prepared during the TAS project: TAS - CORE- prepared during the TAS project: TAS Leonardo da Vinci

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Text of prepared during the TAS project: TAS - CORE- prepared during the TAS project: TAS Leonardo da Vinci

  • TALAT Lectures 2710

    Static Design Example

    82 pages

    Advanced Level

    prepared during the TAS project:

    TAS Leonardo da Vinci Training in Aluminium Alloy Structural Design

    Example developed with the “Mathcad” Software

    Date of Issue: 1999  EAA - European Aluminium Association

  • TALAT 2710 2

    2710 Static Design example Table of Contents (Active)

    2710 Static Design example........................................................................................... 2 1. Introduction.......................................................................................................................6

    2. Materials ............................................................................................................................7

    3. Loads ..................................................................................................................................7

    4. Load Combinations...........................................................................................................9

    5. Loads Effects ...................................................................................................................11 5.1. Loads per unit length and concentrated loads...........................................................................11 5.2 Finite element calculations ........................................................................................................12 5.3. Section forces for characteristic loads ......................................................................................14 5.4. Design moments, shear forces and deflections .........................................................................16

    6. Code Checking.................................................................................................................28 6.1 Column A ..................................................................................................................................28 6.2 Column B ..................................................................................................................................42 6.3 Column C ..................................................................................................................................55 6.4 Floor Beam D............................................................................................................................56 6.5 Roof Beam E .............................................................................................................................64 6.6 Roof Beam F .............................................................................................................................65 6.7 Welded Connections..................................................................................................................74

    Table of Contents (Complete) 1 INTRODUCTION

    1.1 Description 1.2 Sketches 1.3 References 1.4 S.I. units

    2 MATERIALS 2.1 Aluminium 2.2 Other materials

    3 LOADS 3.1 Permanent loads 3.2 Imposed loads 3.3 Environmental loads

    3.3.1 Snow loads 3.3.2 Wind loads

  • TALAT 2710 3

    4 LOAD COMBINATIONS 4.1 Ultimate limit state 4.2 Serviceability limit state

    5 LOAD EFFECTS

    5.1 Loads per unit length and concentrated loads 5.1.1 Permanent loads 5.1.2 Imposed loads, uniform distributed 5.1.3 Imposed loads, concentrated 5.1.4 Snow loads 5.1.5 Wind loads

    5.2 Finite element calculations

    5.2.0 Nodes and elements 5.2.1 Permanent loads 5.2.2 Imposed loads, uniformly distributed 5.2.3 Imposed loads, concentrated 5.2.4 Snow loads 5.2.4 Wind loads

    5.3 Section forces for characteristic loads

    5.3.1 Column A 5.3.2 Column B 5.3.3 Column C 5.3.4 Floor beam D 5.3.5 Floor beam E 5.3.5 Floor beam F

    5.4 Design moments, shear forces and deflections

    5.4.1 Column A 5.4.2 Column B 5.4.3 Column C 5.4.4 Floor beam D 5.4.5 Floor beam E 5.4.6 Floor beam F 5.4.7 Joint A-D 5.4.8 Joint B-D 5.4.9 Joint A-E 5.4.10 Joint B-E 5.4.11 Joint B-F 5.4.12 Joint F-C 5.4.13 Column base

  • TALAT 2710 4

    6 CODE CHECKING 6.1 Column A

    6.1.1 Dimensions and material properties 6.1.2 Internal moments and forces 6.1.3 Classification of the cross section in y-y-axis bending 6.1.4 Classification of the cross section in z-z-axis bending 6.1,5 Classification of the cross section in axial compression 6.1.6 Welds 6.1.7 Design resistance, y-y-axis bending 6.1.8 Design resistance, z-z-axis bending 6.1.9 Axial force resistance, y-y buckling 6.1.10 Axial force resistance, z-z axis buckling 6.1.11 Flexural buckling of beam-column 6.1.12 Lateral-torsional buckling between purlins 6.1.13 Design moment at column base 6.1.14 Deflections 6.1.15 Summary

    6.2 Column B

    6.2.1 Dimensions and material properties 6.2.2 Internal moments and forces 6.2.3 Classification of the cross section in y-y-axis bending 6.2.4 Classification of the cross section in z-z-axis bending 6.2,5 Classification of the cross section in axial compression 6.2.6 Welds 6.2.7 Design resistance, y-y-axis bending 6.2.8 Design resistance, z-z-axis bending 6.2.9 Axial force resistance, y-y buckling 6.2.10 Axial force resistance, z-z axis buckling 6.2.11 Flexural buckling of beam-column 6.2.12 Lateral-torsional buckling between purlins 6.2.13 Design moment at column base 6.2.14 Deflections 6.2.14 Summary

    6.3 Column C

    6.4 Floor Beam D

    6.4.1 Dimensions and material properties 6.4.2 Internal moments and forces 6.4.3 Classification of the cross section 6.4.4 Welds 6.4.5 Bending moment resistance 6.4.6 Bending resistance in a section with holes 6.4.7 Shear force resistance 6.4.8 Deflections 6.4.8 Summary

  • TALAT 2710 5

    6.5 Roof Beam E

    6.6 Roof Beam F

    6.6.1 Dimensions and material properties 6.6.2 Internal moments and forces 6.6.3 Classification of the cross section 6.6.4 Welds 6.6.5 Bending moment resistance 6.6.6 Lateral-torsional buckling between purlins 6.6.7 Bending resistance in a section with holes 6.6.8 Shear force resistance 6.6.9 Concentrated transverse force 6.6.10 Deflections 6.6.11 Summary

    6.7 Welded connections

    6.7.1 Weld properties 6.7.2 Longitudinal weld of floor beam D 6.7.3 Base of column B 6.7.4 Connection between floor beam D and column B

    Software The example is worked out using the MathCad software in which some symbols have special meanin according to the following

    x 50.6 mm. Assign value

    y 2.5 mm. Global assignment

    x y 53.1 mm= Evaluate expression

    a b Boolean equals

    0.5 Decimal point

    c 1 3 2( ) Vector

    d 2 4 3( ) Vector

    a c d.( ) Vectorize (multiply the elements in vector c with corresponding elements in d)

    a 2 12 6( )= Result

    Structure

    The structure was proposed by Steinar Lundberg, who also contributed with valuable suggestions. Part 1 to 6.6 was worked out by Torsten Höglund and 6.7 by Myriam Bouet-Griffon.

  • TALAT 2710 6

    1. Introduction

    1.1 Description The industrial building contains an administration part with offices, wardrobe, meeting rooms etc. and a fabrication hall. The load bearing system consist of frames standing at a distance of 5000 m

    In the serviceability limit state max. allowable deflection is 1/250 of span.

    1.2 Sketches

    1.3 References [1] ENV 1999-1-1. Eurocode 9 - Design of aluminium structures - Part 1-1: General rules. 1997

    [2] ENV 1991-2-1. Eurocode 1 - Basis of design and actions on structures - Part 2-1: Action on structures - Densities, self-weight and imposed loads. 1995

    [3] ENV 1991-2-3. Eurocode 1 - Basis of design and actions on structures - Part 2-3: Action on structures - Snow loads. 1995

    [4] ENV 1991-2-4. Eurocode 1 - Basis of design and actions on structures - Part 2-4: Action on structures - Wind loads. 1995

    [5] ENV 1991-1. Eurocode 1 - Basis of design and actions on structures - Part 1: Basis of design. 1994

    1.4 S.I. units kN 1000 N. MPa 1000000 Pa. kNm kN m. MPa 1

    N

    mm2 =

  • TALAT 2710 7

    2. Materials

    3. Loads

    2.1 Aluminium [1], 3.2.2 The extrusions are alloy EN AW-6082, temper T6

    The plates are EN AW-5083 temper H24

    Strength of aluminium alloys

    EN AW-6082 T6 EN AW-5083 H24

    f o 260 MPa. f u 310 MPa.

    f o 250 MPa. f u 340 MPa.

    [1], 5.1.1 The partial safety factor for the members

    The partial safety factor for welded connections

    Design values of material coefficients

    Modulus of elasticity Shear modulus Poisson´s ratio

    Coefficient of linear thermal expansion

    Density

    γ M1 1.10 γ M2 1.25

    [1], 6.1.1 γ Mw 1.25

    E 700000 MPa. G 27000 MPa. ν 0.3

    α T 23 10 6.

    ρ 2700 kg. m 3.

    2.2 Other materials Comment: Properties of any other materials to be filled in

    3.1 Permanent loads [3], ?? Permanent loads are self-weight of structure, insulation, surface materials and fixed equipment

    Permanent load on roof

    Permanent load on floor

    q´ p.roof 0.5 kN. m 2.

    q´ p.floor 0.7 kN. m 2.

    3.2 Imposed loads [2], 6.3.1 Office area => Category B

    q´ k.floor 3 kN. m 2.

    Uniform distributed load

    Concentrated load Q k.floor 2 kN.

    [2], 6.3.4 Roofs not accessible except for