sofistik manual
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Sofistik ManualTRANSCRIPT
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VG E6 VID SVINESUND O 1319 BRO ver IDEFJORDEN (NYA SVINESUNDSBRON) vid BJLLVARPET
VGVERKET REG. VST Lilla Bommen 8 SE-405 33 GTEBORG
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
KONSTR GRANSK KONSTBYGGNADSNR ANTAL SIDOR (INKL DENNA SIDAN) SOFiSTiK 14-1319-1 2+127 Mannheim 2002-12-19 OBJEKT NR DOKUMENT NR REV
43 36 05 110K1374 0
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Konstruktionshandlingar
List of revisions
Rev. No.
Changes Pages No.
Changed by
Date
433 605 / Deckblatt1374 / 2003-04-15
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STAR2Statics of Beam StructureTheory of 2nd Order
Version 10.20
SOFiSTiK AG, Oberschleissheim, 2000
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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.
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STAR2Statics of Beam Structures
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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. . . . . . . . . . . . . . . . . . . . . . . . .
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STAR2 Statics of Beam Structures
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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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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STAR2Statics of Beam Structures
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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
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STAR2 Statics of Beam Structures
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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.
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STAR2Statics of Beam Structures
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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).
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STAR2 Statics of Beam Structures
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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.
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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
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STAR2 Statics of Beam Structures
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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
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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
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STAR2 Statics of Beam Structures
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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
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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.
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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.
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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.
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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,
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STAR2Statics of Beam Structures
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.
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STAR2 Statics of Beam Structures
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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
Der Bauingenieur 56 (1981), S. 17
/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
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STAR2Statics of Beam Structures
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/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
Der Bauingenieur 59 (1984), S. 381388
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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:
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STAR2 Statics of Beam Structures
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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.
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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.
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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).
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STAR2Statics of Beam Structures
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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.
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3.4. CTRL Parameters Controlling
the Analysis Method
CTRL
Item Description Dimension Default
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
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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)
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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)
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3.5. GRP Selection of an Element
Group
GRP
Item Description Dimension Default
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
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STAR2 Statics of Beam Structures
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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.
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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!
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3.6. STEX External Stiffness
STEX
Item Description Dimension Default
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.
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3.7. INFL Definition of an
Influence Line Loadcase
INFL
Item Description Dimension Default
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
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3.8. LC Definition of a Loadcase
LC
Item Description Dimension Default
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
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program SOFiLOAD, if factors for the dead load are defined for DLX, DLY
and DLZ.
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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.
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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
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3.10. NL Nodal Load
NL
Item Description Dimension Default
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.
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3.11. SL Point Load on a Beam
SL
Item Description Dimension Default
NO
TYPE
P
A
DY
DZ
REF
KTYP
Beam number
Type and direction of the load
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
One can input for TYPE:
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
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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
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3.12. GSL Point Load on a Beam
Group
GSL
Item Description Dimension Default
NO
TYPE
P
A
DY
DZ
REF
KTYP
NOE
STEP
Number of first beam
Type and direction of load
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
Number of the last beam
Increment of the beam numbers
LIT
kN, m
m,
m
m
LIT
1
!
!
0
0
0
S
SPL
*
1
One can input for TYPE:
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
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PX = Load in global Xdirection
PY = Load in global Ydirection
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
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
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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.
See loading on beam group for explanation of REF
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3.13. UL Uniform Load on a Beam
UL
Item Description Dimension Default
NO
TYPE
P
A
L
REF
Beam number
Type and direction of the load
Load value
Distance of load from beginning of beam
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.
See loading on beam group for explanation of REF
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3.14. GUL Uniform Load on a Beam
Group
GUL
Item Description Dimension Default
NO
TYPE
P
A
L
REF
NOE
STEP
Beam number
Type and direction of the load
Load value
Distance of load from beginning of beam
negative: distance measured from end
of beam group
Length of the load
(default: to the end of the beam group)
Reference system for A, L
Number of the last beam
Increment of the beam numbers
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
previous load record are activated.
P (new) = P (old)
A (new) = A+L (old)
For further explanations refer to the records VL and GVL.
See loading on beam group for explanation of REF
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3.15. VL Linearly Varying on a
Beam
VL
Item Description Dimension Default
NO
TYPE
PA
PE
A
L
DYA
DZA
DYE
DZE
REF
Beam number
Type and direction of the load
Start load value
End load value
Distance of load from beginning of beam
negative: distance measured from end
of beam
Length of the load
(default: to the end of the beam)
Eccentricity of the load application at
load start
Eccentricity of the load application at
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
One can input for TYPE:
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)
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
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T1 = Temperature difference in local ydirection in C
T2 = Temperature difference in local zdirection in C
PX = Load in global Xdirection
PY = Load in global Ydirection
PZ = Load in global Zdirection
MX = Moment about global Xdirection
MY = Moment about global Ydirection
MZ = Moment about global Zdirection
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).
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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
previous load record are activated.
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.
See loading on beam group for explanation of REF
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3.16. GVL Linearly Varying Load on
a Beam
GVL
Item Description Dimension Default
NO
TYPE
PA
PE
A
L
DYA
DZA
DYE
DZE
REF
NOE
STEP
Beam number
Type and direction of the load
Start load value
End load value
Distance of load from beginning of beam
negative: distance measured from end
of beam group
Length of the load
(default: to the end of the beam group)
Eccentricity of the load application at
load start
Eccentricity of the load application at
load end
Reference system for A und L
Number of the last beam
Increment of the beam numbers
LIT
kN, m
kN, m
m,
m
m
m
m
m,
1
!
!
PA
0
*
0
0
DYA
DZA
S
*
1
Remarks for distributed loads
One can input for TYPE:
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)
ES = Strain in the axial direction
K1 = Curvature about the local ydirection in 1/m
K2 = Curvature about the local zdirection in 1/m
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TS = Uniform temperature increase in C
T1 = Temperature difference in local ydirection in C
T2 = Temperature difference in local zdirection in C
PX = Load in global Xdirection
PY = Load in global Ydirection
PZ = Load in global Zdirection
MX = Moment about global Xdirection
MY = Moment about global Ydirection
MZ = Moment about global Zdirection
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.
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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
previous load record are activated.
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.
See loading on beam group for explanation of REF
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3.17. CL Loading of Cables
CL
Item Description Dimension Default
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
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3.18. TL Loading of Trusses
TL
Item Description Dimension Default
NO
TYPE
P
Truss number
Type and direction of the load
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)
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3.19. LCC Importing Loads from
another Loadcase
LCC
Item Description Dimension Default
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.
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3.20. LV Generating Loads from
Results of a Loadcase
LV
Item Description Dimension Default
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.
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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
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changes or prestress cables defined with AQBS.
By CSMI 1 the reinforcement defined in AQUA will be brought in with
prestress for the loading.
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See also: DESI
3.21. REIN Specification for
Determining Reinforcement
REIN
Item Description Dimension Default
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
*
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Item DefaultDimensionDescription
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
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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.
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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
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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
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STAR2 Statics of Beam Structures
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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
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See also: REIN NSTR
3.22. DESI Reinforced Concrete
Design, Bending, Axial Force
DESI
Item Description Dimension Default
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
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Item DefaultDimensionDescription
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
4253 Design per OeNORM B 4253
4700 Design per OeNORM B 4700
LIT *
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Item DefaultDimensionDescription
T01
T02
T03
TVS
Shear stress limit
(e.g. DIN 1045 Table 13 line 3)
Shear stress limit
(e.g. DIN 1045 Table 13 line 4)
Shear stress limit
(e.g. DIN 1045 Table 13 line 5)
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:
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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