Sofistik Manual

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BILFINGER BERGER AG Projekt Ny Svinesundsbro Postlda 44 60 SE-452 92 STRMSTAD

Substructures

0 General Descriptions Appendix 0-4:

SOFiSTiK-Manual STAR2 Konstruktionshandlingar

ORT DATUM Godknd

NAMN Knnedom

REV ANT NDRINGEN AVSER KONSTR GODKND DATUM UTARBETAT

TRAGWERKSPLANUNG INGENIEURBAU Mnchen o Mannheim o Kln o Hamburg TECHNISCHES BRO MANNHEIM CARL-REISS-PLATZ 1-5 D-68165 MANNHEIM TELEFON: +49 621 459-0 TELEFAX: +49 621 459-2219

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Konstruktionshandlingar

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433 605 / Deckblatt1374 / 2003-04-15

STAR2Statics of Beam StructureTheory of 2nd Order

Version 10.20

SOFiSTiK AG, Oberschleissheim, 2000

STAR2 Statics of Beam Structures

This manual is protected by copyright laws. No part of it may be translated, copied orreproduced, in any form or by any means, without written permission from SOFiSTiKAG. SOFiSTiK reserves the right to modify or to release new editions of this manual.

The manual and the program have been thoroughly checked for errors. However,SOFiSTiK does not claim that either one is completely error free. Errors and omissionsare corrected as soon as they are detected.The user of the program is solely responsible for the applications. We stronglyencourage the user to test the correctness of all calculations at least by randomsampling.

STAR2Statics of Beam Structures

i

1 Task Description. 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Theoretical Principles. 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1. Introduction 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Definitions 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Beam Elements. 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1. Introduction 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2. Transfer Matrices 23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3. Stiffness Matrix of the Entire Beam 26. . . . . . . . . . . . . . . . . . . . . . 2.3.4. Principle Axes 26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Springs, Trusses, Cables. 27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. Springs 27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Trusses 29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3. Cable Elements 29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Solution of the Complete System. 29. . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Limitations 29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Special Topics. 210. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.1. Predeformations 210. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.2. Creep and Shrinkage 210. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.3. Prestress 211. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.4. Shear Deformations 211. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.5. Design 212. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8. Literature. 212. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Input Description. 31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1. Input Language 31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Input Records 31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. ECHO Control of the Output Extent 34. . . . . . . . . . . . . . . . . . . . 3.4. CTRL Parameters Controlling the Analysis Method 36. . . . . . . . 3.5. GRP Selection of an Element Group 39. . . . . . . . . . . . . . . . . . . . 3.6. STEX External Stiffness 313. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7. INFL Definition of an Influence Line Loadcase 314. . . . . . . . . . . 3.8. LC Definition of a Loadcase 315. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9. Definiton of Beam Loads on Beam Groups. 317. . . . . . . . . . . . . . . . . 3.10. NL Nodal Load 319. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11. SL Point Load on a Beam 320. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12. GSL Point Load on a Beam Group 322. . . . . . . . . . . . . . . . . . . . . . 3.13. UL Uniform Load on a Beam 325. . . . . . . . . . . . . . . . . . . . . . . . . . 3.14. GUL Uniform Load on a Beam Group 326. . . . . . . . . . . . . . . . . . . 3.15. VL Linearly Varying on a Beam 327. . . . . . . . . . . . . . . . . . . . . . . . .


ii

3.16. GVL Linearly Varying Load on a Beam 330. . . . . . . . . . . . . . . . . . 3.17. CL Loading of Cables 333. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18. TL Loading of Trusses 334. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19. LCC Importing Loads from another Loadcase 335. . . . . . . . . . . . 3.20. LV Generating Loads from Results of a Loadcase 336. . . . . . . . . . 3.21. REIN Specification for Determining Reinforcement 339. . . . . . . 3.22. DESI Reinforced Concrete Design, Bending, Axial Force 345. . . 3.23. NSTR Nonlinear Stress and Strain 351. . . . . . . . . . . . . . . . . . . . .

4 Output Description. 41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.1. Load Assembly 41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Output of the Structure 42. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Results 42. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Output during Iterations 42. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Convergence Criteria 43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6. Design Output 43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7. Stiffness Computation 44. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Examples 51. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1. Training Example of Cantilever Column. 51. . . . . . . . . . . . . . . . . . . 5.2. Wind Frame with Cable Diagonals. 57. . . . . . . . . . . . . . . . . . . . . . . . 5.3. Girder. 510. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Threedimensional Frame. 513. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Construction Stages. 522. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1. Introduction 522. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2. Single Span Beam with Auxiliary Support. 522. . . . . . . . . . . . . . . . . 5.5.3. Internal Force Redistribution due to Creep. 525. . . . . . . . . . . . . . . 5.6. Nonlinear Material Behaviour. 532. . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1. Precast Column 532. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2. Steel Frame According to Plastic Zones Theory. 538. . . . . . . . . . . 5.7. Examples in the Internet. 545. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


11Version 10.20

1 Task Description.The programs of the STARfamily enable the computation of the internal

forces in any threedimensional beam structure by 2nd or 3rd order theory

taking into consideration shear deformations as well as various nonlinear

material effects.

STAR1 3D version without design

STAR2 2D version with design

STAR3 3D version with design

Effects of 3rd order theory are available for truss and cable elements.

The static system must be described by the user in terms of discrete elements,

and the corresponding database must be defined by the generation program

GENF.

Available elements are:

Beam element with straight axis and piecewise constant arbitrary

cross section. Analysis by 2nd order theory with consideration of the

shear deformation. Consideration of nonlinear material behaviour

through iteration.

Spring element such as support spring or nodecoupling spring; non

linear effects include slippage, failure, yielding and friction.

Truss element with prestress

Cable element with prestress (only tensile force is possible)

Distributed support element for elastic support of beams

Couplings for special effects like eccentric beam links, rigid links be

tween nodes etc.

Disk or plate elements as well as solid elements, which can be defined by

GENF, can not be processed by STAR2. The foundation definitions for pile el

ements are not available in STAR2 either.

Concentrated forces or moments may act on the nodes, while support transla

tions or rotations can be defined at any support. The beam elements can be

loaded with point loads at any position in the form of eccentrically acting


Version 10.2012

forces, moments, jumps in displacement or rotation, as well as with linearly

varying loads in the form of forces, moments, strains, curvatures or tempera

ture strains. Unintentional eccentricities of linear, quadratic or cubic vari

ation can be defined for the analysis with 2nd order theory. In addition, creep

deformations or unintentional eccentricities can be generated from already

analysed loadcases. Prestress can be considered by specifying an MV0 or NV0

distribution.

The analysis of frames by 2nd order theory with consideration of material be

haviour is a demanding engineering task. The user of STAR2 should therefore

accumulate experience from simple examples, before attempting to take on

more complicated structures. A check of the results by offhand engineering

calculations is indispensable.


21Version 10.20

2 Theoretical Principles.

2.1. Introduction

The static problem is solved by the deformation method. In any iterative tech

nique, nonlinear properties must be decomposed into several individual lin

ear steps by an iterative method. A closed form solution can be computed by

2nd order theory for such a linear step, if the stiffness and the axial force are

assumed constant.

2.2. Definitions

The program uses exclusively righthanded coordinate systems in accord

ance to DIN 1080 for the description of force, moment, displacement or

rotationvectors. The threedimensional global system of coordinates serves

in defining the nodal coordinates and displacements or rotations.

Each beam possesses a local coordinate system, which is defined by GENF.

Beam deformations and section forces are output in this coordinate system.

When confusion is possible, the local xyzsystem is also designated by S12.

Thus, the essential magnitudes for primary bending are:

Cross section values AZ, IY

Forces, displacements, moments Z or 2

Rotations, curvatures Y or 1

Section forces VZ, MY

and for secondary bending:

Cross section values AY, IZ

Forces, displacements, moments Y or 1

Rotations, curvatures Z or 2

Section forces VY, MZ

Section forces are positive if they act in the positive directions of the axes at

an end cross section (when moving in the longitudinal direction of the beam).


Version 10.2022

System of coordinates

2.3. Beam Elements.

2.3.1. Introduction

The individual beam elements are analysed by the reduction method (method

of transfer matrices) under the assumption of piecewise constant axial force.

The following assumptions are made as well:

The beam axis is a straight line. Broken or curved beams must be replaced

by several straight beam segments. The beam axis coincides with the centro

baric axis. The stiffnesses and the axial force for each particular segment are

averaged from their end values. Therefore, in case of highly varying values,

one should be careful to define a sufficient number of segments (usually 5 to

10).

The theory of 2nd order satisfies the equilibrium conditions for the deformed

structure. The orientation of the beam axes (transverse force instead of shear

force) and the forces (conservative loading) remain unaltered. By contrast,

the theory of 3rd order considers large deformations, which alter the orienta

tion of the local system of coordinates. The 3rd order theory is not yet implem

ented for beam elements. Thus, by 3rd order theory all beam elements are

handled in the same ways as by 2nd order theory.


23Version 10.20

The stiffnesses can be modified due to the material by design only (input re

cord NSTR). They remain constant within an iteration step, whereas without

NSTR they remain constant during the entire analysis.

Torsion according to St. Venant (no lateral warping of the cross section).

Warping and torsion according to theory of 2nd order are not implemented in

STAR2.

The effect of shear deformations due to shear force can be taken into consider

ation.

A deviation between the shear centers and the center of gravity can be ulti

mately considered as a rotation of the principal axes with respect to the sys

tem of coordinates of the beam.

2.3.2. Transfer Matrices

Each beam is partitioned into n segments defined by n+1 sections. The status

magnitudes are collected into a vector z:

z

v x,d x,v z,v y,

N,

MT,

d y,d z,

MY,

MZ,

VZ

VY

Components 1 and 2 represent the axial force, 3 and 4 the torsion, 58 the pri

mary bending and 912 the secondary bending. The transfer equation from

section i to section i+1 is given by:

zi1Ui zip

i

where Ui stands for the transfer matrix of the beam segment i and pi for the

component of the loading acting on segment i. The transfer matrix is as

sembled under the familiar assumptions. Its components are:

Normal axial force:

UN1

0

CN

1mitCN 1

2 1EAi

1EAi1

Torsion:

UT1

0

CT

1mitCT 1

2 1GITi

1GITi1


Version 10.2024

Primary bending:

UP

1

0

0

0

C1

C0

C4CH0

CHC2CHC1

C0

0

CHC3CHC2

C1

1

where

CH 12 1EIYi

1EIYi1

CSH 12 1GAZi

1GAZi1

KV CSH

CH l2

(CH N) l

AK 1 2 KV

C0 = COS AK

C1 = l SIN AK /

C2 = l2 ( COS AK 1 ) / 2

C3 = l3 ( SIN AK AK ) / 3

C4 = SIN AK / l

Secondary bending:

US

1

0

0

0

C1

C0

C4CQ0

CQC2CQC1

C0

0

CQC3CQC2

C1

1

with similar constants.

The components of the loading vector p are formed from


25Version 10.20

px,dpx = constant and linear component of a load in the

axial direction

ex,dex = constant and linear component of a strain in the

axial direction

mx,dmx = constant and linear component of a torsional load

py,dpy = constant and linear component of a lateral load

in the secondary bending direction

pz,dpz = constant and linear component of a lateral load

in the primary bending direction

my,dmy = constant and linear component of a moment load

in the primary bending direction

mz,dmz = constant and linear component of a moment load

in the secondary bending direction

ky,dky,d2ky,d3ky = Components of the cubic variation

of a compulsory curvature due to

temperature and prestress in the

primary bending direction

kz,dkz,d2kz,d3kz = Components of the cubic variation

of a compulsory curvature due to

temperature and prestress in the

secondary bending direction

uy,duy,d2uy,d3uy = Components of the cubic variation

of an initial deformation in the

secondary bending direction

uz,duz,d2uz,d3uz = Components of the cubic variation

of an initial deformation in the

primary bending direction

With these loads the resulting loading vector components are:

p1 = CN l2 ( px/2 + dpx/6 ) + l ( ex + dex/2 )

p2 = l ( px + dpx/2 )

p3 = CT l2 ( mx/2 + dmx/6 )

p4 = l ( mx + dmx/2 )

p5 = CH ( C5py + C6dpy/l + C3mz C5dmz/l) C2ky


Version 10.2026

C3dky/l + (C1/l1)duz (2C2/l2+1)d2uz (6C3/l3+1)d3uz

p6 = CH (C3py + C5dpy/l + C2mz + C3dmz/l) +

+ C1ky C2dky/l

+ (C01)/lduz + 2(C11)/l2d2uz (6C2/l3+3l)d3uz

p7 = C2py C3dpy/l C1mz + C2dmz/l

+ (C01)/CNky (C1/l1)/CNdky/l

C4/CN/lduz + 2(C01)/l2d2uz + 6(C1l)/l3d3uz

p8 = lpy ldpy/2

with the additional constants

C5 = ( COS AK 1 + AK2/2) (l/AK)4

C6 = ( SIN AK AK + AK3/6) (l/AK)5

Similar expressions are obtained for the secondary bending (p9 p12).

For the axial force stressing (px) and the torsional loading (mx) STAR2 sim

plifies the load components by an average load value at each section.

2.3.3. Stiffness Matrix of the Entire Beam

By continuous transfer of the status magnitudes and incorporation of the dis

continuities (concentrated load, moment etc.), one obtains a relationship be

tween the state magnitudes at the beginning of the beam and those at its end.

zn1Us z1 rs

This relationship can be used as a linear system of equations for the computa

tion of the stiffness matrix. The matrix obtained this way can now be sub

jected to any modifications caused by hingedjoints and to a transformation

into the global system of coordinates.

2.3.4. Principle Axes

The separate analysis in the primary and secondary direction is correct only

when the axes y and z are the principal axes of the cross section. If this condi

tion is not satisfied, the deformations are not computed correctly in case of

statically determinate structures, whereas in case of statically indetermi

nate structures the section forces are wrong too. STAR2 transforms all the


27Version 10.20

loads and the section forces of three dimensional structures into the direc

tions of the principal axes. Variable rotation along the length of a beam can

not be considered however. This transformation can be suppressed in special

cases. The principal axes are always taken into consideration correctly dur

ing design, when biaxial bending is active.

2.4. Springs, Trusses, Cables.

2.4.1. Springs

Spring elements model structural parts by a simplified force displacement

relationship. This is usually expressed by means of a spring constant in the

form of a linear equation:

P c u

The spring is defined by its direction ( DX, DY, DZ ) and the spring constants.

The direction can be determined as the difference of two nodes (N2 NA), or

it can be specified explicitly. Support springs must be provided with a direc

tion (see GENF).

The element implemented herein allows for the following nonlinear effects:

Prestress (linear effect)

Failure

Yield

Friction with cohesion

Slip

Forcedisplacement diagrams of springs

Geometrically nonlinear effects are not possible for springs.


Version 10.2028

A prestress shifts the corresponding effects and it always generates a loading

upon the structure. A prestressed spring is relaxed in the absence of external

loading or compulsion. The nonlinear effects apply to rotational springs as

well as lateral springs too. Friction can be defined by a lateral spring. The

force components normal to the springs direction of action are equal to the

product of the displacement components in the lateral direction by the lateral

spring constants. This force is at most equal to the product of the force in the

normal direction by the friction coefficient plus the cohesion. If the normally

oriented spring is eliminated, the lateral spring is automatically eliminated

too.

All spring nonlinearities are activated only during a nonlinear analysis. To

this end, a value for the number of iterations must be specified by the analysis

methods in CTRL.

Upon such request (see input record CTRL) either the force corresponding to

a prescribed displacement value will be determined within an iteration

(strain control a) or the displacement for a prescribed force (stress control b).

A secant stiffness results from the values computed in this way.

Iteration methods a / b

Method a should be used by structures, which soften as they are loaded,

whereas method b should be used for stiffening structural members.

The user must take care so that the system does not become unstable in any

step of the iteration through failure of springs or cables. This can happen, for

instance,if one defines additional springs with small stiffness, resulting to a

small remaining stiffness after the main springs failure. This stiffness

should not be less than the stiffness of the main spring divided by 10000.


29Version 10.20

2.4.2. Trusses

Trusses can be analysed by 2nd or 3rd order theory. 2nd order theory is con

sidered as described in /9/; nodal deformations are additionally taken into ac

count in the construction of the element matrices by 3rd order theory.

2.4.3. Cable Elements

Cable elements are handled similarly to trusses. Cables can not sustain any

compressive forces. 2nd and 3rd order theories are applicable as for trusses.

A correct computation is generally possible through several iterations only.

In order to analyse a cable structure, which is usually stable only under load

ing, by 1st order theory too, it is assumed that the elements are subjected to

a small prestress.

2.5. Solution of the Complete System.

A global stiffness matrix is obtained by adding all the individual element stiff

nesses; after incorporating the geometric boundary conditions, the displace

ments and thus the section forces get computed. If nonlinear springs or a re

positioning of the axial force are present, the input of a number of iterations

within the defined limits will force the whole process to be repeated by updat

ing the secant stiffnesses until a solution is obtained.

2.6. Limitations

The number of loadcases is limited to 999.

The number of nodes, beams, sections or loads is only limited by the amount

of the available disk space. 5 digits are usually reserved for the output of their

numbers, thus values above 99999 should not be used.

STAR2 works with double precision. Despite that the following points should

be considered:

1. The stiffness EI/l3 of neighbouring beam elements may not differ

by a factor larger than 105.

2. Beam theory is valid only for structural members, the length of

which is at least twice their height. The length of each individual el

ement should not be smaller than the height of the cross section used.

3. Artificially rigid elements can and must be defined as couplings.


Version 10.20210

If these criteria are not met, reaction forces will arise on free nodes.

STAR2 sets a constant stiffness for each segment. The buckling length coeffi

cient after Petersen /6/ p.489 reaches a maximum of 1.22 for a conical beamunder its own weight compared to 1.12 for a prismatic beam (8% error). If the

dimensions are changed by just 10% (IValue by 27.1%), reaches 1.14, corresponding to an error of about 2%.

2.7. Special Topics.

2.7.1. Predeformations

Initial deformations (unintentional eccentricities) are deviations of the

actual beam axis from the ideal beam axis. These are independent of self

arising deformations. They have no effect on an analysis by 1st order theory.

The following variations are possible:

Linear inclination (e.g. DIN 1045 Sec. 15.8.2)

Input in the form of a point load at the column head.

Arbitrary piecewise linear variation.

Input in the form of distributed load.

Arbitrary shape related to the buckling mode (e.g. DIN 1045 17.4).

Defined either by several positions along the column, connected by a

cubic spline, or by the bending line from an already analysed loadcase.

2.7.2. Creep and Shrinkage

DIN 1045 requires an estimation of the effects of creep and shrinkage accord

ing to Section 17.4, when the slenderness of the compressed member is

greater than 70 for immovable or 45 for movable structures and at the same

time the eccentricity e/d is smaller than 2.

Creep deformations are computed for the permanent loads acting in the ser

vice state as well as for any prescribed permanent beam deflections and ec

centricities including the unintentional ones.

An approximate method using an increased unintentional eccentricity is de

scribed in note 220 of DAfSt.

STAR2, however, can perform a more accurate check. A loadcase is built for

this purpose from the loads that cause creep. The resulting deformations,


211Version 10.20

multiplied by a creep factor, can be used either as initial deformations or as

curvature loads during a subsequent run. The same method allows the con

sideration of construction phases.

2.7.3. Prestress

A fixed prestress can be specified in GENF for springs and trusses. This acts

by every loadcase and generates corresponding stresses. A prestress for each

individual loadcase can be defined in STAR2 as well.

A statically determinate component of the prestress (NV0,MV0) for each

loadcase can be defined separately for bending beams. Then, depending on

the number of parameters, any variation of these values from constant to

cubic can be assumed along the beam axis. The effect of prestress is twofold.

On one hand, the section forces are modified by the corresponding prestress

values, and on the other hand, deformations result from prestress, which in

turn lead to compulsory forces in cases of statically indeterminate structures.

Prestress is considered differently for cables and for beam elements. A cable

or a truss can be only prestressed through the external system. Therefore, the

prestress is then analysed like a temperature stressing caused by a strain im

posed on the element. Forces are generated within the elements of an unde

formable structure, whereas in deformable structures the prestress deterio

rates due to selfarising deformations. If one wants to receive a defined

prestress, one must employ therefore an element with very small strain stif

fness.

For beams, by contrast, prestress is defined as an independent state of stress

(prestressed concrete). Since the prestress is imposed on the element itself,

the resulting forces on freely deformable beams are the input section forces

themselves. If the deformation is hindered, compulsory forces arise. In the li

miting case, e.g. if a beam is prevented from deforming in the longitudinal

direction, the resulting axial force is null, because the forces imposed by the

prestressing steel are resisted by the support instead of the beam.

2.7.4. Shear Deformations

The shear deformation can be also taken into account by the beam elements.

The program AQUA defines the standard shear areas for some cross sections.

The internal force variation in statically indeterminate structures may differ

from the one obtained by pure bending theory, if shear deformation is taken

into consideration.


Version 10.20212

2.7.5. Design

Since the design or stiffness computation by AQB must be activated for an

iteration with nonlinear material behaviour after any static analysis, the

most important records of AQB are also available in STAR2. These are:

CTRL General parameter

REIN Special parameter for ULTI and NSTR

ULTI Reinforcement computation

NSTR Strain state

The complete theory for these records can be found in the AQB manual. Only

the descriptions of the input records are given in this manual.

If not all of the beams are to be dimensioned in the same way, this can be

avoided by an external iteration via the record processor PS.

2.8. Literature.

/1/ Th.Fink, J.St. Kreutz

Berechnungsverfahren nach Fliezonentheorie II. Ordnung fr

rumliche Rahmensysteme aus metallischen Werkstoffen.

Der Bauingenieur 57 (1982), S. 297302

/2/ R. Uhrig

Zur Berechnung der Schnittkrfte in Stabtragwerken nach

Theorie II. Ordnung, insbesondere der Verzweigungslasten unter

Bercksichtigung der Schubdeformation.

Der Stahlbau (2/1981), S. 3942

/3/ V.Gensichen

Zum Ansatz ungnstiger Vorverformungen bei der Berechnung

ebener Stabwerke nach der Elastizittstheorie II. Ordnung


/4/ E.Grasser, K.Kordina, U.Quast

Bemessung von Beton und Stahlbetonbauteilen

Deutscher Ausschu fr Stahlbeton, Heft 220

Wilhelm Ernst & Sohn, Berlin 1977

/5/ D.Hosser

Tragfhigkeit und Zuverlssigkeit von Stahlbetondruckgliedern

Mitteilungen aus dem Institut fr Massivbau der TH Darmstadt

Heft 28, Wilhelm Ernst&Sohn 1978


213Version 10.20

/6/ Chr. Petersen

Statik und Stabilitt der Baukonstruktionen

Vieweg & Sohn, Braunschweig, 1980

/7/ H.Werner, J.Stieda, C.Katz, K.Axhausen

TOP Benutzer und DVHandbuch.

CADBericht KfkCAD67, Kernforschungszentrum Karlsruhe,

1978

/8/ H.Werner

Rechnerorientierte Nachweise an schlanken Massivbauwerken

Beton und Stahlbetonbau 73 (1978),S. 263268

/9/ S. Palkowski

Einige Probleme der statischen Nachweise von

Seilnetzkonstruktionen



Version 10.20214


31Version 10.20

3 Input Description.

3.1. Input Language

The input is made in the CADINP language (see general manual SOFiSTiK:

FEA / STRUCTURAL Installation and Basics).

3.2. Input Records

The input is organised in blocks terminated by the record ENDE. A particular

structure or particular loadcases can be analysed within each block. The pro

gram stops, when an empty block is found:

END

END

Only one loadcase per block must be analysed in case of nonlinear analysis.

The program recognises three operation modes controlled by the extent of the

input.

a. Load generation

During a load generation run the loads are solely read, checked and stored.

The loads generated in such a run can be used as a whole during a subsequent

run or block. A generation run results from an input block with loads but

without any record CTRL.

b. Analysis run

An analysis run is the usual option by input of a record CTRL and loads.

c. Restart

A Restart run can be used to analyse again loadcases defined in the last block

or run with stiffnesses modified after design. A Restart run results from an

input block without any loads.

The following records are defined:


Version 10.2032

Record Items

ECHO

CTRL

GRP

STEX

OPT VAL SELE

OPT VAL

NO VAL STIF SECT SC PRES FACS FACG CS

NAME

INFL

LC

NL

SL

GSL

UL

GUL

VL

GVL

CL

TL

LCC

LV

NO TITL

NO FACT DLX DLY DLZ TITL

NO TYPE P1 P2 P3 PF

NO TYPE P A DY DZ REF KTYP

NO TYPE P A DY DZ REF KTYP NOE

STEP

NO TYPE P A L REF

NO TYPE P A L REF NOE STEP

NO TYPE PA PE A L DYA DZA DYE

DZE REF

NO TYPE PA PE A L DYA DZA DYE

DZE REF NOE STEP

NO TYPE P

NO TYPE P

NO FACT FROM TO INC NFRO NTO NINC TFRO

TTO TINC CFRO CTO CINC

NO PHI EPS FACV FROM TO INC STIF CSMI

CSMA KTYP

*REIN

*ULTI

*NSTR

AM1 AM2 AM3 ED AMAX EGRE NGRE ZGRP TANA

MOD BMOD LCR P7 P8 P9 P10 P11 P12

MOD BMOD STAT SC1 SC2 SS1 SS2 C1 C2

S1 S2 Z1 Z2 KSV KSB SMOD T01 T02

T03 TVS KTAU TTOL

KMOD KSV KSB KMIN KMAX ALPH FMAX SIGS CRAC

CW BB HMAX CW

The records marked by * control the design and the stiffness computation.

They are also included in AQB.

The record STEX can be used only for substructuring techniques in combina

tion with HASE.


33Version 10.20

The records HEAD, END and PAGE are described in the general manual SO

FiSTiK: FEA / STRUCTURAL Installation and Basics.

The description of the single records follows.


Version 10.2034

3.3. ECHO Control of the Output

Extent

ECHO

Item Description Dimension Default

OPT A literal from the following list:

NODE Node coordinates, constraints

BEAM Beams (structure)

SPRI Spring elements (structures)

BOUN Distributed supported ele

ments (structure)

SECT Cross section values (as in

AQUA)

MAT Material constants (as in

AQUA)

LOAD Loads

FORC Internal forces and moments

DEFO Beam deformations

BDEF Nodal displacements

REAC Support reactions

REIN Reinforcements

NSTR Strains and stiffnesses

STEP Output of all iterations

FULL Set all options

LIT FULL

VAL Value of output option

NO no output

YES regular output

FULL extensive output

EXTR extreme output

LIT FULL

The default for options NODE, BEAM, SPRI, BOUN, MAT and SECT as well

as BDEF is NO, for FORC FULL, and for all others YES.

For the effects of all options refer to Chapter 4 (Output description).


35Version 10.20

The option STEP controls the output during nonlinear analyses and its de

fault value is 99. The last iteration is always printed. A negative value for this

option suppresses the output of the initial linear analysis.


Version 10.2036

3.4. CTRL Parameters Controlling

the Analysis Method

CTRL


OPT Control option LIT I

VAL Option value /LIT *

CTRL prescribes control parameters of the analysis. The input of a CTRL re

cord with the theory to be used is mandatory. The following particular options

are available:

LIT Description Value De

fault

I 1st order theory (strain controlled) nIter 1

IB 1st order theory (stress controlled) nIter 1

II 2nd order theory (strain controlled) nIter 1

IIB 2nd order theory (stress controlled) nIter 1

III 3rd order theory (strain controlled) nIter 1

IIIB 3rd order theory (stress controlled) nIter 1

GEN Tolerance for forces and displacements in 0/0 1.0

GENM Tolerance for moments and rotations in 0/0 1.0

AFIX Handling of freely movable degrees of freedom 1

0 Degrees of freedom which can move

freely result into an error

1 Degrees of freedom which are almost

movable are considered movable

2 Degrees of freedom which are movable

get subsequently fixed after a warning

3 Almost movable degrees of freedom get

subsequently fixed in a similar manner

STYP Handling of cable elements LIT CABL

CABL Cables have tension only

TRUS Cables can sustain compression


37Version 10.20

GDIV Group divisor *

Temporary different value for group subdivision

When no CTRL record is input, only the loads are stored, or a restart of the

previous analysis takes place in case there arent any loads.

An analysis by 2nd or 3rd order theory requires an initial analysis by 1st order

theory in order to compute the axial loads. Therefore, except for a restart

upon a structure already analysed by 1st order theory, such an analysis must

precede any higher order analysis.

3rd order theory is only considered for truss and cable elements; the difference

between II and IIB as well as between III and IIIB is similarly of importance

only for spring, truss and cable elements.

The input of CTRL I or Ib and ITER greater than 1 results in an analysis with

nonlinear springs by 1st order theory.

The entry for AFIX controls the programs behaviour, when linearly depend

ent degrees of freedom are encountered. Such examples are the continuous

beam, which does not possess any constraints for torsional or axial force, and

any section forces eliminated by hinges or couplings. Degrees of freedom

which do not possess any stiffness, e.g. rotations of a pure truss, are always

suppressed and therefore, they can not be affected by AFIX.

The input parameter STYP is currently used for cable structures in order to

prevent the occurrence of structural instability during iteration. If TRUS is

input, the results must be manually checked at the end of the analysis, to

make sure that all cables carry only tensional forces. A Restart with STYP

CABL must follow otherwise.

In addition, the following options from AQB are available for the design/

strain computation:

AXIA Type of bending

1 = uniaxial bending (VY=MZ=0)

(default for plane structures)

2 = biaxial bending,

boundary stresses in system of principal axes

(default for threedimensional structures)

VRED Maximum allowed inclination for the conversion of shear forces

at haunches. (Default: 0.3333, 0. = no conversion)


Version 10.2038

SMOO Rounding of moments

0 = no rounding

1 = primary bending only (default)

2 = primary and secondary bending

+128 = no use of reference system

+256 = no shear force conversion by inclined centrobaric axis

+512 = no moment conversion by inclined centrobaric axis

Rounding of the moments takes place only when a support

boundary has been defined in GENF. The shear force at the

support is zero.

INTE Axial stress / shear stress interaction

0 = no consideration

1 = linear reduction

2 = theoretical solution according to Prandtl (default)

3 = shear stresses of prime importance

+4 = additional nonlinear axial strain

VIIA Application of prestress in State II

(for very experienced users only, see AQB manual)

VM Factor with which the axial forces due to shear force from Eqn.

(18) of the AQB manual must be taken up by longitudinal rein

forcement (shift)

0.0 = no consideration (default thus far)

> 0 = factor for value from truss analogy (EC2)

< 0 = factor for cross section height as shift (DIN)

ETOL Tolerance for the computation of the internal section forces

(0.0001)

IMAX Maximum number of AQB iterations (30)

AMAX Maximum LineSearch factor (1000)

AGEN Relative LineSearch tolerance (0.01)

(no input necessary in general)


39Version 10.20

3.5. GRP Selection of an Element

Group

GRP


NO

VAL

STIF

SECT

SC

Group number

Selection

OFF do not use

YES use

FULL use and print results

Stiffness parameters

1 consider rotation of principal

axes

0 do not consider rotation

LIN1 1 + not designed group

LIN0 0 + not designed group

Cross section values

BRUT effective gross cross section

TOTA total cross section

DESI design cross section (1/mmultiple)

Shear centre

NONE do not consider

YES consider by loads only

FULL consider fully

LIT

LIT

LIT

FULL

1

*

FULL


Version 10.20310

Item DefaultDimensionDescription

PRES

FACS

FACG

CS

Prestress loading

FULL consider all effects

NOTO no torsional components

REST restraint components only

UNRE unrestraint components only

URNT UNRE + NOTO

Factor of linear stiffnesses

Dead weight factor

Construction stage number

LIT

FULL

1.0

1.0

The group number of an element is obtained by dividing its element number

by the group divisor (GENF SYST record, e.g.: 1000). The default is the group

selection of the previous analysis run or input block. In the absence of input

all the elements are used. In the case of explicit input only the specified

groups get activated.

Each particular group can contain different directions regarding the special

effects. This is especially meant for controlling inaccuracies in the input or

the modelling in special cases. The user himself must decide whether this is

permissible.

For the cross section values the user has a choice between the total cross sec

tion and the cooperating cross section (default). The area in both cases is sub

stituted by the value of the total cross section.

Some codes (e.g. DIN 18800) require by the analysis with 2nd order theory the

reduction of the stiffnesses by the material safety factor. For all load cases

with a load factor greater than 1.0 the default is DESI, for all other it is BRUT.

For nonlinear analysis with NSTR this input has only minor effects.

In the analysis with rotation of the principal axes the rotation angle must be

constant along the beam. Multiple beams should eventually be defined each

time with prismatic cross section.

The factors FACS and FACG act upon the stiffnesses and the dead weight of

the elements of this group. FACG acts only as additional factor to the values

DLX through DLZ of the LC record.


311Version 10.20

Attention:

Only one group selection can be used inside a block for several loadcases.

When no group selection is found, the old one remains in effect along with all

its parameters!


313Version 10.20

3.6. STEX External Stiffness

STEX


NAME Name of the external stiffness LIT24 *

A complete external stiffness can be added by STEX. External stiffnesses are

generated for the time being only by the program HASE for the halfspace

(stiffness coefficient method) and for substructures.

The project name is the default value for NAME. The mere input of STEX

(without name) usually suffices.


Version 10.20314

3.7. INFL Definition of an

Influence Line Loadcase

INFL


NO

TITL

Loadcase number (1999)

Title of influence line loadcase

LIT24

1

An influence line loadcase is defined by the input of INFL. Any INFLrecord

must be followed by at least one load card describing the type of the influence

line. A separate loadcase INFL must be defined for each point of interest and

each section force. Only the displacements (=influence line) of the structure

are computed and output for an INFLloadcase. Computation by 2nd order

theory is not possible.

Influence line Required loading e.g.

Moment

Axial or shear force

Support reaction

Displacement

Unit rotation

Unit displacement

Nodal displacement

Unit load

SL D.

SL W.

NL W.

SL P.

Example for the influence line of the moment MY at beam 1001 at position

2 by loadcase number 91:

INFL 91 SL 1001 D1 1.0 A 2.0

This concept can be used to compute very particular influence lines too. If e.g.

the influence line for the upper marginal stress of a cross section = N/A M/W is sought, it can be found by the following input (area A is #10, section

modulus W is #11):

INFL 92 SL 1001 WS 1.0/#10 2.0 SL 1001 D1 1.0/#11 2.0


315Version 10.20

3.8. LC Definition of a Loadcase

LC


NO

FACT

DLX

DLY

DLZ

TITL

Loadcase number (1999)

Factor for all loads of type P (forces) and

M (moments) of the loadcase

Factor dead weight load in xdirection

Factor dead weight load in ydirection

Factor dead weight load in zdirection

Title of loadcase

LIT24

1

1

0

0

0

The input of LC results in the analysis or the definition of the corresponding

loadcase. If the LCinput contains only a global factor and if the LCrecord

is not followed by any loads, the old loads including the possibly defined dead

weight are imported with this factor. If some loads do follow the LCrecord

or if a factor of the dead weight is entered, all other loads that were stored by

the same loadcase number are first deleted.

In case of restart of a nonlinear calculation with NSTR no record LC must

be indicated since otherwise the nonlinear strains are extinguished.

STAR2 analyses all loadcases for which LC or INFLinput was generated

in some block. For nonlinear calculations it is sensible to analyse each time

one loadcase per block only.

FACT affects the loads only temporarily, these are copied into another load

case, so the factor of the new loadcase is valid. It does not perform in addition

either onto the loads DLX, DLY or DLZ if these are entered in the same LC

input. Different factors for dead weight and other loads should be defined

therefore with a FACT 1.0 and corresponding DLfactors as well as further

records of the typ LCC with a factor. If FACT is > 1.0, the design values of the

stiffness will be used (see record GRP).

The factor FACG of the record GRP acts as additional multiplier.

If dead loads should be taken over by the program SOFiLOAD, then only the

load case number NO has to be input for LC. No dead loads are used from the


Version 10.20316

program SOFiLOAD, if factors for the dead load are defined for DLX, DLY

and DLZ.


317Version 10.20

3.9. Definiton of Beam Loads on Beam Groups.

The loads of beam elements can be defined either in reference to an individual

element or to beam groups. The records GSL, GUL and GVL are identical

with SL, UL and VL as far as their parameters and meaning. The loading,

however, acts not only upon a single beam but on a series of beams beginning

with the given beam number and including all following beams with the same

group number. The dimensions of the load refer to the entire series of beams.

e.g. NO = 100 generates loads on beams 100,101,...

NO = 156 generates loads on beams 156,157,...

NO = 2350 generates loads on 2350,2351,........

Attention:

The end number is not given any more, as it used to, by the end figure 99, but

through either the specified group divisor (from the database or the value de

fined with CTRL GDIV) or an explicit input of the end number NOE. The load

is limited in either cases, so long as a load length has been defined.

Independently of their actual geometric layout, the beams are interrelated in

the order stored in the database and the numbering increment defined

through STEP. Any entry for REF is taken though into consideration. A warn

ing is issued if the node numbers of two adjacent beams do not match.

Group loads

Explanations about reference system REF:

If a negative A is input, its value will be measured from the end of the beam.


Version 10.20318

The eccentricities are defined in the local beam system of the gravity centre

of the beam. Torsional or bending moments are thus generated from loads of

type P.

REF can define the system in which the dimensions of the load (values A and

L) will be input:

S = in m along the beam axis

XX = projection of the beam axis on the global Xdirection

YY = projection of the beam axis on the global Ydirection

ZZ = projection of the beam axis on the global Zdirection

SS = dimensionless, normalized by the beam length

(0.5 = midbeam)

XY = projection of the beam axis on the global XYplane

XZ = projection of the beam axis on the global XZplane

YZ = projection of the beam axis on the global YZplane

Reference system REF


319Version 10.20

3.10. NL Nodal Load

NL


NO

TYPE

P1

P2

P3

PF

Node number

Type and direction of the load

Load values or directional components

Factor for P1 through P3

LIT

kN, m

kN, m

kN, m

1

!

0

0

0

1

One can input for TYPE:

P = Load (P1,P2,P3) in (X,Y,Z)direction

PX = Load P1 in Xdirection

PY = Load P1 in Ydirection

PZ = Load P1 in Zdirection

M = Moment (P1,P2,P3) in (x,y,z)direction

MX = Moment P1 about Xdirection

MY = Moment P1 about Ydirection

MZ = Moment P1 about Zdirection

WX = Support translation in Xdirection in m

WY = Support translation in Ydirection in m

WZ = Support translation in Zdirection in m

DX = Support rotation about Xdirection in rad

DY = Support rotation about Ydirection in rad

DZ = Support rotation about Zdirection in rad

Attention!

The specification of a support translation for a coupled degree of freedom

deactivates the coupling. A reinstatement of the coupling condition can not

take place.


Version 10.20320

3.11. SL Point Load on a Beam

SL


NO

TYPE

P

A

DY

DZ

REF

KTYP

Beam number


Load value

Distance of load from beginning of beam

Eccentricity of load application point

Reference system for A

Vertex type

POL discontinuous slope

SPL continuous slope

LIT

kN, m

m,

m

m

LIT

1

!

!

0

0

0

S

SPL


PS = Load in local xdirection (axial force)

P1 = Load in local ydirection (secondary bending)

P2 = Load in local zdirection (primary bending)

MS = Moment about local xdirection (torsion)

M1 = Moment about local ydirection (primary bending)

M2 = Moment about local zdirection (secondary bending)

WS = Displacement jump in local xdirection in m

W1 = Displacement jump in local ydirection in m

W2 = Displacement jump in local zdirection in m

DS = Rotation jump about local xdirection in rad

D1 = Rotation jump about local ydirection in rad

D2 = Rotation jump about local zdirection in rad

PX = Load in global Xdirection

PY = Load in global Ydirection


321Version 10.20

PZ = Load in global Zdirection

MX = Moment about global Xdirection

MY = Moment about global Ydirection

MZ = Moment about global Zdirection

Special load directions:

PXS, PYS, PZS Loads similar to PX, PY, PZ

PX1, PY1, PZ1 only the corresponding components in the beam

PX2, PY2, PZ2 directions S, 1 or 2 are set however

Vertices of a prestress or initial deformation variation

See record GSL Point Load on a Beam Group

See loading on beam group for explanation of REF


Version 10.20322

3.12. GSL Point Load on a Beam

Group

GSL


NO

TYPE

P

A

DY

DZ

REF

KTYP

NOE

STEP

Number of first beam

Type and direction of load

Load value


Eccentricity of load application point

Reference system for A

Vertex type

POL discontinuous slope

SPL continuous slope

Number of the last beam

Increment of the beam numbers

LIT

kN, m

m,

m

m

LIT

1

!

!

0

0

0

S

SPL

*

1








WS = Displacement jump in local xdirection in m

W1 = Displacement jump in local ydirection in m

W2 = Displacement jump in local zdirection in m

DS = Rotation jump about local xdirection in rad

D1 = Rotation jump about local ydirection in rad

D2 = Rotation jump about local zdirection in rad


323Version 10.20







Special load directions:

PXS, PYS, PZS Loads similar to PX, PY, PZ

PX1, PY1, PZ1 only the corresponding components in the beam

PX2, PY2, PZ2 directions S, 1 or 2 are set however

Vertices of a prestress or initial deformation variation

By TYPE one can input as well:

U1 = Initial deformation vertex in m (secondary bending)

U2 = Initial deformation vertex in m (primary bending)

U1S = Initial deformation (secondary bending) as a fraction of

the beam length

U2S = Initial deformation (primary bending) as a fraction of

the beam length

VS = Prestress vertex NV0

V1 = Prestress vertex MV0 (primary bending)

V2 = Prestress vertex MV0 (secondary bending)

This defines the vertices of a constant, linear, quadratic or cubic variation, de

pending on the number of these vertices.

For each xvalue only one value per direction should be entered. Jumps in the

variation of the function can be defined by means of two values at a distance

of 0.0001 m. Specifying values for DY or DZ (including 0.) along with VS gen

erates prestress moments V2 or V1 (including 0 !). The default values are not

valid for these parameters.

Only the loads in the defined xregion are applied in case of GSLvariations,

thus at least two entries are necessary. In case of SL on the other hand, the

values for the beginning and/or the end of the beam are automatically sup


Version 10.20324

plemented. Therefore, any missing values of initial deformations at the beam

ends are assumed to be 0. This means, that a single entry at the beginning

or the end of the beam defines a linear lateral deformation, whereas a single

value at the middle of the beam defines a quadratic parabola. In case of pres

tress, the neighbouring values are applied each time at the beginning or the

end of a beam.

Vertices with discontinuous slope can be marked separately by means of

KTYP. If all vertices are of TYPE POL, the result is a broken polygon line.

The definition of several independent sections in the same series of beams can

be described by GSL and distinct numbers, describing though the same beam

series. A definition in separate loadcases and the use of the LCCrecord may

be of further help in general cases.

The entry for STEP is not further processed by the applied loads.



325Version 10.20

3.13. UL Uniform Load on a Beam

UL


NO

TYPE

P

A

L

REF

Beam number


Load value


negative: distance measured from end

of beam

Length of the load

(default: to the end of the beam)

Reference system for A, L

LIT

kN, m

m,

m,

m,

1

!

!

0

*

S

If the literal CONT is defined for TYPE by UL or GUL, the defaults from the

previous load record are activated.

P (new) = P (old)

A (new) = A+L (old)

For further explanations refer to the records VL and GVL.



Version 10.20326

3.14. GUL Uniform Load on a Beam

Group

GUL


NO

TYPE

P

A

L

REF

NOE

STEP

Beam number


Load value



of beam group

Length of the load

(default: to the end of the beam group)

Reference system for A, L



LIT

kN, m

m,

m,

m,

1

!

!

0

*

S

*

1

If the literal CONT is defined for TYPE by UL or GUL , the defaults from the


P (new) = P (old)

A (new) = A+L (old)

For further explanations refer to the records VL and GVL.



327Version 10.20

3.15. VL Linearly Varying on a

Beam

VL


NO

TYPE

PA

PE

A

L

DYA

DZA

DYE

DZE

REF

Beam number


Start load value

End load value



of beam

Length of the load

(default: to the end of the beam)

Eccentricity of the load application at

load start


load end

Reference system for A und L

LIT

kN, m

kN, m

m,

m

m

m

m

m,

1

!

!

PA

0

*

0

0

DYA

DZA

S

Remarks for distributed loads








ES = Strain in the axial direction

K1 = Curvature about the local ydirection in 1/m

K2 = Curvature about the local zdirection in 1/m

TS = Uniform temperature increase in C


Version 10.20328

T1 = Temperature difference in local ydirection in C

T2 = Temperature difference in local zdirection in C







PXP = Load in global Xdirection

PYP = Load in global Ydirection

PZP = Load in global Zdirection

PXS, PYS, PZS = Component loads

PX1, PY1, PZ1

PX2, PY2, PZ2

U1 = Initial deformation (secondary bending) in m

U2 = Initial deformation (primary bending) in m

U1S = Initial deformation (secondary bending) as a fraction

of the beam length

U2S = Initial deformation (primary bending) as a fraction

of the beam length

In case of PXP,PYP and PZP the load values refer to the projected length (e.g.

snow), whereas in case of PX,PY and PZ they refer to the beam axis (e.g. dead

weight).

In case of component loads, the loads act similarly to PX, PY, or PZ. However,

only the components in the corresponding beam directions S, 1 or 2 are ap

plied.

Positive curvature loads cause deformations similar to those from positive

moments.

Positive values of T1, T2 mean that the temperature increases in the direc

tion of the positive 1 or 2 axis. T1, T2 loads can be only set upon beams with

geometrically defined cross sections (AQUA).


329Version 10.20

The eccentricities are defined in the local beam system with respect to the

gravity centre of the beam. Torsional or bending moments are thus generated

from loads of type P.

If by VL or GVL the literal CONT is defined for TYPE, the defaults from the


PA (new) = PE (old)

A (new) = A+L (old)

Roof loads etc. can be defined easier this way, e.g:

VL 101 PZ PE 100 L 2 = CONT PE 120 L 5 = CONT PE 0

This input describes a load, which in the first 2 m from the beginning of the

beam climbs from 0 to 100, increases to 120 within another 5 m, and from that

point on it decreases linearly to zero at the end of the beam.



Version 10.20330

3.16. GVL Linearly Varying Load on

a Beam

GVL


NO

TYPE

PA

PE

A

L

DYA

DZA

DYE

DZE

REF

NOE

STEP

Beam number


Start load value

End load value



of beam group

Length of the load

(default: to the end of the beam group)


load start


load end

Reference system for A und L



LIT

kN, m

kN, m

m,

m

m

m

m

m,

1

!

!

PA

0

*

0

0

DYA

DZA

S

*

1

Remarks for distributed loads








ES = Strain in the axial direction

K1 = Curvature about the local ydirection in 1/m

K2 = Curvature about the local zdirection in 1/m


331Version 10.20

TS = Uniform temperature increase in C

T1 = Temperature difference in local ydirection in C

T2 = Temperature difference in local zdirection in C







PXP = Load in global Xdirection

PYP = Load in global Ydirection

PZP = Load in global Zdirection

PXS, PYS, PZS = Component loads

PX1, PY1, PZ1

PX2, PY2, PZ2

U1 = Initial deformation (secondary bending) in m

U2 = Initial deformation (primary bending) in m

U1S = Initial deformation (secondary bending) as a fraction

of the beam length

U2S = Initial deformation (primary bending) as a fraction

of the beam length

In case of PXP,PYP and PZP the load values refer to the projected length (e.g.

snow), whereas in case of PX,PY and PZ they refer to the beam axis (e.g. dead

weight).

In case of component loads, the loads act similarly to PX, PY, or PZ. However,

only the components in the corresponding beam directions S, 1 or 2 are ap

plied.

Positive curvature loads cause deformations similar to those from positive

moments.


Version 10.20332

Positive values of T1, T2 mean that the temperature increases in the direc

tion of the positive 1 or 2 axis. T1, T2 loads can be only set upon beams with

geometrically defined crosssections (AQUA).

The eccentricities are defined in the local beam system with respect to the

gravity centre of the beam. Torsional or bending moments are thus generated

from loads of type P.

If by VL or GVL the literal CONT is defined for TYPE, the defaults from the


PA (new) = PE (old)

A (new) = A+L (old)

Roof loads etc. can be defined easier this way, e.g:

VL 101 PZ PE 100 L 2 = CONT PE 120 L 5 = CONT PE 0

This input describes a load, which in the first 2 m from the beginning of the

beam climbs from 0 to 100, increases to 120 within another 5 m, and from that

point on it decreases linearly to zero at the end of the beam.



333Version 10.20

3.17. CL Loading of Cables

CL


NO

TYPE

P

Cable number

Type and direction of load

Load value

LIT

1

!

!

The following values are possible for TYPE:

PX Loading in global direction, (kN/m)

PY referring to the beam/cable length (kN/m)

PZ (kN/m)

PXP Loading in global direction, (kN/m)

PYP referring to the projected length (kN/m)

PZP (kN/m)

ES Strain in axial direction ()

VS Prestress (kN)

TS Temperature (C)

The loads are converted by the program to corresponding nodal loads. The

cable sag can be calculated by the expression:

fop l2

8Ho

where: p = load in the direction of the sag

H = component of cable force normal to the direction

of the loading


Version 10.20334

3.18. TL Loading of Trusses

TL


NO

TYPE

P

Truss number


Load value

LIT

1

!

!

The following values are possible for TYPE:

PX Loading in global direction (kN/m)

PY referring to the beam/truss (kN/m)

PZ length (kN/m)

PXP Loading in global direction, (kN/m)

PYP referring to the projected length (kN/m)

PZP (kN/m)

ES Strain in axial direction ()

VS Prestress (kN)

TS Temperature (C)


335Version 10.20

3.19. LCC Importing Loads from

another Loadcase

LCC


NO

FACT

FROM

TO

INC

NFRO

NTO

NINC

TFRO

TTO

TINC

CFRO

CTO

CINC

Number of a loadcase

Factor for load values

Range data for beam numbers

Range data for node numbers

Range data for trussbar numbers

Range data for cable numbers

1

FROM

1

NFRO

1

TFRO

1

CFRO

1

By entering LCC, all previously generated loads of the given loadcase, pro

vided they fall within the specified range, get multiplied by the factor and

added to the current loadcase. This does not hold for dead weight loads (record

LC).

The input of NO and FACT suffices when loads are to imported for all el

ements or nodes.

Creep loadcases from AQB have also still residual stresses, these can not be

incorporated with LCC.


Version 10.20336

3.20. LV Generating Loads from

Results of a Loadcase

LV


NO

PHI

EPS

FACV

FROM

TO

INC

STIF

CSMI

CSMA

KTYP

Number of an analysed loadcase

Creep factor

Shrinkage coefficient

Factor for deformations

Range data for beam numbers

Loadcase number stiffnesses

Lowest construction stage number

Highest construction stage number

Loading type of prestress loads similar to

SL/GSL

SPL cubic variation

POL polygonal variation

SPL1 cubic without secondary ben

ding components

POL1 polygonal without secondary

bending components genera

ted

LIT

0

0

0

FROM

1

NO

CSMI

SPL

Results of earlier analyses can be processed by LV as loads during a new

analysis step. These can be used for the analysis of creep effects and support

changes due to construction phases, as well as for the generation of initial de

formations. Only results of beams and trusses inside the specified range can

be imported. Appropriate separate input of more than one records can be used

e.g. to assign a different creep factor to each beam. If nothing is input for

FROM, all the beams that are defined in the analysed loadcase get loaded.

LV generates three completely different types of loading.


337Version 10.20

1. The input to FACV generates an affine initial deformation out of the

stored elastic line. Buckling modes can e.g. be modelled this way as

undesired eccentricities when addressing the difference of the dis

placement according to 2nd and 1st order theory.

The increase of the undesired eccentricity due to creep can be taken

into consideration as well. There are extremely different opinions for

the value of FACV. Since Version 2.095 the initial deformations are

taken into account by the displacements. Most different opinions exist

for this matter too. If necessary, one can subtract the old initial de

formations with LCC and factor 1.

2. The values of PHI and EPS generate corresponding strains or curva

ture loads.

ES = EPS + PHI N/EF

K1 = PHI MY/EIY

K2 = PHI MZ/EIZ

The most important special cases are:

1.1. Creep deformations of a loadcase (statically determinate)

PHI =

1.2. Constraints from a construction phase (primary state)

PHI = 1.0

1.3. Creep of a constraint from construction phase

PHI 11.0

The stiffnesses can be used by another loadcase too, so long as all in

volved beams exist as well. For applications and further explanations

refer to Chapter 5.5.

3. The input of CSMI/CSMA results in the calculation of the prestress

loads from the prestressing cables stored in the database. Such loads

will usually have already been generated by GEOS. However, these

loads can be also computed by STAR2 for cases of structural system


Version 10.20338

changes or prestress cables defined with AQBS.

By CSMI 1 the reinforcement defined in AQUA will be brought in with

prestress for the loading.


339Version 10.20

See also: DESI

3.21. REIN Specification for

Determining Reinforcement

REIN


AM1

AM2

AM3

ED

AMAX

Minimum reinforcement bending

members

Minimum reinforcement compression

members

Minimum reinforcement statically re

quired cross section

Relative eccentricity for boundary be

tween compression and bending

members, if not defined with record

BEAM.

Maximum reinforcement

EC2 8 %

DIN 9 %

%

%

%

%

0

0.1

0.8

3.5

*

EGRE

NGRE

ZGRP

TANA

Strain limit for design

Only sections with internal forces and

moments whose elastic edge strains are

numerically larger than the value of

EGRE are designed.

Lower limit of axial force relative to plas

tic axial force for "compression members"

Grouping of prestressing tendons

Lower limit inclination of struts of shear

design (tan )

0/00

0.02

0.001

0

*


Version 10.20340


MOD

RMOD

Design mode

SECT Reinforcement in cut

BEAM Reinforcement in beam

SPAN Reinforcement in span

GLOB Reinforcement in all effective

beams

TOTL Reinforcement in all beams

Minimum reinforcement mode

SEPA Crack width doesnt change

reinforcement

SING Single calculation, not saved

SAVE Saved

SUPE Superposition

LIT

LIT

SECT

SING

LCR

P7

P8

P9

P10

P11

Number of reinforcment distribution

Parameter for determining reinforce

ment

(See notes)

1

*

*

*

*

0.20

In the record BEAM the user can define explicitly if this is a bending or com

ressed member. The default value is compressed member if the excentricity

of the load < ED and the magnitude of the compression force > NGRE A r.The minimum reinforcements AM1 to AM3 apply to all cross sections; they

are input as a percentage of the section area.

The relevant value is the maximum of the minimum reinforcements:

Absolute minimum reinforcement (AM1/AM2)

Minimum reinforcement of statcally required section

Minimum reinforcement defined in cross section program AQUA

Minimum reinforcement stored in the database

Any number of types of reinforcement distribution can be stored in the data

base. Under number LCR, the most recently calculated reinforcement for

graphic depictions and for determinations of strain is stored. LCR=0 is re


341Version 10.20

served for the minimum reinforcement. This makes it possible, for instance,

to design some load cases in advance and to prescribe their reinforcements

locally or globally as defaults. The input value RMOD refers to the minimum

and stirrup reinforcement:

SING uses the stored minimum reinforcement without modifying

it

SAVE ignores the stored minimum reinforcement and overwrites

it the current reinforcement. This permits the establish

ment of an initial condition.

SUPE uses the stored minimum reinforcement and overwrites it

with the possibly higher values.

SUPE cannot be used during an iteration, since then the maximum reinforce

ment for an iteration step will no longer be reduced. STAR2 therefore ignores

a specification of SUPE, as long as convergence has not been reached. AQB

can still update the reinforcements at a later time: DESI STAT NO needs to

be specified in that case.

A specification of BEAM, SPAN, GLOB or TOTL under MOD refers to sec

tions with the same section number. For all connected ranges with the same

section, the maximum for the range is incorporated as the minimum rein

forcement. The design is done separately in each case for each load, however,

so that the user can recognize the relevant load cases.


Version 10.20342

Distribution of reinforcements

Use of minimum reinforcement in ultimate load design has a detrimental ef

fect on the shear reinforcement, since the lever of internal forces is reduced.

The user can take the appropriate precautions by specifying a minimum lever

arm in AQUA.

Since this effect is especially strong with tendons, AQBS can give special ef

fect to the latter in ultimate load design. This option is controlled with ZGRP:

ZGRP = 0 Tendons are considered with both their area and their

prestressing. Normal reinforcement is specified at the


343Version 10.20

minimum percentage.

The relative loading capacity is found.

ZGRP > 0 Tendons are specified with their full prestressing, but

with their area (stress increase) only specified in so

far as necessary. Normal reinforcementif installed

only if the prestressing steel alone is not sufficient.

A required area of prestressing steel is determined.

ZGRP < 0 Tendons are specified with their prestressing, only

specified in so far as necessary, otherwise the same

like ZGRP > 0.

If ZGRP < > 0 has been specified, the tendons are grouped into tendon groups.

The group is a whole number proportion which comes from dividing the

identification number of the tendon by ZGRP. Group 0 is specified with its

whole area, the upper group as needed. Any group higher than 4 is assigned

group 4. The group number of the tendons is independent of the group number

of the nonprestressed reinforcement.

Assume that tendons with the numbers 1, 21, 22 and 101 have been defined.

With the appropriate inputs for ZGRP, the following division is obtained:

ZGRP 0 All tendons are minimum reinforcement

ZGRP 10 Tendon 1 is group 0 and minimum reinforcement

Tendons 21 and 22 are group 2 and extra

Tendon 101 is group 4 and extra

ZGRP 100 Tendons 1, 21 and 22 are minimum reinforcement

Tendon 101 is group 1, extra

An example of the effect can be found in Section 5.1.5.3.

Notes: Parameters for determining reinforcement

The following parameters are normally not to be changed by the user:

Default Typical

P7 Weighting factor, axial force 5 0.5 50

When designing, the strain plane is iterated by the BFGS method. The

required reinforcement is determined in the innermost loop according

to the minimum of the squared errors. The default value for P8 leads

to the same dimensions for the errors. The value of P7 has been deter


Version 10.20344

mined empirically. With symmetrical reinforcement and tension it is

better to choose a smaller value, with multiple layers and compression

a larger one. For small maximum values of the reinforcementthe value

of P7 should be increased.

MIN ( (NNI)2 + F1(MYMYI)2 + F2(MZMZI)2 )

where F1 = P7 (zmaxzmin)P8

F2 = P7 (ymaxymin)P8

Default Typical

P9 Factor for reference point of strain 1.0 0.21.0

P10 Factor for reference point of moments 1.0 0.21.0

Lack of convergence in the dimensioning with biaxial loading can gen

erally be attributed to the factors no longer shaping the problem con

vexly, so that there are multiple solutions or none. In these cases the

user can increase the value of P7 or can vary the value of P10 between

0.2 and 1.0, for individual sections. In most cases, however, problems

are caused by specifying the minimum reinforcement.

P11 Factor for prefering outer reinforcement

Reinforcement which is only one third of the lever arm, is allowed to be

maximum one third of the area of the outer reinforcement. P11 is the

factor to set this up. For biaxial bending is P11=1.0, for uniaxial bend

ing is P11=0.0


345Version 10.20

See also: REIN NSTR

3.22. DESI Reinforced Concrete

Design, Bending, Axial Force

DESI


MOD

RMOD

STAT

Design mode

SECT Reinforcement in cut

BEAM Reinforcement in beam

SPAN Reinforcement in span

GLOB Reinforcement in all effective

beams

TOTL Reinforcement in all beams

Minimum reinforcement mode

SING Single calculation, not saved

SAVE Saved

SUPE Superposition

Load condition and code

NO Save reinforcement only

SERV Serviceability loads

ULTI Ultimate loads old DIN 1045

EC2 Load combination EC2

DIN Load combination DIN10451

EC2B Buckling load combination

DINB per EC2 resp DIN 10451

EC2A Accidential load combination

DINA EC2 resp DIN 10451

Additional combinations may be found on

the following pages.

LIT

LIT

LIT

*

*

SERV


Version 10.20346


SC1

SC2

SS1

SS2

C1

C2

S1

S2

Z1

Z2

KSV

KSB

Safety coefficient concrete

Safety coefficient concrete

Safety coefficient steel

Safety coefficient steel

Maximum compression

Maximum centric compression

Optimum tensile strain

Maximum tensile strain

Maximum effective compressive strain

of prestressing steel

Maximum effective tensional strain

of prestressing steel

Control for material of cross section

Control for material of reinforcements

o/oo

o/oo

o/oo

o/oo

o/oo

o/oo

*

*

*

*

*

*

*

*

*

*

UL

UL

SMOD Design mode shear

NO No shear design

EC2 Design per EC2

DIN Design per DIN 10451

1045 Design per DIN 1045

4227 Design per DIN 4227

SIA Design per SIA 162

8110 Design per BS 8110

5400 Design per BS 5400

5402 Design per BS 5400 class 1/2

5403 Design per BS 5400 class 3

(vtu < 5.8)

4250 Design per OeNORM B 4250



LIT *


347Version 10.20


T01

T02

T03

TVS

Shear stress limit

(e.g. DIN 1045 Table 13 line 3)

Shear stress limit


Shear stress limit


Boundary between reduced and full

shear coverage

N/mm2

N/mm2

N/mm2

N/mm2

*

*

*

T02

KTAU

TTOL

Shear design for plates

K1 not staggered for normal

plates (DIN 1045 17.5.5.

equation 14)

K2 not staggered for plates with

constant, evenly distributed

full loading (DIN 1045 17.5.5.

equation 15)

K1S like K1, tension reinforcement

staggered (DIN 1045 17.5.5.

Table 13 1a)

K2S like K2, but staggered

num coefficient k per equation 4.18

EC2

0.0 no shear check

Tolerance fot the limit values

/LIT

*

0.02

Defaults for strain limits and safety coefficients:


Version 10.20348

SC1 SC2 SS1 SS2 C1 C2 S1 S2 Z1 Z2

GEBR

BRUC

DIN

DINA

DINL

DINC

EC2

EC2A

EC2B

OE

OEB

SIA

SIAB

BS

BSU

ACI

AASH

1.75 2.10 1.75 2.10 3.5 2.2 3.0 5.0 2.2 5.0

1.00 1.00 1.00 1.00 3.5 2.2 3.0 5.0 2.2 5.0

1.50 1.50 1.15 1.15 3.5 2.2 3.0 25.0 2.0 5.0

1.30 1.30 1.00 1.00 3.5 2.2 3.0 25.0 2.0 5.0

1.30 1.30 1.30 1.30 3.5 2.2 3.0 25.0 2.0 5.0

1.10 1.10 1.10 1.10 3.5 2.2 3.0 25.0 2.0 5.0

1.50 1.50 1.15 1.15 3.5 2.0 3.0 10.0 2.0 5.0

1.30 1.30 1.00 1.00 3.5 2.0 3.0 10.0 2.0 5.0

1.35 1.35 1.15 1.15 3.5 2.0 3.0 10.0 2.0 5.0

1.50 1.50 1.15 1.15 3.5 2.0 3.0 20.0 2.0 5.0

1.30 1.30 1.00 1.00 3.5 2.0 3.0 20.0 2.0 5.0

1.20 1.20 1.20 1.20 3.5 2.0 3.0 5.0 2.0 5.0

1.00 1.00 1.00 1.00 3.5 2.0 3.0 5.0 2.0 5.0

1.50 1.50 1.115 1.15 3.5 2.0 3.0 5.0 2.0 5.0

1.30 1.30 1.00 1.00 3.5 2.0 3.0 5.0 2.0 5.0

0.90 0.70 0.85(shear)3.0 2.0 2.1 5.0 2.0 5.0

0.90 0.70 0.85(shear)3.0 2.0 2.1 5.0 2.0 5.0

When designing for ultimate load or combinations with divided safety factors,

the load factor must be contained in the internal forces and moments. One

way to accomplish this is with the COMB records.

The maximum strain depends on the stressst

Documents

Sofistik Manual