 300.51 mm

fu 360.00 MPa

BetaW 0.80


aw 5.00 mm


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2.7 PST.07.01 - 07: Bolted connection with column minor axis Description This benchmark consists in a manual verification of a connection by using the minor axis theory combined with Annex J Revised EC3. Those results are compared with the design calculation of EPW 3.20 Project data See input file Reference [1] Eurocode 3



[3] COST C1 Control of the semi-rigid behaviour of civil engineering structural connections Edited by René Maquoi, Université de Liège, Belgium Application of the component method to steel joints

See the chapter "Manual calculation" for the manual calculation according to this reference. Result Manual calculation EPW % Diff. FPunching,Rd,l1,tension 247.1 kN 247.05 kN 0.02 % FPunching,Rd,l1,compression 192.1kN 192.12 kN 0.01 % FPunching,Rd,l2 185.5 kN 185.53 kN 0.02 % FComb,Rd,tension 65.4 kN 65.44 kN 0.06 % FComb,Rd,compression 110.0 kN 110.01 kN 0 % FGlobal,Rd,tension 57.6 kN 56.59 kN 1.75 % FGlobal,Rd,compression 156.2 kN 156.19 kN 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + Calculation note PST070107.epw Modules 2D Frame (PRS.01)


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Connect Frame - Rigid (PST.07.01) Author NEM/CVL Manual calculation The following connection is composed with a endplate, 1 bolt row above the beam flange, 2 bolt rows between the beam flange and 1 bolt row under the beam flange. The plate is made of steel with following properties: S235 and is characterised by properties described in the EPW results document. The present document assumes that all the tensions, the stresses and the most dangerous combination computed by EPW are right. The node use for the check is the minor axis column-beam connection number 4 in PST070107.epw. This connection is composed with a HEA180 column and a IPE240 beam. We assume that the most dangerous combination is the 4th. The verification concerns only the weak axis part. For other controls from Annex J Revised EC3, other benchmarks are available.

AB

IPE240

5

5

4

Section AB

HEA180

80

80


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End plate

120

400

Plate 15

30 61

50

70

160

70

8 x M-12 (DIN601)

Local failure: Punching Punching Loading case 1

Tension zone

mm95.192

199.20

2

dmed m =

+=

+=

mm70c0 = and mm955.87d9.0cc m0 =⋅+=

mm61pitch x boltb0 == and mm955.78d9.0bb m0 =⋅+=

( )kN05.247

3

ftcb2F

0M

ywc

1LRd,Punching =γ⋅

⋅⋅+⋅=

Compression zone:

mm8.9tc fbeam ==

mm120bb beam ==

( )kN11.192

3

ftcb2F

0M

ywcRd,Punching 1L

=γ⋅

⋅⋅+⋅=

Punching Loading case 2

n=4 bolt rows

kN5.1853

ftdnF

0M

ywcmRd,Punching =

γ⋅

⋅⋅⋅π⋅=


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Combined punching and bending

Tension zone

mm152thd fcc =−=

mm5.1294

r32dL =⋅−=

mm5.50bLa =−=

1k5.0L

cb=⇒>

+

0109.4mm Lt

c8.211

c

t82.01Lb

2

wc

2

2

2wc

m >=

⋅++⋅−⋅=

mm3.36bL

bb

L

t

L

c23.0

L

tLx

m

m3

1

wc3

2

wc0 −=

−

−⋅

⋅⋅+

⋅=

bb 0x m≤=

( )( )

kN44.651

xat3

xxc5.1

xa

c2xaLftkF

0Mwc

2

y2wcRd,Comb =

γ⋅

+⋅⋅

+⋅⋅+

+

⋅++⋅⋅π⋅⋅⋅=

Compression zone

mm152thd fcc =−=

mm5.1294

r32dL =⋅−=

mm5.9bLa =−=

1k5.0L

cb=⇒>

+

0.00 Lt

c8.211

c

t82.01Lb

2

wc

2

2

2wc

m =<

⋅++⋅−⋅=

mm23.16bL

bb

L

t

L

c23.0

L

tLx

m

m3

1

wc3

2

wc0 =

−

−⋅

⋅⋅+

⋅=

( )[ ] bb if mm6.23c4xaL2

t3ca5..1aax m0

wc2 >=⋅++⋅⋅π⋅⋅

+⋅⋅−+−=

( )( )

kN1101

xat3

xxc5.1

xa

c2xaLftkF

0Mwc

2

y2wcRd,Comb =

γ⋅

+⋅⋅

+⋅⋅+

+

⋅++⋅⋅π⋅⋅⋅=

Global failure Tension zone

4.55 bL

z=

−=ρ with z=230.1mm


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kN92.1ft25.0

m0M

y2w

pl =γ

⋅⋅=

kN59.571

2z

b2m

2

FF

0Mpl

tension,Rd,ComRd,Global =

γ⋅

ρ⋅+π+

⋅⋅+=

Compression zone

4.55 bL

z=


kN19.1561

2z

b2m

2

FF

0Mpl

ncompressio,Rd,ComRd,Global =

γ⋅

ρ⋅+π+

⋅⋅+=

Calculation note Node 4 : bolted beam-to-column connection side AB

According to COST C1 September 1998 & Revised Annex J EC3

1. Input data

Column HEA180

h 171.00 mm

b 180.00 mm

tf 9.50 mm

tw 6.00 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 240.00 mm

b 120.00 mm

tf 9.80 mm

tw 6.20 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.25

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

End plate

h 400.00 mm

b 120.00 mm

t 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolts M-12 (DIN601)


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Bolts M-12 (DIN601)

type normal

grade 4.6

fu 400.00 MPa

As 84.50 mm^2

do 14.00 mm

S 19.00 mm

e 20.90 mm

h head 8.00 mm

h nut 10.00 mm

Bolt position


1 350.00 61.00

2 280.00 61.00

3 120.00 61.00

4 50.00 61.00

Internal forces


N 0.29 kN

Vz 21.49 kN

My -0.00 kNm

Tension top


2.1. Design resistance of basic components 2.1.1. Column web in bending and punching: Local mechanism

2.1.1.1. Punching Loadcase 1

Tension Zone

dm 19.95 mm

b0 61.00 mm

b 78.95 mm

c0 70.00 mm

c 87.95 mm

FRd,punch,LC1,tens 247.05 kN

Compression zone

b0 0.00 mm

b 120.00 mm

c0 0.00 mm

c 9.80 mm

FRd,punch,LC1,comp 192.12 kN


Tension Zone

dm 19.95 mm

n 4

FRdpunch,LC2,tens 185.53 kN

Compression zone

n 4


2.1.1.3. Combined flexural and punching shear local

Tension Zone

L 129.50 mm

bm 109.42 mm

x0 -36.38 mm


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Tension Zone

x 0.00 mm

a 50.55 mm

k 1.00

FComb,Rd,tens 65.44 kN

Compression zone

L 129.50 mm

bm 0.00 mm

x0 16.23 mm

x 23.61 mm

a 9.50 mm

k 1.00

FComb,Rd,comp 110.01 kN

FLocal,Rd= 65.44kN

2.1.2. Column in bending and punching: Global mechanism

Tension Zone

mpl 1.92 kN

z 230.10 mm

ro 4.55

FGlobal,Rd,tens 57.59 kN

Compression zone

z 230.10 mm

ro 24.22

FGlobal,Rd,comp 156.19 kN

FGlobal,Rd= 57.59kN


Fc,fb,Rd data

Fc,fb,Rd 339.67 kN

section clas 1

Mc,Rd 78.19 kNm

hb-tfb 230.20 mm



Bt,Rd = 24.34 kN

2.1.4.2. Endplate


1 0.0+35.0 - 50.00 24.34 30.43

2 35.0+80.0 6.27 29.50 22.87 28.59

3 80.0+35.0 6.27 29.50 22.87 28.59

4 35.0+ 0.0 - 50.00 24.34 30.43


1 135.48 60.00

2 143.72 143.47

3 143.72 143.47

4 135.48 60.00


1 135.48 60.00 - - - -

2 - - - - 231.86 159.29

3 - - 231.86 159.29 - -


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4 135.48 60.00 - - - -

For individual bolt row :


1 60.00 60.00 60.00 48.67 -

2 143.47 143.47 143.47 48.67 190.04

3 143.47 143.47 143.47 48.67 190.04

4 60.00 60.00 60.00 48.67 -

For bolt group :


1- 1 60.00 60.00 60.00 48.67 -

2- 2 143.47 143.47 143.47 48.67 190.04

2- 3 318.57 318.57 318.57 97.34 421.97

4- 4 60.00 60.00 60.00 48.67 -


row h[mm] Ft[kN]

1 265.10 32.72

2 195.10 24.87

3 35.10 0.00

4 -34.90 0.00

Mj,Rd = 13.53 kNm



VRd data

VRd 83.07 kN

Fv,Rd 16.22 kN

e1,ep 50.00 mm

p1 70.00 mm

alfa,ep 1.00

alfa,fc 1.00

Fb,ep,Rd 129.60 kN

Fb,wc,Rd 51.84 kN

VRd beam 235.93 kN


row k5[mm] k7[mm]

1 11.93 4.04

2 34.39 4.04

Sj data

Sj 1.52 MNm/rad

Sj,ini 7.58 MNm/rad

z 232.31 mm

mu 5.00

k1 1.94 mm

k2 1.21 mm

keq 6.47 mm


Stiffness data

E 210000.00 MPa


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Stiffness data

Ib 38900001.53 mm^4

Lb 6000.00 mm

frame type braced

S1 10.89 MNm/rad

S2 0.68 MNm/rad

System SEMI RIGID


Stiffness data

Fi y 0.00 MNm/rad


Sj,app 0.00 MNm/rad


Sj,upper boundary 0.68 MNm/rad



5. Unity checks

Unity checks

MSd/MjRd 0.00

VSd/VRd 0.26



6.1. Calculation weldsize af / Minium thickness th for stiffener in column

data

MRd 13.53 kNm

Gamma 1.40

h 230.20 mm

FRd 82.26 kN

NT,Rd 251.24 kN

N 82.26 kN

fu 360.00 MPa

BetaW 0.80

minimum af 1.35 mm

af 5.00 mm

Minimum th 3.21 mm

6.2. Calculation aw

data

Ft 24.87 kN

Fv 5.37 kN

lw 143.47 mm

fu 360.00 MPa

BetaW 0.80


aw 4.00 mm


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2.8 PST.07.01 - 08: Welded connection with column minor axis Description This benchmark consists in a manual verification of a connection by using the minor axis theory combined with Annex J Revised EC3. Those results are compared with the design calculation of EPW 3.20 Project data See input file. Reference [1] Eurocode 3



[3] COST C1 Control of the semi-rigid behaviour of civil engineering structural connections Edited by René Maquoi, Université de Liège, Belgium Application of the component method to steel joints

See the chapter "Manual calculation" for the manual calculation according to this reference. Result Manual calculation EPW % Diff. FPunching,Rd, 192.1 kN 192.12 kN 0 % FComb,Rd 72.5 kN 72.55 kN 0 % FGlobal,Rd 112.4 kN 112.39 kN 0 % See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070108.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author NEM -CVL


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Manual calculation The following connection is composed only with a column and a beam welded on the web column around the flange beam. The present document assumes that all the tensions, the stresses and the most dangerous combination computed by EPW are right. The node use for the check is the minor axis column-beam connection number 4 in PST070108.epw. This connection is composed with a HEA180 column and a IPE240 beam. We assume that the most dangerous combination is the 4th. The verification concerns only the weak axis part. For other controls from Annex J Revised EC3, other benchmarks are available. Local failure: Punching Punching Loading case 1

Tension & compression zone

mm8.9tc fbeam ==

mm120bb beam ==

( )kN11.192

3

ftcb2F

0M

ywc

1LRd,Punching =γ⋅

⋅⋅+⋅=


Tension & compression zone

mm152thd fcc =−=

mm5.1294

r32dL =⋅−=

mm5.9bLa =−=

1k5.00023.1L

cb=⇒>=

+

002.56- Lt

c8.211

c

t82.01Lb

2

wc

2

2

2wc

m =<=

⋅++⋅−⋅=

mm2.16bL

bb

L

t

L

c23.0

L

tLx

m

m3

1

wc3

2

wc0 =

−

−⋅

⋅⋅+

⋅=


t3ca5..1aax m0

wc2 >=⋅++⋅⋅π⋅⋅

+⋅⋅−+−=

( )( )

kN55.721

xat3

xxc5.1

xa

c2xaLftkF

0Mwc

2

y2wcRd,Comb =

γ⋅

+⋅⋅

+⋅⋅+

+

⋅++⋅⋅π⋅⋅⋅=

Compression zone

mm152thd fcc =−=

mm5.1294

r32dL =⋅−=

mm5.9bLa =−=


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1k5.0L

cb=⇒>

+

0.00 Lt

c8.211

c

t82.01Lb

2

wc

2

2

2wc

m =<

⋅++⋅−⋅=

mm23.16bL

bb

L

t

L

c23.0

L

tLx

m

m3

1

wc3

2

wc0 =

−

−⋅

⋅⋅+

⋅=


t3ca5..1aax m0

wc2 >=⋅++⋅⋅π⋅⋅

+⋅⋅−+−=

( )( )

kNxat

xxc

xa

cxaLftkF

Mwc

ywcRdComb 5.721

3

5.12

0

22

, =⋅

+⋅⋅

+⋅⋅+

+

⋅++⋅⋅⋅⋅⋅=

γπ

Global failure Tension zone

mm5.71 bL

z=


kN92.1ft25.0

m0M

y2w

pl =γ

⋅⋅=

kN38.1121

2z

b2m

2

FF

0Mpl

tension,Rd,ComRd,Global =

γ⋅

ρ⋅+π+

⋅⋅+=

Compression zone

mm5.71 bL

z=


kN92.1ft25.0

m0M

y2w

pl =γ

⋅⋅=

kNz

bm

FF

M

pl

ncompressioRdCom

RdGlobal 38.1121

22

2 0

,,, =⋅

⋅++⋅

⋅+=γ

ρπ

Calculation note Node 4 : bolted beam-to-column connection side AB

According to COST C1 September 1998 & Revised Annex J EC3

1. Input data

Column HEA180

h 171.00 mm

b 180.00 mm

tf 9.50 mm

tw 6.00 mm

r 15.00 mm


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Column HEA180

fy 235.00 MPa

fu 360.00 MPa


h 240.00 mm

b 120.00 mm

tf 9.80 mm

tw 6.20 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.25

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Internal forces


N 0.18 kN

Vz 0.92 kN

My 0.00 kNm

Tension bottom


2.1. Design resistance of basic components 2.1.1. Column web in bending and punching: Local mechanism


Tension Zone

dm 0.00 mm

b0 0.00 mm

b 120.00 mm

c0 0.00 mm

c 9.80 mm

FRd,punch,LC1,tens 192.12 kN

Compression zone

b0 0.00 mm

b 120.00 mm

c0 0.00 mm

c 9.80 mm


2.1.1.3. Combined flexural and punching shear local

Tension Zone

L 129.50 mm

bm 0.00 mm

x0 16.23 mm


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Tension Zone

x 23.61 mm

a 9.50 mm

k 1.00

FComb,Rd,tens 72.55 kN

Compression zone

L 129.50 mm

bm 0.00 mm

x0 16.23 mm

x 23.61 mm

a 9.50 mm

k 1.00

FComb,Rd,comp 72.55 kN

FLocal,Rd= 72.55kN

2.1.2. Column in bending and punching: Global mechanism

Tension Zone

mpl 1.92 kN

z 166.25 mm

ro 17.50

FGlobal,Rd,tens 112.39 kN

Compression zone

z 166.25 mm

ro 17.50

FGlobal,Rd,comp 112.39 kN

FGlobal,Rd= 112.39kN


Fc,fb,Rd data

Fc,fb,Rd 339.67 kN

section clas 1

Mc,Rd 78.19 kNm

hb-tfb 230.20 mm


Mj,Rd data

F 72.55 kN

h 230.20 mm

Mj,Rd 16.70 kNm

Mj,Rd 16.70 kNm

(inclusive normal force)


VRd =235.93 kN



Sj data

Sj 2163.15 kNm/rad


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Sj data


z 230.20 mm

mu 5.00

k1 1.94 mm

k2 1.94 mm


Stiffness data

E 210000.00 MPa

Ib 38900001.53 mm^4

Lb 6000.00 mm

frame type braced

S1 10892.00 kNm/rad

S2 680.75 kNm/rad

System SEMI RIGID


Stiffness data

Fi y 0.00 kNm/rad


Sj,app 0.00 kNm/rad


Sj,upper boundary 680.75 kNm/rad



5. Unity checks

Unity checks

MSd/MjRd 0.00

VSd/VRd 0.00


6. Design calculations 6.1. Calculation weldsize af / Minium thickness th for stiffener in column

data

MRd 16.70 kNm

Gamma 1.40

h 230.20 mm

FRd 101.57 kN

NT,Rd 251.24 kN

N 101.57 kN

fu 360.00 MPa

BetaW 0.80

minimum af 1.66 mm

af 5.00 mm

Minimum th 3.96 mm

6.2. Calculation aw


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data

M 16.70 kNm

N 0.18 kN

V 0.92 kN

fu 360.00 MPa

BetaW 0.80

a1 5.00 mm

a3 5.00 mm

l1 120.00 mm

l2 180.60 mm

l3 41.90 mm

A 2399.20 mm^2

I 28438455.99 mm^4


aw 4.00 mm


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2.9 PST.07.01 - 09: Bolted connection Description This benchmark consists in a verification of bolted beam-to-column connections compared with the table values given in reference [1], Chapter 5 : "Bemessungshilfen für nachgiebige Stahlknoten mit Stirnplattenanschlüssen", Table 5-25 and 5-26. Project data Column data : HEB280 (S235) Beam data : IPE240, IPE270, IPE300, IPE330, IPE360, IPE400, all made of S235 Bolt grade : 10.9 Reference [1] Stahlbau Kalender 1999

1. Jahrgang DSTV -1999

Result Connection EPW SBK 99 %

MRd [kNm] 58 57 1.7 VRd [kN] 236 236

HEB280/IPE240/M24/20 node 3

Sj,ini [kNm/rad] 10566 12060 MRd [kNm] 74 71 4.1 VRd [kN] 237 273









HEB280/IPE300/M27/25 (1) node 9


HEB280/IPE300/M27/25 (2) node 10


HEB280/IPE330/M24/25 node 11


HEB280/IPE330/M24/35 node 12

Sj,ini [kNm/rad] 24581 26229 HEB280/IPE330/M27/25 (1) MRd [kNm] 112 110 1.8


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VRd [kN] 308 380 node 13 Sj,ini [kNm/rad] 21661 24231 MRd [kNm] 112 111 0.9 VRd [kN] 308 380

HEB280/IPE330/M27/25 (2) node 14


HEB280/IPE360/M24/25 node 15


HEB280/IPE360/M27/25 (1) node 16


HEB280/IPE360/M27/25 (2) node 17


HEB280/IPE360/M30/20 node 18


HEB280/IPE360/M30/25 (1) node 19


HEB280/IPE360/M30/25 (2) node 20


HEB280/IPE400/M24/25 node 21


HEB280/IPE400/M27/25 (1) node 22


HEB280/IPE400/M27/25 (2) node 23


HEB280/IPE400/M30/25 (1) node 24


HEB280/IPE400/M30/25 (1) node 25

Sj,ini [kNm/rad] 44240 46882 Version ESA-Prima Win 3.20.03 Input file + calculation note PST070109.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.01) Author CVL


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2.10 PST.07.02 – 01 : Frame pinned connection (plate welded on the web) Description A pinned connection with a plate welded on the beam web and the column flange is calculated manually in node 2 of the Tutorial Frame project. The results are compared with the results of ESA-Prima Win. Project data The following connection will be calculated : h=0.163 m b=0.164 m t=0.012 m Play=0.01m The connection is composed of two plates welded symmetrically on each side of the beam’s web and to the column’s flange. The plates are made of Fe 360. The node use for the check is the column-beam connection number 2 in the Tutorial Frame project. This connection is composed with a HEA160 column and an IPE 240 Beam. We assume that the most dangerous load combination is the 4th. Considering that the moment approaches 0 precision, we can say that we have a pinned connection. Forces in the connection :

N=262.4939 N Tz=7990 N M≅0 Reference Eurocode 3 : Design of steel structures

Part 1-1 : General rules and rules for buildings ENV 1993-1-1:1992 Revised Annex J ENV 19+93-1-1/pr A2

See the chapter "Manual calculation" for the manual calculation according to this reference. Result See the chapter "Calculation note" for the detailed output of ESA-Prima Win.

0.038m

Weld Part

0.164m

0.01m

0.163m

Play

Weldsize


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Version ESA-Prima Win 3.20.03 Input file + calculation note PST070201.epw Modules 3D Frame (PRS.11) Connect Frame – Pinned (PST.07.02) Author NEM/CVL Manual calculation 1. Calculation of VRd and NRd 1.1. Calculation Design Shear Resistance VRd for Connection Element

Transversal section of the plate : 2plplpl m003912.0th2A =⋅⋅= (2 plates)

Normal stress : 2pl

N mN667.67099

003912.0

4939.262

A

N===σ

Flexion module : 32

plpl m000106276.0

6

ht2W

pl

=⋅

⋅=

Design Shear Resistance : a= 0.082 m is the bolt center

N66.240087

A

3

W

a2

f

N

a4

W

a2

W

a2

V

2pl

2

2

2M

2y2

N2

22

pl

N

pl

N

Rd

pl

0=

+⋅

γ−σ⋅

⋅−

⋅σ⋅+

⋅σ⋅−

=

1.2 Calculation Design Shear Resistance VRd for Beam

Shear Area : ( ) 2fwfv m00191276.0tr2ttb2AA =⋅⋅++⋅⋅−=

Shear Resistance : N57.2359253

fAVRd

0M

yv =γ⋅

⋅=

1.3 Calculation Design Tension Resistance NRd for Connection Element

Area of the element : 2plplpl m003912.0th2A =⋅⋅=

Tension Resistance : N45.835745fA

N0M

yplRd =

γ

⋅=


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1.4 Calculation Design Tension Resistance NRd for Beam

Area of the Beam : 2m003910.0A =

Tension Resistance : N18.835318fA

N0M

yRd =

γ

⋅=

1.5 Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check :

Shear Unity Check : 11038.357.235925

7990

V

V 2

Rd

Sd ≤⋅== − ⇒ Connection OK for Shear

Tension Unity Check : 11014.345.835745

4939.262

N

N 4

Rd

Sd ≤⋅== − ⇒ Connection OK for Tension

2. Weldsize Calculation for Plate, Beam and Column To determine the weldsize a for the plate on the beam and on the column, we must use a iterative process with a as parameter until the Von Mises rules is respected (Annexe M/EC3) :

( )ww

211M

u1

Mw

u222 f and

f3

γ≤σ

γ⋅β≤τ+τ⋅+σ

We’ll only check the weldsize for the final value of a. For the weld between plate and beam we find a=4mm and for weld between plate and column, the weldsize is a=10mm. 2.1 Weldsize Plate/Beam We define the play as the effective distance between the end of the beam and the flange of the column. In this case, the play is 10mm. By using EC3 and the Chapter 11 of the manual, we compute the following parameters : Weldsize : a=0.004 Weld Length : m139.012.02163.0t2hl plpl1 =⋅−=⋅−=

m13.0t2Playbl plpl2 =⋅−−=

m154.001.0164.0Playll pl =−=−=

By EC3 : fuw=360000000N/m2 and βw=0.8 The order parameters are :

( )10.104

la414.1la577.0

lla577.0la707.0g

21

11 =⋅⋅+⋅⋅

⋅⋅⋅+⋅⋅=

30377.0la414.1la577.0

la577.0

21

1 =⋅⋅+⋅⋅

⋅⋅=δ

15603.0hla577.0la117.0

la117.0

pl221

21 =

⋅⋅⋅+⋅⋅

⋅⋅=µ


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3987.0la14.1la707.0

la707.0

21

1 =⋅⋅+⋅⋅

⋅⋅=Γ

g10L +=

Shear force on one plate : N789.1179622

VD Rd == (for one plate)

Normal force on one plate : N24.1312

NN ==

Moment on the plate : Nm781.13459LDM =⋅=

Weld Check 1: 21

211 mN74.115363040

la2

N

la2

M6

1

==⋅⋅

⋅Γ+

⋅⋅

⋅µ⋅=σ=τ

21

2 mN72.64449431

la

D=

⋅⋅δ

=τ

Unity Check : ( )

14.0f

and 1316.0f

3

ww

211

M

u

1

Mw

u

222

≤=

γ

σ≤=

γ⋅β

τ+τ⋅+σ

Weld Check 2 : ( )

22

11 mN8731.55840293

la22

D1=

⋅⋅⋅

⋅δ−=τ=σ

( ) ( )2

222 m

N161.134095932la2

N1

lah

M1=

⋅⋅⋅Γ−

+⋅⋅⋅µ−

=τ

Unity Check : ( )

1193.0f

and 1715.0f

3

ww

211

M

u

1

Mw

u

222

≤=

γ

σ≤=

γ⋅β

τ+τ⋅+σ

2.2 Weldsize Plate/Column Weldsize : a=0.01 m Normal Force : N=262.4939N Moment : Nm89674.19345082.057.235925LDM =⋅=⋅= Stress Calculation :

22pl

11 mN96.154518316

6

ha22

LD

la22

N

W

M

la22

N=

⋅⋅⋅

⋅+

⋅⋅⋅=+

⋅⋅⋅=τ−=σ

22 mN7485.72369806

la2

D=

⋅⋅=τ

Unity Check : ( )

192.0f

3

w

211

Mw

u

222

≤=

γ⋅β

τ+τ⋅+σ


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153.0f

wM

u

1 ≤=

γ

σ

Calculation note Node 2 : frame pinned beam-to-column connection side CD 1. Input data

Column HEA160

h 152.00 mm

b 160.00 mm

tf 9.00 mm

tw 6.00 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 240.00 mm

b 120.00 mm

tf 9.80 mm

tw 6.20 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Welded plate

number 2

h 163.00 mm

b 164.00 mm

t 12.00 mm

position (to top of beam) 38.00 mm

play beam/column 10.00 mm

fy 235.00 MPa

fu 360.00 MPa


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Internal forces


N 0.26 kN

Vz 7.99 kN

My -0.00 kNm

2. Design shear resistance

2.1.Design shear resistance VRd for connection element

data

sigmaN 0.07 MPa


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data

A 3912.00 mm^2

W 106276.00 mm^3

a 82.00 mm

VRd 240.09 kN

2.2.Design shear resistance VRd for beam

data

Av 1912.76 mm^2

VRd 235.93 kN

2.3.Critical design shear resistance VRd = 235.93 kN

3, Design tension/compression resistance NRd

3.1.Design compression/tension resistance NRd for connection element

data

A 3912.00 mm^2

NRd 835.75 kN

3.2.Design compression/tension resistance NRd for beam

data

A 3910.00 mm^2

NRd 835.32 kN

3.3.Critical design tension/compression NRd = 835.32 kN

4. Unity checks

Unity checks

VSd/VRd 0.03

NSd/NRd 0.00


5. Weldsize calculation 5.1. Weldsize plate/beam

data

fu 360.00 MPa

beta 0.80

a 3.00 mm

l1 139.00 mm

l2 130.00 mm

L 114.10 mm

g 104.10 mm

delta 0.30

mu 0.16

tau 0.40

D 117.96 kN

N 0.13 kN

M 13.46 kNm

for weld check 1:

sigma,1 154.28 MPa

tau,1 154.28 MPa

tau,2 85.93 MPa

for weld check 2:

sigma,1 74.68 MPa

tau,1 74.68 MPa

tau,2 178.79 MPa

5.2. Weldsize pate/column


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data

fu 360.00 MPa

beta 0.80

a 10.00 mm

L 82.00 mm

D 235.93 kN

N 0.26 kN

M 19.35 kNm

sigma,1 154.98 MPa

tau,1 154.98 MPa

tau,2 72.37 MPa


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2.11 PST.07.02 – 02 : Frame pinned connection (plate bolted to the web) Description A pinned connection with a plate bolted on the beam web and welded on the column flange is calculated manually in node 2 of the Tutorial Frame project. The results are compared with the results of ESA-Prima Win. In the first part normal bolts are used. In the second part, we replace these bolts by PRESTRESSED BOLTS and develop the calculation note only for points that change by using this type of bolts. Project data The following connection is calculated :

The connection is composed of two plates bolted symmetrically on each side of the beam’s web and welded to column. The plates are made of Fe 360. The node used for the check is the column-beam connection number 2 in the Tutorial Frame project. This connection is composed with a HEA160 column and an IPE 240 Beam. We assume that the most dangerous load combination is the 4th. Considering that the moment approaches 0 precision, we can say that we have a pinned connection.

The forces in the connection :



See the chapter "Manual calculation" for the manual calculation according to this reference.

Weld Part

M-16(DIN601) Normal Bolt

0.189m

0.034m

0.01m

0.024m

0.188m

Play


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Result See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070202.epw Modules 3D Frame (PRS.11) Connect Frame – Pinned (PST.07.02) Author NEM/CVL Manual calculation 1. Dimensions of the Plate and Position according to EC3 The plate is bolted to the web’s beam on each side with M-16(DIN601) normal bolts. The position of the bolts and of the plate on the web’s beam and its dimensions are represented in the figure. First, we must verify, according to EC3, the positioning of holes for bolts in the plate. The EC3 prescribes a minimum and maximum end distance, a minimum and maximum edge distance and a minimum and maximum spacing.

• the end distance e1 from the center of a fastener hole to the adjacent end of any part, measured in the direction of the load transfer must be not be less than 1,5d0, where d0 is the diameter of the hole. We impose e1=24≤1.5d0.

• the edge distance e2 from the center of a fastener hole to the adjacent edge of any part, measured at right angles to the direction of the load transfer must be not less than 1,5d0. We impose e2=24≤1.5d0. 2. Calculation of VRd and NRd 2.1. Calculation Design Shear Resistance VRd for Connection Element

Transversal section of the plate : 2m004512.0012.0188.02th2A =⋅⋅=⋅⋅= (2 plates)

Normal Stress : 2N mN8395.58176

004512.0

4939.262

A

N===σ

Flexion Module : 32

m000141376.06

ht2W =

⋅⋅=

Bolt Center : a=0.0995m Design Shear Resistance :


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N015.266422

A

3

W

a2

f

N

a4

W

a2

W

a2

V

22

2

2M

2y2

N2

22NN

Rd0

=

+⋅

γ−σ⋅

⋅−

⋅σ⋅+

⋅σ⋅−

=


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2.2. Calculation Design Shear Resistance VRd for Beam


Net Area : m56.001689.0dt2AA 0wvnet =⋅⋅−=

For the calculation of VRd in the beam, we use Av because 2v

u

ynet m00124860.0A

f

fA =⋅≥

Shear Resistance: N57.2359253

fAVRd

0M

yv =γ⋅

⋅=

2.3. Calculation Design Tension Resistance NRd for Connection Element

Area : 2m004512.0ht2A =⋅⋅=

Net Area : 20net m003648.0d2t2AA =⋅⋅⋅−=

Tension Resistance :

γ

⋅⋅

γ

⋅=

1

net

0 M

u

M

yRd

fA9.0,

fAminN ( ) N27.96392781.1074501,27.963927min ==

2.4. Calculation Design Tension Resistance NRd for Beam

Area : 2m003910.0A =

Net Area : 20net m0036868.0dt2AA =⋅⋅−=


γ

⋅⋅

γ

⋅=

1

net

0 M

u

M

yRd

fA9.0,

fAminN ( ) N18.83531818.1085930,18.835318min ==

2.5. Calculation Design Shear Resistance VRd for Bolt in Beam The calculation of the shear resistance for bolt in beam is based on the following equation to be solve :

0Qn

N

nI

dNa2V

I

da

I

ca

n

1V 2

2

2

pRd2

p

22

2p

22

22Rd

=−+

⋅⋅⋅⋅

⋅+

⋅+

⋅+⋅

m


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Where : 0.0995ma = 0.094mb = 0.0655mc = 0.07md =

24

1i

22ip m036761.066.95rI ∑ ∑ ===

=

( )( )beam,Rd,bplate,Rd,bRd,v F;Fmin,F2minQ ⋅= =31740.8256N for two plates, where

• N30144Af6.0

FMb

subV dR

=γ

⋅⋅=

• N8256.31740tdf5.2

FMb

upBeam,Rd,b =

γ

⋅⋅⋅α⋅=

444.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

• N712.122867tdf5.2

FMb

plupplate,Rd,b =

γ

⋅⋅⋅α⋅=

444.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

By solving the second-degree equation, we find N89.67907VRd = 2.6. Calculation Design Block Shear Resistance The design value of the effective resistance to block shear is determined by the following expression :

eff,veffv,M

eff,vyRd,eff LtA with

3

AfV

0

⋅=γ⋅

⋅=

We determined the effective shear area Av,eff as follows :

m049.0a1 = m155.0a 2 = m051.0a 3 =

m14.0aahL 21v =−−=

( )

( ) m24.02849.0;24.0min

f

fdnaaL;aaLminL

y

u031v31v3

==

⋅⋅−++++=

( ) m049.0d5;aminL 011 =⋅=

( )

bolt rows 2for 2.5k with

m1685.0f

fdkaL

y

u022

=

=⋅⋅−=

( ) m24.0L;LLLminL 321veff,v =++=

2

eff,v m001488.0A =

a1

Lv

a3

a2

d

c

b

a

ri


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N40.1835343

AfV

0M

eff,vyRd,eff =

γ⋅

⋅=

2.7. Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check :

Shear Unity Check: 11176.089.67907

7990

V

V

Rd

Sd ≤== ⇒ Connection OK for Shear

Tension Unity Check: 11014.345.835745

4939.262

N

N 4

Rd


3. Weldsize Calculation between Plate and Column As before, to determine the weldsize a for the plate on the column, we must use a iterative process with a as parameter until the Von Mises rules is respected:

( )w

211Mw

u222 f3

γ⋅β≤τ+τ⋅+σ and 1

f

wM

u

1 ≤

γ

σ

We’ll only check the weldsize for the final value of a. For weld between plate and column, the weldsize is a=0.004m. The data are : Weldsize : a=0.004 m Normal force : D=67907.89N Moment : Nm835.67560995.089.67907LDM =⋅=⋅=

Flexion module : 352

m106645.66

ha22W pl −⋅=⋅⋅⋅=

l : length of the weld l=0.188m Stress calculation :

22pl

11 mN087.10151858

6

ha22

LD

la22

N

W

M

la22

N=

⋅⋅⋅

⋅+

⋅⋅⋅=+

⋅⋅⋅=τ−=σ

22 mN25.4515604

la2

D=

⋅⋅=τ

Unity Check : ( )

10352.0f

and 10604.0f

3

ww

211

M

u

1

Mw

u

222

≤=

γ

σ≤=

γ⋅β

τ+τ⋅+σ

4.Plate Bolted to Beam, Weld to Column with Prestressed Bolt The following calculation is also based on a connection composed with a plate bolt to beam and weld to column. The difference between this connection and the precedent is that we use prestressed bolt. The settings, meaning the type and the dimension of the plate, the position of the bolt and of the plate in the web’s beam, are exactly the same. Prestressed


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d

c

b

a

ri

bolts use in this connection are M-16(DIN6914) grade 10.9. The results and the calculation of the shear resistance for connection element, the block shear resistance, the tension/compression resistance for the connection element and for the beam, and the unity check for tension are identical. This connection involves only the calculation of the design shear resistance for bolts in beam and the weld size calculation. 4.1. Calculation Design Shear Resistance VRd for Bolts in Beam The calculation of the shear resistance for bolt in beam is based on the following equation to be solve:

0Qn

N

nI

dNa2V

I

da

In

ca2

I

ca

n

1V 2

2

2

pRd2

p

22

p2p

22

22Rd

=−+

⋅

⋅⋅⋅⋅+

⋅+

⋅

⋅⋅+

⋅+⋅

Where: 0.0995ma = 0.094mb = 0.0655mc = 0.07md =

24

1i

22ip m036761.066.95rI ∑ ∑ ===

=

Rd,bFQ = =26376N for two plates, where

• ( ) NN26376F8.0Fnk

F tSdCd,pMs

sRd,b =⋅−⋅

γ

µ⋅⋅=

traction)(no 0F

hole) theof clearance nominal(standart 1k

tion)classifica surface (C 0.3

N109900Af7.0Fwith

Sdt,

s

subCdp,

=

=

=µ

=⋅⋅=

Assuming that there is no traction in the bolt (N=0), the resolution of the second-degree equation give

N126.56430VRd = . This value is the most critical value of the design shear resistance and involves a new calculation of the unity check and of the weldsize between the plate and the column. 4.2. Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check:

Shear Unity Check: 1141.0126.56430

7990

V

V

Rd


Tension Unity Check: 11014.345.835745

4939.262

N

N 4

Rd


3.3. Weldsize between Plate and Column

As before, to determine the weldsize a for the plate on the beam and on the column, we must use a iterative process with a as parameter until the Von Mises rules is respected:

( )1

f and 1

f

3

ww

211

M

u

1

Mw

u

222

≤

γ

σ≤

γ⋅β

τ+τ⋅+σ

We’ll only check the weldsize for the final value of a. For weld between plate and column, the weldsize is a=0.004m. The data are :


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Weldsize : a=0.004 m Normal force : D=56430.126N Moment : Nm79.56140995.0126.56430LDM =⋅=⋅=

Flexion module : 352

m106645.66

ha22W pl −⋅=⋅⋅⋅=

l: length of the weld l=0.188m Stress calculation :

22pl

11 mN46.84624528

6

ha22

LD

la22

N

W

M

la22

N=

⋅⋅⋅

⋅+

⋅⋅⋅=+

⋅⋅⋅=τ−=σ

22 mN59.37520030

la2

D=

⋅⋅=τ

Unity Check : ( )

1293.0f

and 1503.0f

3

ww

211

M

u

1

Mw

u

222

≤=

γ

σ≤=

γ⋅β

τ+τ⋅+σ

Calculation note Normal bolts Node 2 : frame pinned beam-to-column connection side CD

1. Input data

Column HEA160

h 152.00 mm

b 160.00 mm

tf 9.00 mm

tw 6.00 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 240.00 mm

b 120.00 mm

tf 9.80 mm

tw 6.20 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolted plate

number 2

h 188.00 mm

b 189.00 mm

t 12.00 mm


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Bolted plate



fy 235.00 MPa

fu 360.00 MPa

Bolts M-16 (DIN601)

type normal

grade 4.6

fu 400.00 MPa

As 157.00 mm^2

do 18.00 mm

S 24.00 mm

e 26.20 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position

number of rows 2

number of columns 2

x1 34.00 mm

x2 24.00 mm

y1 24.00 mm

y2 24.00 mm


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Internal forces


N 0.26 kN

Vz 7.99 kN

My -0.00 kNm

2. Design shear resistance 2.1.Design shear resistance VRd for connection element

data

sigmaN 0.06 MPa

A 4512.00 mm^2

W 141376.00 mm^3

a 99.50 mm

VRd 266.42 kN


data

Av 1912.76 mm^2

Av,net 1689.56 mm^2

VRd 235.93 kN

2.3.Design shear resistance VRd for bolts in beam

Bolt resistance


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Bolt resistance

e1 24.00 mm

p1 140.00 mm

alfa,el 0.44

alfa,bw 0.44

Fb,el,Rd 122.88 kN

Fb,bw,Rd 31.74 kN

Fv,Rd 30.14 kN

data

a 99.50 mm

b 94.00 mm

d 70.00 mm

c 65.50 mm

Ip 36761.00 mm^2

VRd 67.91 kN

2.4.Design block shear resistance VRd

data

k 1.50

a1 49.00 mm

a2 155.00 mm

a3 51.00 mm

L1 49.00 mm

L2 196.09 mm

L3 240.00 mm

Lv 140.00 mm

Lv,eff 240.00 mm

Av,eff 1488.00 mm^2

VRd 183.53 kN


3, Design tension/compression resistance NRd 3.1.Design compression/tension resistance NRd for connection element

data

A 4512.00 mm^2

A,net 3648.00 mm^2

NRd 963.93 kN


data

A 3910.00 mm^2

A,net 3686.80 mm^2

NRd 835.32 kN


4. Unity checks

Unity checks

VSd/VRd 0.12

NSd/NRd 0.00


5. Weldsize calculation 5.1. Weldsize plate/column

data


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data

fu 360.00 MPa

beta 0.80

a 4.00 mm

L 99.50 mm

D 67.91 kN

N 0.26 kN

M 6.76 kNm

sigma,1 101.82 MPa

tau,1 101.82 MPa

tau,2 45.16 MPa

Prestressed bolts Node 2 : frame pinned beam-to-column connection side CD

1. Input data

Column HEA160

h 152.00 mm

b 160.00 mm

tf 9.00 mm

tw 6.00 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 240.00 mm

b 120.00 mm

tf 9.80 mm

tw 6.20 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bolted plate

number 2

h 188.00 mm

b 189.00 mm

t 12.00 mm



fy 235.00 MPa

fu 360.00 MPa

Bolts M16-10.9 (DIN6914)

type prestressed

grade 10.9

fu 1000.00 MPa

As 157.00 mm^2

do 18.00 mm

S 27.00 mm

e 29.60 mm

h head 10.00 mm

h nut 13.00 mm

Bolt position

number of rows 2


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Bolt position

number of columns 2

x1 34.00 mm

x2 24.00 mm

y1 24.00 mm

y2 24.00 mm


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Internal forces


N 0.26 kN

Vz 7.99 kN

My -0.00 kNm

2. Design shear resistance

2.1.Design shear resistance VRd for connection element

data

sigmaN 0.06 MPa

A 4512.00 mm^2

W 141376.00 mm^3

a 99.50 mm

VRd 266.42 kN


data

Av 1912.76 mm^2

Av,net 1689.56 mm^2

VRd 235.93 kN


Data for high strength bolts

ks 1.00

n 1.00

slip factor 0.30

Fp,Cd 109.90 kN

Ft,Sd 0.00 kN

Fs,Rd 26.38 kN

data

a 99.50 mm

b 94.00 mm

d 70.00 mm

c 65.50 mm

Ip 36761.00 mm^2

VRd 56.43 kN


data

k 1.50


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data

a1 49.00 mm

a2 155.00 mm

a3 51.00 mm

L1 49.00 mm

L2 196.09 mm

L3 240.00 mm

Lv 140.00 mm

Lv,eff 240.00 mm

Av,eff 1488.00 mm^2

VRd 183.53 kN


3, Design tension/compression resistance NRd 3.1.Design compression/tension resistance NRd for connection element

data

A 4512.00 mm^2

A,net 3648.00 mm^2

NRd 963.93 kN


data

A 3910.00 mm^2

A,net 3686.80 mm^2

NRd 835.32 kN


4. Unity checks

Unity checks

VSd/VRd 0.14

NSd/NRd 0.00


5. Weldsize calculation 5.1. Weldsize plate/column

data

fu 360.00 MPa

beta 0.80

a 4.00 mm

L 99.50 mm

D 56.43 kN

N 0.26 kN

M 5.61 kNm

sigma,1 84.62 MPa

tau,1 84.62 MPa

tau,2 37.52 MPa


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2.12 PST.07.02 – 03 : Frame pinned connection (Angles) Description A pinned connection with two angles is calculated manually in node 2 of the Tutorial Frame project. The results are compared with the results of ESA-Prima Win. Project data The following connection is calculated : The connection is composed of two angle profiles bolted symmetrically on each side of the beam’s web and to the column’s flange. The angles are made of Fe 360. The angle used to build this connection is an H60/60/6 profile bolted to the beam on each side and to the column by using normal bolts M-12(DIN601). The settings necessary to verify this connection according to EC3 are represented in the figure. The node use for the check is the column-beam connection number 2 in the Tutorial frame project. This connection is composed with a HEA160 column and an IPE 240 Beam. We assume that the most dangerous load combination is the 4th. Considering that the moment approaches 0 precision, we can say that we have a pinned connection. The forces in the connection :



See the chapter "Manual calculation" for the manual calculation according to this reference.

0.03m

0.018

Colum

View A-A

Beam

0.01

Play

M-12(DIN601)

H60/60/6

0.03m

0.059m

0.018m

0.188m

0.025m

Column A

A


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Result See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070203.epw Modules 3D Frame (PRS.11) Connect Frame – Pinned (PST.07.02) Author NEM Manual calculation 1. Bolted Angle in Beam and Column As we can see, the dimension of the column and the beam allowed only one column of two bolts on the beam and the column, conforming to the rules in the EC3 concerning the position of holes in the connected members. 2. Calculation of VRd and NRd 2.1 Calculation Design Shear Resistance VRd for Connection Element

Transversal section of the corner : 2corcorcor m002256.0th2A =⋅⋅= (2 corners)

Normal Stress : 2cor

N mN67.116353

002256.0

4939.262

A

N===σ

Flexion Module : MOMENT NO m000706.06

ht2 0W 3

2cor

pl

cor

⇔

=

⋅⋅=

Design Shear Resistance :

N7939.278261V0f

A

3V Rd2

M

2y2

N22

Rd

0

=⇔=γ

−σ+⋅

2.2 Calculation Design Shear Resistance VRd for Beam


Net Area : m00173916.0dt2AA 0wvnet =⋅⋅−=

For the calculation of VRd in the beam, we use Av because 2v

u

ynet m00124860.0A

f

fA =⋅≥


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Shear Resistance : N57.2359253

fAVRd

0M

yv =γ⋅

⋅=

2.3. Calculation Design Shear Resistance VRd for Bolt in Beam The calculation of the shear resistance for bolt in beam is based on the following equation to be solve:

0Qn

N

nI

dNa2V

I

da

In

ca2

I

ca

n

1V 2

2

2

pRd2

p

22

p2p

22

22Rd

=−+

⋅

⋅⋅⋅⋅+

⋅+

⋅

⋅⋅+

⋅+⋅

m

Where : 0.03ma = 0.094mb = 0mc = 0.076md =

22ip m011552.0rI ∑ == m018.0e1 = m152.0p1 =

( )( )beam,Rd,bcor,Rd,bRd,v F;Fmin,F2minQ ⋅= =22957.71N for two corners, where

• N16224Af6.0

FMb

subV dR

=γ

⋅⋅=

• N71.22957tdf5.2

FMb

upBeam,Rd,b =

γ

⋅⋅⋅α⋅=

428.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

• N28.44434tdf5.2

FMb

corupcor,Rd,b =

γ

⋅⋅⋅α⋅=

428.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

By solving the second-degree equation, we find N41.42718VRd = 2.4. Calculation Design Block Shear Resistance The design value of the effective resistance to block shear is determined by the following expression :

eff,veffv,M

eff,vyRd,eff LtA with

3

AfV

0

⋅=γ⋅

⋅=

We determined the effective shear area Av,eff as follows :

m043.0a1 = m045.0a 2 = m02.0a 3 =

m152.0aahL 21v =−−=

( )

( ) m24.0324.0;24.0min

f

fdnaaL;aaLminL

y

u031v31v3

==

⋅⋅−++++=

d

b

a

ri

a1

Lv

a3

a2


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( ) m043.0d5;aminL 011 =⋅=

( )

5.0k with

m019914.0f

fdkaL

y

u022

=

=⋅⋅−=

( ) m2149.0L;LLLminL 321veff,v =++=

2

eff,v m001332.0A =

N14.1643513

AfV

0M

eff,vyRd,eff =

γ⋅

⋅=

2.5. Calculation Design Shear Resistance for Bolts in Column The profile use in the present connection is a H60/60/6. To determine the design shear resistance for bolts in the flange of the column, we use a iterative process with hD as parameter until we reach a equilibrium :

γγ=σ

00 M

cor,y

M

beam,yD

f,

fmin

We’ll only consider the check for the final value of hD. As represented in the figure, we have the following data :

m008.0r = m03.0a = m006.0s =

m0128436.0s577.1r4227.0b =⋅+⋅= m0028436.0Playbbs =−=

m011.0h D = 22ipD m029194.0rID

==∑

We compute : 0951.1anI

aK

2pD

=⋅−

=

Corne

Beam

Column

Play

α

s b

r

bs

σD

View A-A

hD

σD

d

Web Beam

Corner A A

a

e

p1

Flange Column


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We define xj=0.03m and zj=0.165m respectively as the maximum horizontal distance between bolts and d and the maximum vertical distance between the bolts and d. Its corresponds to the further bolts how is submitted to the higher force.

( ) 5.0xaKn

1A j =−⋅+= 18069.0zKB j =⋅=

N16224Fn4.1

N1F,FminQ

Rd,tRd,vRd,b =

⋅⋅−⋅= where:

• N16224Af6.0

FMb

subcor,V dR

=γ

⋅⋅= and N24336

Af9.0F

Mb

subRd,t =

γ

⋅⋅=

• N2.22187tdf5.2

FMb

corupcor,Rd,b =

γ

⋅⋅⋅α⋅=

• N28.33281tdf5.2

FMb

flangeupflange,Rd,b =

γ

⋅⋅⋅α⋅=

428.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

With this values, we have :

N94.61032BA

Q2V

22ColFlange,Rd =

+

⋅= ∑ ∑ =⋅⋅= N64.5948zKVQ jRdh

2DD

hD m

N89.209194259bh

Q=

⋅=σ∑

2.6. Calculation Design Tension Resistance NRd for Connection Element

Area : 2m002256.0ht2A =⋅⋅=

Net Area : 20net m001920.0d2t2AA =⋅⋅⋅−=

Tension Resistance:

γ

⋅⋅

γ

⋅=

1

net

0 M

u

M

yRd

fA9.0,

fAminN ( ) N63.481963277.565527,63.481963min ==


Area : 2m003910.0A =

Net Area : 20net m0037364.0dt2AA =⋅⋅−=



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γ

⋅⋅

γ

⋅=

1

net

0 M

u

M

yRd

fA9.0,

fAminN ( ) N175.83531863.1100539,18.835318min ==

2.8. Calculation Design Tension Resistance NRd As prescribed in EC3 Annexe J, we can substituted a bolt joint by a equivalent T-stub to model the resistance of the column flange. The length of the considered T-stub is note leff. 2.8.1. T-Stub Model: Calculation of the equivalent length First, we have to calculate the length leff in the corner for the equivalent T-Stub model by considering the bolts individually (note I) or as part of a group of bolt-rows (note g). Each of this case we’ll be calculate for a circular pattern (note cp) and a non-circular pattern (note nc). We define in the following table p as the pitch of the holes and the parameters m and e as represented in the figures.

Bolt for Element

Start Bolt for Element End Bolt for Element

2tam cor−=

0.027m

( )1i,cp,eff e2m;m2minl ⋅+⋅π⋅π⋅= leff,cp,i,e1=0.1208 leff,cp,i,e2=0.1208

( )1i,nc,eff ee625.0m2;e25.1m4minl +⋅+⋅⋅+⋅= leff,nc,i,e1=0.09075 leff,nc,i,e2=0.09075

( )11g,cp,eff pe2;pmminl +⋅+⋅π= leff,cp,g,e1=0.188 leff,cp,g,e2=0.188

( )p5.0e625.0m2;p5.0eminl 1g,nc,eff ⋅+⋅+⋅⋅+= leff,nc,g,e1=0.094 leff,nc,g,e2=0.094

Bolt for Column-Flange

Start Bolt for Column End Bolt for Column

r8.02t

2t

am col,wbeam,w ⋅−−+= 0.0181m

( )m;m2minl i,cp,eff ⋅π⋅π⋅= leff,cp,i,col1=0.0.1137 leff,cp,i,col2=0.1137

P=0.152

e1=0.018

mCor

eColumn=0.022625

mCol a=0.03m

eelement=0.03


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( )e625.0m2;e25.1m4minl i,nc,eff ⋅+⋅⋅+⋅= leff,nc,i,col1=0.14976 leff,nc,i,col2=0.1497

( )1g,cp,eff p;pmminl +⋅π= leff,cp,g,col1=0.20886 leff,cp,g,col2=0.20886

( )p5.0e625.0m2;p5.0minl g,nc,eff ⋅+⋅+⋅⋅= leff,cp,g,col1=0.15088 leff,cp,g,col2=0.15088

ELEMENT COLUMN

Bolt Consider Individually Start Bolt End Bolt Start Bolt End Bolt

MODE1 ( )i,nc,effi,cp,eff1,eff l,lminl =

0.0907 0.0907 0.1137 0.1137

MODE 2

i,nc,eff2,eff ll = 0.0907 0.0907 0.14977 0.14977

Bolt considered as a part of a group bolt-rows

MODE 1

( ∑∑∑ = g,nc,effg,cp,eff1,eff l,lminl

Min(0.376, 0.188)=0.188

Min(0.4177,0.30177)=

0.30177

MODE 2

∑∑ = g,nc,eff2,eff ll

0.188

0.30177

2.8.2. Failure Mode According to EC3, to obtain the design tension resistance of a connection represented by an equivalent T-Stub flange model, it is necessary to determine the maximum resistance of each bolt-group (element and column) and for each bolt-row. Bolt-Group:

ELEMENT

COLUMN

0

r

M

y2

1,effRd,1,pl

ftl25.0M

γ

⋅⋅⋅=

∑

361.4727Nm

1305.5196Nm

0M

y2

2,effRd,2,pl

ftl25.0M

γ

⋅⋅⋅=

∑

361.4727Nm

1305.5196Nm

Mb

sbolt,uRd,tRd,t

Af9.0FB

γ

⋅⋅==

24336N

24336N

Rd,tboltRd,t BnB ⋅=∑ 97344N

97344N

FAILURE MODE 1

m

M4F

Rd,1,plRd,T

⋅=

53551.51N

288512.634N


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FAILURE MODE 2

nm

BnM2F

Rd,tRd,2,plRd,T +

⋅+⋅=

∑

63916.93N

118193.91N

FAILURE MODE 3

∑= Rd,tRd,T BF

97344N

97344N

Note: nElement=emin=0.03 nColumn=emin=0.022625 Each bolt-row considered individually:

ELEMENT

1ST

ROW

2ND ROW

0M

y2core,1,eff

Rd,1,pl

ftl25.0M

γ

⋅⋅⋅=

174.487Nm

174.487Nm

0M

y2core,2,eff

Rd,2,pl

ftl25.0M

γ

⋅⋅⋅=

174.487Nm

174.487Nm

FAILURE MODE 1

m

M4F

Rd,1,plRd,T

⋅=

25850N

25850N

FAILURE MODE 2

nm

BnM2F

Rd,tRd,2,plRd,T +

⋅+⋅=

∑

31739.21N

31739.21N

FAILURE MODE 3

∑= Rd,tRd,T BF

48672N

48672N

COLUMN

1ST

ROW

2ND ROW

0M

y2fcolcol,1,eff

Rd,1,pl

ftl25.0M

γ

⋅⋅⋅=

491.9926Nm

491.9926Nm

0M

y2fcolcol,2,eff

Rd,2,pl

ftl25.0M

γ

⋅⋅⋅=

647.947Nm

647.947Nm

( ) N51.53551FminF Rd,TGroup,Element,Rd,T ==

( ) N97344FminF Rd,TGroup,Column,Rd,T ==


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FAILURE MODE 1

m

M4F

Rd,1,plRd,T

⋅=

108727.65N

108727.65N

FAILURE MODE 2

nm

BnM2F

Rd,tRd,2,plRd,T +

⋅+⋅=

∑

58860.601N

58860.601N

FAILURE MODE 3

∑= Rd,tRd,T BF

48672N

48672N

The previous table lead to the determination of the design resistance tension for the column flange, the column web and the connected element:

( ) ( )

( ) ( )

( )

0)(M connection pinned ain 0 because 1 where

6826.386820ftl,lmin

N

N9734497344;97344minF,FminN

N5170051.53551;51700minF,FminN

0M

ywbColumn,2,effColumn,1,effColumnWeb,Rd

Group,Column,Rd,TBoltrow,Column,Rd,TBoltColumn,Rd

Group,Element,Rd,TBoltrow,Element,Rd,TtBoltElemen,Rd

==β=ρ

=γ

⋅⋅⋅ρ=

===

===

∑∑

2.9. Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check:


7990

V

V

Rd


Tension Unity Check : 110077.551700

4939.262

N

N 3

Rd

Sd ≤⋅== − ⇒Connection OK for Tension

( )( )∑ =+==

∑ =+==

N973444867248672FminF

N517002585025850FminF

Rd,TBoltrow,Column,Rd,T

Rd,TBoltrow,Element,Rd,T


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Calculation note Node 2 : frame pinned beam-to-column connection side CD

1. Input data

Column HEA160

h 152.00 mm

b 160.00 mm

tf 9.00 mm

tw 6.00 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 240.00 mm

b 120.00 mm

tf 9.80 mm

tw 6.20 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Angle H60/60/6

number 2

h 188.00 mm

b 59.00 mm

t 6.00 mm



fy 235.00 MPa

fu 360.00 MPa

Bolts in beam M-12 (DIN601)

type normal

grade 4.6

fu 400.00 MPa

As 84.50 mm^2

do 14.00 mm

S 19.00 mm

e 20.90 mm

h head 8.00 mm

h nut 10.00 mm

Bolt position in beam

number of rows 2

number of columns 1

x1 30.00 mm

x2 29.00 mm

y1 18.00 mm

y2 18.00 mm

Bolts in column M-12 (DIN601)

type normal

grade 4.6

fu 400.00 MPa


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As 84.50 mm^2

do 14.00 mm

S 19.00 mm

e 20.90 mm

h head 8.00 mm

h nut 10.00 mm

Bolt position in column

number of rows 2

number of columns 1

x1 30.00 mm

x2 30.00 mm

y1 18.00 mm

y2 18.00 mm


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Internal forces


N 0.26 kN

Vz 7.99 kN

My -0.00 kNm


data

sigmaN 0.12 MPa

A 2256.00 mm^2

VRd 278.26 kN


data

Av 1912.76 mm^2

Av,net 1739.16 mm^2

VRd 235.93 kN


Bolt resistance

e1 18.00 mm

p1 152.00 mm

alfa,el 0.43

alfa,bw 0.43

Fb,el,Rd 44.43 kN

Fb,bw,Rd 22.96 kN

Fv,Rd 16.22 kN

data

a 30.00 mm

b 94.00 mm


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data

d 76.00 mm

c 0.00 mm

Ip 11552.00 mm^2

VRd 42.71 kN


data

k 0.50

a1 43.00 mm

a2 20.00 mm

a3 45.00 mm

L1 43.00 mm

L2 19.91 mm

L3 240.00 mm

Lv 152.00 mm

Lv,eff 214.91 mm

Av,eff 1332.47 mm^2

VRd 164.35 kN

2.5.Design shear resistance VRd for bolts in column

Bolt resistance

e1 18.00 mm

p1 152.00 mm

alfa,el 0.43

alfa,cf 0.43

Fb,el,Rd 22.22 kN

Fb,cf,Rd 33.33 kN

Fv,Rd 16.22 kN

Ft,Rd 24.34 kN

data

hd 11.00 mm

bd 2.84 mm

sigma,d 209.19 MPa

a 30.00 mm

Ipd 29194.00 mm^2

zk 165.00 mm

xj 30.00 mm

K 1.10e-003 1/mm

A 5.00e-001

B 1.81e-001

VRd 61.03 kN




data

A 2256.00 mm^2

A,net 1920.00 mm^2

NRd 481.96 kN


data

A 3910.00 mm^2

A,net 3736.40 mm^2

NRd 835.32 kN


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3.3.Design tension resistance NRd


Bt,Rd = 24.34 kN

3.3.1.Column flange

kfc = 1.00

row p (p1+p2) e m n

1 152.00 61.90 18.10 22.63

2 152.00 61.90 18.10 22.63

row leff,cp,i leff,nc,i leff,cp,g leff,nc,g

1 113.73 149.77 208.86 150.89

2 113.73 149.77 208.86 150.89

NRd data

Som Fti,fc,Rd 97.34 kN

Ftg,fc,Rd 97.34 kN

Ft,wc,Rd 386.82 kN

3.3.2.Connection element

row p (p1+p2) e m n

1 152.00 30.00 27.00 30.00 18.00

2 152.00 30.00 27.00 30.00 18.00


1 120.82 90.75 188.00 94.00

2 120.82 90.75 188.00 94.00

NRd data

Som Fti,el,Rd 51.70 kN

Ftg,el,Rd 53.55 kN


4. Unity checks

Unity checks

VSd/VRd 0.19

NSd/NRd 0.01



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2.13 PST.07.02 – 04 : Frame pinned connections (Short endplate) Description A pinned connection with a short endplate is calculated manually in node 2 of the Tutorial Frame project. The results are compared with the results of ESA-Prima Win. Project data The following connection is calculated :

The connection is composed of a endplate made in Fe 360. This endplate is bolted to column’flange and welded to beam’s web. The node used for the check is the column-beam connection number 2 in the Tutorial Frame project. This connection is composed with a HEA160 column and an IPE 240 Beam. We assume that the most dangerous load combination is the 4th. Considering that the moment approaches 0 precision, we can say that we have a pinned connection. The forces in the connection :


Part 1-1 : General rules and rules for buildings

Colum

0.03m

0.018

View A-A

M-12(DIN601)

bendplate=0.159

0.86m

Beam

Play

Column

Endplate

Weld Part

25 mm

0.188mm

A

A


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ENV 1993-1-1:1992 Revised Annex J ENV 19+93-1-1/pr A2

See the chapter "Manual calculation" for the manual calculation according to this reference. Result See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070204.epw Modules 3D Frame (PRS.11) Connect Frame – Pinned (PST.07.02) Author NEM/CVL Manual calculation 1. Dimensions and Position of the Endplate This type of frame pinned connection is composed by a plate placed between the beam and the column. The plate is bolted to the flange’s column by normal bolts and weld to the web’s beam. The following figure specifies the settings. We must note that the disposition of the bolts does not satisfy the rules imposed by EC3. In spite of this, we continue the control this connection so that we can use 3 rows of bolts and the specific calculation that implies (intermediate row of bolts). The solution would be to place 2 rows of bolts in place of three. 2. Calculation of VRd and NRd 2.1. Calculation design local shear resistance VRd for beam

Transversal section of the corner : 2beamwebEndplEndpl m0011656.0thA =⋅=

Normal stress : 2Endpl

N mN669.225200

0011656.0

4939.262

A

N===σ

Flexion module : MOMENT NO 0Wpl ⇔=

Design Shear Resistance : 0f

A

3V

2M

2y2

N22

Rd

0

=γ

−σ+⋅

By solving this second degree, we obtain : 548.143768VRd =


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2.2. Calculation Design Shear Resistance VRd for Bolt in Column The calculation of the design shear resistance for bolt in the column is based on the following expression:

N002.97219F,F4.1n

N1FminV Rd,b

Rd,tRd,vRd =

⋅⋅−⋅= , where

Where : 0.018me1 = 0.152mp1 = 6n =

• N16224Af6.0

FMb

subV dR

=γ

⋅⋅=

• N24336Af9.0

FMb

subRd,t =

γ

⋅⋅=

• N71.33325tdf5.2

FMb

upColumn,Rd,b =

γ

⋅⋅⋅α⋅=

4285.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

• N285.44434tdf5.2

FMb

corupEndpl,Rd,b =

γ

⋅⋅⋅α⋅=

4285.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α


Area of the element: 2wBeamEndpl m0011655.0thA =⋅=

Tension Resistance: N18.24899318fA

N0M

yRd =

γ

⋅=

2.4. Calculation Design Tension Resistance NRd for Bolt and Column Flange As prescribed in EC3 Annexe J, we can substituted a bolt joint by a equivalent T-stub to model the resistance of the column flange. The length of the considered T-stub is note leff. 2.4.1. T-Stub Model: Calculation of the equivalent length The sheme follows to calculate the length leff for the equivalent T-Stub model is the same that we used in bolted angle (Chap.4). As we’ve seen, the computing of the equivalent length is quite complicate by the amount of value to determine. To simplify the presentation, we’ll only calculate leff for the intermediate bolt considered individually and as part of a group of bolt-rows. Each of this case we’ll be calculate for a circular pattern (note cp) and a non-circular pattern (note nc). We define in the following table p as the pitch of the holes and the parameters m and n as represented in the figures. The other equivalent length are calculated in the same way than in the bolted angle connection.

p1=0.076

e1=0.018


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Bolt for Element and Column Flange

Intermediate Bolt for Element Intermediate Bolt for Column Flange

m 0.03537m 0.028m

m2l i,cp,eff ⋅π⋅= leff,cp,i,e1=0.222 leff,cp,i,e2=0.1759

e25.1m4l i,nc,eff ⋅+⋅= leff,nc,i,e1=0.1871 leff,nc,i,e2=0.177

p2l g,cp,eff ⋅= leff,cp,g,e1=0.152 leff,cp,g,e2=0.152

pl g,nc,eff = leff,nc,g,e1=0.076 leff,nc,g,e2=0.076

2.4.2. Failure Mode The maximum resistance of each bolt group (element and column) and for each bolt-row are calculated in the same we that in the bolted angle. The results are: Bolt-Group: ( ) N989.114384FminF Rd,TGroup,Endpl,Rd,T ==

( ) N08.126304FminF Rd,TGroup,Column,Rd,T ==

Bolt-rows individually: ( )∑ == N576.145856FminF Rd,TBoltrow,Endplt,Rd,T

( )∑ == N146016FminF Rd,TBoltrow,Column,Rd,T

The previous results lead to the determination of the design resistance tension for the column flange, the column web and the connected element:

eelement=0.0365 eColumn0.052

m

P=0.076

e1=0.018


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( )

( )

( )N183.421718

ftl,lminN

N08.126304F,FminN

N989.114384F,FminN

0M

ywbColumn,2,effColumn,1,effColumnWeb,Rd

Group,Column,Rd,TBoltrow,Column,Rd,TBoltColumn,Rd

Group,Element,Rd,TBoltrow,Element,Rd,TBoltEndplt,Rd

=γ

⋅⋅⋅ρ=

==

==

∑∑

2.5. Unity Check The most critical design shear resistance and design tension resistance is used to calculate the unity check:


7990

V

V

Rd


Tension Unity Check : 11029.2989.114384

4939.262

N

N 3

Rd

Sd ≤⋅== − ⇒Connection OK for Tension

2.6. Weldsize Endplate/Beam

Weldsize : a=0.04 m Moment: M=0 (Pinned Frame) )f;min(ff Columnu,Endplu,uw =

Normal force : N=262.4939

Shear force : 002.97219VD Rd == N

Stress calculation :

211 mN524.1237800

la22

N

W

M

la22

N=+

⋅⋅⋅=+

⋅⋅⋅=τ−=σ where l=0.188m

22 mN474.64640294

la2

D=

⋅⋅=τ

Unity Check : ( )

11029.4f

and 1311.0f

34

M

u

1

Mw

u

222

ww

211 ≤⋅=

γ

σ≤=

γ⋅β

τ+τ⋅+σ− where βw=0.8

Calculation note Node 2 : frame pinned beam-to-column connection side CD

1. Input data

Column HEA160

h 152.00 mm

b 160.00 mm

tf 9.00 mm

tw 6.00 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


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h 240.00 mm

b 120.00 mm

tf 9.80 mm

tw 6.20 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Endplate

h 188.00 mm

b 159.00 mm

t 12.00 mm


fy 235.00 MPa

fu 360.00 MPa


type normal

grade 4.6

fu 400.00 MPa

As 84.50 mm^2

do 14.00 mm

S 19.00 mm

e 20.90 mm

h head 8.00 mm

h nut 10.00 mm


number of rows 3

spacing 86.00 mm

y1 18.00 mm

y2 18.00 mm


Gamma M0 1.10

Gamma M1 1.10

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Internal forces


N 0.26 kN

Vz 7.99 kN

My -0.00 kNm

2. Design shear resistance 2.1.Design local shear resistance VRd for beam

data

sigmaN 0.23 MPa

A 1165.60 mm^2

VRd 143.77 kN



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Bolt resistance

e1 18.00 mm

p1 76.00 mm

alfa,el 0.43

alfa,cf 0.43

Fb,el,Rd 44.43 kN

Fb,cf,Rd 33.33 kN

Fv,Rd 16.22 kN

Ft,Rd 24.34 kN

data

n 6

VRd 97.22 kN


3, Design tension/compression resistance NRd 3.1.Design tension/compression resistance NRd for beam web

data

A 1165.60 mm^2

NRd 249.01 kN



Bt,Rd = 24.34 kN

3.2.1.Column flange

kfc = 1.00

row p (p1+p2) e m n

1 76.00 52.00 28.00 35.00

2 76.00 52.00 28.00 35.00

3 76.00 52.00 28.00 35.00


1 175.93 177.00 163.96 126.50

2 175.93 177.00 152.00 76.00

3 175.93 177.00 163.96 126.50

NRd data

Som Fti,fc,Rd 146.02 kN

Ftg,fc,Rd 126.30 kN

Ft,wc,Rd 421.72 kN


row p (p1+p2) e m n

1 76.00 36.50 35.37 36.50 18.00

2 76.00 36.50 35.37 36.50 -

3 76.00 36.50 35.37 36.50 18.00


1 147.13 111.56 112.00 56.00

2 222.26 187.12 152.00 76.00

3 147.13 111.56 112.00 56.00


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NRd data


Ftg,el,Rd 114.38 kN


4. Unity checks

Unity checks

VSd/VRd 0.08

NSd/NRd 0.00


5. Weldsize calculation 5.1. Weldsize endplate/column

data

fu 360.00 MPa

beta 0.80

a 4.00 mm

L 0.00 mm

D 97.22 kN

N 0.26 kN

M 0.00 kNm

sigma,1 0.12 MPa

tau,1 0.12 MPa

tau,2 64.64 MPa


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2.14 PST.07.02 - 05 : Frame pinned connection (Angles) with column minor axis Description This benchmark consists in a manual verification of a connection by using the minor axis theory combined with Annex J Revised EC3. Those results are compared with the design calculation of EPW 3.20 Project data See input file. Reference Eurocode 3 : Design of steel structures


See the chapter "Manual calculation" for the manual calculation according to this reference. Result Manual calculation EPW FPunching,Rd,l1,ind 331.8 kN 331.87 kN FPunching,Rd,l1,group 402.8 kN 402.75 kN FPunching,Rd,l2 185.5 kN 185.53 kN FComb,Rd,ind 105.8 kN 105.81 kN FComb,Rd,group 123.6 kN 123.69 kN See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070205.epw Modules 2D Frame (PRS.01) Connect Frame - Rigid (PST.07.02) Author NEM - CVL Manual calculation The following connection is composed with a angle attached respectively on the web beam and the web column through 2 bolt rows. The angle, symmetrically bind around the beam flange, is composed of the profile L70/70/5. The angle is made of steel with following properties: S235 and is characterised by properties described in the EPW results


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document. The present document assumes that all the tensions, the stresses and the most dangerous combination computed by EPW are right. The node use for the check is the minor axis column-beam connection number 4 in PST070205.epw. This connection is composed with a HEA180 column and a IPE240 beam. We assume that the most dangerous combination is the 4th. The verification concerns only the weak axis part. For other controls from Annex J Revised EC3, other benchmarks are available.

AB

IPE240

Section AB

HEA18025

27


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70

18

8

35

14

16

0

2 x M-12 (DIN601)

70

18

8

188

70

14 160

35

2 x M-12 (DIN601)

188

70

Local failure: Punching Punching Loading case 1 The connection is submitted to tension. The bolt will transmit the forces through the column web. Individual bolt row

mm95.192

199.20

2

dmed m =

+=

+=

mm95.17d9.0c m =⋅=

mm2.76x2tmm702b 2wbeam0 =⋅−+⋅=

mm15.94d9.0bb m0indivi =⋅+=


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( )kN8.331n

3

ftcb2nF boltrow

0M

ywcboltrowindividual,1LRd,Punching =⋅

γ⋅

⋅⋅+⋅=⋅

Bolt pattern group

mm2.76d9.0bb m0group =⋅+=

mm160yyhc 21angle0 =−−=

mm95.177d9.0cc m0groupe =⋅+=

( )kN75.402

3

ftcb2F

0M

ywcgroup,Rd,Punching 1L

=γ⋅

⋅⋅+⋅=

Punching Loading case 2

n=2 bolts row*nbolt row=4

kN5.1853

ftdnF

0M

ywcmindividual,Rd,Punching =

γ⋅

⋅⋅⋅π⋅=

kN5.1853

ftdnF

0M

ywcmgroup,Rd,Punching =

γ⋅

⋅⋅⋅π⋅=


Individual bolt row

mm152thd fcc =−=

mm5.1294

r32dL =⋅−=

mm3.35bLa individualindividual =−=

1k5.0L

cbindi

indiindi =⇒>+

0mm1.75 Lt

c8.211

c

t82.01Lb

2

wc

2indi

2indi

2wc

indi,m >=

⋅++⋅−⋅=

mm3.9bL

bb

L

t

L

c23.0

L

tLx

indi,m

indi,mindi3

1

wcindi3

2

wcindi,0 =

−

−⋅

⋅⋅+

⋅=


t3ca5..1aax mindiindi,0indi

wcindiindi

2indiindiindi >=⋅++⋅⋅π⋅

⋅+⋅⋅−+−=

( )( )

kN8.105n1

xat3

xxc5.1

xa

c2xaLftkF boltrow

0Mindiindiwc

2indiindiindi

indiindi

indiindiindiy

2wcindiRd,Comb =⋅

γ⋅

+⋅⋅

+⋅⋅+

+

⋅++⋅⋅π⋅⋅⋅=

Bolt pattern group

mm3.35bLa group =−=

1k5.0L

cb groupgroup=⇒>

+


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112.8mm Lt

c8.211

c

t82.01Lb

2

wc

2group

2

2wc

group,m =

⋅++⋅−⋅=

mm4.35bL

bb

L

t

L

c23.0

L

tLx

group,m

group,mgroup3

1

wcgroup3

2

wcgroup,0 −=

−

−⋅

⋅⋅+

⋅=

groupm,groupgroup bb 0x <=

( )( ) kN

xat

xxc

xa

cxaLftkF

Mgroupgroupwc

groupgroupgroup

groupgroup

groupgroupgroup

ywcgroupgroupRdComb 6.1231

3

5.12

0

22

,, =⋅

+⋅⋅

+⋅⋅+

+

⋅++⋅⋅⋅⋅⋅=

γ

π

Calculation note Node 4 : frame pinned beam-to-column connection side AB

1. Input data

Column HEA180

h 171.00 mm

b 180.00 mm

tf 9.50 mm

tw 6.00 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa


h 240.00 mm

b 120.00 mm

tf 9.80 mm

tw 6.20 mm

r 15.00 mm

fy 235.00 MPa

fu 360.00 MPa

Angle L70/70/5

number 2

h 188.00 mm

b 70.00 mm

t 5.00 mm



fy 235.00 MPa

fu 360.00 MPa


type normal

grade 4.6

fu 400.00 MPa

As 84.50 mm^2

do 14.00 mm

S 19.00 mm

e 20.90 mm

h head 8.00 mm

h nut 10.00 mm


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Bolt position in beam

number of rows 2

number of columns 1

x1 35.00 mm

x2 35.00 mm

y1 14.00 mm

y2 14.00 mm


type normal

grade 4.6

fu 400.00 MPa

As 84.50 mm^2

do 14.00 mm

S 19.00 mm

e 20.90 mm

h head 8.00 mm

h nut 10.00 mm


number of rows 2

number of columns 1

x1 35.00 mm

x2 35.00 mm

y1 14.00 mm

y2 14.00 mm


Gamma M0 1.10

Gamma M1 1.25

Gamma Mb 1.25

Gamma Ms 1.25

Gamma Mw 1.25

Internal forces


N 0.38 kN

Vz 23.74 kN

My -0.00 kNm

Warning : Bending moment is present !


data

sigmaN 0.20 MPa

A 1880.00 mm^2

VRd 231.88 kN


data

Av 1912.76 mm^2

Av,net 1739.16 mm^2

VRd 235.93 kN


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Bolt resistance

e1 14.00 mm

p1 160.00 mm

alfa,el 0.33

alfa,bw 0.33

Fb,el,Rd 28.80 kN

Fb,bw,Rd 17.86 kN

Fv,Rd 16.22 kN

data

a 35.00 mm

b 94.00 mm

d 80.00 mm

c 0.00 mm

Ip 12800.00 mm^2

VRd 32.72 kN


data

k 0.50

a1 39.00 mm

a2 25.00 mm

a3 41.00 mm

L1 39.00 mm

L2 27.57 mm

L3 240.00 mm

Lv 160.00 mm

Lv,eff 226.57 mm

Av,eff 1404.76 mm^2

VRd 173.27 kN


Bolt resistance

e1 14.00 mm

p1 160.00 mm

alfa,el 0.33

alfa,cf 0.33

Fb,el,Rd 14.40 kN

Fb,cf,Rd 17.28 kN

Fv,Rd 16.22 kN

Ft,Rd 24.34 kN

data

hd 18.00 mm

bd 1.69 mm

sigma,d 201.63 MPa

a 35.00 mm

Ipd 29870.50 mm^2

zk 165.50 mm

xj 35.00 mm

K 1.28e-003 1/mm

A 5.00e-001

B 2.11e-001

VRd 53.06 kN





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data

A 1880.00 mm^2

A,net 1600.00 mm^2

NRd 401.64 kN


data

A 3910.00 mm^2

A,net 3736.40 mm^2

NRd 835.32 kN



3.3.1. Column web in tension

NRd individual bolt row local punching

# bolt row 2

dm 19.95 mm

b0 76.20 mm

b ind 94.15 mm

c ind 17.95 mm

FPunch,Rd,ind, L1 331.87 kN

FPunch,Rd,ind, L2 185.53 kN

FPunch,Rd,ind 185.53 kN

NRd Bolt group local punching

# bolt row 2

b0 76.20 mm

b gr 94.15 mm

c0 gr 160.00 mm

c gr 177.95 mm

FPunch,Rd,gr,L1 402.75 kN

FPunch,Rd,gr,L2 185.53 kN

FRd,Punch 185.53kN

NRd individual bolt row local combined

L 129.50 mm

bm ind 57.14 mm

x0 ind 9.30 mm

x ind 8.38 mm

a ind 35.35 mm

k ind 1.00

FCombRd,ind 105.81 kN

NRd Bolt group local combined

L 129.50 mm

bm gr 112.89 mm

x0 gr -35.43 mm

x gr 0.00 mm

a gr 35.35 mm

k gr 1.00

FCombRd,gr 123.69 kN

FRd,Punch 105.81kN


row p (p1+p2) e m n

1 160.00 35.00 32.50 35.00 14.00


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row p (p1+p2) e m n

2 160.00 35.00 32.50 35.00 14.00


1 130.10 100.88 188.00 94.00

2 130.10 100.88 188.00 94.00

NRd data


Ftg,el,Rd 30.90 kN


4. Unity checks

Unity checks

VSd/VRd 0.73

NSd/NRd 0.01



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2.15 PST 07 03 01: Hollow section joint design Annex K Description Benchmark for hollow section connection design following EC3 Annex K, Revised Annex KK and CIDECT design Guide for circular hollow section (CHS) under predominantly static loading. Project data The project tested is a Warren truss consisting of circular hollow section. To limit the number of joints, a K-joint configuration is chosen. The following dimension are assumed: Span: 36m Depth: 2,4m Purlins: 6m K angle: 38.66° The load P=108kN including the weight of the truss is applied in each node and a pin-jointed analysis is performed. Reference CIDECT Design guide for circular hollow section (CHS) joints under predominantly static loading J. Wardenier, Y. Kurobane, J.A. Packer, D.Dutta, N. Yeomans Verlag TUV Rheinland Work example p.46 See the chapter "Manual calculation" for the calculation according to this reference. Result

CIDECT EPW Manual

Unity Check 1.17 1.12 1.12

Version ESA-Prima Win 3.20.03 Input file + calculation note PST070301.epw Modules 2D Frame (PRS.01) Truss connections (PST.07.03)

φ219.1/7.1

φ139.7/4.5

φ88.9/3.6

φ193.7/6.3


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Author NEM/CVL Manual calculation

Calculation following CIDECT reference

Configuration of the node: Connection combination: CC Connection type: K joint Calculation type: K joint (one bracing in compression and one bracing in tension) Profile used: Chord: 219.1/7.1 Bracings: 139.7/4.5 88.9/3.6 Partial security factor: γM1=1.1 Geometrical data:

521.0d2

dd

0

21 =⋅

+=β

429.15t2

d

0

0 =⋅

=γ

( )mm38.91

sin2

d

sin2

d

sinsin

sin

2

deg

2

2

1

1

21

210 =θ⋅

−θ⋅

−θθ

θ+θ

+= with e=0

Range of validity

1405.0d

d2.0 and 163.0

d

d2.0 :1 Criterion

0

2

0

1 ≤=≤≤=≤

2534.12t2

d and 2552.15

t2

d :2 Criterion

2

2

1

1 ≤=≤=

°≤°=θ=θ≤° 9066.3830 :3 Criterion 11

2542.15t2

d :4 Criterion

0

0 ≤==γ

25.00d

e0.55- :5 Criterion

0

≤=≤

mm1.8ttmm38.91g :6 Criterion 21 =+≥=

22y2y1 mmN355

mmN275ff :8Criterion ≤==

RANGE OF VALIDITY OK for calculation Design of the joint The function f(n’) that appear in the chord plastification failure mode incorporates the chord prestress in the joint. The prestress in the joint designs the load in the chord not necessary for the equilibrium of the bracing load components.

220

opop mm

N38.71mm4728

N337500

A

Nf −=

−== pinned joint -> no moment in the connection


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201.0

mmN355

mmN38.71

f

f'n

2

2

0y

op−=

−==

( ) 927.0'n3.0'n3.01'nf 2 =−+=

( ) 735.11e

024.01'g,f

33.1'g5.0

2.12.0 =

+

γ⋅+⋅γ=γ

−⋅ with 87.12

t

g'g

0

==

Joint strength: Chord Plastification

( ) ( ) ( ) N13.3828431.1

'nf'g,f2.108.1sin

tfN

1M1

20yo

Rd,1 =γ

⋅⋅γ⋅β⋅+⋅θ

⋅=

N13.382843sin

sinNN

2

1Rd,1Rd,2 =

θ

θ⋅=

Unity Check: 1128.113.382843

432210

N

N

Rd

maxSd >==

Punching shear

N13294591.1

sin2

sin1td

3

fN

1M201

0yRd,1 =

γ⋅

θ⋅

θ+⋅⋅⋅

⋅π=

N8460191.1

sin2

sin1td

3

fN

1M202

0yRd,2 =

γ⋅

θ⋅

θ+⋅⋅⋅

⋅π=

Weldsize calculation

Following EC3 a1=a2≥0.87t1=4mm Calculation note

Node 14: Welded truss connection

1. Input data

Chord: Member 12 13 B219.1/7.1

d 219.00 mm

t 7.10 mm

fy 355.00 MPa

fu 510.00 MPa

Bracing: Member 24 B139.7/4.5

d 140.00 mm

t 4.50 mm

teta 38.66 deg

fy 275.00 MPa

fu 430.00 MPa


d 88.90 mm

t 3.60 mm

teta 38.66 deg

fy 275.00 MPa


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fu 430.00 MPa

2. General node data

Node characteristics

References CIDECT Design Guide CHS Fig.8&24

Standard configuration K Joint

Standard combination CC Type

Type of calculation K type

Gamma M1 1.10

Gamma Mw 1.00

Geometrical data

beta 0.52

gamma 15.42

e 0.00 mm

gap (g) 90.54 mm

Range of Validity

0.2<di/d0<=1.0 OK

di/2ti<=25 OK

30°<=tetai<=90° OK

gamma<=25 OK

-0.55<=e/d0<0.25 OK

g>=t1+t2 OK

fyi<= 355.00 MPa OK

3. Failure mode and results

Chord plastification

Nop -337.50 kN

fop -72.11 MPa

n' -0.20

g' 12.75

f(n') 0.93

f(gamma,g') 1.74

NRd,c Bracing 24 383.32 kN

NRd,t Bracing 25 383.32 kN

NSd,c Bracing 24 -432.21 kN

NSd,t Bracing 25 259.33 kN

Unity Check bracing 24 1.13


Punching shear

NSd bracing 24 -432.21 kN

NRd bracing 24 1332.32 kN


NSd bracing 25 259.33 kN



4. Weldsize CalculationEC3 Annex K.5

Weldsize bracing 24

alfa weld 0.80

a 4.00 mm


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Weldsize bracing 25

alfa weld 0.80

a 4.00 mm

Critical loadcase:2 Critical NRd: 383.32 kN

Unity Check 1.13 Chord plastification


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2.16 PST 07 03 02: Hollow section joint design Annex K Description Benchmark for hollow section connection design following EC3 Annex K, Revised Annex KK and CIDECT design Guide for rectangular hollow section (RHS) under predominantly static loading. Project data The project tested is a Warren truss consisting of rectangular hollow section. To limit the number of joints, a K-joint configuration is chosen. The following dimension are assumed: Span: 36m Depth: 2,4m Purlins: 6m K angle: 38.66° We must note that the chord is composed with a square profile. The load P=108kN including the weight of the truss is applied in each node between the support and the load P=54kN on each extremity. A pin-jointed analysis is performed. Reference CIDECT Design guide for rectangular hollow section (RHS) joints under predominantly static loading J. Wardenier, Y. Kurobane, J.A. Packer, D.Dutta, N. Yeomans Verlag TUV Rheinland Work example p.46 See the chapter "Manual calculation" for the calculation according to this reference. Result

CIDECT EPW Manual

Unity Check 0.74 0.73 0.73

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file PST070302.epw

180/180/8

120/120/4

80/80/3.2

150/150/6.3


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Modules 2D Frame (PRS.01) Truss connections (PST.07.03) Author NEM - CVL Manual calculation


Configuration of the node: Connection combination: RR square Connection type: K joint Calculation type: K joint (one bracing in compression and one bracing in tension) Profile used: Chord: 180/180/8 Bracings: 120/120/4 80/80/3.2 Partial security factor: γM1=1.1 Geometrical data:

555.0b4

hhbb

0

2121 =⋅

+++=β

25.11t2

b

0

0 =⋅

=γ

( )mm92.64

sin2

h

sin2

h

sinsin

sin

2

heg

2

2

1

1

21

210 =θ⋅

−θ⋅

−θθ

θ+θ

+= with e=0

Range of validity

3252.0t

b01.01.044.0

b

b and 3252.0

t

b01.01.066.0

b

b :1 Criterion

0

0

0

2

0

0

0

1 =⋅+≥==⋅+≥=

3522.5t

b51 :2 Criterion

0

0 ≤=≤

3.1833.0b2

bb.60 :3 Criterion

1

21 ≤=⋅

+=β≤

( ) ( ) mm1.7tt 64.92mmg and 66.015.136.0b

g22.0-10.5 :4 Criterion 21

0

=+≥==β−⋅≤=≤=β⋅

25.00d

e0.55- :5 Criterion

0

≤=≤

°≤°=θ=θ≤° 9066.3830 :6 Criterion 11

8.0696.0f

f

8.0696.0f

f

mmN355

mmN355ff :7Criterion

u2

y2

u1

y1

22y2y1

≤=

≤=

≤==


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in tensionmember 3525t

b

ncompressioin member 4.30f

E25.130

t

b :8Criterion

2

2

1y1

1

≤=

=⋅≤=

RANGE OF VALIDITY OK for calculation Design of the joint The function f(n) that appear in the chord yielding face incorporates the effect of the maximum aplied axial stress in the chord or the maximum stress due to axial force and bending moment.

220

oo mm

N199.162mm5410

N877500

A

Nf −=

−== pinned joint -> no moment in the connection

456.0

mmN355

mmN199.162

f

fn

2

2

0y

o −=−

==

( ) 97.0n4.0

3.1nf =⋅β

+=

Joint strength: Chord face yielding

( ) N76.5850641.1

nfb2

bb

sin

tf9.8N

1M

21

0

21

1

20yo

Rd,1 =γ

⋅⋅γ⋅

⋅

+⋅

θ

⋅⋅=

N76.585064sin

sinNN

2

1Rd,1Rd,2 =

θ

θ⋅=

Unity Check: 1738.0585064

432210

N

N

Rd

maxSd <==

Weldsize calculation

Following EC3 a1 ≥1.01t1=5mm a2 ≥1.01t2=4mm Calculation note Node 14: Welded truss connection

1. Input data

Chord: Member 12 13 SC180/180/8

h (in plane) 180.00 mm

b (out plane) 180.00 mm

t 8.00 mm

fy 355.00 MPa

fu 510.00 MPa


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Bracing: Member 24 SC120/120/4



t 4.00 mm

teta 38.66 deg

fy 355.00 MPa

fu 510.00 MPa

Bracing: Member 25 SC80/80/3.2



t 3.20 mm

teta 38.66 deg

fy 355.00 MPa

fu 510.00 MPa



References Cidect Design Guide RHS Table 2&2a


Standard combination RR Type


Gamma M1 1.10

Gamma Mw 1.00

Geometrical data

beta 0.56

gamma 11.25

e 0.00 mm

gap (g) 64.92 mm

Range of Validity

hi/b0&bi/b0>=0.1+0.01b0/t0 & beta>=0.35 OK

15<=b0/t0<=35 OK

0.6<=b1+b2/2b1<=1.3 OK

0.5(1-Beta)<=g/t0<=1.5(1-Beta) g>=t1+t2 OK

-0.55<=e/h0<=0.25 OK

30°<=tetai<=90° OK

fyi<= 355.00 MPa fyi(orfyj)/fui<=0.8 OK

bc/tc&hc/tc<=1.25sqrt(E/fyc) and bc/tc&hc/tc<=35 OK

bt/tt&ht/tt<=35 OK


Chord face plastification

fo -159.55 MPa

n -0.45

f(n) 0.98

gamma 11.25

NRd,c Bracing 24 588.94 kN

NRd,t Bracing 25 588.94 kN

NSd,c Bracing 24 -432.21 kN

NSd,t Bracing 25 259.33 kN





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Weldsize bracing 24

alfa weld 0.80

a 4.00 mm

Weldsize bracing 25

alfa weld 0.80

a 4.00 mm


Unity Check0.73 Chord face plastification


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2.17 PST 07 03 03: Hollow section joint design Annex K Description Benchmark for hollow section connection design following EC3 Annex K, Revised Annex KK and CIDECT design Guide for rectangular hollow section (RHS) under predominantly static loading. Reference CIDECT Design guide for circular hollow section (CHS) joints under predominantly static loading J. Wardenier, Y. Kurobane, J.A. Packer, D.Dutta, N. Yeomans Verlag TUV Rheinland See the chapter "Manual calculation" for the calculation according to this reference. Result

EPW Manual

Unity Check 0.97 0.97

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070303.epw Modules 2D Frame (PRS.01) Truss connections (PST.07.03) Author NEM - CVL Manual calculation

Calculation following CIDECT reference Configuration of the node: Connection combination: RR square Connection type: X joint Calculation type: X joint Profile used: Chord: 150/75/5 Bracings: 110/70/3 110/70/3 Partial security factor: γM1=1.1 Geometrical data:

933.0b

b

0

1 ==β


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419

5.7t2

b

0

0 =⋅

=γ

Range of validity

25.0866.1b

h and 25.093.0

b

b :1 Criterion

0

2,1

0

2,1 ≥=≥=

22b

h.50 :2 Criterion

1,2

1,2 ≤=≤

3530t

h and 3515

t

b :3 Criterion

0

0

0

0 ≤=≤=

°≤°=θ≤° 904030 :6 Criterion 1

8.0652.0f

f

8.0652.0f

f

mmN355


u2

y2

u1

y1

22y2y1

≤=

≤=

≤==

in tensionmember 3533,23t

b

ncompressioin member 35 35 ; 36.37f

E25.1min33,23

t

b :8Criterion

2

2

1y1

1

≤=

=

=⋅≤=

RANGE OF VALIDITY OK for calculation Design of the joint The function f(n) that appear in the chord yielding face incorporates the effect of the maximum applied axial stress in the chord or the maximum stress due to axial force and bending moment.

20

0

ooup mm

N19.120W

M

A

Nf −=+= in upper fiber and 2

0

0

oobot mm

N19.120W

M

A

Nf −=+= in bottom fiber

56.0

mmN235

mmN19.120

f

fn

2

2

0y

oupup −=

−== and 51.0

mmN235

mmN19.120

f

fn

2

2

0y

obotbot −=

−==

( ) 108.1n4.0

3.1nf up ≤=⋅β

+= and ( ) 1nf bot =

Joint strength: Chord face yielding with β=0.85 η=h1/b0=1.866

( )( ) ( ) N29.448

1.1nf14

sin

2

sin1

tfN

1M

5.0

11

20yo

Rd,2&1 =γ

⋅⋅

β−+

θη⋅

⋅θ⋅β−

⋅=

Chord Side Wall Failure (β=1)

Slenderness: 83.120sin

12

t

h46.3

5.0

10

0 =

θ⋅

−⋅=λ


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420

Euler slenderness: 91.93f

E

0y1 =⋅π=λ

Reduced slenderness: 286.11

red =λλ

=λ

Reduction factor: ( )

478.01

5.022=

λ−φ+φ=χ with

( )( ) =λ+−λ⋅α+⋅=φ 22.015.0

and 21.0=α

Buckling stress: 219.1021

ff1M

0ynk =γ

⋅⋅χ=

Member in compression: connection Xfor 2.565fsin8.0f nk1k =⋅θ⋅=

N55.1981.1

t10sin

h2

sin

tfN

1M0

1

1

1

0kRd,2&1 =

γ⋅

⋅+

θ

⋅⋅

θ

⋅=

Interpolation with 1933.085.0 ≤=β≤ between chord face yielding and side wall failure

N82.312N erpol,intRd =


280

N

N

Rd

maxSd <==

Effective width

( ) 65.2871.1

b2t4h2tfN1M

e1111yRd2,1 =γ

⋅⋅+⋅−⋅⋅⋅=

with 7077.77btf

tf

tb10

b 111y

00y

0

0e ≤=⋅

⋅

⋅⋅=


65.287

N

N

Rd

maxSd <==

Calculation note Node 2: Welded truss connection

1. Input data

Chord: Member 1 2 AC150/75/5



t 5.00 mm

fy 235.00 MPa

fu 360.00 MPa

Bracing: Member 3 AC140/70/3



t 3.00 mm

teta 40.00 deg

fy 235.00 MPa

fu 360.00 MPa


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t 3.00 mm

teta 40.00 deg

fy 235.00 MPa

fu 360.00 MPa




Standard configuration X Joint


Type of calculation X type

Gamma M1 1.10

Gamma Mw 0.00

Geometrical data

beta 0.93

gamma 7.50

Range of Validity

bi/b0&hi/b0>=0.25 OK

0.5<=hi/bi<=2 OK

b0/t0&h0/t0<=35 OK

30°<=tetai<=90° OK


bc/tc&hc/tc<=1.25sqrt(E/fyc) and bc/tc&hc/tc<=35 Not OK

bt/tt&ht/tt<=35 OK


Interpol. of chord face yielding and side wall failure

eta bracing 3 1.87

fo bracing 3 -120.19 MPa

n bracing 3 -0.51

f(n) bracing 3 1.00

eta bracing 4 1.87

fo bracing 4 -120.19 MPa

n bracing 4 -0.51

f(n) bracing 4 1.00

NRd f.yield (Beta=0.85) bracing 3 448.29 kN

NRd f.yield (Beta=0.85) bracing 4 448.29 kN

slenderness 120.84

reduced slenderness 1.29

imperfection factor 0.21

reduction factor 0.48

fkn 102.09 MPa

fk 52.50 MPa

NRd SideWall bracing 3 198.30 kN

NRd SideWall bracing 4 198.30 kN

NRd interpol bracing 3 309.41 kN

NRd interpol bracing 4 309.41 kN






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Effective width

be bracing 3 70.00 mm

be bracing 4 70.00 mm








Weldsize bracing 3

d1 Galvanisation hole out plane 0.00 mm


d3 Galvanisation hole in plane 0.00 mm


Weld factor 1.00

Betaw 0.80

sigma1, weld 0.00 MPa

tau1, weld 0.00 MPa

tau2, weld 0.00 MPa

Unity check (Von Mises) 10.00

Unity Check (sigma1) 10.00

a 0.00 mm

Weldsize bracing 4





Weld factor 1.00

Betaw 0.80


tau1, weld 0.00 MPa

tau2, weld 0.00 MPa



a 0.00 mm


Unity Check0.97 Effective width


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2.18 PST 07 03 04: Hollow section joint design Annex K Description Benchmark for hollow section connection design following EC3 Annex K, Revised Annex KK and CIDECT design Guide for rectangular hollow section (RHS) under predominantly static loading. Reference CIDECT Design guide for circular hollow section (CHS) joints under predominantly static loading J. Wardenier, Y. Kurobane, J.A. Packer, D.Dutta, N. Yeomans Verlag TUV Rheinland See the chapter "Manual calculation" for the calculation according to this reference. Result

EPW Manual

Unity Check 0.91 0.908

See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PST070304.epw Modules 2D Frame (PRS.01) Truss connections (PST.07.03) Author NEM - CVL Manual calculation


Configuration of the node: Connection combination: RR square Connection type: K joint Calculation type: K joint Profile used: Chord: 150/75/5 Bracings: 110/70/3 (40°) 110/70/3 (70°) Partial security factor: γM1=1.1 Geometrical data:

3.1b4

hhbb

0

2121 =⋅

+++=β


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424

5.7t2

b

0

0 =⋅

=γ

Range of validity

25.0t

b01.01.046.1/86.1

b

h 25.0

t

b01.01.093.0

b

b

35.046.1b

h and 35.086.1

b

h 35.093.0

b

b :1 Criterion

0

0

0

2,1

0

0

0

2,1

0

2

0

1

0

2,1

=⋅+≥==⋅+≥=

≥=≥=≥=

257.1b

h.50 22

b

h.50 :2 Criterion

2

2

1

1 ≤=≤≤=≤

3530t

h and 3515

t

b :3 Criterion

0

0

0

0 ≤=≤=

( ) ( ) OKNot 15.1b

g-10.5

OKNot 6tt7.3g :4 Criterion

0

21

β−⋅≤≤β⋅

=+≤=

25.023.0h

e0.55 :5 Criterion

0

≤=≤−

°≤°=θ≤°°≤°=θ≤° 907030904030 :6 Criterion 21

8.0652.0f

f

8.0652.0f

f

mmN355


u2

y2

u1

y1

22y2y1

≤=

≤=

≤==

in tensionmember 3533,23t

b

ncompressioin member 35 35 ; 36.37f

E25.1min33,23

t

b :8Criterion

2

2

1y1

1

≤=

=

=⋅≤=

RANGE OF VALIDITY Not OK Design of the joint The function f(n) that appear in the chord yielding face incorporates the effect of the maximum applied axial stress in the chord or the maximum stress due to axial force and bending moment.

20

0

oo mm

N76.720W

M

A

Nf =+=

06.3

mmN235

mmN76.720

f

fn

2

2

0y

o ===

( ) 124.2n4.0

3.1nf ≤=⋅β

+=

Joint strength: Chord face yielding


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( )( )

kN1.198sin

sinNN

kN603.2891.1

nfb4

hhbb

sin1

tf9.8N

2

1Rd,1Rd,2

M

5.0

0

2121

1

20yo

Rd,11

=θ

θ⋅=

=γ

⋅⋅γ⋅

⋅

+++⋅

θ⋅β−

⋅=

Chord Shear

Reduced Area: ( ) 76.0

t3

g41

1th wi1785.09mm tbh2A

5.0

20

22

000v =

⋅

⋅+

=α=⋅⋅α+⋅=

Plastic Shear: kN2,2423

AfV

v0ypl =

⋅=

kN74.2571.1

sin3

AfN and kN796.376

1.1

sin3

AfN

11 M2

v0yRd2

M1

v0yRd1 =

γ⋅

θ⋅

⋅==

γ⋅

θ⋅

⋅=

( ) kN44.369V

V1fAfAAN

5.02

pl

Sd0yv0yv0)Gap In(Rd,0 =

−⋅⋅+⋅−=

Effective width

( )( )

mm70bmm77,70btf

tf

tb10

b with

kN34.245bbt4h2tfN

kN64.287bbt4h2tfN

1111y

00y

0

02&e1

e22222yRd1

e11111yRd1

=≤=⋅⋅

⋅⋅=

=++⋅−⋅⋅⋅=

=++⋅−⋅⋅⋅=


180

N

N

ieldingRdChordFaceY

maxSd <==

Effective width

( ) 65.2871.1

b2t4h2tfN1M

e1111yRd2,1 =γ

⋅⋅+⋅−⋅⋅⋅=

with 7077.77btf

tf

tb10

b 111y

00y

0

0e ≤=⋅

⋅

⋅⋅=


65.287

N

N

Rd

maxSd <==

Calculation note Node 2: Welded truss connection

1. Input data

Chord: Member 1 2 AC150/75/5



t 5.00 mm

fy 235.00 MPa

fu 360.00 MPa


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t 3.00 mm

teta 40.00 deg

fy 235.00 MPa

fu 360.00 MPa




t 3.00 mm

teta 70.00 deg

fy 235.00 MPa

fu 360.00 MPa







Gamma M1 1.10

Gamma Mw 0.00

Geometrical data

beta 1.30

gamma 7.50

e 0.00 mm

gap (g) -50.75 mm

p 117.06 mm

q 50.75 mm

overlap Ov(%) 43.35

Overlapping member 7

Overlapped member 3

Range of Validity

bi/b0&hi/h0 >=0.25 OK

0.5<=hi/bi<=2 OK

b0/t0&h0/t0<=40 OK

25%<=Ov<=100% ti/tj<=1.0 & bi/bj>=0.75 OK

-0.55<=e/h0<=0.25 OK

30°<=tetai<=90° OK


bc/tc&hc/tc<=1.1sqrt(E/fyc) Not OK

bt/tt&ht/tt<=35 Not OK


Effective width

Overlap Ov(%) 43.35

be1 70.00 mm

be2 70.00 mm

be(Ov) 30.00 mm

NSd bracing 7 180.00 kN





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Effective width




Weldsize bracing 3





Weld factor 1.00

Betaw 0.80


tau1, weld 0.00 MPa

tau2, weld 0.00 MPa



a 0.00 mm

Weldsize bracing 7





Weld factor 1.00

Betaw 0.80


tau1, weld 0.00 MPa

tau2, weld 0.00 MPa



a 0.00 mm


Unity Check0.91 Effective width


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2.19 PST.07.03 -5: KLS Truss connection: weldsize calculation Description Control of weld size in connection composed with special Voest KLS profiles according to Voest specifications. The node controlled has the index 2. Only members 1,2 and 32 are activated to form a Y-connection. Project data See input file. Reference See the chapter "Manual calculation" for the calculation according to the Voest specifications. Result Manual calculation EPW σ1 61.6 N/mm² 61.28 N/mm² τ1 189.4 N/mm² 188.63 N/mm² unity check 0.97 0.97 kN unity check 0.22 0.21 kN See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file PST070305.epw Modules 2D Frame (PRS.01) Truss connections (PST.07.03) Author NEM - CVL Manual calculation The chord is composed with a K180/100/10 profile and the bracing is composed by a KLS70/70/5 profile. Properties of those profiles are listed in the results document of EPW. The frame type following CIDECT documentation is a Y-type RHS-KLS joint. The angle between the chord and the bracing is 26,57°.

kN168.19657.26sin57.438sinNT

kN57.39257.26cos57.438cosNV

=°⋅=α=

=°⋅=α=


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( ) mmvvBN

mmvB

D

mmBC

mmB

E

mmEBN

mmvBB

v

mmRABB

8.225²35.012

5.87²32

12

7.5312

31

13.692

22

4.207221

26.138*12

23.2sin

1

628701

=++=

=+=

==

==

=+=

==

==

=−=−=

α

To determine the weld size a in the connection, we use a iterative process with a as parameter until the Von Mises rules is respected (Ref[1],Annex M/EC3). This benchmark controls only the optimal value found by the iterative process. With a weldsize a=10 mm, we have:


SCIA Software

430

²/6.612

1

221 mmNaN

T=

⋅== τσ

²/4.18911 mmN

aN

V=

⋅=τ

( )122.0 and 197.0

3

w

211

M

1

222

≤=≤=

⋅

+⋅+

γ

σ

γβ

ττσ

u

Mw

u ff

w

with βw=0.8 Calculation note Node 2: Welded truss connection

1. Input data

Chord: Member 1 2 K180/100/10



t 10.00 mm

fy 355.00 MPa

fu 510.00 MPa

Bracing: Member 32 KLS70/70/5

B 70.00 mm

B1 62.00 mm

RA 8.00 mm

t 5.00 mm

teta 26.57 deg

fy 235.00 MPa

fu 360.00 MPa



Standard configuration Y Joint

Standard combination RHS-KLS Type

Type of calculation Only weld size

Gamma M1 1.10

Gamma Mw 1.25

No range of validity and failure calculation

3. Geometry and internal forces of bracings


N 438.57 kN

V 392.27 kN

T 196.13 kN

v 2.24

B2 138.64 mm

E2 69.32 mm

N1 207.95 mm

C1 53.69 mm

D2 87.68 mm


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N2 226.32 mm

4. Weldsize CalculationEC3 Annex K.5 : Default weldsize and Optimisation

Weldsize bracing 32: a=0.7.t

Weld factor 1.00

Betaw 0.80


tau1, weld 471.58 MPa




a 4.00 mm

Weldsize bracing 32 Optimisation

Weld factor 1.00

Betaw 0.80






a 10.00 mm

Critical Member32 Critical loadcase:1

Unity check2.42


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2.20 PST.07.04 – 01 : Bolted diagonal connections Description Bolted diagonal connections are calculated manually. The results are compared with the results of ESA-Prima Win. Project data Reference Eurocode 3 : Design of steel structures


See the chapter "Manual calculation" for the calculation according to this reference. Result Manually

[kN] EPW [kN]

Node 12 Npl,Rd (diagonal) 479 480 Nu,Rd (diagonal) 282 282 Fv,Rd 60.28 60.28 Fb,Rd (diagonal) 68.8 68.8 Npl,Rd (plate) 320 320 Nu,Rd (plate) 342 342 Fb,Rd (plate) 69.12 69.12 Node 10 Nu,Rd (diagonal) 238.74 239.42 Fb,Rd (diagonal) 67.52 67.52 Fb,Rd (plate) 56.44 56.53 Node 8 Fp,Cd 109.9 109.9 Fs,Rd 26.4 26.4 Node 4 Npl,Rd (diagonal) 725 725 Nu,Rd (diagonal) 629.5 629 Node 2 Nu,Rd (diagonal) 639.7 639 See the chapter "Calculation note" for the detailed output of ESA-Prima Win. Version 3.20 Input file PST070401.epw Modules 3D Frame (PRS.11) Bolted Diagonal Connection (PST.07.04)


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Author CVL Manual calculation Partial safety factors : γM0 = 1.10 γM2 = 1.25 γMb = 1.25 Node 12 Diagonal element : • H100/100/10 • fy = 275 N/mm² • fu = 430 N/mm² • A = 1915 mm²

The design plastic resistance for the angle section is kN4791.1

2751915AfN

0M

yRd,pl =

⋅=

γ=

Bolts :

• M16 - 8.8 • d = 16 mm • d0 = 18 mm • fub = 800 N/mm² • A = 157 mm² • e2 = 50 mm • e1 = 27 mm

The design ultimate resistance of the net section for angle diagonal with 1 bolt :

( ) ( )kN282

25.1

10185.0500.2tfd5.0e0.2N

2M

uo2Rd,u =

⋅−=

γ

−=

The shear resistance per shear plane and per bolt is

kN28.6025.1

1578006.00.1

Af6.0F

Mb

subLfRd.v =

⋅⋅=

γβ=

The bearing resistance (in the angle section) is


SCIA Software

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50.0183

27)0.1,

f

f,

4

1

d3

p,

d3

emin(

kN8.6825.1

101643050.05.2dtf5.2F

u

ub

0

1

0

1

Mb

uRd.b

=⋅

=−=α

=⋅⋅⋅⋅

=γ

α=

For single lap joints with one bolt, Fb,Rd is limited by

kN56.8225.1

10164305.1dtf5.1F

Mb

uRd.b =

⋅⋅⋅=

γ=

� Fb,Rd = 68.8 kN Gusset element : • b= 150 mm • t = 10 mm • e1=40 mm

The design plastic resistance for the plate is kN3201.1

2351500AfN

0M

yRd,pl =

⋅=

γ=

The design ultimate resistance of the net section is

kN34225.1

360)10*181500(9.0fA9.0N

2M

unetRd,u =

−⋅=

γ=

The bearing resistance (in the plate) is

741.0183

40)0.1,

f

f,

4

1

d3

p,

d3

emin(

kN33.8525.1

1016360741.05.2dtf5.2F

u

ub

0

1

0

1

Mb

uRd.b

=⋅

=−=α

=⋅⋅⋅⋅

=γ

α=

For single lap joints with one bolt, Fb,Rd is limited by

kN12.6925.1

10163605.1dtf5.1F

Mb

uRd.b =

⋅⋅⋅=

γ=

� Fb,Rd = 69.12 kN Node 10 Identical characteristics as in node 12, but with 2 bolts per row, p=40 mm The design ultimate resistance of the net section for angle diagonal with 2 bolts :


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kN74.23825.1

430)10*181915(40.0fAN

2M

unet2Rd,u =

−⋅=

γ

β=

There p < 2.5 d0 ( 40 < 45 ), β2 = 0.4 The bearing resistance (in the angle section) is

49.0)49.0,5.0min()25.0183

40,

183

27min()0.1,

f

f,

4

1

d3

p,

d3

emin(

kN52.6725.1

101643049.05.2dtf5.2F

u

ub

0

1

0

1

Mb

uRd.b

==−⋅⋅

=−=α

=⋅⋅⋅⋅

=γ

α=

The bearing resistance (in the plate) is

49.0)25.0183

40,

183

40min()0.1,

f

f,

4

1

d3

p,

d3

emin(

kN448.5625.1

101636049.05.2dtf5.2F

u

ub

0

1

0

1

Mb

uRd.b

=−⋅⋅

=−=α

=⋅⋅⋅⋅

=γ

α=

Node 8 Identical characteristics as in node 12, but with prestressed bolt M16-10.9

kN9.10915710007.0Af7.0F subCd,p =⋅⋅=⋅⋅=

kN37.269.10925.1

3.011F

nkF Cd,p

Ms

sRd,s =

⋅⋅=

γ

⋅µ⋅⋅=

Node 4 Diagonal element UPE200

• fy = 275 N/mm² • fu = 430 N/mm² • A = 2900 mm²

The design plastic resistance for the channel section is kN7251.1

2752900AfN

0M

yRd,pl =

⋅=

γ=

Bolts :

• M16 - 8.8 • d = 16 mm • d0 = 18 mm • fub = 800 N/mm² • A = 157 mm² • e1 = 27 mm • 2 bolts in the web of the channel, w=100 mm

The design ultimate resistance of the net section for channel diagonal :


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644.016289843

9843

AA3

A3

²mm20331628644.0984AAA

kN5.62925.1

43020339.0fA9.0N

21

1

21n

2M

unRd,u

=+⋅

⋅=

+=ξ

=⋅+=ξ+=

=⋅⋅

=γ

=

A1 = 200 x 6 - 2 x 18 x 6 = 984 mm² A2 = 2 ( 74 x 11) = 1628 mm² Node 2 Identical characteristics as in node 12, but with 2 bolts per row (p=80 mm), staggered position (s=40 mm) The design ultimate resistance of the net section for channel diagonal :

65.0162810083

10083

AA3

A3

²mm2066162865.01008AAA

kN75.63925.1

43020339.0fA9.0N

21

1

21n

2M

unRd,u

=+⋅

⋅=

+=ξ

=⋅+=ξ+=

=⋅⋅

=γ

=

²mm10081004

²40181850100506

p4

²sddepetA

2002221 =

⋅+−−++⋅=

+−−++⋅=

A2 = 2 ( 74 x 11) = 1628 mm² Calculation note

Bolted connection

Node: 12

Diagonal item: H100/100/10

Equal legs connection

b 100mm

t 10mm

fy 275.000MPa

fu 430.000MPa

Non-Staggered bolt position

w 50mm

e1 27mm

p1 0mm


Gama M0 1.10


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Gama M2 1.25

Gama Mb 1.25

Gama Ms 1.25

Gama Mw 1.25

Gusset plate

b 150mm

t 10mm

fy 235.000MPa

fu 360.000MPa


e2 75mm

p2 0mm

e1 40mm

M16-8.8 (DIN960)

Type Normal

Grade 8.8

fu 800.000MPa

As 157mm^2

d0 18mm

S 24mm

e 27mm

h head 10mm

h nut 13mm

Total number of bolts 1

Number of bolt rows 1


Internal forces

Group of load case(s) : 1

N1 100.000kN

Member resistance

Resistance of the gross section of diagonal1

A 1920mm^2

Npl,Rd 480.000kN

Resistance of the net section of diagonal1

Anet 820mm^2

Nu,Rd 282.080kN

Resistance of the gross section of gusset

A 1500mm^2

Npl,Rd 320.455kN


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Resistance of the net section of gusset

Anet 1320mm^2

Nu,Rd 342.144kN

Connection resistance

Shear resistance

Lj 0mm

Beta Lf 1.000

Fv,Rd 60.288kN

Bearing resistance for diagonal

Alfa 0.500

Fb,Rd 68.800kN

Bearing resistance for gusset

Alfa 0.741

Fb,Rd 69.120kN

The design shear force per bolt

Fv,Sd,diagonal1 100.000kN

Unity check

Member resistance 0.35

Connection resistance 1.66

The connection satisfies !

Weld size calculation for gusset plate

a 5mm

La 58mm

NRd 60.288kN

Beta W 0.80

Fw,Rd 1039.230kN/m

Node: 10



b 100mm

t 10mm


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fy 275.000MPa

fu 430.000MPa


w 50mm

e1 27mm

p1 40mm


Gama M0 1.10

Gama M2 1.25

Gama Mb 1.25

Gama Ms 1.25

Gama Mw 1.25

Gusset plate

b 150mm

t 10mm

fy 235.000MPa

fu 360.000MPa


e2 75mm

p2 0mm

e1 40mm

M16-8.8 (DIN960)

Type Normal

Grade 8.8

fu 800.000MPa

As 157mm^2

d0 18mm

S 24mm

e 27mm

h head 10mm

h nut 13mm




Internal forces


1

N1 100.000kN

Member resistance


A 1920mm^2

Npl,Rd 480.000kN


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Anet 1740mm^2

Nu,Rd 239.424kN

Beta2 0.400


A 1500mm^2

Npl,Rd 320.455kN


Anet 1320mm^2

Nu,Rd 342.144kN


Shear resistance

Lj 40mm

Beta Lf 1.000

Fv,Rd 60.288kN


Alfa 0.491

Fb,Rd 67.526kN


Alfa 0.491

Fb,Rd 56.533kN



Unity check





a 5mm

La 109mm

NRd 113.067kN


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Beta W 0.80

Fw,Rd 1039.230kN/m

Node: 8



b 100mm

t 10mm

fy 275.000MPa

fu 430.000MPa


w 50mm

e1 27mm

p1 0mm


Gama M0 1.10

Gama M2 1.25

Gama Mb 1.25

Gama Ms 1.25

Gama Mw 1.25

Gusset plate

b 150mm

t 10mm

fy 235.000MPa

fu 360.000MPa


e2 75mm

p2 0mm

e1 40mm

M16-10.9 (DIN6914)

Type PreStressed

Grade 10.9

fu 1000.000MPa

As 157mm^2

d0 18mm

S 27mm

e 30mm

h head 10mm

h nut 13mm




Internal forces



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Internal forces

1

1

N1 100.000kN

Member resistance


A 1920mm^2

Npl,Rd 480.000kN


Anet 820mm^2

Nu,Rd 282.080kN


A 1500mm^2

Npl,Rd 320.455kN


Anet 1320mm^2

Nu,Rd 342.144kN


Shear resistance

Fp,Cd 109.900kN

ks 1.00

mi 0.30

n,diagonal1 1

Fs,Rd,diagonal1 26.376kN


Alfa 0.500

Fb,Rd 68.800kN


Alfa 0.741

Fb,Rd 69.120kN



Unity check


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a 5mm

La 25mm

NRd 26.376kN

Beta W 0.80

Fw,Rd 1039.230kN/m

Node: 4

Diagonal item: UPE200

Web connection

b 200mm

t 6mm

fy 275.000MPa

fu 430.000MPa


w 100mm

e1 27mm

p1 0mm


Gama M0 1.10

Gama M2 1.25

Gama Mb 1.25

Gama Ms 1.25

Gama Mw 1.25

Gusset plate

b 300mm

t 6mm

fy 235.000MPa

fu 360.000MPa


e2 100mm

p2 100mm

e1 40mm

M16-8.8 (DIN960)

Type Normal

Grade 8.8


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M16-8.8 (DIN960)

fu 800.000MPa

As 157mm^2

d0 18mm

S 24mm

e 27mm

h head 10mm

h nut 13mm




Internal forces


1

1

1

N1 100.000kN

Member resistance


A 2900mm^2

Npl,Rd 725.000kN


Anet 2033mm^2

A1 984mm^2

A2 1628mm^2

Zeta 0.645

Nu,Rd 629.514kN


A 1800mm^2

Npl,Rd 384.545kN


Anet 1584mm^2

Nu,Rd 410.573kN


Shear resistance

Lj 0mm

Beta Lf 1.000

Fv,Rd 60.288kN


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Alfa 0.500

Fb,Rd 41.280kN


Alfa 0.741

Fb,Rd 51.200kN



Unity check





a 3mm

La 132mm

NRd 82.560kN

Beta W 0.80

Fw,Rd 623.538kN/m

Node: 2

Diagonal item: UPE200

Web connection

b 200mm

t 6mm

fy 275.000MPa

fu 430.000MPa

Staggered bolt position

s 40mm

w 100mm

e1 27mm

p1 80mm


Gama M0 1.10

Gama M2 1.25

Gama Mb 1.25

Gama Ms 1.25

Gama Mw 1.25


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Gusset plate

b 160mm

t 6mm

fy 235.000MPa

fu 360.000MPa


e2 30mm

p2 100mm

e1 40mm

M16-8.8 (DIN960)

Type Normal

Grade 8.8

fu 800.000MPa

As 157mm^2

d0 18mm

S 24mm

e 27mm

h head 10mm

h nut 13mm




Internal forces


1

1

1

1

N1 100.000kN

Member resistance


A 2900mm^2

Npl,Rd 725.000kN


Anet 2066mm^2

A1 1008mm^2

A2 1628mm^2

Zeta 0.650

Nu,Rd 639.717kN


A 960mm^2

Npl,Rd 205.091kN


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Anet 768mm^2

Nu,Rd 199.066kN


Shear resistance

Lj 120mm

Beta Lf 1.000

Fv,Rd 60.288kN


Alfa 0.500

Fb,Rd 41.280kN


Alfa 0.741

Fb,Rd 51.200kN



Unity check





a 3mm

La 265mm

NRd 165.120kN

Beta W 0.80

Fw,Rd 623.538kN/m

4 x M16-8.8 (DIN960)Channel: UPE200

80 4027

50

100

50


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First Diagonal, Node 2

Gusset: th. 6mm4 x M16-8.8 (DIN960) 80 4040

30

100

30

Gusset plate Node 2

Whole connection Node 2


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3. TIMBER 3.1 PTR.06.01 – 01 : EC 5 Timber Code Check Description The unity checks in ULS and the deformation in SLS are compared with literature results. Project data See input file. Reference [1] Eurocode 5

Design of timber structures Part 1-1 : General rules and rules for buildings ENV 1995-1-1:1993 E

[2] Informationsdienst Holz Holzbau Handbuch Reihe 2 - Tragwerksplanung Eurocode 5 - Holzbauwerke Bemessungsgrundlagen und Beispiele 1995

Result Example 1.2.4. is considered. Ref.[2] EPW unet,fin - member 1 51 mm (1/207) 50.58 mm (1/209) ULS unity check member 1 1.02 1.02 See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PTR060101.epw Modules 3D Frame (PRS.11) EC5 Timber code check (PTR.06.01) Author CVL Calculation note


SCIA Software

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Relative deformation on member(s) with creep. Member extreme Values of kdef

Permanent : 0.60

Long term : 0.50

Medium term : 0.25

Short term : 0.00

Group of member(s) :1/3

Group of serviceability combi :1/2

memb cr.nr combi dx

[m]

ux

[mm]

uz

[mm]

fiy

[mrad]

1 1 2 5.278 -0.04

1/265242

-50.58

1/209 0.00

1 1 2 2.111 -0.03

1/414441

-30.05

1/351

2.93

1 1 2 8.445 -0.03

1/414441

-30.05

1/351

-2.93

2 1 2 5.278 -0.04

1/265241

-50.58|

1/209 -0.00

2 1 2 2.111 -0.03

1/414440

-30.05

1/351

2.93

2 1 2 8.445 -0.03

1/414442

-30.05

1/351

-2.93

3 2 2 12.209 -0.00 0.00 0.00

EUROCODE 5 - DESIGN OF TIMBER STRUCTURES, ENV 1995-1-1.

Tension paralel to the grain (5.1.2)

Compression paralel to the grain (5.1.4)

Bending (5.1.6a and 5.1.6b)

Shear (5.1.7.1)

Torsion (5.1.8)

Combined bending and axial tension (5.1.9a and 5.1.9b)

Combined bending and axial compression (5.1.10a and 5.1.10b)

Columns and beams (5.2.1e and 5.2.1f)

Detailed output, element extremes.

Macro :1 Member :1 L=10.556m CS : 1 - REC (160,550)

Material: BS14k

Service class : 1

gamma m =1.30 k m =0.70 (rectangle)

section=5.278m ult.combi=4 k mod = 0.90

Section check

N Vy Vz Mx My Mz

Design force -162.5[kN] 0.0[kN] 0.0[kN] 0.0[kNm] 137.8[kNm] 0.0[kNm]

Design stress -1.8[MPa] 0.0[MPa] 0.0[MPa] 0.0[MPa] 17.1[MPa] 0.0[MPa]

Limit stress 19.0[MPa] 1.9[MPa] 1.9[MPa] 1.9[MPa] 19.4[MPa] 19.4[MPa]

Unity check 0.10 0.00 0.00 0.00 0.88 0.00

Bending : 0.88 (5.1.6a)

Shear : 0.00 (5.1.7.1)

Compression + bending : 0.89 (5.1.10a)

Stability check

L0

m

k L

m

lam sigma krit

MPa

lam_rel beta c k

k crit

kc

Y 10.56 1.00 10.56 66.49 22.3 1.110 0.10 1.146 0.70

Z 10.56 0.33 3.44 74.51 17.8 1.244 0.10 1.311 0.58

LTBy 10.56 0.33 3.44 106.1 0.514 1.00

LTBz 10.56 0.33 3.44 4311.3 0.081 1.00

Compression (5.2.1) : 1.02 (5.2.1f)

Bending (5.2.2) : 1.02


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Maximal unity check = 1.02 The member does NOT satisfy the check !


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3.2 PTR.06.01 – 02 : EC 5 Timber Code Check Description The unity checks in ULS are compared with literature results. Project data See input file. Reference [1] Eurocode 5


[2] Informationsdienst Holz Holzbau Handbuch Reihe 2 - Tragwerksplanung Eurocode 5 - Holzbauwerke Bemessungsgrundlagen und Beispiele 1995

Result Example 1.3 is considered. Ref.[2] EPW ULS unity check member 1 0.95 0.96 ULS unity check member 2 0.95 0.92 See the chapter "Calculation note" for detailed output of ESA-Prima Win. Version ESA-Prima Win 3.20.03 Input file + calculation note PTR060102.epw Type of calculation 3D Frame (PRS.11) EC5 Timber code check (PTR.06.01) Author CVL Calculation note



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Shear (5.1.7.1)

Torsion (5.1.8)






Material: BS 11

Service class : 1



Section check

N Vy Vz Mx My Mz

Design force -86.4[kN] 0.0[kN] 31.5[kN] 0.0[kNm] -128.4[kNm] 0.0[kNm]

Design stress -0.7[MPa] 0.0[MPa] 0.4[MPa] 0.0[MPa] -12.9[MPa] 0.0[MPa]


Unity check 0.04 0.00 0.20 0.00 0.77 0.00

Bending : 0.77 (5.1.6a)

Shear : 0.20 (5.1.7.1)


Stability check

L0

m

k L

m

lam sigma krit

MPa

lam_rel beta c k

k crit

kc

Y 6.43 2.70 17.36 125.29 5.8 2.037 0.10 2.651 0.23

Z 6.43 1.00 6.43 85.67 12.4 1.393 0.10 1.515 0.47

LTBy 6.43 1.00 6.43 158.4 0.389 1.00

LTBz 6.43 1.00 6.43 996.7 0.155 1.00

Compression (5.2.1) : 0.96 (5.2.1f)

Bending (5.2.2) : 0.96

Maximal unity check = 0.96 - satisfies.


Material: BS 11

Service class : 1



Section check

N Vy Vz Mx My Mz




Unity check 0.16 0.00 0.00 0.00 0.31 0.00

Bending : 0.31 (5.1.6a)

Shear : 0.00 (5.1.7.1)


Stability check

L0

m

k L

m

lam sigma krit

MPa

lam_rel beta c k

k crit

kc

Y 5.83 1.00 5.83 77.68 15.0 1.263 0.10 1.336 0.56

Z 5.83 1.00 5.83 126.22 5.7 2.052 0.10 2.683 0.23

LTBy 5.83 1.00 5.83 122.1 0.443 1.00

LTBz 5.83 1.00 5.83 524.1 0.214 1.00

Compression (5.2.1) : 0.92 (5.2.1e)


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Bending (5.2.2) : 0.92



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3.3 PTR.06.01 – 03 : EC 5 Timber Code Check Description The unity checks in ULS are compared with literature results. Project data See input file. Reference [1] Eurocode 5


[2] Timber Engineering STEP 2 Design - Details ans structural systems First Edition, Centrum Hout, The Netherlands 1995

Result Example of a truss made from glulam is considered. Ref.[2], pp. E7/5 - E7/8 Ref.[2] EPW remarks ULS unity check macro 2 - top chord 0.70 0.66 In Ref.[2] the value for km is taken as 1.0, in EPW

km=0.7. ULS unity check macro 1 - bottom chord 0.73 0.63 In EPW the netto section is ignored for tension forces.

In EPW the moment is taken into account.

Version ESA-Prima Win 3.20.03 Input file + calculation note PTR060103.epw Modules 3D Frame (PRS.11) EC5 Timber code check (PTR.06.01) Author CVL Calculation note



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Shear (5.1.7.1)

Torsion (5.1.8)






Material: GL32h

Service class : 1



Section check

N Vy Vz Mx My Mz

Design force 273.2[kN] 0.0[kN] -0.0[kN] 0.0[kNm] 1.7[kNm] 0.0[kNm]

Design stress 8.5[MPa] 0.0[MPa] -0.0[MPa] 0.0[MPa] 1.6[MPa] 0.0[MPa]


Unity check 0.56 0.00 0.00 0.00 0.07 0.00

Bending : 0.07 (5.1.6a)

Tension + bending : 0.63 (5.1.9a)

Stability check

L0

m

k L

m

lam sigma krit

MPa

lam_rel beta c k

k crit

kc

Y 2.25 2.54 5.73 99.17 10.6 1.693 0.10 1.993 0.33

Z 2.25 1.00 2.25 48.71 44.1 0.832 0.10 0.863 0.92

LTB 2.25 1.00 2.25 473.3 0.260 1.00

Compression (5.2.1) : 0.07 (5.2.1f)

Bending (5.2.2) : 0.07



Material: GL32h

Service class : 1



Section check

N Vy Vz Mx My Mz




Unity check 0.34 0.00 0.00 0.00 0.24 0.00

Bending : 0.24 (5.1.6a)

Shear : 0.00 (5.1.7.1)


Stability check

L0

m

k L

m

lam sigma krit

MPa

lam_rel beta c k

k crit

kc

Y 2.29 1.00 2.29 39.58 66.8 0.676 0.10 0.737 0.97

Z 2.29 1.66 3.79 65.71 24.2 1.122 0.10 1.160 0.69

LTB 2.29 1.00 2.29 728.0 0.210 1.00

Compression (5.2.1) : 0.66 (5.2.1e)

Bending (5.2.2) : 0.24


Documents

ESA-Prima Win STEEL AND TIMBER DESIGN BENCHMARKSdocumentatie.nemetschek.ro/documentatie/7scia/tutoriale/en/STEEL... · ESA-Prima Win Steel and timber design benchmarks ... EXAMPLE