ASE General Static Analysis of Finite Element Structures SOFiSTiK 2014
ASE General Static Analysis of Finite Element Structures ASE Manual, Version 2014-9 Software Version SOFiSTiK 2014 c 2015 by SOFiSTiK AG, Oberschleissheim, Germany. Copyright
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Office Nuremberg Burgschmietstr. 40 90419 Nuremberg Germany
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This manual is protected by copyright laws. No part of it may be translated, copied or reproduced, in any form or by any means, without written permission from SOFiSTiK AG. 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 omissions are corrected as soon as they are detected. The user of the program is solely responsible for the applications. We strongly encourage the user to test the correctness of all calculations at least by random sampling.
Front Cover Project: Yas Hotel, Abu Dhabi | Client: ALDAR Properties PJSC, Abu Dhabi | Structural Design and Engineering Gridshell: schlaich bergermann und partner | Architect: Asymptote Architecture | Photo: Björn Moermann
Contents | ASE
Contents
Contents 1
Task Description
2
Theoretical Principles 2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Implemented Elements - licence level . . . . . . . . . . . . . 2.3 Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Geometric nonlinear Theory 2nd and 3rd Order . 2.3.2 Coordinate System of Forces, Center of Gravity . 2.3.3 Warping torsion . . . . . . . . . . . . . . . . . . . . . . 2.3.4 SOFiSTiK - T-Beam Philosophy . . . . . . . . . . . 2.4 Pile Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Winkler Coefficient . . . . . . . . . . . . . . . . . . . . 2.4.2 Numerical Solution and Accuracy . . . . . . . . . . 2.5 Truss and Cable Elements . . . . . . . . . . . . . . . . . . . . . 2.6 Spring Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Boundary Elements BOUN and FLEX . . . . . . . . . . . . . 2.8 Shell Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8.1 Plate Structural Behaviour . . . . . . . . . . . . . . . 2.8.2 Membrane Structural Behaviour . . . . . . . . . . . 2.8.3 Elastic Foundation . . . . . . . . . . . . . . . . . . . . 2.8.4 Rotations around the Shell Normal . . . . . . . . . 2.8.5 Twisted Shell Elements . . . . . . . . . . . . . . . . . 2.8.6 Eccentrically Connected Shell Elements . . . . . . 2.8.7 Tendons in QUAD Elements . . . . . . . . . . . . . . 2.8.8 Non-conforming Formulation . . . . . . . . . . . . . 2.9 Volume Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Primary Load Cases . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Non-linear Analyses . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 Non-linear Analysis of Plates and Shells . . . . . . . . . . . 2.12.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12.2 Input of the Materials . . . . . . . . . . . . . . . . . . 2.12.3 Analysis Basics . . . . . . . . . . . . . . . . . . . . . . 2.12.4 Rounding off over Punching Points . . . . . . . . .
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2-1 2-1 2-2 2-3 2-3 2-4 2-4 2-6 2-11 2-12 2-12 2-14 2-14 2-15 2-16 2-18 2-21 2-22 2-24 2-24 2-24 2-25 2-25 2-26 2-27 2-28 2-29 2-29 2-30 2-37 2-50
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2.13
2.14 2.15 2.16 2.17 2.18
2.12.5 Output of the Results . . . . . . . . . . . . . . . . . 2.12.6 Miscellaneous Information . . . . . . . . . . . . . . Membrane Structures: Formfinding and Static Analysis 2.13.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 2.13.2 The Membrane Element . . . . . . . . . . . . . . . 2.13.3 Formfinding . . . . . . . . . . . . . . . . . . . . . . . . 2.13.4 Static Analysis . . . . . . . . . . . . . . . . . . . . . . 2.13.5 Unstable Membrane Forms . . . . . . . . . . . . . 2.13.6 Calculations of Cable Meshes . . . . . . . . . . . . 2.13.7 Check List - Notes - Problem Solutions . . . . . 2.13.8 Overview about the Used Examples . . . . . . . 2.13.9 Necessary Program Versions . . . . . . . . . . . . Dynamic Modal Analysis . . . . . . . . . . . . . . . . . . . . . Buckling Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Damping Elements . . . . . . . . . . . . . . . . . . . . . . . . . Modal Damping and Modal Loads . . . . . . . . . . . . . . .
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2-51 2-52 2-55 2-55 2-55 2-63 2-76 2-80 2-82 2-84 2-86 2-86 2-87 2-87 2-88 2-88 2-88
Literature
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3-1 3-1 3-2 3-5 3-18 3-22 3-24 3-33 3-37 3-38 3-41 3-43 3-46 3-52 3-55 3-56 3-57 3-59 3-60 3-61 3-63 3-65 3-67
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Input Description 3.1 Input Language . . . . . . . . . . . . . . . . . . . 3.2 Input Records . . . . . . . . . . . . . . . . . . . . 3.3 CTRL – Control of the Calculation . . . . . . . 3.3.1 SOLV Equation solver . . . . . . . . . 3.3.2 CORE Parallel computation control 3.4 SYST – Global Control Parameters . . . . . . 3.5 STEP – Time Step Method Dynamics . . . . 3.6 HIST – Storage STEP-LCST . . . . . . . . . . 3.7 ULTI – Limit Load Iteration . . . . . . . . . . . . 3.8 PLOT – Plot of a Limit Load Iteration . . . . . 3.9 CREP – Creep and Shrinkage . . . . . . . . . 3.10 GRP – Group Selection Elements . . . . . . . 3.11 GRP2 – Expanded Group Selection . . . . . 3.12 ELEM – Single Element Settings . . . . . . . . 3.13 LEN0 – Unstressed Length . . . . . . . . . . . 3.14 HIGH – Membrane High Points . . . . . . . . . 3.15 PSEL – Selection of Piles . . . . . . . . . . . . 3.16 TBEA – Reduction of the Width for T-Beams 3.17 REIQ – Reinforcement in QUAD Elements . 3.18 STEX – External Stiffness . . . . . . . . . . . . 3.19 OBLI – Inclination . . . . . . . . . . . . . . . . . . 3.20 SLIP – SLIP Cable . . . . . . . . . . . . . . . . .
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3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 4
VOLU – Air Volume Element . . . . . . . . . . . . . . . . . . . . MOVS – Moving Spring . . . . . . . . . . . . . . . . . . . . . . . . LAUN – Incremental Launching . . . . . . . . . . . . . . . . . . SFIX – Fixing Stiffness . . . . . . . . . . . . . . . . . . . . . . . . LC – Load Case and Masses . . . . . . . . . . . . . . . . . . . . TEMP – Temperature from HYDRA . . . . . . . . . . . . . . . . LAG – Loads from Support Reactions . . . . . . . . . . . . . . PEXT – Prestress of External Cables . . . . . . . . . . . . . . . LCC – Copy of Loads . . . . . . . . . . . . . . . . . . . . . . . . . EIGE – Eigenvalues and -vectors . . . . . . . . . . . . . . . . . MASS – Lumped Masses . . . . . . . . . . . . . . . . . . . . . . V0 – Initial Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . REIN – Specification for Determining Reinforcement . . . . DESI – Reinforced Concrete Design, Bending, Axial Force NSTR – Non-linear Stress and Strain . . . . . . . . . . . . . . . Non-linear Material Analysis in ASE . . . . . . . . . . . . . . . ECHO – Output Control . . . . . . . . . . . . . . . . . . . . . . . .
Output Description 4.1 Check List of the Generated Structure . . . . . . 4.2 Check List of the Non-linear Parameters . . . . 4.3 Check List of the Analysis Control Parameters 4.4 Check Lists of the Loads . . . . . . . . . . . . . . . 4.5 Process of the Analysis . . . . . . . . . . . . . . . 4.6 Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . 4.7 Element Results . . . . . . . . . . . . . . . . . . . . . 4.8 Non-linear Results . . . . . . . . . . . . . . . . . . . 4.9 Nodal Results and Support Reactions . . . . . . 4.10 Internal Forces and Moments at Nodes . . . . . 4.11 Error Estimates . . . . . . . . . . . . . . . . . . . . . 4.12 Distributed Support Reactions . . . . . . . . . . . 4.13 Strain Energy of Groups . . . . . . . . . . . . . . . 4.14 Wind Load Generation . . . . . . . . . . . . . . . .
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3-68 3-70 3-72 3-74 3-75 3-78 3-80 3-82 3-84 3-86 3-89 3-91 3-92 3-97 3-103 3-105 3-109 4-1 4-1 4-1 4-1 4-2 4-2 4-3 4-4 4-7 4-8 4-10 4-11 4-12 4-13 4-13
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Task Description | ASE
1
Task Description
ASE calculates the static and dynamic effects of general loading on any type of structure. To start the calculations the user divides the structure to be analyzed into an assembly of individual elements interconnected at nodes (Finite Element Method). Possible types of elements are : haunched beams, springs, cables, truss elements, plane triangular or quadrilateral shell elements and threedimensional continuum elements. The program handles structures with rigid or elastic types of support. An elastic support can be applied to an area, a line or at nodal points. Rigid elements or skew supports can be taken into account. ASE calculates the effects of nodal, line and block loads. The loads can be defined independently from the selected element mesh. The generation of loads from stresses of a primary load case allows the consideration of construction stages, redistribution and creep effects. Non-linear calculations enables the user to take the failure of particular elements into account, such as: cables in compression, uplifting of supported plates, yielding, friction or crack effects for spring and foundation elements. Non-linear materials are available for three-dimensional and shell elements. Geometrical nonlinear computations allow the investigation of 2nd and 3rd order theory effects by cable, beam, shell and volume structures. In case of beam structures, the program can calculate warping torsion with up to 7 degrees of freedom per node. The user of ASE should therefore gather experience from simple examples before tackling more complicated structures. A check of the results through approximate engineering calculations is imperative. The basic version of ASE performs the linear analyses of beams, cables, trusses, plane and volume structures. Plain strain and rotational systems can be analyzed with TALPA.
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Extended versions of ASE offer calculations of: •
Influence surfaces
•
Non-linear analyses
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Pile elements with linear/parabolic soil coefficient distribution
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Creep and shrinkage
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Forces from construction stages
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Modal analysis, Time step method
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Material non-linearities
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Geometrical non-linearities
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Membrane elements
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Evaluation of collapse load
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Non-linear dynamics
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Theoretical Principles | ASE
2 2.1
Theoretical Principles General
A continuum or a plane structure can be interpreted as a statically or geometrically infinitely indeterminate structure. If an analytical solution is unknown, every numerically approximate method is based on converting this infinite system into a finite one, in other words to discretizing it. The advantage of the finite elements lies in their universal applicability to any geometrical shape and almost to any loading. This is achieved by a modular principle. Single elements which describe parts of the structure in a computer oriented manner are assembled into a complete structure. The continuous structure is represented thus by a large but finite number of elements. A discrete solution consisting of n unknowns is calculated instead of the continuous solution. In general, the approximate solution may represent the exact solution better with the use of more elements. The single elements of an area can be of arbitrarily small dimensions in comparison to the dimensions of the overall structure without giving rise to any incompatibilities with the presented theory. The refinement of the subdivision is, however, subjected to certain limitations due to numerical reasons. The Finite Element Method (FEM) employed in ASE is a displacement method, meaning that the unknowns are deformation values at several selected points, the so-called nodes. Displacements can be obtained with an element-wise interpolation of the nodal values. The calculation of the mechanical behaviour is based generally on an energy principle (minimisation of the deformation work). The result is a so-called stiffness matrix. This matrix specifies the reaction forces at the nodes of an element when these nodes are subjected to known displacements. The global force equilibrium is generated then for each node in order to determine the unknowns. A force in the same direction which is a function of this or another displacement corresponds to each displacement. This leads to a system of equations with n unknowns, where n can become very large. Numerically beneficial banded matrices result, however, due to the local character of the element-wise interpolation. The complete method is divided into four main parts: 1.
Determination of the element stiffness matrices.
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2.
Assembly of the global stiffness matrix and solution of the resulting equation system
3.
Application of loads and determination of the corresponding displacements.
4.
Determination of the element stresses and support reactions due to the computed displacements.
The second step is that with most CPU time. It may use up to 90 percent of the total CPU time. However, it has to occur only once for a static system. The stresses jumps from element to element. The size of the jump is thus a direct measure of the quality of the FE analysis.
2.2
Implemented Elements - licence level
The elements shown in the following table are available in ASE. A non-linear analysis can occur also for some types of elements. A detailed list of the implemented nonlinear effects is written in section 3.36. Program ASE runs with licences to ASE, SEPP and PFAHL. Depending on the licence not all elements can be used - see following table. Nonlinear analsis also require a higher licence level. Non-linear
Geometrical
Material
Non-linearity
SPRI
yes
yes
TRUS
yes+tension failure
yes
Element
CABL
yes+compression failure yes + cable sag
BEAM
yes
yes
PILE1
elastic bedding only
yes
QUAD2
yes
yes
BRIC12
yes
yes
BOUN
-
-
FLEX12
-
-
yes
-
Halfspace2
1
not available on licence SEPP
2-2
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Theoretical Principles | ASE
2
not available on licence PFAHL
2.3
Beam Elements
The beam element in ASE is an arbitrary haunched beam element including shear deformations and hinge effects. It can be defined also eccentrically to the node connecting line. For haunched cross sections in bridge analysis all nodes can be defined on the top face of the superstructure. 2.3.1
Geometric nonlinear Theory 2nd and 3rd Order
The following figures shall clarify the essential characteristics between SOFiSTiK theory 2nd and 3rd order (TH2 and TH3). Pz P
d − TH2
− TH3
Figure 2.1: Column geometric nonlinear theory 2nd and 3rd order
In the column example in figure 2.1 the effect of theory TH2 causes a stiffness reduction in the column due to the compression normal force (geometric stiffness). This creates an additional deflection dux in x direction (no duz!). The beam can get longer than in the original shape. The bottom bending moment increases due to the displacement of the vertical load Pz. This type of analysis is also known as pi-delta method. In the complete geometric nonlinear analysis TH3 the column head follows the physically correct path. Equilibrium is iterated on the real deformed shape. In figure 2.2 a horizontally fixed bending girder is loaded vertically. In TH2 the girder just deflects vertical without a normal force N. In the TH3 analysis the vertical displacement causes a lengthing of the beam. The created normal force N carries a part of the load and reduces the vertical deformation.
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TH2 : N = 0
TH3 : N
Figure 2.2: girder geometric nonlinear theory 2nd and 3rd order
Examples see SYST 2.3.2
Coordinate System of Forces, Center of Gravity
In TH2 the forces are related to the original coordinate system. So the shear forces are transversal forces. In the column example in figure 2.1 N stays vertical and VZ stays horizontal. In TH3 the forces are always related to the deformed beam coordinate system. The beam forces N, MY and MZ are related to the center of gravity of the actual active partial section (not to node connecting line). MT, VY and VZ are related to the center of shear. Dead load is applied in the stiffness center (and not in the center of mass that may differ in case of composite sections). 2.3.3
Warping torsion
Warping torsion can be used for straight beam structures with CTRL WARP 1. Warping effects can also appear without warping support. In the following picture to example ase11_girder_overturning.dat in loadcase 11 a single moment MT=1 kNm (2*0.50 kNm) is applied in midspan of a single girder 90 % of it work via warping torsion as force pairs in the flanges - see MTs = 0.45 kNm. 10 % go directly into the section via Saint Venant shear - see MTp = 0.05 kNm. Warping parts (ASE output): The total torsional moment Mt has 3 parts (MT= MTp +MTs +MTn): MTp - primary torsional moment from Saint Venant shear stresses MTs - secondary tors. moment (flange shear from warping longitudinal stresses) MTn - theory 2. order torsional moment from twisted normal stresses Mb warping moment (from warping longitudinal stresses - creates MTs at other beam sections) You can imagine the behavior as follows: the flange forces in midspan deflect
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the flanges opposite and transport a part of the loading via longitudinal stresses to the support. The longitudinal warping stress due to Mb in midspan create a flange shear force at the supports. The corresponding torsional momennt MTs at the support is about 0.05 kNm. At the support itself, the longitudinal warping stresses are zero (free end) - see Mb = 0 kNm. The effects are as follows:
MT
MTp
MTs
Mb
The warping effects are also explained in warping_mtp_mts_mtn.dat. There the interaction of MTs and Mb for a MT load on a cantilever is interpretet as follows:
•
Please notice that at the cantlever end (beam 10 x= 0.4) already a part of the load MT= 10 kNm is carried by warping although there are no longitudinal
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warping stresses at that location (free end)! •
You can imagine this in the following way: The top flange longitudinal warping stresses at beam 1 x=0 want to pull pack the top flange at the cantilever. The bottom flange longitudinal warping stresses want to pull pack the bottom flange as well.
•
This pair of forces (flange shear from warping longitudinal stresses) carries a part of the MT loading.
•
So the longitudinal warping stresses at the beginning of the beam create a MTs at the end - and oposite.
•
An MTs at a beam section x1 creates longitudinal warping stresses at another beam section x2.
2.3.4
SOFiSTiK - T-Beam Philosophy
Automatic addition of the T-beam parts for FE plates with beams Example see ase3_t_beam_test.dat Usage in bridge construction see also tbeam_philosophy_e.pdf
Figure 2.3: T-Beam Philosophy
Attention: This model can not be used for influence line evaluation with ELLA because ELLA does not add the slab parts to the beam! A 2D slab analysis is usually sufficient and desirable for beams and continuous beams with effective cross section widths in a slab. Only in a 2D slab analysis normal forces are not determined in the slab or in the beam! The advantage is that the slab can be simply designed (without normal forces) particularly for the shear checks. In addition the determined beam moments can be designed directly with the right T-beam cross section. Procedure: The user or the graphical input program positions a centric defined beam in the node plane (with the T-beam cross section see picture on the right). The QUAD elements are also defined centric. As the beam is positioned in 2-6
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Theoretical Principles | ASE
the centre of gravity (a little bit below the slab center), the upper edge of the T-beam looks a little bit out of the slab - this is also visible in WinGRAF. The ANIMATOR displaces the cross section a little bit downwards, so that the upper edges beam+slab appear at the same position for a better visualization. So in the standard case the beam section is defined with the corresponding effective slab width. Looking from the side (see picture left below) you see that cross section parts and slab overlap and concrete areas are defined twice. These double parts are now corrected in the T-Beam philosophy: Therefore in the stiffness analysis the slab part (I-slab = bVh3/12 with b=effective width = width of the cross section) is substracted automatically from the stiffness of the beam I-Tbeam. An equivalent (reduced) beam is used: I–equivalent beam = I–Tbeam – I–slab In the same way the deadload of the equivalent beam is modified to avoid double dead load. Then the program at first determines a bending moment of this equivalent beam in a FE analysis. The internal forces parts of the slab (M-slab = m-slab V b) are added automatically immediately. Thus the complete T-beam internal forces are available for the following beam design: M–Tbeam = M–equivalent beam + M–slab The bending moments My and the shear forces Vz are added as default, for shells also the normal forces N. The torsional moment Mt is not added as default. Output: •
The parts of the slab are already included in the printout of the beam forces.
•
A statistic of the slab parts follows. The maximum slab parts are compared with the maximum beam internal forces: Statistic Beam - Additional Forces from a Slab Loadcase 2 The printed beam-forces include max. additional forces of a slab: max. beam-force without slab-addition max. slab-addition cno bm Vz My Vz My [m] [kN] [kNm] [kN] [kNm] 1 2.20 max 48.60 243.78 43.63 5.95 min -48.60 0.00 -43.63 0.00
For safety the internal forces are not reduced in the FE plate elements, although it would be possible about the amount of the increase of the beam internal
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forces. So this method can be uneconomical for smaller beam heights. Beams which are connected with kinematic constraints at the slab are also processed, if the beams are positioned in the slab plane. Defaults for the addition of the plate internal forces to the beam internal forces: For slab structures: •
The single beam must have a cross section with a defined width at the start and the end. A defined width can be generated from a T-beam (e.g. record SREC in AQUA) and from general cross sections (e.g. AQUA record SECT and following). The maximum width of the cross section is used in each case (independent of the position of the plate, above or below). A cross section which is input without dimensions however with stiffnesses (e.g. with record SVAL) does not known any defined width. A plate part can therefore not be added for these beams!
•
The single beam is connected generally directly with the nodes of the plate.
•
After an automatic mesh generation or a free mesh definition the straight beam which is positioned in the plate plane can be combined also with the FE mesh via kinematic constraints.
•
The beam reads the plate thickness and the modulus of elasticity from these plate nodes. Different plate thicknesses are possible at the beam start and end.
Additionally for three-dimensional slab structures (ASE): The feature can be used also for three-dimensional slabs however with following restrictions: •
The beams must be positioned in the same plane as the plate. The plate parts are not added for beams which are connected eccentrically.
Special features with the input: •
The beam cross section must represent the effective cross section, therefore the web and the effective plate. If a concrete slab on a steel girder should be considered as a composite construction, the steel girder must be defined with the effective concrete plate as cross section! The determined internal forces and moments refer then to this composite cross section.
•
The effective width (cross section width) should be chosen a little bit smaller than to large especially over the columns, because for the plate moment to be added only the moment near the node at which the beam and the plate
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Theoretical Principles | ASE
are combined is used (see CTRL PLAB V2). This plate moment is processed then unchangeable acting about the whole width. The internal forces and moments are therefore not exactly integrated about the effective width! •
The plate stiffness I-plate (without the part of Steiner) is diverted from the total cross section stiffness I-cross. If the subtrahend I-plate is bigger than 0.8·I-cross, a warning is printed and the minimum stiffness of 0.2·I-cross is used.
•
For three-dimensional systems the subtrahend is maximal 0.9·A-cross for the area A-plate. At least 0.1·A-cross are available then for the fictitious beam in the FE system.
Special features with the output: •
The attenuated stiffnesses are printed with ECHO PLAB FULL. If a cross section is available at beams with different plate thicknesses (e.g. haunches), the attenuated stiffness is printed for the minimal and maximal plate thickness.
•
The plate parts are already available in the printed beam internal forces and moments and can be designed directly. beam at FE node
beam which is connect ed wit h kinemat ic const r aint s
CTRL PL AB 0 added plat e par t s
Figure 2.4: Beam internal forces
For comparison a load case can be calculated once without input of CTRL PLAB and the second time with CTRL PLAB 0 and another load case number. The beam internal forces and moments of both calculations can be represented then with the same scale in a picture. (More precise) calculation possibilities: Also with the above describes method, the normal forces occur in the compression zone (plate) first during the design of the T-beam. Normal forces are not
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considered during the calculation of the FE system. The effective width has to be estimated manually and defined. In reality the normal forces act from the supports into the plate. For a more precise calculation three possibilities are described here. For all three variants the effective width is realized automatically via the normal force calculation and has not to be input: 1.
The web part which is positioned below the plate can be defined as a beam which lies eccentrically below the plate. Then two nodes lying upon each other are however necessary for the system input. This complicates the input. Problems occur also for the design, because the sum of the internal forces from web+plate including the parts of Steiner are necessary for a design of the total T-beam. The method is therefore only reasonable for composite slabs with eccentrically defined steel beams (see ASE example 5.3).
kinemat ic const r aint
Figure 2.5: Eccentrical defined steel beam
2.
The web can be also generated with shell elements. The same problems for the design result as for the eccentrical beam. In addition it should be noted that the area in the intersection point plate-web is not defined twice:
Figure 2.6: Shell elements
3.
2-10
The SOFiSTiK offers the eccentrical plate elements as a real alternative. The system is generated here with different thick plate elements. The plate elements get a larger thickness in the area of the beams. A simply defined node plane which lies at the upper edge of the plate is here necessary in the input. All elements can be defined eccentrically below the node
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Theoretical Principles | ASE
plane. Thereby all elements have the same upper edge, the thicker beam elements stand only below out. Normal forces which are considered for the design are produced due to the eccentrical position of the elements. Thereby the usual plate design is done simultaneously the beam design a special beam design is therefore not necessary. The FE analysis uses here automatically the real effective width via the simultaneous analysis of the normal force distribution. This method is therefore applicable not only for the analysis of building slabs but also for analysis of concrete bridges. Each elements is processed for themselves alone during design and not the total T-beam cross section! This method is however only correct for beams with moderate thickness. The design can be uneconomical for larger beams (web height larger than 2.5·plate thickness), but it is in each case at the sure side. The simple method with fictitious beams lying in the plate is more practical for larger web heights. See also tbeam_philosophy_e.pdf
eccent icit y plane of t he node point s
under side of t he QUAD element s
cent r oid line of QUAD lying below t he node plane
Figure 2.7: Eccentrical plate element
For all analysis methods the resultant internal forces and moments can be determined with the program SIR (Sectional Results). Afterwards a design as beam cross section is possible, also for system 2 from folded structure elements. This is especially necessary in bridge design for checks of the ultimate limit state and for checks for safety against cracking. Attention: This model can not be used for influence line evaluation with ELLA because ELLA does not add the slab parts to the beam! Literature: K ATZ [10]
2.4
K ATZ
AND
S TIEDA [11], W UNDERLICH
ET AL .
[18], B ELLMANN [2],
Pile Elements
A single pile is idealized through a straight, elastically supported beam with shear deformations and 2nd order theory. It is numerically integrated with the
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complete system of 12 differential equations. Pile elements get a minimal constraint of the rotational spring in order to prevent instabilities. Example see single_pile.dat These equations are integrated numerically with the Runge-Kutta method. PLC analysis for piles: In this way also system with pile elements can be used including creep in CSM. Shrinkage will never be taken into account for piles, creep acts for the pile and the bedding! If GRP PHIF is input this value is taken for both the pile and the bedding. The pile element is not contained in the basic licence of ASE. 2.4.1
Winkler Coefficient
The definition of the bedding constants requires a good engineering understanding of the problem. For their definition it is most important to take into account that the Winkler coefficient is not a simple material property but depends on the system dimensions and the loading. The Winkler coefficient defines the stress caused by a given deformation whereas the influence of adjacent points (shear deformations) is not taken into account. The dimension of a bedding is therefore given as kN/ m3 . A displacement causes a stress (kN/ m2 ). However, the pile bedding is defined in kN/ m2 since the pile ”width” has to be integrated into this value. In this case, a displacement causes a load (kN/ m). Since the pile width influences also the Winkler coefficient, the pile dimensions are dropped possibly from the equation and the pile Winkler coefficient can be estimated also from the elastic modulus of the soil and a form factor. For circular pile cross sections and a Poisson’s ratio of 0.4 a form factor of 1.12 can be derived. For a Poisson’s ratio of 0.0 the form factor would be 1.57. In EBK 82 of the Road Traffic Department in Rheinland-Pfalz the extreme values of the form factor are scheduled to be 0.5 and 2.0. Simplifying to DIN 4014 a foundation modulus ks = Es / D (at D > 1.0m D = 1.0m may be used) can be determined and from that a beam foundation k = D · ks as line-shaped foundation per m pile length. 2.4.2
Numerical Solution and Accuracy
In general, the set of differential equations can not be solved directly. Therefore, for each pile, these equations are integrated numerically by the Runge-Kutta method. The step width is controlled automatically to maintain a relative accuracy of 0.01 percent. The setting of higher error limits results in a reduction of the
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CPU time. The setting of smaller error limits is reasonable up to a certain value, which depends on the machine accuracy of the computer used. The reduction of the error limit below a certain value is not reasonable because the computational error increases again due to the rounding errors in the high number of the necessary additions. In the case of an unbedded beam the step width can be set very large. By contrast, for large Winkler coefficients the numerical calculation becomes more difficult. As a criterion the characteristic length is used, defined as: L=
p 4
4 · E/ K
(2.1)
This value is an estimation of the distance between the zero points of the solution function. For reasons with reference to the numerical integration, the characteristic length should not become less than 1/5 up to 1/10 of the element length. If this condition is not satisfied, great accuracy problems may occur resulting in differential forces in the nodes which are pointed out in an error message. These problems can be overcome by subdividing a pile into more subelements. In the case that a pile is subdivided into more elements, the placing of the nodes at points of changing soil parameters (layers) is to be preferred over an uniform subdivision. Pile elements get a minimal constraint of the rotational spring in order to prevent instabilities. If otherwise nothing was specified, a linear analysis is performed. Non-linear effects are: •
Different bedding in various transverse directions (F1 - term of the series sequence)
•
Limitation of the maximum bedding stresses
•
Second order theory
For these cases an iterative calculation has to be carried out. The program uses the ”Quasi-Newton” method with constant stiffness matrix. To obtain a better convergence the single increments are modified according to the Crisfield method. Literature: K ATZ [9]
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2.5
Truss and Cable Elements
Truss and cable elements can transfer only axial forces. In the case of non-linear analysis the cable elements can not sustain compressive forces. Example see ase5_cable_trestle.dat An internal cable sag is considered for geometrically non-linear analysis. In this case the transverse loading of the cable is calculated for the cable geometry (extensible plane prestressed cable). Without using internal cable sag a cable can be subdivided into shorter individual cables. The resulting cable chains can be analysed in a stable way with a prestress. For the control of the internal cable sag please look at CTRL CABL too.
2.6
Spring Elements
Spring elements idealize structural parts by means of a simplified forcedisplacement relationship. This is usually a linear equation which is based on the spring constant: P=C·
(2.2)
A spring is defined with a direction (dX, dY, dZ) and three spring constants. The here implemented element allows the following non-linear effects which are of course only usefully during a non-linear analysis: • •
prestress (linear effect) failure
•
yield friction with cohesion slip spring nonlinear work laws, please refer to section 3.36
•
springs with a reference area AR and a nonlinear material work law
• • •
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Figure 2.8: Spring force-displacement diagrams
A prestress displaces the corresponding effects and produces always a loading which acts on the structure. A prestress should not be defined in the system generation because it acts in all loadcases. It is better to use the prestress in ASE...PREX. A prestressed spring gets a relaxation in the absence of external loading or constraints. The non-linear effects are considered both for rotational and displacement springs. Friction can be defined with a lateral spring. The force component perpendicular to the spring effect direction results from the product of the displacement component in the lateral direction multiplied by the lateral spring constant. The maximum value of this force, however, is equal to the force in the primary direction multiplied by the friction coefficient plus the cohesion. If the primary spring fails, the lateral spring gets eliminated too. Spring loads are not included. A bearing lifting can be modelled in ASE with the group prestress GRP PREX also for coupling springs. Springs with a work law (see SOFIMSHA SARB) work with hysteresis by shifting the zeropoint of the work law curve after plastification. Examples see a1_spring_overview.dat e.g. spring_law_3_pkin_curve.dat
2.7
Boundary Elements BOUN and FLEX
The elastic boundary conditions do not represent actual elements. They describe the additional stiffnesses of the structure. Results are not saved in the case of FLEX. The effect of the elements appears directly in the form of support reactions at the corresponding nodes. For BOUN additional distributed boundary forces are stored for graphical output. Distributed support reactions are determined for boundary elements with number (compare program SOFIMSHA/SOFIMSHC). If two boundaries are defined at an edge, the distributed support reactions are calculated once only and they are output for the boundary with the smaller boundary number. Single supports
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can not be considered by boundary elements. A boundary element interpolates linearly the displacements between two nodes. The resultant distribution of the stiffness matrix at the two nodes is CR + 3 · CL
CR + CL
CR + CL
CL + 3 · CR
(2.3)
with: CR = CA · L/ 12 CL = CB · L/ 12
CA,CB
spring constants at beginning/end
L
distance of nodes.
2.8
Shell Elements
The shell element implemented in program ASE is a surface element. The individual elements are plane and they lie in each case in a plane whose normal is generated through the vector product ((X3-X1)·(X2-X4)) of the diagonals. The deviation of the element’s plane from the nodes is taken into consideration by means of additional eccentricities. The local coordinate system is oriented in such a way that the z axis is given with the normal to the element’s plane and the local x axis can be selected freely. The default orientation is parallel to the global XY plane with an angle smaller-equal than 90 degrees to the global X axis. If the observer looks into the positive direction of the z axis (thus from ”above ”), then he watches the nodes numbered counter-clockwise. If the element’s plane coincides with the global XY plane, the local and the global coordinate systems are then identical.
Figure 2.9: Local coordinate system
The element is implemented as a triangular as well as a quadrilateral element.
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The triangular element is considerably worse than the quadrilateral element and it should be used only, if no other choice of mesh partitioning can be found. Generally it should not to be used in the vicinity of supports.
Figure 2.10: Internal forces and moments
Because the normal element remains plane, the bending and the membrane structural behaviour of the individual element are decoupled. The element properties can be defined thus separately for the both components. Additionally the consideration of the components of an elastic support and a numerically conditional stiffness for the rotations around the shell normal occurs still. For a twisted element the membrane and plate parts are generated by decoupling. Then they are coupled with each other via the twist of the element. Thus the element is able to represent curved shells very exactly. This was demonstrated with corresponding benchmarks. The consideration of each structural behaviour can be specified in the program SOFIMSHA/SOFIMSHC for each particular element. The defaulted values are: SYST FRAM
membrane structural behaviour only
SYST GIRD
plate structural behaviour only
SYST SPAC
additionally rotations around the normal
The elements defined in SOFIMSHA/SOFIMSHC without load bearing behaviour are not considered for the structure. They can be referenced, however, in the case of load cases with free loads. In this way, a load area which consists of QUAD elements can be used for block loading of girders or three-dimensional elements. The ASE element is defined as a general quadrilateral. The accuracy of the solution, however, depends on the geometry of the element, thus not all conceivable element shapes are permitted. The optimum element is the square or the equilateral triangle. Rectangles and parallelograms are the second-best shape and the general quadrilateral the SOFiSTiK 2014
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third-best. General quadrilaterals with re-entrant corners are not allowed in the element formulation. A rectangle with a large side ratio a/b has difficulties in the representation of the twisting moments and also for the bending near a corner. A ratio of 1:5 is still tolerated in the program SOFIMSHA/SOFIMSHC and it should be exceeded only in exceptions. The size ratio of two adjacent elements should not be smaller than approx. 1:5. However, this value is relatively uncritical. The ratio thickness to element dimension is uncritical, because a shear correction factor is applied. It should be clear to the user, however, that the shear deformations in the case of thick plates result in deviations from the Kirchhoff’s theory. The ratio of the thicknesses of two adjacent elements should not be smaller than 1:10 due to its cubic effect. 2.8.1
Plate Structural Behaviour
The ASE element for the plate structural behaviour is based on Mindlin’s plate theory, as described in the implementations of H UGHES AND T EZDUYAR [8], T ESSLER AND H UGHES [16] and C RISFIELD [4], with an extension of a nonconforming formulation. The cross sections remain plane also according to Mindlin’s theory, however, they are not perpendicular anymore to the neutral axis. The same shape functions as for the displacements are used for the additional shear rotations. The total rotation is then the sum of the shear deformation and the bending rotation.
θ =
δ δ
+ θS
(2.4)
with:
deflection
θ
total rotation
θS
shear rotation
δ / δ
derivative w.r.t. x (similarly for y)
For the curvature and the shear angle we then have: k =
2-18
δθ δ
(2.5)
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Theoretical Principles | ASE
ky =
δθy
ky =
(2.6)
δy
δθ δ
+
θS = θ −
θSy = θy −
δθy
(2.7)
δy
δ
(2.8)
δ
δ
(2.9)
δy
A general orthotropic accretion which includes the thicknesses as well as the elastic moduli is formulated for the internal forces and moments: m = −B · k − μ · By · ky
(2.10)
my = −By · ky − μ · By · k
(2.11)
my = −Bd · ky
(2.12)
= S · θS
(2.13)
y = Sy · θSy
(2.14)
and
with the stiffnesses B =
By =
E · t3 12 · (1 − μ Ey · ty3 12 · (1 − μ
SOFiSTiK 2014
) 2
S =
) 2
Sy =
5 6
5 6
G · t
(2.15)
G · ty
(2.16)
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transverse bending stiffness By =
3 E · ty
12 · (1 − μ2
)
(2.17)
torsional stiffness Bd =
G · td3
(2.18)
12
with E , Ey
elastic moduli
G
shear modulus
μ
Poisson’s ratio
t , ty , ty , td plate thicknesses
In the isotropic case one must set t = ty = ty = td = t and E = Ey = E. The orthotropic elastic moduli and thicknesses are rotated through the input of an orthotropy angle OAL in the record MAT! a) For orthotropic material (e.g. mathematical cross section of prestressed concrete or wood) it can be set: By = Bd =
Æ
(2.19)
B · By
To reach this the mathematical thickness for ty and td must be input in addition to the orthotropic input of E and Ey . ty = td = t ·
Æ 3
(2.20)
By/ B
with B > By and ty = t . b) For corrugated steel can be applied (Timoshenko)
z = ƒ · sin π ·
B =
2-20
1
;
E · t3
· α 12 · (1 − μ2 )
α =1+
πƒ 2
2
(2.21)
(2.22)
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B y = 1 −
0.81 E · t · ƒ2 · 2 ƒ 2 1 + 2.5 2
(2.24)
By ≈ 0
Bd =
(2.23)
E · t3
α
· 2 12 · (1 − μ2 )
(2.25)
c) For web plates (y-axis in longitudinal direction) one can set: ty = t · 1 +
b · to3
1/ 3
· t3
(2.26)
ty = t
(2.27)
Bd = Bd (t ) + C/ (2 · )
(2.28)
where: C
torsional stiffness of the web,
, b
spacing and width of the web,
t , to
thickness of the plate and web.
Examples for orthotropic cases can be found e.g. in the book by T IMOSHENKO AND W OINOWSKY-K RIEGER [17]. 2.8.2
Membrane Structural Behaviour
The element formulation of the membrane stress state occurs either via a classical isoparametric formulation or probably via a similarly classical non-conforming formulation written by Wilson and Taylor. The thicknesses as well as the elastic moduli in different directions are taken into consideration. The poisson ratio corresponding to Ex is used. For anisotropic poisson’s ratio see chapter membrane structures and example membrane_poisson_ratio.dat n = S · ε − μ · Sy · εy
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(2.29)
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nyy = Sy · εy − μ · Sy · ε
(2.30)
ny = G · ty · γy
(2.31)
with the stiffnesses: S =
Sy =
E · t 1 − μ2 Ey · ty 1 − μ2
Sy =
2.8.3
E · ty 1 − μ2
(2.32)
(2.33)
(2.34)
Elastic Foundation
The QUAD element can be expanded with stiffness components in order to describe an elastically supported area. Only appropriate inputs can activate this foundation component. The foundation can be defined both perpendicularly and tangentially to the area. The non-linear effects like failure, yielding and friction may be specified. An elastic foundation is an engineering trick used for the approximate modelling of subsiding structures. The method is known from foundation engineering, however, it can be used also for the description of support conditions in structural engineering. The foundation coefficient indicates the stress resulting at a point which is subjected to a certain displacement. It is not a material constant, it is calculated later with a settlement analysis. In principle, its value always consists of an elastic modulus together with a geometrical dimension. The displacements of adjacent points are independent of each other, since shear deformations are not taken into consideration with this method. A more exact analysis of foundations according to the stiffness modulus method is possible with the program HASE. The easiest case is a single compressible layer of uniform thickness h. The
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calculation of the Winkler coefficient is achieved by applying a constant stress and by computing the resultant displacement. In the case of hindered lateral strain the result is C=
(1 − μ)
E ·
h (1 + μ) · (1 − 2μ)
=
Es h
(2.35)
In analog mode one can obtain Winkler coefficients for multi-layered systems. These coefficients are more acceptable as the layer becomes thinner in comparison to its deformation. If, however, the layer is relatively thick in comparison to the loaded area, or if it is infinitely thick, the Winkler coefficient has to be estimated in a settlement analysis at the point of interest. The horizontal foundation has usually the same order of magnitude. Column heads are defined sometimes with elastic foundations, especially in the case of masonry. By defining the Winkler coefficient one must keep in mind, that a two-dimensional foundation develops a certain rotational spring effect which is more important to the loading of a plate than the perpendicular displacement spring. A column of the height h which is supported articulated at its foot has a rotational stiffness equal to Cϕ =
3 · E h
(2.36)
This stiffness should correspond to a rotational spring foundation with Cϕ = C ·
(2.37)
From that follows C=
3·E h
(2.38)
The corresponding value for a column fixed at its foot is 4 · E/ h. Therefore it is correct to define a foundation three till four times higher, instead of the Winkler coefficient E/h, in order to describe the rotational foundation properly. If, however, the plate is supported articulated on the column, this type of foundation should not be used in any case because of its clamping effect against rotation. In this case it is recommended to use a single point support of a node and distribute the load by means of rigid or elastic elements (kinematic constraints). The foundation can be considered optionally as a single springs at the element
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nodes or as distributed foundation with a matrix. The use of single springs is advised in the case of very stiff foundations and severe load concentrations. The selection occurs with the input CTRL BTYP. CTRL BTYP > 0 consistent foundation matrix (default) CTRL BTYP < 0 single springs Support reactions which result from a QUAD foundation are printed and stored as nodal support reactions. Thus a graphical check of the support reactions is facilitated. 2.8.4
Rotations around the Shell Normal
The rotational degree of freedom around the shell normal is not contained in both load bearing behaviours. In order to prevent numerical difficulties for threedimensional structures, the Inplane-rotation of the nodes is coupled via a weak torsional spring at the displacements of the corner nodes in an intern way. 2.8.5
Twisted Shell Elements
If not all four nodes of an element lie in a plane (e.g. in the case of a hypershell), then the program defines an eccentric kinematic constraint of the corner nodes at a plane element in a median plane in an intern way. Three-dimensional curved structures may be analysed in this way with sufficient accuracy. In the case of twisted shell elements as well as geometrically non-linear analyses (twisted elements are generated automatically with the latter), internal springs are used now instead of the rotational stiffnesses mentioned in the previous paragraph. These springs convert the moment loading of a node around the shell normal to axial forces in the shell. The shear stiffness of the elements is modified slightly with this method, however, this is the only way to achieve moment equilibrium at the nodes of three-dimensional curved structures. 2.8.6
Eccentrically Connected Shell Elements
In the case of T-beams, it is an advantage to lay all nodes in the plane of the top surface of the plate and to connect the elements with different thicknesses eccentrically to this plane. Then the T-beam effect is realized correctly. The position of the elements is input in the program SOFIMSHA/SOFIMSHC (e.g. QUAD ... POSI=BELO). Additional explanations can be found in the school example ”Prestressed
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Skewed T-beam Bridge”. 2.8.7
Tendons in QUAD Elements
Prestressed cables defined with the program TENDON have the same element number as the QUAD element that contains them. They are characterised additionally with a cable number and with construction stage numbers for installation, grouting and a possible removal. They possess their own stiffness and are processed independently from the QUAD elements. Thus not only the deflecting loads are applied to the structure, but also stress changes in the tendon are calculated. The input occurs by the means of GRP CS. Prestressing cables in the QUAD elements can be used only in a geometrically linear analysis. 2.8.8
Non-conforming Formulation
The regular 4-node element is characterised through a bilinear accretion of the displacements and rotations. This accretion describes a uniform variation of the shear force and of the bending moment via a transformation. This element is called conforming, because the displacements and the rotations between elements do not have any jumps. The results at the gravity centre of the element represent the actual internal force variation fairly well, whilst the results at the corners are relatively useless, especially the ones at the edges or at the corners of a region. Taylor and Wilson came up with the idea to describe more stress states through additional functions that value is zero at all nodes. As a rule, these functions lead to a substantial improvement of the results, however, they violate the continuity of displacements between elements. Thus they are called non-conforming elements. Two element variations are available in the program ASE. The selection of the variations occurs via the CTRL option QTYP. QTYP 0
regular conforming element according to H UGHES [8] or Zienkiewicz
QTYP 1
non-conforming element with six functions based on H UGHES T EZDUYAR [8] or Wilson (default value)
AND
T EZDUYAR AND
Elements of type 0 can describe only uniform moments and membrane forces inside them. Elements of type 1 can describe a linear moment variation, if they are rectangular, whereas a general quadrilateral element can only do that approximately. Membrane forces can vary linearly.
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A corresponding non-conforming triangular element does not exist. Therefore the use of these elements in combination with triangles should be avoided, if possible. More explanations of the element properties can be found in the manual of the program TALPA.
2.9
Volume Elements
The volume element (BRIC) represents an elastic body and it is defined by means of 8 nodes. Even uniform bending states of a structure can be realized exactly via non-conforming accretions using hexaeders. Tetraeder should not be used as the used linear shape functions can not represent a uniform bending states! Please use WINTUBE for a graphical input or extrude Quad areas to a hexaedral mesh - see example SOFIMSHA/SOFIMSHC e.g. hex_handle.dat But also with pure SOFIMSHA simple structures can be created using hexaeder, e.g. bric_bucl.dat or more sofisticated water.dat Orthotropic material properties can be defined with the help of a meridian and a descend angle. The following options are available in extensions: •
Yield criteria for plastic analyses including analytical primary stress states
•
Import of temperature fields from program HYDRA (they can be applied to the structure as loading)
Material laws of AQUA-NMAT are implemented especially for tunnel analysis, e.g.: •
Mise-Drucker-Prager (also for steel)
•
Mohr Coulomb
•
Lade (for concrete)
Materials CONC and STEE are only computed linear in volume elements! For a nonlinear analysis with concrete or steel see: Concrete: bric_concrete.dat Steel: bric_steel_van_mise.dat
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2.10
Primary Load Cases
For the analysis of construction stages or for the definition of load steps in geometrical non-linear analyses it is possible to use a previous load case. The parameters of the primary stress state are defined group-wise for this purpose. A detailed description of the method is also given in the TALPA manual. Construction stages can be considered with different accuracies. The easiest way, of course, is to analyse the construction stages with the respective structural system independently on each other and then proceed with the superposition and the design of the structure. The different statical systems can be selected through the assignment of the elements in groups. ASE has, however, also a very efficient possibility to use stresses and deformations of a primary load case which allow the complete consideration of effects from creep or system change. See also module CSM Construction stage manager. During application the user must keep in mind that each stress state in a single element corresponds to an external loading of the element and is in equilibrium with that loading. ASE calculates now equivalent forces from the internal forces or stresses of the elements and can apply them as loading (GRP...FACL). These forces create a deformation state which counteracts the internal forces and makes them to zero when the statical system is not changed. If a system change has taken place in the meanwhile or if these loads have been applied with different factors, corresponding inherent stress states result. Following principal cases have to be distinguished: 1.
If the old loading is activated together with the primary state with a factor GRP...FACL=1.0, new loads do not result. The stresses remain the same, the deformations are zero. According to SYST...PLC the total deformations or at SYST...PLC=0 only the addition deformations are output.
2.
If only the primary state is applied as loading with a factor GRP ... FACL=0, the resultant loading is the primary load case with inverted sign. This gives rise to unloading deformations that generate a stress state which becomes zero together with the primary stress state in the case of free deformability. This FACL=0 method should only be used in special cases. FACL=1 is the usual default.
A graphical explanation to this can also be found in figure 2.18 :taking over the primary load case
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If some elements are removed from the system of the primary stress state along with their corresponding loads, the initial equilibrium is disturbed and forces arise at the boundary nodes of the removed parts. The remaining elements expand to the direction of the removed parts. If the primary state is generated analytically, the removed parts do not have to be defined once, because all necessary information can be extracted from the remaining elements. Using ECHO LOAD EXTR one can obtain an output of the internally generated loading at every node. This option should be used generally during analyses with primary states, because it is the best means for tracking down errors in the description of the states. The really applied nodal loads (nodal load vectors) can be represented with the program WinGRAF. Further instructions can be found in the description of the record GRP in the TALPA manual or in the examples. See also figure 2.18 :taking over the primary load case
2.11
Non-linear Analyses
Non-linear effects can be analysed only with iterations. This is done in ASE usually with a modified Newton method with constant stiffness matrix. The advantages of the method are that the stiffness matrix does not need to be decomposed more than once and that the system matrix remains always positive definite. The speed of the method is increased through an accelerating algorithm written by Crisfield. This method notices the residual forces developing during the iterations and calculates the coefficients e and f for the displacement increments of the current and the previous step. A damping of the method can be specified in the case of critical systems (SYST...FMAX Summary of example overviews Following non-linear effects are implemented currently: please also refer to NSTR in section 3.36: •
Spring elements (failure, yield, slip, friction, work laws)
•
QUAD foundation elements (failure, yield, slip, friction)
•
Cable elements ( compression failure, material work laws)
•
Truss elements (tension failure, material work laws)
•
Nonlinear bedding for PILE elements
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•
Nonlinear beam elements
•
Non-linear material laws for QUAD and BRIC elements
•
Geometrically non-linear analyses for all elements, cable sag, membranes
Tendons defined in the QUAD elements with the program TENDON can be used only in geometrically linear analysis. For TRUS, SPRI, CABL, BEAM, QUAD and BRIC in a geometrically non-linear analysis the initial stress matrix is added to the stresses of the primary stress state (for TRUS, SPRI and CABL without reference to a primary stress state, the prestress from the program SOFIMSHA/SOFIMSHC is used for this purpose see CTRL CABL). Thereby the iterations are markedly more stable when referring to a primary load case and the ultimate load can be calculated more precisely. A stability failure is recognized also in this way, even in the cases without unplanned initial deformation (an unstable system is reported, if the stresses of the primary state exceed the buckling load, i.e. the total stiffness matrix is negative). Since it is reported here, that the PLC was actually unstable, this feature is only meaningful in the case of small load steps. A module for the ultimate load calculation ULTI increases or decreases the load step-by-step until it reaches a still sustained loading. Initial deformations of the structure can be read as results of already analysed load cases with the record SYST...PLC...FACV. With GRP...FACL=0 and FACP=0 the initial deformation is applied without stresses. This can also be done more clearly with OBLI (the OBLI oblique position or predeformation can also be mixed with a primary stress state SYST PLC). In the stored results, the initial deformation is added to the incremental displacements of the actual loadcase. With CTRL DIFF the increment can be stored separately. Deformations from a modal analysis (bucling eigenvalue) can be used as initial deformation via scaling with FACV or OBLI see ase9_quad_euler_beam.dat task (ULTI iteration ... with predeformation) Non-linear analyses are not possible with the basic version.
2.12
Non-linear Analysis of Plates and Shells
2.12.1
Overview
The Layer-Model allows the layering of the material properties in a QUAD-shell element. The model can be implemented for laminated glass, laminated wood plates or other composite plates. The layer technique can be also implemented for the non-linear calculation of elements consisting of a homogeneous materi-
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al. In this case it is used to establish the positions of the individual layers. This method is especially suited for the non-linear calculation of plates and shells consisting of steel and reinforced concrete. Up to now the non-linear construction material models, steel and concrete, have been implemented for the shellelements. Example
Input file
Concrete
a1_introduction_example.dat
Steel
ase12_buckling_slab.dat
Ulimate load - verification
nonlinear_quad_concrete_beam.dat
pdf for that
nonlinear_quad_concrete_beam.pdf
Arch pure concrete
arch_bridge.dat
Steel_fibre_concrete
steel_fibre_concrete.dat
Sector tank
concrete_tank_cracked.dat
Fire design
quads_on_fire_1.dat
pdf for that
quads_on_fire_1_english.pdf
-> Example overviews
-> Summary of example overviews
The relaxation in individual layers, due to former plastification, is considered by consistently saving the results in all the layers of the elements (hysteresis effect for the bending of plates). This could create residual stresses over the crosssectional height, even after total relaxation. By means of the concrete law one can even consider creep and shrinkage effects for a cracked shell-element (The redistribution of stress, from concrete to the reinforced steel, due to creep and shrinkage). Several other advantages of the layer technique become apparent during the visualisation of the results. Besides the output of the numerical results in the different layers of the element one also has the option to graphically view the stresses over the element thickness in the program called ANIMATOR (choose a loadcase and double klick an element). 2.12.2
Input of the Materials
The calculation program ASE can evaluate an analysis for either the workingor the failure-stress level. It is advisable to use the option ECHO MAT YES in ASE, which checks the material values. The really used stress-strain curves of the material are plotted then and the significant values are printed. Examples for a free work law input:
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Work law input
Input file
Spring work law
a1_spring_overview.dat
.z.B. kinematic hardening
spring_law_3_pkin.dat
Concrete work law
steel_fibre_concrete.dat
Steel work law
ase12_buckling_slab.dat
Layer Sperrholzplatte
ase.dat/english/special/timber_quad_layer.dat
Layer Hohlkörperbeton
bubble_deck.dat
-> Example overviews
-> Summary of example overviews
Preset Stress-Strain Curves in AQUA Without any different defaults for the material parameters one gets from AQUA with following input: ECHO MAT FULL $ for output of the stress-strain curves $ NORM DIN 1045-1 $ acc. to DIN 1045-1 $ $----------------Concrete:----------------------------------$ CONC 1 TYPE C 25 $ standard C25/30 $ STEE 2 BST 500SA $ reinforcement $
the stress-strain curves which are represented below for the desired concrete. Here are according to chapter 9.1.5 of DIN 1045-1 (02.07): sig-u (red)
Stress-strain-curve for the cross section design (parabolarectangle-diagram) according to equation (65) and (66) [ 4] .
sig-r (blue)
Stress-strain-curve for non-linear methods of the determination of internal forces and moments according to equation (62) with fc = fcR [ 4] .
sig-m (green) Stress-strain-curve for non-linear methods of deformation analysis according to equation (62) with fc = fcm [ 4] .
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Figure 2.11: AQUA plot of the standard stress-strain curves for concrete C 25/30 according to DIN 1045-1 (07.02)
In analog mode one gets the stress-strain curves for the reinforcement according to chapter 9.2.3 and 9.2.4 of DIN 1045-1 (07.02):
Figure 2.12: AQUA plot of the standard stress-strain curves for reinforcement 500S(A) according to DIN 1045-1 (07.02)
ASE uses the stress-strain curves from AQUA. In this way also arbitrary stressstrain curves which are defined manually can be considered. Following requirements are to be considered for the input of the stress-strain curve type in order to select the correct curve during calculation in ASE with record NSTR. The stress-strain curve for concrete as well as for steel is defined with the item KSV in record NSTR and without the input for KSB. If a stress-
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strain curve is defined for KSV and for KSB, KSV sets the curve for concrete and KSB for the reinforcement. In this way arbitrary combinations are possible. Types and designations of the stress-strain curves in AQUA and ASE Designation of the stress-strain curve
Type in AQUA record SSLA
sig-u (red): design
ULTI
Selection in ASE NSTR without/with safety coefficient UL / ULD
sig-r (blue): non-linear internal forces and moments sig-m (green): non-linear deformations
CALC
CAL / CALD
SERV
SL / SLD
Following AQUA input defines a new serviceability stress-strain curve for concrete as well as for reinforcement with the safety 1.3: $-- Input of an example stress-strain curve for serviceability limit state: $ SSLA SERV 1.3 $ first SSLA record defines the type of the stressstrain curve $ $ The value after type of the stress-strain curve sets the corresponding $ $ safety coefficient $ SSLA EPS SIG TYPE 0.30 0.0 $ tensile zone $ 0.09 2.1 0 0 $-------------$ -1.1 -17.8 spl -2.0 -24.0 spl -3.5 -23.0 $ compression zone $ -4.5 0 $---------------- reinforcement: --------------------------------$ STEE 2 BST 500SA $-- Input of an example stress-strain curve for serviceability limit state: - $ SSLA SERV 1.3 $ first SSLA record defines the type of the stressstrain curve $ $ The value after type of the stress-strain curve sets the corresponding $ $ safety coefficient $ SSLA EPS SIG TYPE=POL -50 -525 $ compression zone $ -25 -525
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-2.3 0 2.3 25 50
-500 0 500 525 525
$-------------$ $ tensile zone $
The stress-strain curves which are input in this way can be seen and checked as modified serviceability stress-strain curve (sig-m / green) in the AQUA output of the material values and in the plot of the stress-strain curves:
Figure 2.13: AQUA plot with manually defined stress-strain curve sig-m (green) for concrete
Temporary Material Control Parameters in ASE In ASE record CTRL item CONC there are extended input possibilities for the material law for non-linear reinforced concrete. On the one hand the control parameters can be input here for consideration of the multiaxial stress state. On the other hand a temporary modification of the in AQUA defined material values FCT and FCTK, which is only valid in the current ASE calculation, can be done here also. Selection of a Stress-Strain Curve for an ASE Calculation The selection of a preset or manually defined stress-strain curve is done with an input in the ASE record NSTR (items KSV and /or KSB). Possible temporarily different inputs for the concrete tensile strengths and the consideration of the multiaxial stress state can be done with record CTRL CONC.
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Check of the Material Values in ASE In order to increase the transparency of the calculation the material values and further definitions for the non-linear material law which is in each case used in the calculation are also output in ASE. For this purpose it is necessary to set ECHO MAT YES. Then it follows here a definition of the analysis method for consideration of the crack widths and the tension stiffening as well as the output of all relevant parameters. In addition a presentation of the actually used stress-strain curves of the materials as well as a detailed plot of the concrete stress-strain curve in tensile zone are printed in the URSULA output.
Figure 2.14: Plot of the used concrete stress-strain curve in ASE
Figure 2.15: Detailed plot of the tensile zone of the concrete stress-strain curve in ASE
For laminated timber or laminated glass calculations a QUAD element can be defined about the height also with variable material composition. The materials for the individual layers are saved at first in AQUA how usual in separate
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material numbers. Then MLAY is used to define a composite material, which is input according to the layer arrangement. First the layer-thicknesses t0, t1, t2, t3 and t4 are defined, which are then followed by the respective material numbers: Layer t0 6 mm thick out of material 11, Layer t1
3 mm thick out of material 12 etc... :
PROG AQUA MATE 11 E 60e3 MUE 0.2 MATE 12 E 0.8e3 MUE 0.3 $ glass-plastic-glass $ MLAY NO 1 T0 0.006 11 $$ T1 0.003 12 $$ T2 0.003 12 $$ T3 0.003 12 $$ T4 0.006 11 END
$ glass $ $ plastic $
Figure 2.16: Heterogeneous Layers
The intermediate layers t2+t3 were defined only for a more clear output! The layer material No. 1 can be used only for QUAD elements. Example MLAY input see bubble_deck.dat or for a timber slab: timber_quad_layer.dat Note: The analysis is according to plate theory, i.e. assuming that the crosssection does not have planar deformation! The displacement of the plates between each other is not taken into account. For this one would have to couple the plates with springs! This model is not suited for the analysis of local failure at the coupling points of laminated glass plates, because for such an analysis the planar deformation of the cross-sections is very important. At these points one could evaluate a spatial stress-state, which can only be depicted by volume elements. Any arbitrary material can be used basically also orthotropic as layer for nonlinear analyses.
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Figure 2.17: Laminated plate
At the moment only layers from the material concrete or steel are processed non-linearly. The loading and unloading curve is generated independent on each other (hysteresis). 2.12.3
Analysis Basics
Linear Analysis Bending The total moment of inertia of a layered element is made up by the sum of each layer’s moment of inertia and the Steiner-part of the individual layers. Here an eccentricity of the centroid’s position could be created due to stiffer layers on one side of the element, e.g. sandwich-element with different top-layer thicknesses. The eccentricity is established automatically and is considered for simple plate bending, it also leads the correct length deformation of the elements. This effect also becomes apparent for an eccentric connection with a homogeneous element. The input of orthotropic materials is not allowed, due to the occurrence of various eccentricities in various directions. This is blocked by the program and leads to an error message. Linear normal-stresses in the layers are generated by the strains in the layers. They are calculated as usual by the stress-strain matrix D of the material in a layer: δσ = D · δϵ
(2.39)
where the matrix D can also be orthotropic. The linear total stress is made up of all the stress components including the allowed factors out of the ASE-GRP input: σ = FACP · FCREEP2 · σ,PLC + + FACS · FCREEP1 · D · (δϵ + ϵ,LOAD ) + σ (2.40)
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σ,PLC
Primary stress (initial stress)
FACP
Factor of the primary stress record ASE-GRP
FACS
Factor of the stiffness record ASE-GRP
FCREEP1
Stiffness reduction creep and shrinkage without PLC FCREEP1 = 1 / (1+PHI) with PHI from record ASE-GRP
FCREEP2
Reduction of the primary stress through creep and shrinkage, by taking over the primary load case with ro and dphi from record GRP FCREEP2 = 1 - dphi/(1 + ro·dphi)) (dphi = creep increment of a creep step component)
ε,LOAD
Load expansion (temperature or expansion load)
σ
Pre-stress (record GRP-PREX)
The GRP factor FACL is generally multiplied to the primary load-case as a value of 1.0. It generates the expansion loads from the primary stresses σ,PLC . If the stresses of the PLC together with the loads of the PLC are multiplied with the factors FACL=1.0 and FACP=1.0, then the system will remain in equilibrium and no additional expansions or displacements are created. The FACL expansion loads are then in equilibrium with the external loads:
Figure 2.18: Load equilibrium when taking over the primary load case without any new loads
The nodal load resulting from FACL and the element stress is generated because the element wants expand due to the primary compressive stress. The internal forces and moments are calculated by integrating the stresses in the layers, over the element thickness of each layer.
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Shear Initially the shear stiffnesses of the individual layers are summed up for the stiffness determination. The following equation is used to calculate the shear stress from the shear force q. τ =
q · S ·b
(2.41)
For homogenous material definitions, in the linear domain, this would result in a parable-shaped shear stress distribution over the height of the element, with the maximum value of τm = 1.5 · q/ h. For sandwich elements, with thick (strong) top-layers, it would mean that a nearly constant shear stress is present in the middle of the element; given by τm = 1.0 · q/ h (h=element thickness). Non-linear Analysis STEEL Example see ase12_buckling_slab.dat For a non-linear analysis, the calculation of the new linear stresses is initially made by assuming a linear material behaviour for every layer xi. The following applies when proceeding with the primary load case: σ = σ,PLC + D · dϵ
(2.42)
τ = τ,PLF + dτ
(2.43)
and
(simplified) The total stress σ is therefore not just put together by the total strain multiplied with the stiffness, instead it might be that the non-linear eigen-stresses of the individual layers of σ,PLC have to be considered. For the consistent treatment of the problem, including the correct generation of the loading- and unloading curves of the layer model, it is of importance that not only the internal forces and moments are stored in the database, but also all the stress in all the layers and all the Gauss-points. This information is needed for the next load case as σ,PLC . From these initial linear stresses a new linear comparison stress is calculated: For QUAD elements the following applies: σ =
r
2 + 3τ 2 + 3τ 2 σ2 + σy2 − σ · σy + 3τy y
(2.44)
where τy = disc shear and τ , τy = plate shear perpendicular to the plate.
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If the so calculated linear comparison stress σ, is above the allowed stress (by considering the hardening, which is calculated by summing up the plastic strains, by entering a trilinear stress-strain curve); then first of all the linear component is established (Break-through point through the plastic area). Then the remaining strain increment δdε with the elastoplastic material matrix D-P is applied incrementally, with the consideration of possible hardening. The non-linear relaxation lies on the surface of the plastic area. The number of plastic increments of the strain increment can be changed in the input CTRL MSTE. The non-linear material behaviour is according to the elasto-plastic plastic-law, described in TALPA, which is according to van MISE and includes hardening. For more information on this topic you are referred to Z IENKIEWICZ [21]. The following diagram results from uniaxial stress:
Figure 2.19: Uniaxial stress
In the case of combined stress, which is made up of normal stress (N/ A ± M/ ) and shear force stress, it is assumed that on reaching the elasticity limit (plastic area) the shear stress (from the shear force) remains constant and can not be increased any further through hardening. The thus established shear force stress is then basically substituted as a constant component into the calculation of the comparison stress. It has started to plasticising. This would then lead to the following: e.g. in plate bending; the shear stresses in the plastified plate edge would not increase anymore, however in the middle of the plate they would still get bigger, this in turn would cause a deviation from the parable-shaped shear stress distribution over the plate thickness, which would in turn cause a concentration of the shear stresses in the middle of the plate.
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Non-linear Analysis CONCRETE Examples see ase.dat\...\nonlinear_quad\ a1_introduction_example.dat The following literature was consulted on the concrete material law: S TEMPNIEWSKI AND E IBL [14], F EENSTRA AND D E B ORST [6], S CHIESSEL [12] Following current assessments and explanations are mentioned here additionally: XX [20], Z ILCH AND R OGGE [22], B ELLMANN AND R ÖTZER [3], XX [19], S CHNEIDER [13] The material behaviour of reinforced concrete can be described by the following properties: •
Non-linear stress-strain curve in tension and compressive zone
•
Contribution of the concrete between cracks (tension stiffening)
•
Non-linear material behaviour of the steel inserts
•
Simplified check of the plate’s shear stress
Usual procedure: The element is subdivided into NLAY layers. The stresses sigma-x, sigma-y and tau-xy and the principal stresses sigma-I and sigma-II are calculated for every layer’s boundary. For each principal stress direction a stress-strain curve is generated, which results from the principal stress relation in the respective direction. The thus established non-linear stresses are then integrated over all the layers to find the internal forces. After this all the forces of the reinforcement including the tension-stiffening-effect are added. Finally an independent check is made for the plate’s shear stresses. The following is a list of the concrete parameters taken from record CONC: CONC-FC
= calculation value of the concrete stiffness
CONC-FCT
= average tension stiffness for tension stiffening
CONC-FCTK
= lower fractile of the tension stiffness for bare concrete
CONC-GC
= GC compression fracture energy
CONC-GF
= GF tension fracture energy
CONC-MUEC = friction value in the crack splice Further inputs in ASE:
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LC - BET2
= load duration coefficient (beta2)
CTRL - NLAY = number of layers to be calculated >=6, default = 10 Analysis on Serviceability Stress Level Using the 1.0-times serviceability loads the maximum desired stress is input for this serviceability state at the material. The deformation and crack width to be expected is in this case mostly interesting. The input of the concrete tensile strength of the (pure) concrete layer is particularly important. This value is input in AQUA in CONC...FCTK and it can be modified subsequently temporarily in ASE with CTRL CONC V3+V4. The serviceability stress-strain curve without any additional material safeties is requested then in ASE (NSTR KSV SL = default). The selection of a realistic concrete tensile strength fctk (pure strength without reinforcement) is here very important. If fctk or CTRL CONC V4 is not input, the plate remains in uncracked state I. It can be therefore reasonable to decrease the value e.g. onto 60 % in order to consider a crack predamage from construction stage (hydration heat). On the other hand realistic deflections are resulted often only with a high initial value for fctk. Analysis with gamma-times Loads If using gamma-times loads the corresponding material stress-strain curve has to be selected in record NSTR in ASE. There are two possibilities that are also well shown in the beam example aseaqb_1_column_cracked.dat : •
Analysis according to "non-linear method": Here an averaged material safety of 1.3 is used. The material strengths are modified for this purpose. They are available AQUA and can be requested in ASE with NSTR KSV CALD.
•
Analysis in ultimate limit state NSTR KSV ULD
In both cases the pure concrete alone must include any tensile strengths. CTRL CONC V4 0.0 or 0.01 must be input! The increase of the steel stress due to the concrete action between the cracks may be brought into approach (default for fct or CTRL CONC V3). A non-linear analysis for the ultimate limit state is particularly necessary for additional effects from second-order theory. Such an analysis with temporarily switched-off tensile strength of the pure concrete causes however often big deformations and bad convergences. A reasonable procedure is therefore often also a determination of the internal
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forces and moments with average values of the material strengths (analysis in serviceability limit state) and a definitive design of the redistributed internal forces and moments with an average load safety coefficient (e.g. 1.45) Futher explanations see example a2_nonlinear_slab.dat Non-linear Stress-Strain Curve in the Compressive Zone The maximum concrete compression stiffness beta-ic, found in the compressive zone, is deduced from the principal stress relation. Beta-ic can either be read from the Kupfer curve, or it can be calculated by the respective equations [ 1] , pg. 260.
Figure 2.20: Biaxial failure curve according to Kupfer-Hilsdorf-Ruesch
With this maximum value beta-ic an uniaxial stress-strain line can be generated according to the concrete stress-strain curve for every of both principal stress directions. An increase value higher than 1.0 is only allowed for calculations in serviceability limit state. For calculations with gamma-times loads (ultimate limit state) this increase is deactivated in the default, because it is mostly desired that the maximum stress increases about the basic value of the concrete compressive strength beta-ic - see CTRL CONC V2. A reduction of the permissible compressive stresses is always considered for lateral tension. If the stress which is determined at first linearly is higher than the allowed stress, SOFiSTiK 2014
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the stress is reduced parallelly. The calculation is repeated again with the possible modified principle stress ratio. Tensile zone In the tensile zone of concrete, the maximum value beta-z, is always taken as the lower fractile of the concrete stiffness fctk. The length of the descending curve results from the tension crack energy GF of the processing zone. Typical values lie between 0.10 and 0.25 Nmm/mm2 . The program restricts the length of the descending curve to 5·epslin - see CTRL CONC VAL. If a stress-strain curve for concrete is already defined in the tensile zone in AQUA, then this one is used instead of the here described programinternal curve! Thus it is possible to calculated steel fibre concrete -> steel_fibre_concrete.dat
Figure 2.21: Uniaxial stress-strain curve for the tensile zone
The element is seen as cracked as soon as the tensile-strain crosses the linear limit value of epslin. Any further strain is stored as plastic tensile-strain and is taken into account for reloading after an element has been unloaded (hysteresis). Due to the possibility of excessive tensile stiffness perpendicular to the first crack, the program has to store two plastic tensile-strains at each point (first crack and second crack). It could be that a crack has already emerged when a primary load case is taken over. In this case the fixed crack direction of the primary load case is used for the calculation of the stresses. For this calculation the strains in the direction of the crack and perpendicular to it are used. When a possible shear stress is present at the crack it is lowered by a simple friction consideration (Crack-toothing input with AQUA-CONC-MUEC). This would prevent the occurrence of a second crack perpendicular to the first crack. For biaxial coated material, without the primary load case, two cracks are always perpendicular to each other.
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Reinforcement The program takes the defined reinforcement as the default reinforcement. The non-linear analysis is then performed for the default reinforcement. An automatic increase in lacking structural safety does not take place! It is therefore the users responsibility to check the certainty of the convergence of the analysis! Possible residual forces of the non-linear iteration have to be checked. Since these residual forces are stored as support forces they can be checked with the program WinGRAF, this is done by generating a plot of the support forces. During a plate analysis residual forces are also generated in the plate’s plane (normal forces), this is because the program needs to find equilibrium of the normal stresses. The reinforcement parameters and a given minimum reinforcement is taken from BEMESS-PARA or from the corresponding SSD design parameter dialog. REIQ is used to import a reinforcement from a previously generated BEMESS-analysis. The recommended method is used in the example a2_nonlinear_slab.dat . An analysis can also be made with non-reinforced concrete, when no reinforcement is defined. Further information on the program ASE can be found in the chapter ’Definition of Reinforcement’ as well as the latest TEDDY-Help . The consideration of the tension stiffening is done generally with a modification of the steel stress-strain curve described in [ 2] page 269. Since ASE 11.76-21 the consideration in serviceability limit state (NSTR SL/SLD) occurs according to the method of SchieSSl (DAfStB Heft 400) or EC 2, because more realistic deformation values result here. For the ultimate limit state and the non-linear determination of the internal forces and moments (NSTR UL/ULD or CAL/CALD) the consideration of the tension stiffening is done according to the simplified method of the modified steel strains according to DAfStB Heft 525. For a better clarity the in each case used method in ASE is output again at the non-linear properties of the plane elements. Please note, that the serviceability analysis (NSTR KSV SL) should be done usually according to Heft 400 also for DIN 1045-1 and respectively acc. EN 1992-1-1, because it leads to a better agreement with the test result according our experiences.
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Figure 2.22: Simplified method of the tensile stiffening acc. to Heft 525 (Bild H 8-4)
As the pure concrete layers also work in tension, the following working method is used: •
In a first step the strains in the steel layers in reinforcement direction are determined. These strains are equal to the mean steel strains εsm according to S CHIESSEL [12].
•
Using the tensile working law the two majoring strains I and II are determined based on the actual tensile strength amd the process zone length LZ (see below): I:
average strain when cracking starts
II: average strain for finished crack development = at the end of the decreasing part of the tensile work law •
•
The streel stress is now calculated as follows: –
In interval 0-I the steel stress is linear, concrete works linear.
–
In interval I-II the additional strain due to tension stiffening is interpolated linear. Concrete descends linear.
–
After II the full effect of tension stiffening is applied, concrete stress is 0. Reaching the steel yielding point a trilinear part follows,e.g. the steel working law is used.
The process zone length LZ is calculated as follows:
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example EC=27700 GF=0.3 fctk=3.71: Process zone length LZ = GF*EC/FCTK/FCTK = 0.3*27.7/3.71/3.71 = 0.605 m In SOFiSTiK this length is limited to 0.400 m, because otherwise an FCTK of e.g. 0.5 N/mm2 would result in a very long and unrealistic length. In ˇ TFinite Elemente im Stahlbeton - Betonkalender 1993/I StempniewskiTˇ a value between 200-600 mm is recommended. •
With this process zone length LZ and GF a crack opening delta= 2 * GF / FCTK can be calculated. With eps=delta/LZ the length of the descending part will be DEPSX= 0.404 promille (relative to LZ). This value is then limited to 5*length of the increasing part = 5*0.134 - not controlling here. This strain ˝ that means DEPSX is used in ASE for the plot of the stress strain curve U for an element with the element gauss point size LZ.
•
In the real analysis now this strain DEPSX= 0.404 promille is scaled to the actual element gauss point size. e.g. element area = 0.05m*0.05m = 0.0025m2 = per gauss point 0.000625m2 -> element gauss point size L_Gauss = squareroot(0.000625m2) = 0.025m. –
For an actual element with L_Gauss > LZ, DEPSX_GAUSS is calculated to DEPSX_GAUSS = DEPSX*LZ/L_Gauss (descending part is shortened).
–
For an actual element with L_Gauss < LZ, DEPSX_GAUSS = DEPSX. That means that the descending part will not be elongated!
So for an element size of 0.05m*0.05m a descending part of DEPSX_GAUSS = DEPSX = 0.404 promille is taken into account. •
For the new design codes (and without the input of CTRL CONC V5 400) the crack width is then calculated according to DIN 1045.1 11.2.4 or according to the Eurocode equation. The average force of the steel insert is calculated by multiplying the steel stress for the crack cross section in the cracked condition (state II) σs with the reinforced concrete area. This value is added to the concreteŠs internal forces and moments. The crack widths are first calculated in the direction of the reinforcement! If the crack direction is not perpendicular to the reinforcement, the crack distance and the crack width are modified according to EN 1992-I-I 7.3.4(4). For non-reinforced elements it is only possible to calculate one crack direction, but the crack width can not be established. The the average strain is plotted as crack width.
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The coefficient describing the connection properties is to be defined in AQUASTEE. The factor for the influence of the load period is input in ASE-LC. For ultimate limit state the calculation is done according to Heft 525, if DIN 10451, DIN FB 102 or EN 1992-1-1 is set. Shear force The shear stresses for the concrete law are not calculated for each layer, as is the case for the plastic yield criteria of STEEL, instead a simple shear limitation of the shear force is set with an assumed shear stress in the cracked condition (state II) of τ = q/ z = q/ (0.8 · h)
(2.45)
where h represents average of all the reinforcement layers. If the linear calculated shear stress τ rises over the input value τ02 , then the shear force is reduced accordingly and the element undergoes plastic shear deformation. The value τ02 is input with ASE-CTRL FRIC in N/mm2 and the default value is set to 2.4 N/mm2 . With TAU2...V2 a descending part with a final strength can be defined. The shear limitation is only calculated for the centre of gravity. Then it is proportionally assigned to all the Gauss points. If a BEMESS calculation with punching occurs before the non-linear ASE calculation, then a check of the shear stresses in ASE is not done in the areas of the punching point. In fine meshes around a punching node also the support force is distributed to round up the bending (peak smoothing see following chapter and CTRL BETO V7). If this is not the case or if the permissible shear stress is exceeded at other singular points, an undesirable shear plasticity can be switched off with an increase of CTRL TAU2 onto e.g. 9.9 N/mm2 if required. Then a shear or punching check has to be done however separately. Procedure of a Reinforced Concrete Plate Analysis Usually the system is to be defined as a three-dimensional system, this is because the crack opening will cause horizontal node displacements, even in the plate analysis. For the special case of a reinforced-concrete plate analysis the system can also be entered as a girder grid SYST ROST - the program will then automatically introduce a horizontal statically determinate support. The first step would involve a linear analysis of the individual load cases, a su-
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perposition of the load cases and a reinforced concrete design calculation of the linear internal forces and moments. BEMESS will store the required reinforcement dimensions under the design case number 1 (see BEMESS-CTRL-LCR). Subsequently a state load case has to be put together for the non-linear analysis. For the calculation of long-term deformations the load case components consist of self weight and a portion of the imposed load. A linear analysis of this load case is made, which is needed as a comparative reference later on. Now the non-linear analysis of this load case, under a different load case number and with a predefined reinforcement, is calculated (design parameter from BEMESSPARA and input for ASE-REIQ). The convergence of this non-linear analysis needs to be checked. The program finds a stable solution for the case where the energy remains the same (Energy convergence). Varying residual forces might occur due to inadequate convergence in the normal force directions. These are generally not of importance, but should be checked with WinGRAF...nodes...residual forces. The first load case of the non-linear analysis is usually calculated by excluding creep and shrinkage. Subsequently another non-linear calculation is made, including creep and shrinkage, under a different load case number. This is done so that the different effects can be compared and evaluated. It is also advisable to generate several calculations where the concrete stiffness FCTK is altered, due to the fact that this parameter has a significant impact on the entire analysis. The entire analysis should then be verified with the following load case results: •
linear analysis of the state load case
•
non-linear analysis without creep and shrinkage
•
non-linear analysis with creep and shrinkage
Definition of the Reinforcement The input REIQ...LCR...FACT is used to take over the reinforcement from the design load case LCR, generated in BEMESS, with a factor FACT. But the amount of reinforcement is limited by a minimum and maximum value, defined in the design parameters in BEMESS-PARA or the SSD design parameter dialogue box. A minimum reinforcement is applied also without a REIQ input. The new reinforcement is saved under the design load case LCRS (default LCRS=99) and can or should be visualized and checked with WinGRAF.
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The following rules apply for the concrete cover, the steel bar diameters and the reinforcement directions: Concrete cover: Distance to the centroid of the reinforcement: Is taken over from the design parameters (BEMESS-PARA or SSD) or: – from a SOFiPLUS definition from the database – or used as a default of 60 mm Steel bar diameter: Same procedure as the centroid distance – default 10 mm Reinforcement directions: They are: – taken over at first from the design parameters (BEMESS-PARA or SSD) – possible overwrote with a SOFiPLUS definition. – For the case where BEMESS results are taken over and no directions have been defined by SOFiPLUS: Then the directions of BEMESS are used Otherwise: – The reinforcement direction from SOFiPLUS is used. The smallest angle deviation is added to already defined directions, for reinforcements from BEMESS. – 0 and 90 degree steel is assumed for the case where nothing has been defined.
2.12.4
Rounding off over Punching Points
Enhanced computation on singular support points in the material non-linear concrete analysis (SYST NMAT YES): Following problem exists: Such singular supports caused singular forces that could not be carried in the concrete non-linear material model, especially in combination with singular rotational constraints. At punching nodes from BEMESS now a first singular support or connection force (and bending moment) will be distributed on neighbouring nodes inside the column perimeter to simulate a constant distributed support pressure. Thus the feature only works after a BEMESS ultimate design with PUNC YES or PUNC
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CHEK! The support force of the centre is distributed via an internal coupling ring around the centre node and elastic springs to further nodes inside the column area. The processing is documented in the statistic print out "rounding singular punching nodes". It can be switched off with CTRL CONC V7 0. It only works on BEMESS punching nodes but also if they come from beam connections in a 3D analysis. It also converts singular connection bending moments in a triangular connection pressure. The effect can be studied well by comparing a run with CTRL CONC V7 0 and a run with CTRL CONC V7 1. Especially at fine discretized punching points a rotational constraints will be analyzed more realistic (stronger). On such points the singular support moment caused a strong singular curvature in the fine mesh and thus a lower constraint. In a material linear analysis this feature is switched off by default, but can be enforced with CTRL CONC V7 1. 2.12.5
Output of the Results
Graphical Representation The graphical output of the results over the thickness of the QUAD elements is another side effect of the consistent saving of the results in all the layers. The ANIMATOR can be used for the visualization of the results (choose a loadcase and double klick an element). The following picture shows the stresses in a single QUAD element. The element is a sandwich element, where the soft inner layer is covered by two harder top-layers.
Figure 2.23: Element info
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The next picture shows the non-linear stresses in a concrete arched shell. Here the cracks can be seen in the tensile zone. The thin lines are the stresses in the reinforcement layers. The significant numerical values, e.g. the maximum steel stress, are output in addition in the dialogue box. Example tunnel shell quads_on_fire_2.dat
Figure 2.24: Visualization of the non-linear results
The visualization of the non-linear results from the steel and concrete law is still possible with WinGRAF, e.g. the visualization of the crack distribution at the underside of a plate, like in example of the reinforced concrete slab in cracked condition. Numerical output of the Results The entire non-linear results, like the crack widths or stresses in the cracked condition (state II), can only be released numerically in the ASE calculation. For this the ECHO FORC record is used. Statistics of Non-linear Effects The available non-linear effects are logged at the end of a non-linear calculation in ASE in ’STATISTIC NONLINEAR EFFEKTS’ 2.12.6
Miscellaneous Information
Iteration Control - Improvement of the Convergence Concrete Law Usually a tolerance of 0.002 is sufficient for the concrete law (record SYST ...TOL). This tolerance is also needed for the energy convergence. With negative TOL -1.50 a fixed absolute tolerance of 1.5 kN can be defined, if necessary not before 40% of the iterations: TOL4 -1.50 The convergence problems in non-linear calculations, which consider the 2-52
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concrete law, could initially be solved by increasing the number of iterations (SYST...ITER). If after, for example, 50 iteration the energy still increases, the load can not be taken up anymore, this is because: – a lack of reinforcement (tensile forces can not be compensated anymore) – the plate is to thin (compression failure) – the elements next to the singularity are to small (shear problem)
All these three problems lead to a point where the load can not be compensated anymore, due to an increase in strain. So the product of load·strain = energy will increase constantly. This can only be resolved by altering the system: – increase reinforcement – adjust the dimensions – decrease the load (try a lower load step) If the program does not reach a residual force equilibrium, even if the energy converges (the energy seems to remain close to the limiting value), then generally it could be attributed to the following reason: The program does not reach equilibrium in the normal direction of the plate - small changes in the strain plane generate large normal forces. Although this phenomena is usually insignificant for plate calculations and only has a local influence on the result. This becomes apparent when a check is performed on the residual forces (WinGRAF...nodes...residual forces). Often a damping of the iteration is successful with SYST...FMAX 0.90 (FMAX smaller than 1.0 or FMAX 1.10). If no convergence is found, the intermediate results of the iterations are saved with the load case numbers from 90001. They can be checked in the ANIMATOR with displacements and in WinGRAF with residual forces in order to find out the cause of the lacked convergence. With ECHO RESI 7 this can be enforced also for a convergent run. Often the convergence can be improved by the lowering of the concrete tension stiffness e.g. to 0.5 N/mm2 . This is because the negative stiffness, on the decreasing curve of the concrete stress-strain curve, is not that big and it can be equilibrated by the positive stiffness of the reinforcement including the tension stiffening. On the other hand it is possible that a bigger concrete tension stiffness
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could instantaneously release a large amount of concrete failure energy. This energy would then spread like a chain reaction through the system and convergence would be prevented. An increase in the minimum reinforcement would also improve the convergence, because the reinforcement would counteract the negative stiffness of the decreasing stress-strain curve. Steel Law Steel plates or shells do not encounter instantaneous tension failure, as is the case for the concrete law. Besides being able to increase the number of iterations (SYST...ITER), one also has the possibility to generate a trilinear instead of a bilinear stress-strain curve, which has its advantages. The tangential stiffness in a bilinear curve is equal to zero, i.e. a strain correction of the program would not alter the stress. Another advantage is the slowly increasing curve, which is favourable for the Newton-Raphson-method. In addition the steel law allows a step-wise increase of the load, as described in chapter "bearing load iteration". Tangential Stiffness For non-linear material calculations one always works with linear initial stiffness and compensation of the unabsorbed residual forces. An experimental material stiffness was implemented for improving the convergence of the iterations, but it did not achieve the desired effect and was thus deactivated. Non-linear material calculations, according to the first-order theory, utilize the Crisfield standard (CTRL ITER 0) in the iteration control. The line-search with the geometric-tangential stiffness matrix is only utilized in case of second-order theory are crack springs (CTRL ITER 3). The material matrix is always substituted with the linear initial stiffness and is not tangentially updated. You can always try both variants CTRL ITER 0 or CTRL ITER 3 but please start with the default (no input to CTRL ITER). Bearing Load Iteration In a lot of cases it is of interest to establish the maximum bearing load of a given system. To do this the bearing load iteration is applied. Here the load is increased step-wise until the point of failure is reached. The point of failure is interpreted as a lack in energy convergence, i.e. the system starts to fail if the energy is steadily increased during a bearing load iteration. A simple bearing load iteration can be found in example ase9_quad_euler_beam.dat , for cracked concrete also in the verification examples nonlinear_quad_concrete_beam.dat ( nonlinear_quad_concrete_beam.pdf)
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For non-linear material calculations it often happens that this automatic method does not reach adequate equilibrium, due to a lack in normal force convergence, even if the bearing load has not been reached yet. This can be overcome by entering a negative input for STEP under the record ULTI. Now the load is continuously increased, even if no convergence is reached after every individual load step. The user has to be assessed then the systems bearing capacity according to the energy convergence, the remaining residual forces and the load deflection curve. Alternatively the procedure could gain stability through the dynamic calculation.
2.13
Membrane Structures: Formfinding and Static Analysis
2.13.1
Overview
Membrane structures are characterized by transferring of loads only with normal forces. Bending moments and shear forces are not available. The analysis with real membrane elements is more comfortable and more exactly unlike the simplified processing with a truss model, because the geometry and the stress state can be generated any exactly. An orientation of the truss elements in defined directions is not necessary. The first task is the formfinding during the analysis of membrane structures. A corresponding form is searched for a desired stress state in the membrane. A soap skin is only result here for the isotropic prestress. Forms which are different to the soap skin need a normal force distribution which modifies itself about the structure. If the membrane form is found, real load cases can be calculated with this new form as initial system. The membrane must be omitted here for compression. Further textile properties are realized mostly by a simplified linear- elastic orthotropic material law. Edge stiffenings with edge cables, inside cables or compression arches have to be considered in real structures. 2.13.2
The Membrane Element
The membrane element implemented in ASE can be used only for calculations with large deformations with SYST ... PROB TH3. It is activated with the material input AQUA NMAT MEMB or with an input in SOFiMSHA...QUAD...NRA=2 (QUAD only with membrane action). The program configuration levels ASE1-3 are necessary for the material non-linear element and ASE4 for compression
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failure. Properties The membrane element described here is implemented in the FE program ASE of the SOFiSTiK AG. It has following properties: •
The membrane element processes only membrane internal forces and moments (NX, NY, NXY).
•
It bears arbitrary large strains and rotations.
•
It bears large twists and transmits the membrane forces from the twist into the right direction (here forces are available perpendicular to the thought element centre area).
•
It is possible to use three-noded or four-noded elements for it.
•
A prestress can be defined (also orthotropic).
•
Stress modifications can be suppressed for the formfinding.
•
It failures for compression (adjustable).
•
Orthotropic material properties can be considered (linear-elastic approximation). For anisotropic poisson’s ratio see example membrane_poisson_ratio.dat
Figure 2.25: Nodal forces at twisted membrane element
The stiffness of the membrane element consists of the normal strain stiffness in the element plane and of a initial stress stiffness from the prestress of the element. K
=
K0 + Ks
(2.46)
Input of the Membrane element Membrane elements are input like normal shell elements as element type QUAD.
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If the element formulation NRA=2 (see SOFiMSHA-QUAD) is set immediately, the element is marked as membrane. Otherwise a normal QUAD element can be defined as membrane with a non-linear material input AQUA NMAT Non-linear properties can be activated in AQUA with AQUA NMAT MEMB P1 P2. P1
Yield strength for tension maximum tensile strength in kN/m in warp and fill direction, practical e.g. for geo-textiles The input P1=0.0 is taken as ’no input’. The old input P1=1.0 is not considered (P1 was used formerly with another meaning.)
P2
Factor for compression survey P2=1.0 The membrane can sustain the compression. P2=0.0 The membrane cannot sustain the compression. (only reasonable after formfinding) P2=0.1 Intermediate values are possible, the elastic modulus is reduced correspondingly for the compression strains.
Nonlinear warp-fill material law In ASE a "‘Nonlinear yarn-parallel warp-fill behaviour"’ is implement according to: Dr. Cédric Galliot + Dr. Rolf Luchsinger ’A simple non-linear material model for PVC-coated polyester fabrics’ Tensinews Newsletter Nr. 18 April 2010 The definition of additional parameters AQUA NMAT MEMB P3+P4 activates this law. The nonlinear behavior is expressed as a stress-strain relation. This means that for a given stress sigma-w, sigma-f (w=warp direction, f=fill direction) it gives a corresponding nonlinear strain eps-w, eps-f. The values of the stressstrain matrix depend on the ratio of sigma-w to sigma-f using the factors γ und γƒ : γ = Æ
σ σ 2 + σƒ 2
γƒ = Æ
σƒ σ 2 + σƒ 2
(2.47)
Stress-strain relation:
ε
εƒ
=
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1 (γ ) E−ν ƒ E (γ )
−νƒ
E (γ ) 1 Eƒ (γƒ )
σ σƒ
(2.48)
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with the stress-ratio depending warp and fill stiffness: E (γ ) = ΔE
Eƒ (γƒ ) = ΔEƒ
1 + E1:1 γ − p 2
1 γƒ − p + E1:1 ƒ 2
(2.49)
(2.50)
Special Features for the System Input The system should be already defined, if possible, three-dimensionally with boundary arches. The boundary cables can be introduced then with full stiffness in the first formfinding step, because they have already the right length. The three-dimensional input has also the advantage, that the span cables and columns can be already input in the three-dimensional system. Then the still inaccurate form of the membrane is smoothed via ”shrinkage” of the membrane - see formfinding. Only for systems with high reference point it is reasonable to input the system at first two-dimensionally, because the input is significantly simpler here. The membrane can be hoisted then at marked points via nodal point displacements. Mesh selection Automatically generated meshes are unproblematic for systems without high reference points. They should be avoided at high reference points. At high reference points a radially and tangentially oriented mesh is numerically more stable and optically more beautiful due to the often orthotropic prestress. Mesh macros Pregenerated macros can be used for high reference points. Macros which are read in such a way are optimized for the registration of the stress conditions at the high reference points and delivers a good geometry for high reference points (The distance of the inner elements is selected deliberately near in the initial system, because they are stretched due to the hoisting during formfinding). The macros are placed in the plan, adjusted to the size (stretched) and the remaining membrane area is closed with a normal element mesh. Boundary cables Boundary cables should be always defined with the desired final curvature at an arch during input in the plan - see chapter ”Free Cable Edges defined in the
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Figure 2.26: A boundary cable left with small, right with large prestress
Figure 2.27: Left a too small, right a too large prestress
Initial System with Radius”. Mixed systems If the membrane should be calculated together with other structural members (walls, pylons, girders), the input is mostly urgently necessary with threedimensional initial system. Prestress and Formfinding As in outline mentioned in chapter ”Overview”, the prestress is decisive for the formfinding. Different membrane forms can be generated with different prestressing states. This phenomenon becomes especially clear for boundary cables: If a boundary cable is more prestressed for a given membrane prestress, a larger cable radius will result and thus a smaller pass of the boundary cable: At high reference points a too large prestress ties up the ”neck”: The user has to be known the desired form at the beginning. The pass of the boundary cable should be used already during the system input. The input FE mesh should include therefore the boundary cable curvature. Soap skin In a soap skin an isotropic prestress is available in all points of the membrane. This prestress is determined about the surface tension of the liquid for the genuine soap skin.
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The strain stiffness disappears here in the mathematical model. The equilibrium results only from the three-dimensional equilibrium of the isotropic stresses. The stiffness of the membrane results to: K
= Kσ
(2.51)
The stiffness keeps the membrane in its form perpendicularly to the membrane area. Thought points are freely movable in the plane of the membrane area. For the genuine soap skin the phenomenon is visible at the blurring of the points (bubbles) on the skin surface. The in all directions constant prestress is input in ASE with the record GRP ... PREX,PREY (acts on all element types, also on cables, beams ...). Constant orthotropic prestress The direction of effective span is often dominating in one direction for rectangular membrane areas. Then it is desired to set a larger prestress in this direction than perpendicularly to it. Nevertheless the prestress is of the same size in all points, if also orthotropically.
Figure 2.28: Orthotropic prestress - in longitudinal direction larger than in transverse direction
The orthotropic constant prestress is input in ASE either with the record GRP ... PREX,PREY in local element direction or with the record HIGH with a high reference point distance > 999 m in global direction. Orthotropic high reference point prestress If genuine high reference points are available for membranes, the orthotropic prestress is often desired with a fixed ratio of tangential/radial prestress in order to avoid a large tying up of the membrane at the high reference point. A radial stress which increases to the high reference point is necessary for that.
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A such axisymmetric stress state of the high reference point is generated with HIGH. The ratio of the tangential to the radial prestress is input with the item PTPR. In dependence on PTPR the stress increases much or not so much to the high reference point. Example of a high refence point at X = 5.0 m, Y = 0.0 m: HIGH X 5.0 Y 0.0 PR1 20 PTPR 0.4 produces: sig-r in distance of 1m = 20.00 kN/m sig-t in distance of 1m
=
8.00 kN/m (0.4*20)
and due to equilibrium reasons in distance of e.g. 10 m: ˆ sig-r in distance of 10m = PR1*1/r*e(PTPR*ln(r))
sig-t in distance of 10m
=
20*1/10*exp(0.4*ln(10))
=
5.02 kN/m
=
2.01 kN/m (0.4*5.02)
see example file: high_point.dat input: HIGH XM YM ZM NX NY NZ PR1 PTPR NOG
As a default an input for a high reference point has an effect for all QUAD elements, also for elements which are not a membrane. For mixed systems the prestress is allocated therefore with NOG to the corresponding group. It is also possible to input some high reference points per group. The program generates then the average value from the inputs in each element in dependence on the distance to the different high reference points. In the following example there are four high points and one low point in a membrane area. The tangential part PTPR may not be too large for the high reference points, because the membrane constricts itself and tears off. The factor PTPR is input therefore different for the five high reference points in this example.
Figure 2.29: Orthotropic high reference point prestress with some high reference points ( membran5.dat)
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If the distance is larger than 1000 m, the constant prestress is assumed with a stress in direction to the high reference point always of PR1 and a stress perpendicularly to it always of PTPR·PR1 and therefore without radial reduction. The advantage of this input is the simple definition of skewed prestress independently on the direction of the local element coordinate systems! The stress in the QUAD elements results from the global directions! Elastic skin A membrane can be defined from the beginning with the real stiffness and can be hoisted from the plane initial system at the high reference points or at the boundary cables. It results then large stresses in direction to the high reference points in dependence on the material properties. They can be scaled, however, by using this state with the group factors FACL+FACS. The use of a elastic skin formfinding is described in chapter ”Unstable Membrane Forms”. Input of the Prestress for Different Groups Definition in different groups For membrane analyses the system has to be got already in the first step an information about a prestress in the elements, because otherwise the system is unstable - the stiffness is zero perpendicularly to the membrane without prestress! A load prestress is still not considered for the system stiffness. The prestress has to be input therefore with GRP or HIGH. The different elements of the structure like: • • • • •
membrane areas boundary cables structural cables pylones and other beams massive support elements (concrete walls ...)
are defined in different groups and can get thus different prestresses from GRP and HIGH. If different radii in boundary cables should be kept exactly (formfinding also for boundary cables), then also the boundary cables should be defined in different groups. If the boundary radii were already input graphically (is absolutely recommended), it is possible to refrain the exact input of the boundary cable prestress, because the boundary cable force results from the radius and the membrane prestress during the formfinding.
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Criteria for the Input of the Prestress Free cable edges (free membrane edges reinforced with cables) should be input already as arch with the desired curvature radius in the initial system. The radius is preset in any case by the architect. If the boundary cable is defined as line in the initial system and the final edge circle should be determined by the program, then impermissible element angles are often available due to the distorsions. The iterations are much faster and clearer, if the edge arch has approximately the final position already in the initial system. The prestress which should be input for the boundary cable results to: cable force = membrane force radius P = n · r It is to be noted, that physical impermissible inputs do not arise. Unconsistent inputs can arise especially at the connection points of cables. In the following example an equilibrium is possible without an angle of the cable forces, because P1 > P2+P3+P4.
cable 2
cable 1
cable 3
Figure 2.30: Illogical preset cable prestress can not be right
2.13.3
Formfinding
System Definition - Two Options The initial structure can be defined with two options for the formfinding: •
Definition of a three-dimensional initial system with at first plane partial areas: The boundary points of the structure are input three-dimensionally. The remaining areas are defined e.g. as folded structure. The program takes over the formfinding of the inner area.
•
Definition of a plane initial system: The structure is input two-dimensionally. At arbitrary points the structure is ”hoisted” then at support nodes.
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Three-dimensional Initial System Three-dimensional initial system without cable edges Example angle, example file simple_angle.dat. A system is defined three-dimensionally from two planes (folded structure). All boundary points are supported, the lower edge is free.
Figure 2.31: Three-dimensional initial system - angle
The membrane prestress is defined isotropic with GRP ... SIGX SIGY in kN/m during the formfinding step. Because the strains should not lead to stress modifications due to the formfinding, the element stiffness is set almost to 0: GRP FACS=1E-10. The QUAD elements with the material number 1 are defined as membrane elements ( AQUA NMAT 1 MEMB). ASE input: PROG ASE HEAD Formfinding for Three-dimensional Initial Systems SYST PROB TH3 $ for geomatrical non-linear iterations $ GRP 0 FACS 1E-10 PREX 10 PREY 10 $ prestress definition 10 kN/m $ LC 1 TITL Formfinding $ formfinding without further load $ END
A load case with real 1.0-times stiffness should be follow after each formfinding load case for the check of the formfinding in order to guarantee that possible constraints do not lead to impermissible differences during formfinding (see constraints during formfinding CTRL FIXZ 1). PROG ASE HEAD Compensation of Possible Residual Forces SYST PROB TH3 PLC 1 $ uses the primary load case 1 $ GRP 0 FACS 1 $ elemets with full stiffness, stresses $ LC 2 $ are used from load case 1 (see record GRP) $ END
The iterations are necessary due to the effects from third-order theory. The vertical force parts (sinus(α) 6= α) change due to the large displacements. In
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addition the element geometries change also in part considerably. The first ASE calculations ends successfully after 9 iterations: Iteration 1 Residual 1.889 Update nonlinear stiffness Iteration 2 Residual 0.239 Iteration 3 Residual 0.222 Update nonlinear stiffness Iteration 4 Residual 0.134 Iteration 5 Residual 0.017 Iteration 6 Residual 0.008 Update nonlinear stiffness Iteration 7 Residual 0.003
energy 22.6089 Step 1-1 f= 1.000 energy 30.7733 Step 2-1 f= 1.487 energy 32.4090 Step 3-1 f= 1.814 energy 32.7557 Step 4-1 f= 1.838 energy 32.6185 Step 4-2 f= 0.604 energy 32.6450 Step 5-1 f= 0.607 energy 32.6701 Step 6-1 f= 1.178
The convergence has to be checked by the user. Indeed the programs prints a warning in the case of inadequate convergence, but it saves the results nevertheless. The result of the formfinding of load case 1 is shown in the following picture. The load case 2 does not deliver any modifications. The check of the formfinding does not show disturbances.
Figure 2.32: Result of the formfinding -three-dimensional initial system angle
For orthotropic prestress other forms which are all free form areas result in dependence on the prestress condition:
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Figure 2.33: V-long/V-lat=1:5 V-long/V-lat=1:2 orthotropic prestress -threedimensional initial system angle-
Corresponding input files: PROG ASE HEAD Angle with Orthotropic Prestress SYST PROB TH3 GRP 0 FACS 1E-10 HIGH 9999 0 PR1 10 PTPR 0.2 $ PR1 = prestress radial in a distance of 1m from high reference point $ $ PTPR = prestress ration tangential/radial $ LC 1 TITL Formfinding END
Free Cable Edges defined in the Initial System with Radius Example stand roofing, example file roof.dat If possible, a cable radius should be considered already during the graphical input. That means the cable should be input in an arch (see chapter ”Boundary cables”). Following system was generated three-dimensionally as folded structure with plane partial meshes during a graphical input. The cable edges are displaced only horizontally in the plane at a circle:
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Figure 2.34: Stand roofing - initial system plane left and angular picture right
Group classification: group 1:
membrane
expected membrane force X-Y=10-5 kN/m
group 2:
edge cable left
expected radius = 16 m
group 3:
edge cable right
expected radius = 46 m
Here the cable radius is preset instead of the cable force. The membrane prestress should have 10 kN/m in x direction, however, only 5 kN/m in y direction! Thus a first estimated cable force of P = n · r with a membrane force n=10 kN/m perpendicular to the cable results (group 2: N = 16m· 10 kN/m = 160 kN). Because the cable radius is not to be modified significantly, the cable elements are considered with their normal stiffness (GRP ... FACS 1.0) during the calculation. A cable force modification is possible thereby. Here it is important, that the radius of the input is kept approximately in the final result (specification of the architect). Otherwise the membrane should be kept the stress. The membrane stiffness is set therefore as usual with GRP ... FACS 1E-10: PROG HEAD CTRL SYST GRP GRP GRP LC 1 END
ASE Formfinding CABL 0 $ without inner cable PROB TH3 1 FACS 1E-10 PREX 10 PREY 5 2 FACS 1 PREX 160 $ 3 FACS 1 PREX 460 $ DLZ 1 TITL ’Formfinding with DL’
sag of the single cable $ $ membrane 10 KN/m - 5 KN/m2 $ cable N= p*r = 10*16 = 160KN $ cable N= p*r = 10*46 = 460KN $
The dead load is used simultaneously. The form is searched therefore for the loading prestress + dead load. Only the elimination of possible constraint forces is done again in a following calculation in load case 2:
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PROG ASE HEAD Compensation of Possible Residual Forces with FACS=1.0 SYST PROB TH3 PLC 1 $ uses primary load case 1 $ GRP - FACS 1 $ elements now with full stiffness, stresses $ LC 2 DLZ 1 TITL ’end of formfinding FACS=1.0’ END
Because the displacement picture is not different for load case1 and 2, only the final result of load case 2 is shown here:
Figure 2.35: Found form with prestress + dead load
Free cable edges defined straightly in initial system Example angle, example file simple_angle2.dat. Such a process should be avoided, because the QUAD elements are deformed possibly impermissible during the deformation of the boundary cable. This distortion and rotation of the QUAD elements is very unfavourable for orthotropic prestress, because the local coordinate system of the elements and the direction of the orthotropic prestress are turned. Following example should demonstrate nevertheless the possibility of the formfinding for cable edges which are input straightly. The first example simple_angle.dat is so modified, that a upper boundary is defined as free edge (without support conditions) and a boundary cable is generated at the boundary nodes. The membrane is defined in group 0 and the cable in group 1. The iteration is very fast for the system and the result is reasonable, because boundary cable curvature does not distort the QUAD elements. The cable radius is resulted always according to following formula: cable force = membrane force · radius P = n · r
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or r = P / n = 8 kN / 2 kN/m = 4 m
Figure 2.36: Free cable edge - result of the formfinding
Plane Initial System Plane initial system without high reference point Example file innenhof.dat Without additional elements like columns it is possible to define systems in plane and to hoist at corners. Only corner nodes in the plane, boundary cables with desired edge radii as well as meshes which are hooked in are generated here. The system is simple hoisted then at the corner nodes about the support displacements. The membrane becomes mostly a soap skin prestress which is input with GRP ... PREX,PREY. The boundary cables have mostly a fixed radius. The first estimation of the prestress of the boundary edges results from the membrane force multiplied by this radius.
Figure 2.37: Patio - left plane initial system - right result of the formfinding
Plane initial system with high reference point The plane system input is very advantageous for systems with high reference points. The high reference points are hoisted using the support displacements and remain in this position for further calculations. Following input generates the formfinding for a small tangential prestress (HIGH - ratio tangential/radial prestress = PTPR=0.1): example file high_point.dat SOFiSTiK 2014
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PROG ASE HEAD Input of highe reference point SYST PROB TH3 GRP 0 FACS 1E-10 $ membrane $ HIGH 0 0 PR1 10 PTPR 0.1 LC 1 DLZ 1 TITL Formfinding LCC ... copy nodal displacement from SOFILOAD - see input file ase. dat..membranes \sofExampleFile{ase}[english/membranes]{high\_point. dat}[] END HEAD Compensation with FACS=1.0 SYST PROB TH3 PLF 1 GRP FACS 1.0 $ membrane $ LC 2 DLZ 1 TITL ’Compensation with FACS=1.0’ END
Figure 2.38: Angular picture: plane initial system - result of the formfinding principle membrane force
The formfinding which begins with a plane initial mesh is to be seen also very well for another example with four high points and one low point. The system is here also generated very fast in the plane by copying the high reference point macro (example file membran5.dat). Mesh Control It exists the danger in the formfinding step, that the nodal points become blurred in the membrane plane. In order to avoid that, intern disc stiffnesses are generated with the so-called mesh control during formfinding. If this automatic mesh control does not function, further variants can be activated with the manual control CTRL ... FIXZ:
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Figure 2.39: Possible displacements of membrane nodes - constraints are generated perpendicularly to the drawn vectors at FIXZ=2
The automatic fixation of the nodes in the membrane plane is only used for the formfinding QUAD elements. A formfinding is assumed, if the stiffness factor of all QUAD elements which adjoin to a node is smaller than 0.5 (e.g. GRP ... FACS=1.E-10). If other static elements (e.g. QUAD) exists with full stiffness or bending beams are available at a node, then no fixation is done at this node. After end of the formfinding (e.g. for calculation of wind load cases) the membrane is used with full stiffness GRP ... FACS=1.0 and no fixation of the nodes is done in the membrane plane. Possible variants: CTRL FIXZ=1
automatic mesh control = default
CTRL FIXZ=2
fixes the nodes in the membrane plane for all iteration steps
CTRL FIXZ=3
fixes generally all nodes in global X-Y
CTRL FIXZ=4
fixes the local z coordinate in the first iteration step the transverse direction in further steps
CTRL FIXZ=5
fixes the local z coordinate in all iteration steps
CTRL FIXZ=4
can be used for the formfinding of boundary
or 5
cable radii
Saving of the Found Form If the formfinding is completed, it is basically possible to put always on the found form with SYST PLC for further calculations. A result representation with WinGRAF is actually always desired at the formfinding system. In addition it is desired, that the ANIMATOR lets swing e.g. the deformations from wind in rela-
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tion to the formfinding system. Without further control, however, the ANIMATOR would swing between the input system and the system deformed by the wind. In addition a new selection of the local coordinate system of the membrane elements is sometimes reasonable, if e.g. a fibre direction of the cloth should be defined from the high reference point. A function SYST ... STOR is therefore available in ASE. With this function the coordinates and the local coordinate systems of the elements can be generated newly by using the deformations of a load case PLC. Displacements of the load cases which put on that are only output as difference displacements to this updated system. Following literals are indicated in this case for STOR: STOR YES The position of the new local coordinate system of the QUAD elements results from the strains of the primary load case PLC. STOR NEW, XX, YY, ZZ, NEGX, NEGY, NEGZ The local coordinate systems are calculated newly from the new coordinates. · see manual SOFiMSHA record QUAD - KR Example simple_angle.dat The local coordinate systems and the stresses of the load case 2 are printed as follows in the initial system:
Figure 2.40: Coordinate system and representation of the internal forces and moments at the initial system
After the update of the geometry with: PROG ASE HEAD SYST PLC 2 STOR YES END
the same representation is printed considerably more beautifully. The undeformed (!) structure of the updated system is represented now: 2-72
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Figure 2.41: Representation of the coordinate system and the internal forces and moments at the updated system
With STOR YES the internal forces and moments of the primary load case can be used and represented furthermore, because the internal forces and moments refer to the new coordinate system. With STOR NEW,XX ... NEGZ the internal forces and moments do not match the new coordinate system and they are deleted during an ASE calculation with SYST ... STOR NEW...NEGZ. The displacements of the primary load case are deleted in any case, because they are included now in the geometry - in the new coordinates. The current database can be saved with SYST ... STOR before an update, e.g. with +sys copy $(project).cdb sichxyz.cdb. Formfinding with Loading The dead load of the construction was input during formfinding already in the example of the stand roofing. The found form lies then a little deeper as the pure membrane form without dead load. The effect does not strike for a small dead load. Also the boundary cable is very light. It is also possible to search deliberately a form with consideration of an outside loading, e.g. with constant internal pressure. An internal pressure of 2 kN/m2 is used during the formfinding in the example simple_angle.dat. The membrane prestress is selected with 2 kN/m2 . The formfinding is done now in several steps in order to consider the new orientation of the load area- see following chapter. PROG ASE HEAD New formfinding with additional internal pressure2 KN/m2 SYST PROB TH3 GRP 0 FCKS 1E-10 PREX 2 PREY 2 $ membrane 2 KN/m $ LC 11 TITL ’Formfinding internal pressure 1’
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LCC ... loads see .dat inputfile END PROG ASE HEAD Update formfinding internal pressure SYST PROB TH3 PLC 11 GRP 0 FACS 1E-10 $ once more formfinding without stress increase $ $ due to strain of the loading ! $ LC 12 TITL ’Update formfinding internal pressure’ LCC ... loads see .dat inputfile END PROG ASE HEAD Compensation with FACS=1.0 SYST PROB TH3 PLC 12 ITER 90 NMAT YES GRP FACS 1.0 LC 13 TITL ’Compensation with FACS=1.0’ LCC ... loads see .dat inputfile END
The membrane eigenstiffness is switched off again in the formfinding load cases 11+12 in order to prevent stress modifications in the membrane force due to strains. The load case 12 shows following deformation picture:
Figure 2.42: Example angle with internal pressure
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Figure 2.43: load case 11 load case 12 Angle with internal pressure
Because the local coordinate systems are directed inwards, the internal pressure was input negatively. The lower picture shows the formfinding of a compressed air tennis hall beginning with a plane mesh. The calculation as ideal soap skin results here in a curios corner generation. Real tennis halls leave mostly the ideal soap skin form for the benefit of a better space utilization in the corner with the disadvantage of an orthotrop stress distribution with disturbance areas in the corner.
Figure 2.44: Tennis hall: pumping up of a soap skin with plane initial system tennis.dat
A further example for formfinding with internal pressure is to be found in six_corners.dat:
Figure 2.45: Hexagon: six_corners.dat
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pumping up of a spherical shell (increase 1.0) -
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Load Direction and Load Area A setting up onto the load case 11 with the same load is urgently necessary in load case 12 for the last example, because the conversion of the load into nodal loads can be done only on basis of the element geometry of the primary load case. On the one hand the used nodal load is to small in load case 11 - the elements become larger due to the pumping up. On the other hand the load direction of the nodal loads is not correct, because the local z axis is twisted. A new setting up onto the load case 11 is urgently necessary in load case 12 with a new calculation of the nodal loads using the coordinates of the load case 11, if loaded systems have large deformations! This is done, however, fully automatically, if the load case 11 is used in the further calculation with SYST ... PLC 11! Furthermore a compensation in xyz is necessary in load case 12 also due to the large curvatures. It can be recognized at the obvious horizontal expanding of the ”bubble”. For all element loading it is generally valid: The load is converted into nodal loads at the system of the primary load case. Deformations of the current calculated load case do not twist the load anymore. It has to be calculated therefore always with small load steps and with a new setting up onto a primary load case also for a girder which is designed for buckling, if e.g. the load should be twisted to the local z axis of the beam in conformity with the beam rotations! Formfinding for Compression Arch Shells The form which is found with the soap skin and e.g. using negative dead load can be used also as initial system for a compression shell. In this case the element thicknesses and the material parameters can be redefined after formfinding and the membrane elements can be converted into normal shell elements which can carry then the positive dead load and the real loads with compressive forces, bending moments and shear forces. In SOFiMSHA the definition NRA=2 may not be input. The switching over from the membrane to the concrete is done with a first AQUA calculation withAQUA MAT + NMAT MEMB for the formfinding. Then the material CONC is redefined with a following AQUA calculation. 2.13.4
Static Analysis
In general the formfinding is only a first step during the calculation of membrane structures. The loading wind and snow which is essentially for the design of the building structure must be carried by the system which is determined during formfinding. The snow load can be defined mostly very simple. The wind load,
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however, depends on the height, position and direction of the single element. Generation of the Wind Load If the possibilities for the input of the wind load are not sufficient in SOFiMSHA, the wind load can be defined also as block load: example membrane_compression.dat . With a little more expenditure the wind load can be input also as a function of the height in dependence on the position with angle functions. The output of all elements including the definition of the element centre of gravity as well as the printout of the local z axis (normal) can be done in ASE with ECHO ELEM 4. If the list is read into a table calculation program, it can be fast converted into a load input by using of formulas. Then each element get its own local loading. A system has not to be calculated using ECHO ELEM 4 in an ASE calculation - CTRL SOLV 0 can be input here. The output values refer to the system which was displaced possibly with the primary load case SYST ... PLC. Following input generates the subsequent output: PROG ASE HEAD Element centre of gravitiy and normal vector for wind loading ECHO FULL NO ECHO ELEM 4 CTRL SOLV 0 SYST PLC 12 LC 13 DLZ 1 END S H E L L E L E M E N T S EL-No XM(m) YM(m) ZM(m) 1 -22.267 6.178 -.398 2 -21.832 8.165 -.326 3 -20.999 3.618 -.633 4 -19.828 1.022 -.817 5 -20.687 8.110 -.628 6 -20.635 5.709 -.978 7 -20.237 7.585 -.902 element centre of gravity
nx ny nz .342 .082 .936 .222 -.264 .939 .381 .105 .919 .412 .123 .903 .251 -.283 .926 .364 .069 .929 .249 -.264 .932 normal vector
Wind pressure till compression failure The tensile stresses due to the prestress can not be sufficient for large wind forces in the reality. Further compressive strains lead to folds in the membrane. They have, however, no influence on the structural behaviour for these special cases. The system is mostly stable also with folds. The program ASE can realized the load transfer which exists here with switching off of the compressive SOFiSTiK 2014
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stresses. A wind pressure from below which uses the prestress in transverse direction up is used in the example stand roofing ( roof.dat). It would produce therefore folds in reality. At first the system is updated in the calculation by setting up onto formfinding load case 2: PROG HEAD HEAD SYST END
ASE System update for calculation of new displacements from formfinding state LC 2 PLC 2 STOR YES
Figure 2.46: Updated system - coordinate systems
Figure 2.47: Side view
All elements with the stiffness factor 1.0 have to be input now for the following wind loading, because strains should generate now stress modifications in the system. In the following picture the stress in the centre are actually only uniaxial for full wind. The stress is omitted biaxially even in four elements:
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Figure 2.48: Membrane forces wind from below - - rigth: in initial system
Textile Material Laws Essential membrane properties can be described with an orthotrop but otherwise linear-elastic material according to an article in Bauingenieur 70, 1995 on page 271 by R. Münsch and H. W. Reinhardt. Such a material can be defined at SOFiSTiK with the record AQUA MAT . It means here: AQUA MAT
E
elastic modulus in x direction
EY
elastic modulus in y direction
MUE
Poisson’s ratio related to E
G
shear modulus
The material law reads then:
σ
1 σ = y 1 − μ2 τy
E
· μ · E 0
μ·E
0
Ey
0
0
G · (1 − μ2 )
ϵ
· ϵ y
(2.52)
γy
A textile material can be input therefore with different elastic modules in warp and fill direction. Only a Poisson’s ratio which relates to E is possible due to the necessary symmetry condition in the material law see membrane_poisson_ratio.dat The warp direction of the elements should lie in the local x direction of the elements. This direction has to be defined during the (graphical) input of the elements. In special cases it is also possible to input the angle in the material law with the angle of anisotropy OAL. The failure of the membrane elements for compression is activated with ASE input SYST ... NMAT YES. Withj AQUA NMAT ...
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lected - see nonlinear_warp_fill_behaviour.dat Examples for material input see atrium.dat Relaxation and Cutting Pattern The membrane can be cut, detensioned and developed in the plane after formfinding with the program TEXTILE. Further information see manual for TEXTILE. 2.13.5
Unstable Membrane Forms
The tangential prestress can not be chosen in an any large way already in the simple example membhoch.dat. If the tangential prestress is input in record HIGH about the factor 0.3, ASE prints a divergence. An ANIMATOR picture of the load case which is nevertheless saved shows following picture:
Figure 2.49: Initial system tent roof - generated in plane - bottle_nec.dat
Corresponding input - bottle_nec.dat: PROG ASE HEAD Bottleneck HEAD ASE prints divergence - nevertheless look at load case 1 with ANIMATOR SYST PROB TH3 GRP 0 FACS 1E-10 HIGH 0 0 PR1 10 PTPR 1.0 $ soap skin - not possible! $ LC 1 DLZ 1 TITL ’ Bottleneck’ LCC ... loads see .dat inputfile $ lifting node 481 to 6 m $ END
Obviously the large tangential stress cords up the bottleneck (PTPR=0.25) so strong, that the membrane or soap skin cracks.
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The phenomenon keeps on being examined at following example. A membrane structure is generated again in the plane. The high reference points are not discretized here - a upper rigid ring which can be displaced constantly upwards about a support spring is accepted. An isotropic prestress = formfinding of a soap skin is defined. The stiffness factor with 0.01 is input, however, to large for the generation of the desired phenomenon of the bottleneck. Example tent roof, example file tent.dat .
Figure 2.50: Initial system tent roof - generated in the plane
The formfinding with 4 m ring lifting has a still stable form:
Figure 2.51: Initial system three-dim. representation Membrane hoisted 4 m
Due to a further lifting the neck cords up always more during the xyz compensation calculation. By looking at the picture for 4 m lifting the closing forces of the defined membrane prestress in ring direction can be already seen at the bottleneck. The calculation for 7 m lifting is only convergent, if the elements get a residual stiffness with FACS 0.005. The following pictures do not show any correct membrane stress state, but they point out at an unstable formfinding process:
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Figure 2.52: Membran 7 m hochgezogen Weiteriteriert 7 m
This effect can be shown at a soap skin which should be hoisted with a small ring. After a critical height the soap skin constricts itself and is detached suddenly. Following process is trusted by the human eye: The stress modification due to strains are not suppressed anymore but they are allowed. The stress in the ring area increases due to the lifting of the inner rings. The usual picture of a deformed soap skin (or of tights which are tensed over the initial mesh) results thereby.
Figure 2.53: Elastic mesh 1 m till 6 m hoisted
2.13.6
Calculations of Cable Meshes
With the same methods formfindings can be done also for cable meshes. Discrete cable elements are defined here instead of the membrane. As for the membrane the cable elements can be used either as elements with constant prestress and known length or as elements with full strain stiffness and planned initial length. Latter one is mostly desired for the simpler filling measuring of sin2-82
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gle cables with the same length. But it leads to distortions in the grid in the plane projection of the displaced mesh. The lower picture shows the concept design of a footbridge which is supported on a cable mesh - it is a research paper for the bridging of the railway station place in Braunschweig. At first the system is patitioned in an element grid in the plane with cables of the same length. The boundary arches are connected at first at an approximate form. In the following formfinding steps in which the corner points of the mesh are compulsory displaced into the desired vertical position the boundary cables were defined at first as very elastic. That means they might change their length arbitrarily, while the inner cables were defined with normal strain stiffness, because they should not change their position. The four cables which are generated around the inner deep points as well as single cables in the nearness are an exception. They have to be defined also partially elastically in order to get a sufficient lowering of the deep points and thus a double curvature of the cable mesh. These during formfinding more elastic inner cables have to be produced and installed therefore with a larger length. Foremost the double curvature of a membrane or of a mesh creates, however, the possibility to carry outer loads without larger deformations. The stability becomes thereby clearly better also for the dynamic vibration inclination. The point-wise loading due to the footbridge which is not shown here leads to a further local subsidence of the cable mesh. This is, however, favourably for the stability. The compliance with a structure clearance for the lower street (shown in the side view) which is necessary also during load action was decisive for the concept design.
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Figure 2.54: Cable mesh with the necessary structure clearance
2.13.7
Check List - Notes - Problem Solutions
System input: •
If possible, the system should be already defined three-dimensionally with boundary arches (set local coordinate system for the arches). The boundary cables can be used then with the full stiffness in the first formfinding step, because they have already the correct length. The three-dimensional input has the advantage that the span cables and the columns can be already defined in the three-dimensional system. Then the still inaccurate form should be smoothed by ”shrinkage” of the membrane - see -> Formfinding.
•
Without staying construction it is also possible to input the system in plane. Foremost then the system is hoisted by using the support displacements. In this way corrections of the height position are possible. The input of the boundary arches is indeed simpler. Because the cable length of a boundary arch becomes clearly longer during lifting, the first step has to be done with elastic cables (FACS 0.001).
•
Definition of the boundary arches with the approximate curvature radius during input
•
Usage of macros which are like a spider net for modelling of the high reference points
•
Input of a central support node at the high reference points and connection of the surrounding membrane nodes at the structural points
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•
The first calculation with SOFiPLUS is also reasonable with a triangular mesh (mesh generation - triangles)
Formfinding: •
Estimation of the planned prestress of the elements (N=p·r) and definition about GRP and HIGH
•
Input of these elements which should keep their stress in the formfinding with GRP ... FACS 1E-10 - The strains does not generate then additional stresses.
•
Calculation of the cables without inner cable sag (CTRL CABL 0)
•
Termination of the formfinding always with a following load case with full stiffness GRP ... FACS=1.0, setting up onto the last load case as primary load case
Setting up onto a primary load case: •
Input of it in SYST ... PLC
•
A prestress may not be input at GRP ..., because it would be added to the primary stresses. Exception: The primary stresses are not used with GRP ... FACL=0.
•
GRP ... FACL=1 (default) adopts the primary stresses. So that they are in equilibrium with the applied loads, the external loads like dead load, internal pressure or wind load have to be used again and again. Exception: Constraint loads like support displacements, temperature or prestress loads, because they are not external loads.
Static loading: •
For problems with the convergence the loading (wind) should be used with a small factor and then further increase of the load after setting up onto this convergent state as primary state.
Problems during iterations: •
A stable system is reported, then calculate only one iteration step with CTRL ... ITER 1 and check the displacements with the ANIMATOR (first step force density method)
•
Do not input the factor GRP ... FACS for the cables too small (better FACS=0.01) or calculate it with CTRL ITER 3 V2 1
•
If the cables are set with full stiffness in the first formfinding but the membrane elastically , iteration problems may be available - then use the cable
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stiffness with FACS 0.01. It is better set the boundary curvatures with preset cable prestresses. For insistent problems, mail the input file to the SOFiSTiK support. 2.13.8
Overview about the Used Examples
-> Example overviews
Example
-> Summary of example overviews
Special feature
Introduction examples: - see ...\ase.dat\english\membranes atrium.dat
simple plane example with boundary cables
tennis.dat
plane initial system - formfinding with internal pressure - air hall formfinding three-dimensional initial system (angle), update with new local coordinates, internal pressure simple example with high point comparison of different PTPR ratios three-dimensional initial system (folded structure) boundary cables, failure for large wind pressure from below
simple_angle.dat high_point.dat roof.dat Further examples:
same example as membhoch.dat with unstable bottleneck result membrane_compression.dat same example as membhoch.dat with compression failure for strong wind membran5.dat plane initial system with 4 high points and a deep point bottle_nec.dat
plane initial system - formfinding with constant internal pressure tent.dat plane initial system and two high points defined as rings, unstable formfinding, soap skin, comparison with rubber simple_angle2.dat formfinding with at first straight boundary cable, comparison four-node and three-node elements air_volume_tennis.dat Air hall with active aur volume VOLU six_corners.dat
2.13.9
Necessary Program Versions
For the membrane analysis the extensions ASE1 and ASE3 are necessary additionally to the ASE basic packet, for non-linear material analysis (compression
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failure) also ASE4.
2.14
Dynamic Modal Analysis
For dynamic eigenvalues there are two main analysis methods available: 1. Direkt method according to Lanczos 2. Simultaneous inverse vector iteration The method according to Lanczos is usually always the quickest one. Especially in the case of many eigenvalues (more than 10) it is the only practical method. The number of the required eigenvalues depends in turn on the expected excitation frequencies. The simultaneous inverse vector iteration should be used, if the interest is limited to a few eigenvalues only or if a check of the number of eigenvalues below a certain frequency is required (Sturm sequence). The modal shapes are saved like regular load cases. They can be further processed as desired, and then they can be used chiefly with the program DYNA for a dynamic analysis. For the simultaneous vector iteration the higher eigenvalues converge much more worse than the lower. Therefore it is reasonable, if enough memory is available, to iterate a few more vectors than one needs. The method is, however, inappropriate for a large number of eigenvalues. The number of iterations is predetermined by the program. If the convergence is slow, one should switch generally to the Lanczos method instead of increasing the number of iterations. The iteration is interrupted, if the number of the maximum iterations is reached or if the maximum eigenvalue has changed only by the factor less than 0.00001 opposite to the previous iteration. For the method according to Lanczos the number of the Lanczos vectors should be selected usually twice so large as the number of the desired eigenvalues. An iteration is not necessary in this case. Example see ase4_eigenfrequencies.dat
2.15
Buckling Eigenvalues
For buckling eigenvalues only the default method with EIGE ... BUCL should be used: The Pardiso Solver CTRL SOLV 4 should not be used here as he has problems with determinants going to 0.0. The default solver CTRL SOLV 3 is better for buckling eigenvalues.
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If too many or only negative eigenvalues aer found you can choose an automatic eigenvalue shift with EIGE...LMIN AUTO. Example see buckling_eigenvalue_shift.dat Simple slab buckling see ase12_buckling_slab.dat
2.16
Masses
For dynamis eigenvalues only for beams consistent mass matrix are used - vgl. CTRL MCON. All other elements use a diagonal mass matrix (lumped mass matrix). See also program DYNA. In a time step analysis all elements use a diagonal mass matrix . The mass center is printed in the output. The complete calculated mass vector including the dead weight can be output with ECHO LOAD EXTR. A conversion of loads to masses can occur with the record MASS LC. Example see ase4_eigenfrequencies.dat In earthquake analysis: a1_dynamic_overview.dat
2.17
Damping Elements
Damping values e.g. method.
in spring elements are considered for the time-step
Example see spring_with_damping.dat exponential: springdampexpo.dat
2.18
Modal Damping and Modal Loads
The modal damping dj is defined as a product of the modal shape i multiplied by the damping matrix multiplied by the modal shape j. This matrix is not generally diagonal. However, ASE calculates only the diagonal terms of this matrix and saves them as modal damping values. Different damping of the individual modal shapes can be calculated easily in this way by specifying different damping for particular element groups. For evaluation of modal load, SOFILOAD can multiply a loadvector of an ASE loadcase e.g. 3 with an eigenform e.g. lc 1004 (SOFILOAD: LC 3 rest ; EVAL RU no 1004).
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Literature | ASE
Literature [1] K.J. Bathe and E.N. Dvorkin. A Four-Node Plate Bending Element Based on Mindlin/Reissner Plate Theory and a Mixed Interpolation. Int.Journal.f.Numerical Meth. Engineering Vol.21 367-383, 1985. [2] J. Bellmann. Vorgespannte schiefwinklige Plattenbalkenbrücke. SOFiSTiK Seminar, 1994.
7.
[3] J. Bellmann and J. Rötzer. Beispiele zur Bemessung nach DIN 1045-1, Müllbunkerwand. DBV: Band2: Ingenieurbau Beispiel 15, 2003. [4] M.A. Crisfield. A Quadratic Mindlin Element Using Shear Constraints. Computers & Structures, Vol. 18, 833-852, 1984. [5] Timothy A. Davis. Ldl: a consise sparse cholesky factorization package. http://www.cise.ufl.edu/research/sparse/ldl, 2003-2012. [6] P.H. Feenstra and R. De Borst. Aspects of robust computational modeling for plain and reinforced concrete. Heron Volume 38 No.4, 1993. [7] T.J.R. Hughes and E. Hinton. Finite Elements for Plate and Shell Structures. Pineridge Press International, Swansea, 1986. [8] T.J.R. Hughes and T.E. Tezduyar. Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element. Journal of Applied Mechanics, 48/3, 1981. [9] C. Katz. Berechnung von allgemeinen Pfahlwerken. Bauingenieur 61 563568, 1986. [10] C. Katz. Neues zu Plattenbalken. 7. SOFiSTiK Seminar, 1994. [11] C. Katz and J. Stieda. Praktische FE-Berechnungen mit Plattenbalken. Bauinformatik 1, 1992. [12] P. Schiessel. Grundlagen der Neuregelung zur Beschränkung der Rissbreite. Heft 400 DAfStb, 1994. [13] W. Schneider. Zustand II Berechnungen in der Praxis (Beitrag). SOFiSTiK Seminar Leipzig, 2003. [14] Stempniewski and Eibl. Finite Elemente im Stahlbeton. Betonkalender 1993-Teil 1 S. 249., 1993. [15] R.L. Taylor, P.J. Beresford, and E.L. Wilson. A Non-Conforming Element for Stress Analysis. International Journal for Numerical Methods in Engineering, Vol. 10:1211-1219, 1976.
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[16] A. Tessler and T.J.R. Hughes. An improved Treatment of Transverse Shear in the Mindlin-Type Four-Node Quadrilateral Element. Computer Methods in Applied Mechanics and Engineering 39, 1983. [17] Timoshenko and Woinowsky-Krieger. MacGraw-Hill, New-York, 1959.
Theory of Plates and Shells.
[18] W. Wunderlich, G. Kiener, and W. Ostermann. Modellierung und Berechnung von Deckenplatten mit Unterzügen. Bauingenieur, 1994. [19] xx. mit Berichtigung 1, Juli 2002 z.B. in [2]. DIN 1045-1 Ausgabe Juli 2001, 2002. [20] xx. Erläuterungen zu DIN 1045-1. Heft 525 DAfStb September, 2003. [21] O.C. Zienkiewicz. Methode der finiten Elemente, 2.Auflage. Hanser Verlag München, 1984. [22] K. Zilch and A. Rogge. Bemessung von Stahlbeton- und Spannbetonbauteilen im Brücken- und Hochbau. Betonkalender 2, 2004.
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Input Description | ASE
3 3.1
Input Description Input Language
The input is made in the CADINP language (see general manual SOFiSTiK: ’Basics’). Three categories of units are distinguished: mm
Fixed unit. Input is always required in the specified unit.
[mm]
Explicit unit. Input defaults to the specified unit. Alternatively, an explicit assignment of a related unit is possible (eg. 2.5[m] ).
[mm] 1011
Implicit unit. Implicit units are categorised semantically and denoted by a corresponding identity number (shown in green). Valid categories referring to the unit ŠlengthŠ are, for example, geodetic elevation, section length and thickness. The default unit for each category is defined by the currently active (design code specific) unit set. This input default can be overridden as described above. The specified unit in square brackets corresponds to the default for unit set 5 (Eurocodes, NORM UNIT 5).
SOFiSTiK 2014
3-1
ASE | Input Description
3.2
Input Records
The statical system is input with a graphic input program or with the program SOFIMSHA/SOFIMSHC. Material values can be modified, however, in ASE. The input is divided into blocks which are terminated with an END record. A particular system or load case can be analysed within each block. The program ends, if an empty block (END/END) is found. The following records are defined: Record
Items
CTRL
OPT
VAL
SYST
TYPE
PROB
ITER
TOL
FMAX
FMIN
EMIN
PLC
FACV
NMAT
STOR
CHAM
N
DT
INT
ALF
DEL
THE
LCST
FAK1
FAKE
DFAK
PRO
DL
PRIM
STEP
EMAX
SELE ULTI
STEP DMIN
PLOT
LC
TO
NNO
DIRE
TYPE
CREP
NCRE
RO
T
RH
TEMP
BEAM
GRP
NO
VAL
FACS
PLC
GAM
H
K
SIGN
SIGH
FACL
FACD
FACP
FACT
HW
GAMA
RADA
RADB
MODD
CS
PREX
PREY
PHI
EPS
RELZ
PHIF
PHIS
T1
HING
FACB
CSDL
MNO
NO
STEA
QUEA
QUEX
QUEY
ALP0
ULUS
QEMX
EXPO
GEOM
ELEM
ETYP
NO
FACS
FACL
LEN0
ETYP
NO
L0
TYPE
HIGH
XM
YM
ZM
NX
NY
NZ
PR1
PTPR
NOG
*PSEL
FROM
TO
INC
REDP
REDA
REDT
TBEA
NC
b
REIQ
LCB
FACT
STEX
NAME
GRP2
LCRS
Table continued on next page.
3-2
SOFiSTiK 2014
Input Description | ASE
Record
Items
OBLI
SX
SY
SZ
LC
FACV
VMAX
DIRE
MNO
V0
P0
PLC
STOR SLIP
NOSL
NOG
NOEL
VOLU
NO
GRP
POSI
DV
DT
MASS
MOVS
NO
TYPE
FROM
TO
INC
L0
LAUN
GRP
DX
DY
DZ
XM
YM
SFIX
LC
PLC
LC
NO
FACT
DLX
DLY
DLZ
BET2
TITL
TYPE
GAMU
GAMF
PSI0
PSI1
PSI2
PS1S
CRI1
CRI2
CRI3
NO
T1
T2
NOG
FACT
EMOD
RELA
TEMP
EXPO LAG
LCNO
FACT
TYPE
Z
TOL
PROJ
PEXT
NOG
NOEL
P0
SIDE
BETA
MUE
SS
LCC
NO
FACT
NOG
NFRO
NTO
NINC
ULTI
PLC EIGE
NEIG
ETYP
NITE
MITE
LMIN
SAVE
LC
MASS
NO
MX
MY
MZ
MXX
MYY
MZZ
V0
NO
VX
VY
VZ
REIN
MOD
RMOD
LCR
ZGRP
SFAC
P6
P7
P8
P9
P10
P11
P12
TITL
STAT
KSV
KSB
AM1
AM2
AM3
AM4
AMAX
SC1
SC2
SS1
SS2
C1
C2
S1
S2
Z1
Z2
SMOD
TSV
MSCD
KTAU
TTOL
TANA
TANB
SCL
KMOD
KSV
KSB
KMIN
KMAX
ALPH
FMAX
CRAC
CW
BB
HMIN
HMAX
CW-
CHKC
CHKT
CHKS
FAT
SIGS
TANS
TANC
DUMP
OPT
VAL
DESI
NSTR
ECHO
The record PSEL is only available in the ASE version which was expanded by the pile element.
SOFiSTiK 2014
3-3
ASE | Input Description
The records HEAD, END and PAGE are described in the general manual SOFiSTiK: ’Basics’.
3-4
SOFiSTiK 2014
Input Description | ASE
3.3
CTRL – Control of the Calculation
See also: ECHO, SYST, GRP, ULTI
CTRL
Item
Description
Unit
Default
OPT
Control option
LT
-
SOLV
Solver options for ASE
CORE Parallel computing control ITER
Iteration method
QTYP
Formulation of QUAD+TENDON elements AFIX Handling of movable degrees of freedom MSTE Number of the Runge-Kutta steps CABL Cable handling for geometrically non-linear calculation NLAY Parameters for QUAD layers FRIC PLAB
Maximum allowable shear stress for QUAD concrete rule T-beam components
FORM Yield process cross section reduction FIXZ
Global and local xy constraint, Formfinding for membrane structures WARP Warping torsion STII
Non-linear beam stiffness
RMAP Return-mapping UNRE BEAM prestress from the program TENDON SFIX Linearization of beam calculation according to OeNORM B4702 INPL Inplane stiffnesses CONC Concrete in cracked condition Table continued on next page.
SOFiSTiK 2014
3-5
ASE | Input Description
Item
Description
Unit
Default
STEA
Formfinding cable-stayed bridges: normal force stiffness component of beams QUEA Formfinding cable-stayed bridges: normal force stiffness component of QUAD elements DIFF Saving of the difference internal forces between a load case and the primary load case BRIC Control of BRIC elements CANT
Primary displacements
SOFT
Replacement of rigid supports in dead load direction with soft spring supports SPRI Consideration of the eccentricity of springs MCON Activation of a consistant mass matrix GIT Reduction of non-linear torsional stiffness WARN to switch off specific error messages GRAN Activation of the old GRAN material model for BRIC non-linear material with GRAN 0 AXIA, EIGE, AMAX, AGEN, ETOL, IMAX, SVRF, VRED, SMOO, VM, PIIA, INTE, USEP, VERT, COUN, ELIM, NLIM, ED: See manual for the program AQB VAL
Value of the option
−
-
V2
possible 2nd value of the option
−
-
V3
possible 3rd value of the option
−
-
3-6
SOFiSTiK 2014
Input Description | ASE
ITER
Iteration method for the elimination of residual forces VAL 0
Crisfield method
VAL 1
Linesearch method
VAL +2
An update of the tangential stiffness occurs, if required.
VAL 3
1+2 Default: - for PROB NONL: VAL 0 = Crisfield method - for PROB NONL and non-linear springs: VAL 3 - for PROB TH3: VAL 3 = Linesearch with tang. stiffness
V2 1
for every step stiffness update
V2 x
interval stiffness update is extended to x steps Default: dependent on the system size With an input for V2 failure mechanisms can be calculated well for second-order and third-order theory. ASE shows a better iteration in possible failure mode shapes with following input (possible also without PLC): CTRL ITER 2 V2 1 $ new total stiffness after every step $ SYST PROB TH3 ITER -30 PLC 15 $ -30 : simple residual force iteration $
Then the iteration load cases 9001-9030 determine the failure mechanism. V3 x
Update of the AQB stiffness in every xth step with CTRL ITER 3 V3 x Default: 4-8 depending on the number of iterations
V4 x
Smooth change of updated stiffness in the first x iterations. On TH2, TH3 or WARP sometimes an unrealistic normal force in the first iterations leads to negative stiffness. Default: no smoothing - full updated stiffness also in first iteration
V5 x
bits for variations of Chrisfield acceleration +1 also accelerate going downhill +2 high acceleration also in high iterations Default: 0 - Standard Chrisfield
V6 0
no damping of updated spring stiffness in iterations
V6 1
damping method 1
SOFiSTiK 2014
3-7
ASE | Input Description
V6 2
damping method 2 (incremental launching) Default: V6 2
QTYP
Formulation of QUAD elements and tendons The various additional options of the QUAD elements are defined as the sum of the following values: VAL 0
standard element
VAL 1
non-conforming formulation
VAL +10 use of rotational masses (dynamic only) Default: 1 If Tendon parts are not assigned to a quad element in TENDON, it must be defined how these parts shall be treated - as a hole or external tendon. You should also check if it is better to use real cable elements for such extern QUAD tendons (see PEXT and extern_prestress_cables.dat) : V2 0
These parts are interpreted as hole without force
V2 1
These parts are treated as external tendons with acting force (are not taken into account in SIR cuts)<
Default: not set - with version 2016: 1
Figure 3.1: Tendon going through a hole with QTYP V2 1
AFIX
Control of the handling of the movable degrees of freedom Recognizable undefined degrees of freedom (e.g. node rotations of a truss) are assigned a priori a small stiffness. Loads which act on such degrees of freedom cause very large displacements. Instability check: If the solver detects an instability, 6 single load cas-
3-8
SOFiSTiK 2014
Input Description | ASE
es are calculated automatically for the graphical checks under the consideration of dynamic auxiliary stiffnesses. Furthermore the first three eigenvalues are calculated with the same auxiliary stiffness. An input unequal to 1 for CTRL AFIX turns off this instability check. 0
Degrees of freedom which are movable exactly get announced by an error message. The calculation is interrupted.
1
Degrees of freedom which are movable within the numeric accuracy get announced by an error message. The calculation is interrupted. The instability check is realized.
2
Degrees of freedom which are movable exactly are not used and get a warning. The calculation is continued.
3
Degrees of freedom which are movable within the numeric accuracy are not used and get a warning. The calculation is continued.
4
as 0, however, recognizable undefined degrees of freedom get a rigid support.
5
as 1, however, recognizable undefined degrees of freedom get a rigid support.
6
as 2, however, recognizable undefined degrees of freedom get a rigid support.
7
as 3, however, recognizable undefined degrees of freedom get a rigid support.
Default: 1 MSTE
Maximum number of Runge-Kutta steps fory non-linear material MSTE acts only for the yield criteria for BRIC elements. Default: 4 Explanations can be found in the TALPA manual. In many examples the program converges better with MSTE= -110.
CABL
Cable handling 0
No consideration of the internal cable sag
1
Consideration of the internal cable sag The consideration is not done for cables with FACS not equal 1.0 (formfinding).
2
Calculation of cables with FACS not equal 1.0 (formfinding) with inner cable deflection
Default: 2
SOFiSTiK 2014
3-9
ASE | Input Description
PLAB
T-beam philosophy The plate components are deducted automatically during the stiffness calculation for beams inside plates with cross section widths defined in the program AQUA. The dead load is adjusted to avoid double dead load. The components of the plate internal forces are added then to the results of the beam internal forces for a subsequent dimensioning. Restrictions: •
Processing only for cross sections with defined cross section outline (SREC,SECT...) which were defined with the program AQUA. Also composite sections are allowed. The acting width is taken from the concrete parts only.
•
Beams which are connected to the plate via kinematic constraints are processed too, however, only if they lie in the plane of the plate (program MONET: BEAM-abs+coup).
Details: •
During the calculation of plate components the plate internal forces at the beam nodes are multiplied by the cross section width. Therefore, the beam width should not be chosen too large above columns.
•
If some QUAD groups meet at a node, the average value of the plate internal forces is used.
Control: +1
moments My are added
+2
shear forces Vz are added too
+4
axial forces N are added too
+8
torsional moments MT are added too
Default: 7 = My + Vz + N The processing is cancelled with CTRL PLAB 0 V2: With Ctrl PLAB V2 1 also the next quad node rigth and left is used to evaluate the added quad forces (to take into account the quad force distribution more acccurate). With Ctrl PLAB V2 0 only the central node is used. Default: 1 Output: •
3-10
The plate components are included always in the output of the
SOFiSTiK 2014
Input Description | ASE
beam internal forces and moments. Therefore the printout does not occur before the plate node results! •
A statistic of the plate components follows after the beam internal forces and moments. The maximum plate components are compared with the maximum beam internal forces.
Control of the statistic with the input ECHO PLAB 0-1-2. Attention: This model can not be used for influence line evaluation with ELLA because ELLA does not add the slab parts to the beam! Examples see also Theoretical Principles. NLAY
Number of layers for QUAD layers Fire analysis implemented for QUAD shell elements. With SOFILOAD now nonlinear temperature gradients can be defined via QUAD...TYPE=’T’...Z0 and plottet in the ANIMATOR element info after the analysis. Then ASE can use non-linear temperature curves (AQUA ARBL...TEMP) in the QUAD layers. An input of CTRL NLAY V2 V3 V4 is necessary and allows addional settings: VAL
Number of layers
V2 +1
fine layers on positive local z axis
V2 +2
higher layer refinement on +z
V2 +3
extreme refinement on +z
V2 -1 bis -3 : refinement on negative local z axis Default: 0 = constant division V3
start temperature in the quad layers Default: 20 degree celsius The non-linear temperature strain behaviour is taken into account and plotted in the URSULA output.
V4 1
Take alfa-t value from material input (CONC-ALFA) and not from work law SSLA-EPST. Default: V4=0.
V5 1
Concrete uses the maximum temperature found up to now in a layer and does not cure on falling temperature. Default: V5=1.
V9
With V9 a temperature for the plot of the work law can be input, e.g. V9 600., +10000 e.g. 10100=every 100 degree.
Example see quads_on_fire_1.dat FRIC
Maximum allowable shear stress for the QUAD concrete rule
SOFiSTiK 2014
3-11
ASE | Input Description
For point supported slabs the allowable shear stress is exceeded often in support-near elements. It results in shear plastification. For this shear plastification the punching information of BEMESS is taken into account in a non-linear slab analysis. At punching node, the shear plasticity check will be switched off inside an radius of columnedge+hm. Thus an increase of FRIC to for example 9.9 N/mm2 for elimination of these sometimes unwanted shear plastification effects is only necessary in special cases. Default: 2.40 [ N/mm2 ] V2
final stress. With CTRL FRIC 3.00 V2 1.40 a descending final max. allowable shear stress (here 1.40 N/mm2) can be defined. The stiffness in the descending part is equal to the increasing one.
FORM
Yield process Control of the thickness reduction for large deformations 1
volume-constant behaviour (ideal plastic)
2
elastic behaviour using the Poisson’s ratio
effective for QUAD, TRUS and CABL elements Default: 0 FIXZ
Global or local xy constraint Formfinding membrane structures: For membrane elements and FACS < 0.5 a formfinding is calculated. All inner membrane nodes in the membrane plane are fixed then: 1
fixes all internal membrane nodes in the membrane plane from the second iteration step
2
fixed the nodes in the membrane plane in all iteration steps
3
fixes generally all nodes in global XY = formfinding in global Z can be used also for a cable nets
4
fixes the local z coordinate in the first iteration step, in further steps the transverse direction (as for FIXZ 2)
5
fixes the local z coordinate in all iteration steps
0
no such effects
After a formfinding calculation an additional calculation should occur with a stiffness factor multiplied by 1.0 in order to balance possible residual forces in the membrane plane. CTRL FIXZ 4 or 5 can be used for the formfinding of the radii of edge cables.
3-12
SOFiSTiK 2014
Input Description | ASE
Default: 1 WARP
Warping torsion 1
activates the warping torsion with formulation of a seventh degree of freedom per node.
Default: 0 STII
Linear beam stiffness factor in a nonlinear analysis T-beams (beams) are calculated linear in a normal non-linear slab calculation with SYST NMAT YES (without NSTR S1). In this case an overall reduction of the beam stiffness is done. The input CTRL STII 0.4 for example processes the beams with 40 % stiffness. A normal force stiffness is not used then. For slab calculations (program SOFIMSHA/SOFIMSHC ... SYST GIRD) according to cracked condition STII is preset with 0.25 (0.75*1/(1+phi) with phi=2.0).. The default is 1.0 for all other calculations. Using nonlinear T-beams in combination with a quad slab is problematic due to the change of centre of stiffness in cracked beams and the elongation of beams due to crack opening. In such a case it is better to use only excentric quad elements as shown in example csm32_slab_design.dat
RMAP
Return-Mapping BRIC For BRIC yield rules the Return-mapping method is preset (default CTRL RMAP 1). With CTRL RMAP 0 it is possible to change to the method with plastic displacement increments. With CTRL RMAP 2 the material routines can be activated from the program TALPA for non-linear BRIC volume elements (is used automatically). The Return-mapping method has particularly in the area of tensile fracture zone a definite better convergence behaviour.
UNRE
For the use of the BEAM prestress from the program TENDON following inputs are possible: 1
Only the static determinate part of prestress is stored. The curvature loads are not used.
-1
Only the static indeterminate part is calculated and stored.
0
The static indeterminate part is calculated and stored together with the static determinate part. The beam internal forces and moments includes both parts (= default).
example see bridge_design_manual_aqb.dat INPL
Inplane stiffnesses: Connecting beams to quads
SOFiSTiK 2014
3-13
ASE | Input Description
The decisive connection nodes for the beam and disk elements are searched for the transfer of the moments around the local z axis. The stiffnesses of the bordering QUAD elements are increased by an inplane moment spring. Thus a pile can transmit moments around both beam axis to the wall disks. The appropriate node numbers are printed. The method can be switched off with CTRL INPL 0. With CTLR INPL value it can be factorized, e.g. CTLR INPL 0.001. CONC
Concrete in cracked condition For QUAD elements: The length of the decreasing part of the concrete stress-strain curve in the tensile zone is defined with CTRL CONC VAL: VAL 0.2 defines this length to 0.2 per mille VAL 0
The length is determined from the tensilefailure energy. This energy is not limited with 5·eps1 as in the default (without an input for CTRL CONC).
CTRL CONC V2: the increase of the maximum concrete compressive stress for uniaxial compression according to Kupfer/Rüsch is deactivated as a precaution for calculations according to ultimate limit state: V2 0
no limitation, increase permissible, default for NSTR KSV SL, SLD
V2 1
maximum concrete compressive stress = 1.0 · value from uniaxial AQUA stress-strain curve, default for NSTR UL, ULD, CAL, CALD
V3
temporarily sets the concrete strength fct for the QUAD concrete material law W3 = tensile strength for tension stiffening
V4
temporarily sets the concrete strength fctk for the QUAD material law [ N/mm2] W4 = tensile strength for pure concrete layers Should be reduced for ULS analysis.
The method of tension stiffening is controlled with CONC V5: V5 525 plates in cracked condition exactly according to Heft 525 DAfStb (Eurocode) V5 400 plates in cracked condition exactly according to Heft 400 DAfStb (old EC2) without input: for SL,SLD: Heft 400 with modifications for realistic deflection, for UL,ULD: Heft 525 V6
3-14
Bit 1 : the concrete compression strength again reach-
SOFiSTiK 2014
Input Description | ASE
es the uniaxial value in case of a transverse crack (tension stress=0). Without this bit 1 the compression strength is reduced by the transverse tension strain (and not by the stress). The strength reduction is limited to 75 % fc. Please also refer to BEMESS CTRL TENS. Bit 2 : With CTRL CONC V6 +2 the worklaw is not only deformed in vertical direction but also in strain direction to keep the starting E modulus constant. Default V6=2 (=only bit 2) V7
Computation on singular support points in the material nonlinear concrete analysis (SYST NMAT YES): Problem: such singular supports caused singular forces that could not be carried in the concrete nonlinear material model, especially in combination with singular rotational constraints. At punching nodes from BEMESS now a first singular support or connection force (and bending moment) will be distributed on neighbouring nodes inside the column perimeter to simulate a constant distributed support pressure. Thus the feature only works after a BEMESS ultmate design with PUNC YES or PUNC CHEK! The support force of the center is distributed via an internal coupling ring around the center node and elastic springs to further nodes inside the column area. The processing is documented in the statistik print out "rounding singular punching nodes". It can be switched off with CTRL CONC V7 0. It only works on BEMESS punching nodes but also if they come from beam connections in a 3D analysis. It also converts singular connection bending moments in a triangular connection pressure. The effect can be studied well by comparing a run with CTRL CONC V7 0 and a run with CTRL CONC V7 1. Especially at fine discretized punching points a rotational constraints will be analyzed more realistic (stronger). On such points the singular support moment caused a strong singular curvature in the fine mesh and thus a lower constraint. In a material linear analysis this feature is switched off by default but can be enforced with CTRL CONC V7 1.
BRIC yield criteria for non-linear concrete application: A decreasing tensile strength curve can be chosen with the additional input CTRL CONC EPSY. Here EPSY is interpreted as uniaxial strain
SOFiSTiK 2014
3-15
ASE | Input Description
length of the decreasing part of the stress strain-curve in per mille (e.g. CTRL CONC 0.1). The input is possible for the BRIC yield criteria MOHR, LADE and GUDEHUS. Without the input of CTRL CONC the tensile strength is treated as a constant yielding value. V2 -1
The parameter AQUA NMAT ..LADE...P6 is interpreted a length of decresing tension stress.
STEA
With CTRL STEA the normal force stiffness component of beams can be increased. The bending stiffness remains unchangeable. STEA can also use groupwise in GRP2 Example see suspension_bridge_formfinding.dat
QUEA
With CTRL QUEA the E·A part of the QUAD elements can be modified. QUEA can also use groupwise in GRP2 Example see steel_composite_orto.dat
DIFF
With CTRL DIFF the difference internal forces (and displacements) between a load case and the primary load case are saved (nodal displacement differences = difference to SYST PLC load case!). With that for instance the difference results (e.g. the part from creep and shrinkage) are immediately available for a superposition in the program AQB. Only a multiple of thousand is allowed. Usage see program CSM Construction Stage Manager.
BRIC
Control for BRIC elements 1
use normal BRIC element
2
use BRIC element with hyperplastic rubber material Total Lagrangian
+16
CTRL BRIC 17 = use BRIC elements geometric linear
Default: BRIC 1 CANT
3-16
If new groups and new nodes are activated for instance in cantilevering construction, a primary displacement has to be determined for these new nodes, although they were not still available in the primary load case SYST PLC. Using complex FE cantilever parts, the parts sometimes distorted too much. Thus the new member is attached as a whole (block) freely of stress. This can be controlled with CTRL CANT. Usage see program CSM Construction Stage Manager. 0
no action
1
only consideration of displacements
2
consideration of displacements and rotations = tangential cantilevering construction
3
adaption of a new segment in its shop shape (only if using
SOFiSTiK 2014
Input Description | ASE
CSM), example: csm7_cant_3.dat +4
retention of the XY position
11,12
In analog mode to 1 and 2 with the feature: It adds a new part not as a block but each node separate. This allows much better to add an in situ slab on an already deformed grid of beam elements.
Default: CANT 0 = no action SOFT
Replacement of rigid supports in dead load direction with soft spring supports, also for linear analysis If in a graphical input a rigid line support was defined for simplification purposes, this rigid support can be changed subsequently into a soft edge support. The support width is considered here. However, single supports get a factor which is increased with the spring value multiplied with 5, therefore 5·support area·SOFT. The value SOFT is here the bedding value in kN/m3 . Values which are smaller than 1000 are not possible. CTRL SOFT can be input also simultaneously for a non-linear analysis with corners which are displaced upwards (see SYST PROB LIFT). Default: 5E7
SPRI
Spring options: +1 and +8: Consideration of the eccentricity of springs. Coupling spring elements can account for the real distance of the nodes with an implicit KP kinematic constraint. A transverse spring force will transfer a moment to the nodes. Without +1 and +8 the transverse force is transported without a moment - which is mechanically not correct. +4: direction change of coupling springs. 0
= without +1 or +8: do NOT apply excentricity of springs from real distance =without +4: couplings springs bahave like a truss and can change the force direction
+1
apply excentricity in any case
+8
automatic decision: For BRIC and inplane-QUAD connections the eccentricity is not applied, because in that cases a smeared friction is assumed and QUADs and BRICs cannot transfer such bending moments. The eccentricity effect is also not applied for truss and cable connections without beam connections.
+4
SOFiSTiK 2014
coupling springs in geometric nonlinear analysis:
3-17
ASE | Input Description
With +4 a coupling spring will always keep its direction and not work like a truss. +4 is the perfect default for transvers free bridge bearings. If the direction of a coupling spring does not fit to the direction of the nodal connection vector, the spring will always keep its direction! Normally a direction fixed spring should be defined with nodes with the same coordinate ( distance 0). Option V2: With CTRL SPRI V2=2 the shift of the zeropoint of the work law curve after plastification (=hysteresis) can be switched off. This is senseful for work law curves that shall simulate a gap. V2 not equal 2 = with hysteresis. Default: CTRL SPRI 8+4 V2 0 MCON
Activation of a constant mass matrix For eigenvalue analysis with solver LANC, SIMU and RAYL a consistant mass matrix is activated with default CTRL MCON 2 (implemented for beam elements only). MCON 3 includes warping effects. Further comments can be found in the DYNA manual.
GIT
Additional reduction of non-linear torsional stiffness for lateral buckling analysis (NSTR S1) see example: aseaqb_4_lateral_buckl_prestress.dat
3.3.1
SOLV Equation solver
SOLV
Description
VAL
Selection of equation solver 1 Direct Skyline Solver (Gauss/ Cholesky) 2 Iterative Sparse Solver 3 Direct Sparse LDL Solver 4 Direct Parallel Sparse Solver (PARDISO)
Unit
Default
−
3
For solving the equation systems of the Finite-Element problem, SOFiSTiK provides a number of solvers. Which solver is used best depends highly on the type of the system and requires knowledge of relevant system parameters. Following types are available:
3-18
SOFiSTiK 2014
Input Description | ASE
•
Direct Skyline Solver (Gauss/Cholesky) This is the classical solver of the FE-Method. The current implementation works best on a skyline oriented matrix. The storage needed depends on the internal optimization of the node numbers and may become quite large for 3D structures.
•
Iterative Solver (Conjugate Gradients) One advantage of the iterative solver lies in its reduced requirements for storage, but it may also provide reduced computing time compared to the previous two types especially in case of large volume structures.
•
Direct Sparse Solver These types of solvers correspond to state of technology. A quite efficient version based on the work of DAVIS [5] is available as well as a direct parallel solver PARDISO.
The advantage of the direct solvers is especially given in case of multiple right hand sides, as the effort for solving them is very small compared to the triangulization of the equation system. Thus they are the first choice for any dynamic analysis or in case of many load cases. In order to minimize computational effort, the solvers need an optimized sequence of equation numbers. This optimization step is usually performed during system generation. The programs SOFIMSHA/C by default always create a sequence which is suitable for the direct sparse solver (3). The solvers (1) or (2) however require a skyline oriented numbering which may be obtained using the option (CTRL OPTI 1) or (CTRL OPTI 2) during system generation. The correct setting will be checked and a warning will be issued in case a correct numbering is not available. The iterative (CTRL SOLV 2) and the parallel sparse solver (CTRL SOLV 4) can be run in parallel providing an additional reduction in computing time. A parallelization basically requires a license of type ”HISOLV”. More information about parallelization can be found in subsection 3.3.2 describing the input parameter (CTRL CORE). The equation solvers are selected using the parameter (CTRL SOLV). The first value defines the type of the solver, followed by optional additional parameters. Direct Skyline Solver (Gauss/ Cholesky)
SOFiSTiK 2014
3-19
ASE | Input Description
SOLV VAL
Description
1
Direct Skyline Solver (Gauss/ Cholesky)
Unit
Default
−
!
No additional parameters are required. However it is mandatory to optimize the equation numbers in SOFIMSHA/C using (CTRL OPTI 1) or (CTRL OPTI 2) in order to minimize computation time as well as storage requirements. Iterative equation solver SOLV VAL
Description
2
Iterative equation solver
Unit
Default
−
!
V2
Maximum number of iterations
−
*
V3
Tolerance in numeric digits (5 to 15)
−
*
V4
Type of preconditioning: 0 Diagonal Scaling (not recommended) 1 Incomplete Cholesky 2 Incomplete Inverse
−
1
V5
Threshold value of preconditioning
−
*
V6
Maximum bandwidth in preconditioning
−
*
The iterative solver uses a conjugate gradient method in combination with preconditioning. For the preconditioning, following variants are supported: •
Diagonal scaling (V4=0) Although this is the fastest method with the least memory requirements, it will need a considerable high amount of iterations and is therefore not recommended in most cases.
•
Incomplete Cholesky (V4=1) This type of preconditioning performs a partial triangulization of the input matrix. Compared to a full triangulization with the Cholesky method, the Incomplete Cholesky saves time by ignoring the so called Fill-In during decomposition.
•
Incomplete Inverse (V4=2) This type of preconditioning is generally inferior to the Cholesky method. This applies to the convergence-rate as well as the time required for com-
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Input Description | ASE
puting the inverses. It shows however better performance in case of more densely populated matrices (Recommended threshold V5: 0.01). For any kind of preconditioning the number of matrix entries taken into account during preconditioning can be reduced either by giving a relative threshold value at V5 or via a maximum bandwidth size at V6. The optimum choice depends on the type of the structure and may only be found by some tests. Hint The correctness of the solution of the iterative solver depends primarily on the tolerance threshold. Therefore, changing the default setting V3 is not recommended. In any case the analyst should carry out a proper assessment of the computation results.
Direct Sparse LDL Solver (Default) SOLV VAL
Description
3
Direct Sparse LDL Solver
Unit
Default
−
!
Additional parameters are not required. The mesh generators SOFiMSHA/C generate by default an equation numbering required for this type of solver which minimizes the so-called Fill In of the matrix. PARDISO - direct parallel sparse solver SOLV WERT
Description
4
Direct parallel sparse solver
Unit
Default
−
!
This solver PARDISO uses processor optimized high performance libraries from the Intel Math Kernel Library MKL. It usually provides the least computing times. It does not require an a priori optimization of the equation numbers during system generation. Hence, the equation optimization in SOFiMSHA/C could also be deactivated using (CTRL OPTI 0) in order to save memory during system generation. On the other hand however, this solver does not allow reusing the factorized stiffness matrix in other programs. Thus, a usage in combination with the program ELLA is not possible.
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ASE | Input Description
Further options CTRL SOLV 0 suppresses the solution of the system. This is a useful feature to check the effective system loads. STEU SOLV 999 prevents a rebuild of the stiffness matrix within a load case loop in each step. 3.3.2
CORE Parallel computation control
CORE
Description
VAL
Number of used threads
Unit
Default
−
*
SOFiSTiK supports parallel computing for selected equation solvers. Additionally, some programs offer parallel element processing capabilities – independent of the chosen equation solver (CTRL SOLV). Activation of parallel computing By default parallel computing is triggered automatically where it is feasible. Parallel computing requires corresponding harware and operation system support. In addition, availability of an adequate SOFiSTiK license is obligatory. Hint Parallel computing requires availability of a HISOLV license (ISOL granule).
Number of available threads for parallel computing If parallel computing is active, the number of adopted threads is determined as follows (listed with increasing priority): a) The software retrieves the information about the number of available physical processor cores on the system. This number defines the default number of threads that are used when a parallel computation is activated. b) This default can be modified via the environment variable SOF_NUM_THREADS, which is also available as sofistik.def parameter. c) Finally, an explicit statement CTRL CORE NN (or as relative input CTRL CORE NN[%]) temporarily assigns the number of available threads for the
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Input Description | ASE
respective run. Hint Neither option b) nor option c) state an explicit parallel computation request. The decision if a parallel computation is triggered, depends on the actual analysis option (parallel processing must be supported for the specific task) and the availability of an adequate license. Parallel computing can be suppressed by explitly setting the number of available threads to 1 (or 0).
Parallel options for equation solvers License Solver
CTRL SOLV
Serial
Parallel
Skyline Gauss/ Cholesky
1
–
n.a.
Iterativ
2
Sparse LDL (default)
3
Sparse Parallel (Pardiso)
4
SOFiSTiK 2014
HISOLV HISOLV –
n.a.
HISOLV HISOLV
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ASE | Input Description
3.4
SYST – Global Control Parameters
See also: CTRL, GRP, ULTI
SYST
Item
Description
Unit
Default
TYPE
Control option
LT
*
LT
LINE
ITER
Analysis of plates with corners which are displaced upwards Number of iterations
−
90
TOL
Iteration tolerance
−
0.001
* This input is not analyzed, the value is taken over from generation program. PAIN and AXIA only run with TALPA. PROB
Type of the analysis LINE
Linear analysis
NONL Non-linear analysis TH2 TH3 TH3b
Analysis according to second order theory Analysis according to thirdorder theory Limited TH3
LIFT
The tolerance refers to the maximum load of analysis. value multiplied with maximum nodal load generates the tolerance limit for residual forces -value Absolute tolerance limit TOL4
tolerance after 40 % iterations
−
-
TOL8
tolerance after 80 % iterations
−
-
FMAX
Max. f value Crisfield method
−
4.00
> 0.1 or negative
FMIN
Min. f value Crisfield method > 0.1
−
0.25
EMAX
Max. e value Crisfield method ≥ 0.0
−
0.60
EMIN
Mini. e value Crisfield method ≤ 0.1
−
-0.40
PLC
Primary load case of the system
−
-
Table continued on next page.
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Input Description | ASE
Item
Description
FACV
Factor for displacements of PLC
Unit
Default
−
*
−
-
LT
NO
LT
NO
−
-
Default 1.0 for buckling eigenvalue analysis: for geometric nonlinear PLC: 1.0 otherwise for buckling: 0.0 VMAX
Factor for imperfection
NMAT
Yield criteria for QUAD and BRIC elements YES
Yield criteria are used.
NO
Yield criteria are not used.
STOR
Geometry update
CHAM
Magnification calculation in connection with program CSM no magnification 1.0
magnification calculation
Non-linear analyses are not possible with the basic version of program. Further explanations to PROB: LINE
linear analysis
NONL non-linear analysis non-linear springs tension cut off for QUAD elements non-linear pile bedding non-linear halfspace contact material non-linearities: - stress-strain curves for springs, beams, cables and trusses (requires the record NSTR) - concrete and steel rule for QUAD elements (SYST NMAT YES is additionally necessary) - yield criteria for BRIC volume elements (SYST NMAT YES is additionally necessary) TH2
= NONL + analysis according to the second-order theory for calculation of columns and frames according to the second-order theory (pi-delta) Beam elements are calculated with TH2 with a iteration method in
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ASE | Input Description
analog mode to STAR2 (the normal ASE iteration method with residual forces is used for TH3 or CTRL ITER 3) TH3
= NONL + geometrically non-linear analysis contains TH2 and additionally the effects of the geometrical system modification, e.g. snape through, length modification for big deformations, behaviour after buckling On TH2-TH3 Difference see Theoretical Background - Beam Element
TH3b
= NONL + TH2 + effects of the geometrical system modification only for cables, trusses and springs (CTRL SPRI) with kinematic constraint. Beams and QUAD elements are used only according to the second-order theory.
LIFT
Analysis of plates with corners which are displaced upwards A nonlinear analysis is started, at which also fixed supports and elastic edges can be displaced upwards due to tension; see CTRL SOFT
Examples: SYST PROB LINE:
Input file
ASE introduction
ase1_overview.dat
BEMESS slab design
bemess6_design.dat
CSM prestressed bridge
csm31_design.dat
SYST PROB NONL:
Input file
Spring work law
a1_spring_overview.dat
Beam Ship impact plastic
ase_nstr_pld_pile_crash.dat
Quad concrete cracked
a1_introduction_example.dat
Bric tunneling
ase14_tunnel_3d.dat
SYST PROB TH2:
Input file
Beam overturning
ase11_girder_overturning.dat
Beam column cracked
aseaqb_1_column_cracked.dat
SYST PROB TH3:
Input file
Overview examples geo-nonl
ase_geo_nonl_overview.dat
Suspension bridge
suspension_bridge_formfinding.dat
Cable sag
ase5_cable_trestle.dat
Quad geometric nonlinear
ase9_quad_euler_beam.dat
Quad shell buckling
ase13_shell_buckling.dat Table continued on next page.
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Input Description | ASE
SYST PROB LINE:
Input file
Quad web buckling
webblecbuckling.dat
Quad membranes
tennis.dat
Bric buckling
bric_beul.dat
Summary of all example overviews: Example overview
see
Work laws
-> Work law input
Copy loads
-> LCC
Mass conversion
-> MASS
Creep and shrinkage
-> KRIE
Nonlinear effects
-> SYST PROB ...
Quad nonlinear
-> NMAT YES
Membranes
-> MEMB
Ultimate load iteration
-> TRAG
Incremental launching
-> TAKT
Contact Moving Springs
-> MOVS
Dynamic time steps
-> STEP
Halfspace analysis
-> HASE
Plot - diagrams
-> PLOT
An overview over all examples can be found in TEDDY menue file - examples in folder ASE-english. Then look further e.g. to folder ’nonlinear_quad’. Or you go over the SOFiSTiK installation folder to c:/program...sofistik/2014/ANALYSIS_30/ase.dat/english/nonlinear_quad Further input remarks: The value of PLC defines a global primary load case. This is used subsequently as default for the primary load case of all group inputs. Furthermore the displacements of the primary load case are added then and only then to the displacements of the current load case, if the PLC has been defined in the SYST input. In the case of geometrical non-linear analysis the stiffness is calculated for the deformed structure. A predeformation with PLC and FACV effects the internal forces moments only for PROB TH3, see Chapter 2: Non-linear Analyses and Chapter
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ASE | Input Description
5: example Buckling Mode Shapes in Supercritical Region. The application of a non-stressed predeformation is explained in the school example ase9_quad_euler_beam.dat. The stresses of the primary load case are used with GRP FACL=FACP=1. If the loads of the primary load case are applied simultaneously, then the system is in equilibrium and no additional displacements arise (if no changes are made in the system). If a primary load case with TH3 is defined for an eigenvalue determination, one obtains the eigenfrequencies of the system under the stresses of the primary load case (accompanying eigenvalue analysis). With GRP FACL=FACP=0 the deformation of a load case can be defined here as non-stressed scaled predeformation (see Chapter 5: example Buckling Mode Shapes in Supercritical Region). The inputs ITER to EMIN are evaluated only for non-linear analysis. Such an analysis is allowed only for a single load case. Buckling eigenvalues on a deformed structure can be requested with explicit SYST...FACV 1.0. Explanations to the non-linear iteration method: Residual forces New displacements and thus stresses are determined after every iteration step. It is checked, whether plasticising, cracks or any other non-linear effects have occurred at any elements. The plasticized elements generate different nodal loads compared to those of the linear analysis. These nodal loads which were generated by the elements are not anymore in equilibrium with the external nodal loads (after the first iteration step). The remaining residual forces are applied as additional loading during the next iteration step. Additional deformations and a new stress state which in general is closer to equilibrium result. The maximum residual force is printed for every iteration. If all residual forces should be output, this can be controlled with the option ECHO RESI. Graphical control of the residual forces If an iteration ends with residual forces, a picture of the residual forces can be requested in the program WING with NODE SV.
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Input Description | ASE
Since unbalanced residual forces are stored as supported reactions, the problem zone can be localized with that. Here the real support areas should not be printed. Often, it is advisable to fade out the real support areas with BOX and to draw only the interior of the structure. Tolerance limit of the iteration The tolerance limit can be defined with the record SYST. Here the reference value is the largest nodal value which is available in the system. E.g. for a maximum nodal load of 200 kN the tolerance limit for the residual forces is = 200 ·0.001 = 0.2 kN (for TOL=0.001). In this case all loads of the system are used including the inherent stress nodal loads of the elements. The tolerance for non-linear analysis can be input also absolutely with SYST PROB NONL TOL -value. Example: With the input SYST PROB NONL TOL -0.5 the iteration is interrupted, if the maximum residual force is smaller than the value 0.5 kN. Iteration method The default method for problems according to the second-order theory is the Linesearch method with the update of the tangential stiffness (see record CTRL). The load increment is reduced here internally according to the available residual forces. If an iteration step proceeds into the right direction, i.e. in the direction of an energy minimum, then a new tangential stiffness which enhances the further iteration’s behaviour is generated, if necessary. Cracked elements are considered here also with a reduced stiffness. The Crisfield method is the default (CTRL ITER 0) for non-linear calculations according to the first-order theory. For convergence problems the user should attempt also the in each case other method (CTRL ITER 0 or CTRL ITER 1). Variation of iteration factors For convergence difficulties an improvement of the convergence behaviour can be achieved often via reduction of the maximum f value, e.g. FMAX 1.5. If the system still not converges, FMAX can be reduced until 0.7. However, many iteration steps are needed then. The Crisfield method which is implemented for the improvement
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ASE | Input Description
of the convergence modifies the displacement increments of the current and of the last iteration step with the two factors f and e. f values which become alternately larger and smaller than 1.0 are an indication of serious problems. The method can be influenced in such cases by specifying maximum and minimum values of factors. A negative value for ITER switches off this method completely. By contrast, it may occur for tensile failure of stiff elements that the residual forces change very slowly. Here it is useful to select large values for e and f (e.g. EMIN = -9999., EMAX = 9999. , FMAX = 1000.). Generally applicable recommendations can not be given here. It has been observed, however, that the limit values of e should be defined essentially more generously, even if FMAX has to be limited. The values FMAX to EMIN are increasingly limited during the iteration process. Thereby the convergence is improved for many iterations. The FMAX value is decreased automatically during the iteration process with the input of a negative value for FMAX. Failed foundation and tensile springs For analyses without consideration of tensile support reactions (non-linear foundation or springs) the basic foundation values should not be defined too large, because the program reduces gradually these values until the foundation fails. For too large initial values for the foundation the iteration converges extremely slowly. For tensile failure in large regions the residual forces of the non-linear analysis can not be redistributed anymore. The iteration becomes divergent. Additional elements with a small stiffness parallel to the failing ones may be helpful here. Imperfection The imperfection can be scaled automatically with the item VMAX. The inputs -1, -2, -3 for SYST ... FACV control then the direction of the scaling, if desired. SYST PLC 101 FACV - VMAX 0.05 defines the imperfection of the primary load case 101 with a three-dimensional deformation of 5 cm. SYST PLC 101 FACV -1 VMAX 0.5 defines the primary load case 101 with a maximum imperfection u-X of |5 cm|. All other deformations are scaled with the same factor. SYST PLC 101 FACV -1 VMAX -0.05 as before, however, the imperfection figure is defined with a negative sign.
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Input Description | ASE
Failure Mode Shapes With a special control it is possible to get a more precise iteration process for the failure mode shapes in ASE. An analysis according to the second-order and third-order theory does not converge in many cases and it is unknown which failure mechanism will occur. At first a smaller stable load step should be calculated in advance. Then the following input should be startet: PROG ASE HEAD delivers the failure in the iterations load cases 9001-9009. $ Method: $ $ - new total stiffness after every step, $ $ - then continuation of the calculation without manipulation of the residual $ $ force $ CTRL ITER 2 W2 1 $ new total stiffness after every step $ SYST PROB TH3 ITER -30 PLC 15 $ !!minus!! -30 $ LC 201 FACT ... $ Factor, that will cause failure $
In the same way dynamic eigen mode shapes with the last stable load case may give an information about failure problems, because the critical natural vibration shapes in the natural frequency are clearly smaller with increasing load. See example ase9_quad_euler_beam.dat Geometry-Update With SYST STOR the system which was displaced with the displacements of the load case PLC can be stored with the updated nodal coordinates. A calculation does not occur then. SYST STOR=YES: The new local coordinate systems of the QUAD elements are twisted by the rotations of the load case PLC. They, however, keep the direction defined in the input. Beam lengths are nor updated for loading . SYST STOR=NEW: The local coordinate systems of the QUAD elements are defined again, despite their definition in the input. Beam lengths are updated for loading . SYST STOR=XX,YY,ZZ and NEGX,NEGY,NEGZ: The direction of the local x axis is preset for the new installation of the coordinate system of the elements, cf. program SOFIMSHA/SOFIMSHC. Beam lengths are updated for loading. STOR=NEW to STOR=NEGZ acts only to QUAD elements. The local coordinate systems of beams are twisted generally with the PLC displacements. Caution: All results of the nodal displacements are extinguished during the geometry up-
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ASE | Input Description
date. Therefore the data base must be saved absolutely before! With the input STOR=NEW to STOR=NEGZ all other results are extinguished too, because the local directions are twisted. With the input STOR=YES it is possible to use the old stresses via the record GRP, if no beam elements are available. With SYST STOR UZ only the z displacements are corrected. For the x or y displacements are also possible STOR UX and STOR UY.
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Input Description | ASE
3.5
STEP – Time Step Method Dynamics
See also: SYST, GRP
Item
Description
N
STEP Unit
Default
Number of time steps
−
!
DT
Time step
−
!
INT
Output interval all INT steps (not implemented yet) Parameter of the integration method
−/ LT
1
−
0.40
−
0.55
−
1.
−/ LT
-
BET DEL THE
(alpha method with THE input)
LCST
Storage load case number CONT = append on PLC sequence
SELE
Selection of results to be stored
−
-
LCSM
Storage number of min.-max values of all time steps time step division
−
-
−
-2
old input - please use BET as first parameter
−
DIV ALF
The analysis of a time step of duration NVDT with direct (Newmark-Wilson) integration is requested with STEP. The defaults for BET, DEL, THE correspond to a Newmark method with numerical damping of higher frequencies for nonlinear analysis. Following input is possible: BET 0.25 0.50 1.00
$ Original Newmark without numerical damping
BET 1/6 1/2 1.40
$ Original Wilson with large damping in higher modes
BET 0.4 0.55 1.00
$ good numerical damping of high frequencies
THE 0.70
$ alpha method acc. Hilber-Hughes-Taylor with THE= 1-|alpha|(without BET+DEL input ! ) e.g. alpha -0.3 -> STEP 50 dt 0.05 THE 0.7
For nonlinear dynamics we recommend: THE 0.70 or BET 0.4 0.55 1.00
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ASE | Input Description
Examples to STEP
Input file
Introduction
a1_a1_dynamic_overview.dat
BEAM Ship impact plastic
ase_nstr_pld_pile_crash.dat
Quad swinging cracked
step_nonl_concrete_girder.dat
Glass window impact TH3
pendulum_impact_test.dat
SEIL Impact
cable_dynamics.dat
Intelligent load
step_intelligent_load.dat
Bettung abhebend
step_intelligent_load_nonl.dat
Contact car collision
movs_car_collision.dat
Beulen dyn. relaxation
dynamic_relaxation_buckling.dat
Membran dyn. relaxation
dynamic_relaxation_air_cushion.dat
-> Example overviews
-> Summary of example overviews
Damping parameters are to be input with record GRP. Loadfunctions: In ASE usually nonlinear dynamic is calculated. Therefore the complete stress state including dead load must be genereated. To the permanent part (dead load) the variable part of the loading (earthquake, impuls, initial velocity) must be added. It is best to combine the loading directly in ASE, e.g.: SYST PLC 1 $ static state STEP N 100 DT 0.01 LCST 1001 LC 2 DLZ 1 LCC 801 $ permanten additional dead load without load function LCC 901 $ variable load with load function from SOFILOAD see step_sofiload_ase.dat When the variable load starts, the static state already exists. If you first analyze the steady state in a separate loadcase without time dynamic (e.g. loadcase 1) you can then continue with the time dynamic analysis using the steady state as a primary loadcase - see SYST PLC 1 above. If you would activate the dead load in the time step analysis for the first time, the system would accelerate from the unstressed start state and then swing arround the steady state. This would be the case if you would suddenly remove the formwork from a concrete girder, see step_nonl_concrete_girder.dat Saving of the results
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Input Description | ASE
In order to avoid large databases for the time step method the calculation can occur only with two load cases which vary in each case. This works automatically using STEP N>1 and LCST. The results which are important for the user can then be stored in separate storage load cases with STEP LCST ... SELE ... (bit pattern). For N>1 LFST is increased in each step (see example a2_introduction_earthquake.dat). With STEP 0 LCST ... this feature can also be used for normal loadcases. Following inputs are possible: STEP 1 LCST ... SELE +1
= displacements
STEP 1 LCST ... SELE +2
= support reactions
STEP 1 LCST ... SELE +4
= velocities
STEP 1 LCST ... SELE +8
= accelerations
STEP 1 LCST ... SELE +16
= beam internal forces and moments
STEP 1 LCST ... SELE +32
= nonlinear beam results
STEP 1 LCST ... SELE +64
= spring results
STEP 1 LCST ... SELE +128
= truss+cable+boundary results
STEP 1 LCST ... SELE +256
= QUAD results
STEP 1 LCST ... SELE +512
= QUAD results in nodes
STEP 1 LCST ... SELE +1024
= non-linear QUAD results
STEP 1 LCST ... SELE +2048
= foundation results
STEP 1 LCST ... SELE +4096
= BRIC results
STEP 1 LCST ... SELE +8192
= BRIC results in nodes
STEP 1 LCST ... SELE +16384
= loads
default: no generation of a separate storage load case Beispiel
a2_introduction_earthquake.dat
Further examples for the dynamic calculations with ASE can be found in the example folder ase.dat\english\dynamics. With STEP...DIV a time step division can be controlled, if the nonlinear Iteration does not achieve a necessary equilibrium: DIV=0 -
no time step division
DIV=1-9
divide time step max. DIV times, create internal time step division but loadcase output for the requested time steps
DIV=11-19
adapt time step but store each time step. The resulting load-
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ASE | Input Description
case seqence then has variable delta-t. Feature not active now - reserved for new time function input LCC...FUNC Default DIV=-2 For negative DIV, the analysis continues in the shortest time step division also if no sufficient equilibrium is reached. For DIV>0 the progranm stops. At the end of the ASE run, a summary of the calculated time steps is printed.
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Input Description | ASE
3.6
HIST – Storage STEP-LCST
See also: STEP, GRP
HIST
Item
Description
Unit
Default
TYPE
Elementtype
LT
-
−
-
NODE BOUN BEAM TRUS CABL SPRI QUAD BRIC TEND: FROM
Elementnumber
TO INC
Selection of elements to be stored via STEP-LCST: With HIST now nodes and elements can be selected for storage STEP-LCSTSELE to keep the database small: If no HIST command is defined for a certain elementtype, all elemente of this type are stored. For example: STEP ... LCST 1001 SELE 1+2+4+8+16+256+1024 HIST NODE from 701 to 750 HIST QUAD 318,319
stores nodal results for nodes 701-750, all beam results and und Quad results for elements 318+319.
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ASE | Input Description
3.7
ULTI – Limit Load Iteration
See also: CTRL, SYST, GRP, PLOT
Item
Description
STEP FAK1
ULTI Unit
Default
Number of limit load iterations
−
5
Start factor of 1st load case
−
1
(overwrites the factor in record LC - FACT!) FAKE
End factor or accuracy (-0.005 = 0.5%)
−
-0.005
DFAK
First step of the load factor
−
1
PRO
Progression of the load factor
−
2
DL
The factor acts on the dead weight too
LT
YES
PRIM
(only if a dead weight has been activated with GRP - FACD or LC - DLZ) NO Dead weight retains the initially input factor Automatic introduction of a primary load case NO A new load step is not added automatically to the latest LC Minimum step width of the load factor
LT
YES
−
0
DMIN
The limit load iteration begins with the factor given for FAK1. Any factor which was input in the record LC FACT is not considered in this case and it is ineffective. If the first calculation ends with a convergent iteration (notice the iteration parameters ITER and TOL in the SYST record), a new load case is generated with a load case number increased by 1 and the load factor is increased by DFAK. Examples to ULTI: Ultimate load iteration
Input file
Stability quad column
ase9_quad_euler_beam.dat
Slab buckling
ase12_buckling_slab.dat
Shell buckling
ase13_shell_buckling.dat
Concrete girder ULTI
nonlinear_quad_concrete_beam.dat Table continued on next page.
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Input Description | ASE
Ultimate load iteration
Input file
Push Over Beam+Quad
push_over_quad_beam_frame.dat
Push Over Quad Frame
push_over_quad_deformation_controlled.dat
-> Example overviews
-> Summary of example overviews
If a primary load case has been defined in SYST PLC or GRP PLC the first calculation makes already use of this given primary load case. If a load should not be increased during the limit load iteration, this can be requested via the function ’Copy Loads’ with ULTI=NO in the record LCC. With PRIM YES the new load case makes use of the stable first load case. With PRIM NO the analysis starts as in the first load case (PLC according to SYST PLC or GRP PLC). If the second load case ends with convergence too, the last step of the load factor (DFAK) is multiplied by the progression PRO and used as new step. The third load case obtains then the load factor FAK1 + DFAK + DFAK·PRO and so on. The default values FAK1=1, DFAK=1 and PRO=2 result in the following load steps: Load case 1
Factor 1.00
Load case 2
Factor 2.00
Load case 3
Factor 4.00
Load case 4
Factor 8.00
Load case 5
Factor 16.00
Load deformation curves can be calculated with FAK1=1, DFAK=1 and PRO=1 (can be represented graphically, see example ase9_quad_euler_beam.dat): Load case 1
Factor 1.00
Load case 2
Factor 2.00
Load case 3
Factor 3.00
Load case 4
Factor 4.00
Load case 5
Factor 5.00
If an iteration is divergent, i.e. equilibrium could not be reached, the last load step is halved, if no input occurred for DMIN. With DMIN local stability problems
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ASE | Input Description
may be eliminated. The user has to convince himself of the accuracy of the final solution because also non-convergent results may be saved! The limit load iteration ends, if FAKE or the maximum number STEP are reached. For negative FAKE also if the acceracy is reached. Input -0.02 = 2% (when the two last factors differ less than 2%). If a new stable primary load case is used, the program generates always the new tangential geometry stiffness matrix.
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Input Description | ASE
3.8
PLOT – Plot of a Limit Load Iteration
See also: ULTI
PLOT
Item
Description
Unit
Default
LC
First load case number
−
!
TO
Last load case number
−
-
NNO
Node number
−
-
DIRE
Direction
−
-
TYPE
Plot type
LT4
*
−
-
−
-
−
1
NO
FACT
load-displacement plot
FACR
” but factor to the right
TIME
displacement plot on time axis
LCNO displacement plot on load case number EX sig-eps hysterese plot →ase.dat\dynamics\ step_nonl_concrete_girder.dat EX sig-eps Hysterese Plot →ase.dat\dynamics\ step_nonl_betonbalken.dat Element number for spring and quad results
XI
QUAD-layer depth (nur bei RICH= SX, SY, SXY, TAUX, TAUY, SS1 oder SS2)
NULL
connection to the (0,0) nullpoint 0=no, 1=yes
A plot of a limit load iteration can be generated with an input for PLOT. If no input for TO is done, than the last load case number of a sequence is used automatically. Without input for NNO the node number with the largest displacement is selected then automatically and without input for DIRE the direction with the largest displacement. Following directions can be input for DIRE:
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ASE | Input Description
UX,UY,UZ
(or X,Y,Z) displacement
PHIX,PHIY,PHIZ
rotation
VX,VY,VZ,
nodal velocity
VPHX,VPHY,VPHZ
rotation
AX,AY,AZ
nodal acceleration
APHX,APHY,APHZ
rotation
PX,PY,PZ
support reaction
MX,MY,MZ
support moment
N,M,PT,V
spring normal force, moment, PT, displacement for element NO
NV
springforce-springdisplacement diagram
SX,SY,SXY,TAUX,TAUY
QUAD layer stress for element NO
SS1,SS2
QUAD layer reinforcement stress
The definition for PLOT can be done also in a separate ASE input, e.g. PROG ASE HEAD PLOT 101 NNO 200 DIRE Y END
Examples to PLOT: Task
Input file
Load deformation curve
ase9_quad_euler_beam.dat
Quad layer stress
step_nonl_concrete_girder.dat
Spring force hysterese
spring_law_3_pkin_curve.dat
Plots with prog results:
ase1_overview.dat
Beam-MY curve
ase_nstr_pld_pile_crash.dat
Cross section stresses
aseaqb_1_column_cracked.dat
” in bridge design
csm31_design.dat
-> Example overviews
-> Summary of example overviews
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Input Description | ASE
3.9
CREP – Creep and Shrinkage
See also: CTRL, SYST, GRP
Item
Description
NCRE
CREP Unit
Default
Number of creep steps (1-99)
−
5
RO
Relaxation coefficient according to Trost
−
0
T
Effective duration of period
dys
0.0
RH
Relative humidity or maturity
%
40
TEMP
Temperature of concrete or time factor
deg
20
BEAM
Control for take-over of the creep calculation for bending beams via creep curvatures from the program AQB or for the calculation in ASE AQB Take over from AQB
−
ASE
ASE
Calculation in ASE
Additional inputs are necessary in the record GRP ... PHI EPS RELZ PHIF: PHI
Total creep factor of NCRE creep steps
EPS
Total shrinkage coefficient of NCRE creep steps (negative)
RELZ
Relaxation of the prestressing steel (is applied only in the first creep step fully)
PHIF
Total creep step for springs + foundation
Creep and shrinkage with construction stages or in bridge design should be done with module CSM (see examples below). Using pure ASE there are two different 1st Plate calculation according to cracked condition
creep
calculations:
For plates in cracked condition a simplified consideration of creep and shrinkage effects was implemented in a step. With an input of CREP 1 and GRP PHI EPS creep and shrinkage are calculated as follows in a load case step without input of a primary load case: - The elastic modulus of concrete is reduced to E=E0/(1+PHI). - The concrete is given a pre-strain of EPS. Because the shrinkage shortening acts only on the compression side at a
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ASE | Input Description
cracked cross section, shrinkage causes an enlargement of the bending also at plates. At the cracked tensile side shrinkage acts only on the cracked width. The creep and shrinkage values affect all elements with material concrete, PHIF affects springs, edges and QUAD foundations, also with a reduction of the stiffness of 1/(1+PHIF). 2nd More complex calculation with use of a primary load case (is used by CSM) At that the total creep is dismantled in NCRE creep intervals which are calculated in NCRE load cases. The load cases generated automatically by the first LC load case number ascendingly. The stresses of a primary load case which are accepted as constant during a creep step (or of the last creep step) are converted into strains. These strains are multiplied by the (with the modified relaxation coefficient RO) partial creep coefficient DPHI and used as a load for alle concrete elements . Middle stresses which generates creep are not determined. Abrupt constraint is applied for creep of the stresses from PLC (reduction of a constraint internal force): ZK = Z0 ( 1 - dϕ/(1 + RO·dϕ))
see STAR2 manual
ZKF = Z∞( 1 - dϕf/(1 + RO·dϕ))
(springs + foundation)
For shrinkage a gradual constraint is assumed: ZS = Z∞ ( 1 /(1 + RO·dϕ))
(shrinkage)
with dϕ=PHI/NCRE Computation: The program uses the stresses of the primary load case as stresses producing creep. It applies the primary load case in an internal way with FACL=FACP=ZK for the corresponding elements. For tendons the PLC is scheduled only in the first creep step with the factor (1-relz), in all further creep steps with the factor 1.0. At shrinkage the partial shrinkage coefficient which was reduced according to Trost is used: load-strain = dε·ZKF = ε·ZKF/NCRE The program allows in the case of calculations with primary load case only creep values with dphi < 0.4. If the stresses producing creep are hardly reduced by creep and shrinkage, RO has to be defined in a correspondingly small way or more creep steps have to be input. For a prestress from the program TENDON only RO=0 is possible generally in order to avoid an unintentional reduction of
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Input Description | ASE
the creep effect for the statically determinate part of the prestress - possible increase of NCRE. Values in the region of 0.8 are reasonable for creep of a constraint condition, for example from construction stage. For values which are smaller than dϕ=0.2 the importance of RO comes in the background. Creep and shrinkage are effective for all concrete elements of type BEAM, TRUS, CABL, QUAD + BRIC. PHIF acts on spring and boundary elements and on pile- and quad bedding. Thereby the QUAD foundation can get another creep coefficient (settlement) independently of the QUAD element. RELZ acts only on tendons of the plate prestress. With CREP BEAM it can be controlled, whether the creep calculation for bending beams via creep curvatures is taken over from AQB (CREP BEAM=AQB) or whether it should be determined in ASE (CREP BEAM=ASE = default). Caution: Prestressed beams have to be calculated with AQB! Please refer to program CSM. The program extension ASE1 is necessary for creep calculations. Examples to CREP
Input file
Technique by hand
ase7_creep_two_span_girder.dat
Creep on cracked quad
a1_introduction_example.dat
Long term slab deflection
a2_nonlinear_slab.dat
Intruduction CSM
csm1_4span_centering.dat
Twospan creep example
csm2_simplecreep.dat
Prestressed bridge
csm31_design.dat
-> Example overviews
-> Summary of example overviews
SOFiSTiK 2014
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ASE | Input Description
3.10
GRP – Group Selection Elements
See also: SYST, PSEL, LC, GRP2
Item
Description
NO
Group number
GRP Unit
Default
−
ALL
LT
FULL
−
-
−
*
kN/ m3
0
m
0
−
1
default ALL = all groups VAL
Selection OFF
The group is not used
YES
The group is used
FULL
Use of group + result output
LIN
YES, but material linear
LINE
FACS PLC
FULL, but material linear (TH2, TH3 not affected) Factor for group stiffness / see also GRP2 STEA-QUEA Number of the primary load case Default as in SYST
GAM
Parameter of an additional
H
analytical primary state
K SIGN
σ -z = GAM · (Z-H) + SIGN
kN/ m2
0
SIGH
σ -x = σ -y = K · σ -z + SIGH
kN/ m2
0
FACL
Factor of loads from primary stress PLC
−
1
FACD
Factor of dead weight in defined dead weight direction (SYST GDIR from SOFIMSHA, SOFIMSHC) Factor of stress from primary load case PLC
−
0
−
FACL
m
± 99999.
FACP (FACT HW
Temperature replaced by the record TEMP from HYDRA) Ordinate of the ground water level
GAMA
Weight under water
kN/m3
γ-10
RADA
Raleigh damping factor for mass proportional damping
1/ sec
0.
Table continued on next page.
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Input Description | ASE
Item
Description
Unit
Default
RADB
sec
0.
MODD
Raleigh damping factor for stiffness proportional damping Modal damping factor
−
-
CS
Construction stage for tendons
−
-
PREX
Element prestress in local x direction
kN, m
0
PREY
QUAD prestress in local y direction
kN, m
0
PHI
Creep coefficient (see record CREP)
−
0
EPS
Shrinkage coefficient
−
0
RELZ
Relaxation of prestressing steel
−
0
−
PHI
−
0
dys
-
−
ACTI
−
FACS
−
-
−
-
AUTO automatic determination input 0.03 means loss of 3% PHIF
Creep coefficient for springs and foundation Creep coefficient for elements which do not consist of concrete (composite structures)
PHIS T1
HING
Stiffness development of elements with concrete according to the modified concrete age T1 Beam pin-joint temporarily for precast bridges ACTI pin-joint FIX
FACB CSDL MNO
fixed connection
example: Single Span Girder with Auxiliary Support Factor for bedding properties of the QUAD elements Dead load of a later construction stage Material number of PHI and EPS if in a group different materials occur → CSM
The record GRP defines the participating elements as well as the stress state which is available at the beginning of the analysis. At first the defaults for all groups are defined with GRP ALL or GRP - , e.g. GRP -FULL. The following input for a group overwrites then this default, e.g. GRP 5 NO.
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ASE | Input Description
An input to GRP usually enforces a newbuilding of stiffness file $d1. It will also be unusable for further load cases. The storage of this stiffness file is possible with the record CTRL. The group number of each element is obtained by dividing the element number by the group divisor GDIV (see SOFIMSHA/SOFIMSHC manual SYST..GDIV). The defaulted group selection is that one of the last analysis call or input block. Without any inputs all elements are used. With an input only the specified groups are activated. If the subdivision of the elements occurs in groups, it should be kept in mind that the specification of the analytical primary state may require in certain cases a finer subdivision than the one assumed initially by the user. GRP input without any group number set only the given parameters for the previous defined groups. Example: GRP 1,2 GRP CS 5 $ without group number $
Only the groups 1 and 2 are activated with CS 5. A stiffness reduction may be defined with FACS for beams with calculation according to 2nd /3rd order theory (1/γm -multiple). The values GAM-SIGH, FACT, HW and GAMA are only applicable to volume elements (BRIC), i.e. only then an analytical primary stress state is reasonable. By contrast, all control parameters of a primary state from a previous analysis have effect to all elements. The processing of a temperature field from the program HYDRA was expanded essentially with the record TEMP. The input GRP FACT is not anymore permissible. The primary state is necessary for non-linear analysis and in addition it facilitates the determination of loads due to changes of the static system. The analytical component is defined with the load SIGN which is effective in a height H and an increase GAM. The horizontal component is obtained by means of the lateral pressure coefficient and the vertical stress. The item GAM has usually the same values as the items GAM/GAMA of the material record, however, it is independent of them.
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Input Description | ASE
Figure 3.2: Analytical stress states
The loading components from the stresses of the primary state are multiplied by FACL to the load case which is to be calculated. FACD defines a dead weight loading with the values GAM/GAMA of the material record in dead weight direction. This loading is usually in equilibrium with the primary state. The loads from FACL and FACD act in all load cases of the input block. If the old loads of the primary load case ( PLC) are applied simultaneously to a system with the loads from the primary stresses with FACL=1, these both loading cancel themselves. New deformations do not result. Therefore the loads from the primary stresses oppose the old loads. The item HW specifies the phreatic level in the corresponding group. Continuum elements (BRIC) located below HW are analysed under buoyancy. The default setting fo HW is "infinitely deep". Depending on the direction of gravity the phreatic level is set to ± 99999m, in this case. The analysis of the tendons is controlled by CS similar to the program AQBS. Depending on the value of CS the empty duct or the duct with the tendon or of the grouted duct are used. If CS is not input, tendons are used with CS 998 (=bonded, if not ICS1=999 in TENDON for unbonded tendons). More explanations see prestressed_slab.dat Prestress of elements via record GRP: GRP - PREX PREY In the program SOFIMSHA/SOFIMSHC a prestress which is considered during the calculation of stiffness can be input only at TRUS-CABL-SPRI. With GRP ... PREX PREY a real prestress can be defined in addition to TRUSCABL-SPRI also for QUAD and BEAM elements. This acts, first of all, as a normal prestressed load. However, it is considered also with the factor CTRL PRES for the initial stiffness. In this way membrane and cable structures can be calculated more simply according to the third-order theory. A membrane high
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ASE | Input Description
point should be input via the record HIGH. The value from GRP ... PREX PREY is interpreted in kN/m for QUAD, and in kN for BEAM, TRUS, CABL and SPRI. The GRP prestress acts also for linear calculation. A stabilization for the error estimate can be achieved in this way at displaced systems. In addition the prestress is considered also for an eigenvalue determination! Differences of the input of a truss or cable prestress in the program SOFIMSHA/SOFIMSHC for the GRP prestress: -
PRE acts in all load cases as long as a primary load case (PLC) is not used.
-
GRP-PREX acts only in ASE calculations in which it is input, however, in the record GRP in addition to a prestress of a primary load case.
Creep for composite systems concrete + steel A separate item PHIS can be input in the record GRP for elements which do not consist of concrete. Elements of concrete are processed with GRP ... PHI,EPS. Springs, boundary elements and elastic foundations are processed with GRP ... PHIF without shrinkage. Elements whose cross section material is not concrete are processed with GRP ... PHIS. Shrinkage of these elements is considered with the value EPS·PHIS/PHI. For BEAM composite cross sections and BEAM prestressed concrete cross sections creep and shrinkage have to be processed with the program AQB. The prestressing steel relaxation of the QUAD tendons is determined automatically with the input RELZ AUTO in combination with the time duration input T in record CREP. The material values STEE ... REL1+REL2 from the program AQUA are used.. Stiffness development of elements with concrete For input of the temperature adjusted concrete age T1 in GRP...T1, the development of stiffness of concrete elements is taken into account. The program CSM (version 11.57) automatically adjusts T1 in dependence on the given temperature. The development is plotted for the first concrete material (for ECHO MAT FULL for all concrete materials and also for calculations with primary load case). Function for prefabricated bridges
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Input Description | ASE
Temporary BEAM pin-joints can be fixed with GRP HING FIX. Thus a construction stage can be calculated with pin-joint and a final stage without pin-joint. The results can be superpositioned and designed. All pin-joints are active with the default GRP HING ACTI. Example see ase6_two_span_girder_construction_stages.dat Later construction stages With GRP CSDL the dead load of a later construction stage can be activated already for composite beam cross sections with activated stiffness of the cross section construction stage CS (green concrete dead load). Example see csm3_composite_beam.dat
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ASE | Input Description
3.11
GRP2 – Expanded Group Selection
See also: GRP, TEMP
Item
Description
NO
GRP2 Unit
Default
Group number
−
-
STEA
Formfinding cable-stayed bridges:
−
-
QUEA
normal force stiffness component of beams Orthotropic slabs:
−
-
QUEX
normal force stiffness component of QUAD elements Orthotropic slabs:
−
-
QUEY
reduction of the QUAD axial force stiffness only in local x Orthotropic slabs:
−
-
−
0.001
−
-
−
-
−
-
−
1/2
−
2
−
0.55
ALP0
ULUS QEMX QEMY EXPO
GEOM
BWES
STEA
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reduction of the QUAD axial force stiffness only in local y Lower threshold for stiffness development for BRIC elements HYDRA temperature field Limitation of QUAD stresses in ultimate limit analysis Reduction of the elastic modulus of QUAD elements in local x direction Not implemented - use QEMX - see below Exponent for the elastic modulus according to "Braunschweiger Stoffmodell" separated according to groups Group-wise control of the geometric stiffness from primary load case for buckling eigenvalues β value value in the formula according to Wesche
With STEA the normal force stiffness component of beams can be increased. The bending stiffness remains unchangeable. Example see suspension_bridge_formfinding.dat
SOFiSTiK 2014
Input Description | ASE
QUEA
With QUEA the E·A part of the QUAD elements can be modified. Example see steel_composite_orto.dat
QUEX
With QUEX it is possible to reduce the QUAD axial force stiffness only in local x direction for orthotropic slabs.
QUEY
With QUEY it is possible to reduce the QUAD axial force stiffness only in local y direction for orthotropic slabs.
ALP0
With ALP0 varying material stiffness due to different hydration degrees can be taken into account in an stress analysis of a HYDRA temperature field. The lower threshold for stiffness development can be input here (default 0.001). With TEMP EMOD OFF this stiffness modification can be switched off. Example see ripe_creep_comparision.dat
ULUS
Limitation of QUAD stress in ultimate limit analysis With GRP2 ULUS (ultimate limit iteration - capacity usage) the load will not be enlarged, if the maximum van Mise stress in a layer element (non-linear concrete, steel of MLAY-material) reaches the value ULUS*strength. For concrete, strength is fc in AQUA, for steel fy.
QEMX
with QEMX the elastic modulus of QUAD elements can be modified in local x direction, e.g. GRP2 - QEMX 0.001. Example see steel_composite_orto.dat
QEMY
Not implemented. To achieve e.g. 30% reduction in y direction in group 5, you can use GRUP 5 FACS 0.70 ; GRP2 QEMX 1/0.70 (-> E-X 100%, E-Y 70%). Alternatively rotate local coordinate system.
EXPO
BRIC hydration: The exponent for the BRIC hydration E-modulus can now be input for each group. The default is the value of TEMP EXPO.
GEOM
Group-wise control of the geometric stiffness from primary load case for buckling eigenvalues To avoid negative eigenvalues, now in each group the geometric stiffness from the primary loadase can be switched variabel: Input GRP2 GEOM: 0
don’t scale geometric stiffness in buckling eigenvalues
1
normal geometric stiffness in buckling eigenvalues
2
as 1, but don’t scale geometric stiffness for membrane elements
3
as 1, but don’t scale geom. stiffness for membranes and cables
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ASE | Input Description
-1
don’t use geometric stiffness at all (also in static analysis and natural frequencies)
’don’t scale’ means, that the geometric stiffness is added to the linear stiffnesss matrix, deleted in the total geometric stiffnesss matrix and thus is not scaled with the buckling factor. Default: GRP2 - GEOM 2 BWES
β value value according to Wesche in the formula ƒβ
=
e
−·/ z· te−BWES −28−BWES
a·w/z = value can be defined in record TEMP EMOD default: 0.55 (Technische Empfehlung Bautechnick BAW / Wesche) te = effective concrete age resulting from the HYDRA analysis Thus the elastic modulus that is used is determined as follows: E
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=
ƒβ 1/ 3
·
E28
SOFiSTiK 2014
Input Description | ASE
3.12
ELEM – Single Element Settings
ELEM Item
Description
Unit
Default
ETYP
Elementtype - possible input:
LT
BEAM
BEAM TRUS CABL SPRI QUAD BRIC NO
Elementnumber
−
!
FACS
stifness factor Overwrites GPR-FAFC. FACS=0 deactivates one single element (collaps analysis). as GRP FACL
−
-
−
-
N/ mm2
-
FACL
for element damage, both FACS and FACL should be reduced! FCTK
Tension strength - ONLY for cracked concrete quads (SYST NMAT YES) (has no effect, if stress strain law is also defined in tension). See example tunnel_shell.dat
Input for collaps analysis: in big sytems it is often necessary to check the behaviour under failure of one single element. With ELEM ETYP NO FACS one single element can be switched off or weakened. Usually also the element force of the PLC must be reduced → usually also FACL has to be reduced!
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ASE | Input Description
3.13
LEN0 – Unstressed Length
LEN0 Item
Description
ETYP
Element type TRUS
Truss elements
CABL
Cable elements
Unit
Default
−
CABL
NO
Element number (GRP see below)
−
!
L0
Unstressed length
m
!
TYPE
Input of system length
LT
TOTA
LC
Input of total cable installation length DELT Input of difference L0 to the system length in the undeformed system LCL0 Input of difference L0 to unstressed length of loadcase LC Loadcase for TYPE-LCL0
−
-
GRP
instead of NO: all elements of group GRP
−
-
TOTA
Example: cable_unstressed_length.dat LEN0 CABL 501 L0 67.000 TYPE TOTA $ install cable with length 67.000m$ LEN0 CABL 502 L0 -0.100 TYPE DELT $ 100 mm shorter than system length$ LEN0 CABL GRP 50 L0 0 TYPE LCL0 LF 7 $ with unstressed length of LC 7$
If a cable is activated in a CS for the first time and a LEN0 input is found for it, the cable is installed stressfree with this length, independant of deformations in the primary loadcase PLC! Internally it gets an additional prestress that shortens it so that the desired length appears. Without LEN0 (normal behaviour) a cable is installed in that way that on the PLC deformations it has force 0 (without prestress and load on internal cable sagging).
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3.14
HIGH – Membrane High Points
See also: GRP
Item
Description
XM
Coordinates of the high point
HIGH Unit
Default
m/ LT
*
m/ −
*
Alternatively Literal ’NNO’ YM is taken as the node number of the high point YM ZM
(ZM is not used yet)
m
0
NX
Normal vector of the high point axis
−
0
NY
Default: Z axis
−
0
−
1
kN/ m
*
−
*
−
-
NZ PR1 PTPR
Radial stress in 1 m distance to the high point or to the direction XM, YM, ZM Ratio of tangential to radial prestress
NOG
Group for which this prestress is valid Default: all groups
If genuine high points at membranes are available, an orthotropic prestress with a fixed ratio of the tangential/radial prestress is wanted also mostly. A radial stress which increases itself to the high point is necessary here. This axisymmetric high point-stress state is generated with the record HIGH. Here PR1 defines the radial stress in 1 m distance to the high point. PTPR defines the ratio of the tangential to the radial prestress. Examples see Theoretical principles. Example of a high point at X = 5.0 m, Y = 0.0 m: HIGH 5 0 PR1 20 PTPR 0.4
shows: σ -R in 1m distance = 20.00 kN/m
corresponding-σ -T = 8.00 kN/m (0.4*20) and from causes of the equilibrium for example in 10 m distance:
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ASE | Input Description
σ -R= PR1·1/r·eˆ (PTPR·ln(r))= 20·1/10·exp(0.4·ln(10))= 5.02 kN/m
corresponding-σ -T = 2.01 kN/m (0.4·5.02) If the distance is larger than 1000 m, a constant prestress is assumed. The stress in direction to the high point is then always PR1, the stress orthogonal to this direction is PTPR·PR1, therefore without radial reduction as described above. The advantage is in the simple input of skew prestress independently of the direction of the local element coordinate systems! The stress in the QUAD elements results from the global directions!
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3.15
PSEL – Selection of Piles
See also: GRP, ECHO
Item
Description
FROM
PSEL Unit
Default
Lower pile number
−
1
TO
Upper pile number
−
FROM
INC
Increment
−
1
REDP
Reduction factor for pile stiffness
−
1.0
REDA
Reduction factor for axial foundations
−
1.0
REDT
Reduction factor for lateral foundation
−
1.0
PSEL can be used to deactivate certain piles or for the reduction of their bedding due to shadowing inside of a pile group. The reduction factors are determined according to code specifications or experiments. If otherwise nothing is specified, all piles are used. Piles which are not used have to be specified with REDP=0. PSEL inputs are saved permanently. They are valid for every pile during any subsequent inputs so long as they are not redefined. Any input of PSEL causes the recalculation of the system matrix. The record PSEL is only available in the ASE version which was expanded with the pile element.
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ASE | Input Description
3.16
TBEA – Reduction of the Width for T-Beams
TBEA Item
Description
Unit
Default
NC
Cross section number
−
-
B
Reduced cross section width
−
-
For bridge superstructures thin cantilevers get small bending moments or shear forces in longitudinal direction. The multiplication of the internal forces and moments of the FE nodes with the whole plate is then too unfavourable. The cross section width per cross section NC can be reduced now with the record TBEA for the consideration of the haunched cover plate. Attention: This model can not be used for influence line evaluation with ELLA because ELLA does not add the slab parts to the beam! Example see tbeam_philosophy_4.dat ( tbeam_philosophy_e.pdf ) and: steel_composite_tbeam.dat (compare steel_composite_real.dat)
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3.17
REIQ – Reinforcement in QUAD Elements
See also: SYST, GRP
Item
Description
LCR
FACT LCRS
REIQ Unit
Default
Design case number from the program BEMESS (number of a reinforcement distribution) Multiplication factor
−
1
−
1.0
Stored number of the reinforcement distribution
−
99
With REIQ a reinforcement of design case LCR can be used from the program BEMESS for a non-linear calculation of plates and shells according to cracked condition. Nodal reinforcements are applied in all adjacent elements to get enough reinforcement in the gauss points - = shift of reinforcement. Element reinforcement is applied as well. Example see a2_nonlinear_slab.dat For beam elements input for reinforcement cases are possible in BEW. With minimum reinforcement and further datea from BEMESS PARA or the design parameter dialog then a reinforcement distribution is fixed and stored in design case LCRS for graphical checks. For the concrete cover, the bar steel diameters and reinforcements directions the following rules are valid: Concrete cover (centre of gravity distance of the reinforcement bars): These values are used from the BEMESS PARA or the design parameter dialog or as default with 60 mm. Bar diameter: same procedure as for centre of gravity distance: - default 10 mm Reinforcement directions: They are: - used at first from BEMESS PARA or the design parameter dialog - BEMESS or SOFICAD-B reinforcement is taken into acSOFiSTiK 2014
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ASE | Input Description
count with the smallest angle deviation to already existing directions. - If nothing is defined, reinforcement bars are used with an angle of 0 and 90 degree.
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3.18
STEX – External Stiffness
See also: GRP, SYST
Item
Description
NAME
Name of the external stiffness file
OPT
ITER: treat halfspace stiffness iteratively (without full conditioned stiffness matrix)
STEX Unit
Default
LT24
*
−
-
A complete external stiffness can be added with STEX. External stiffnesses are generated currently only by the program HASE for the halfspace (stiffness coefficient method). The project name is the default for NAME. The mere input of STEX (without name) suffices usually. With STEX OPT ITER the halfspace stiffness can be used iteratively. Then only the diagonal therms are used and the off diagonal therms are treated iteratively (residual force iteration). For big systems this is also senseful for linear calculations because full conditioned stiffness matrix is often too big for the solver or the calculation time too long. Usage: – SYST PROB LINE $ siehe Beispiel -> hase1_bottomslab.dat STEX LC 1,2,3 Linear analysis with the full conditioned stiffness matrix for small systems. – SYST PROB LINE $ siehe Beispiel -> hase2_3d.dat STEX OPT ITER LC 1 Linear iterative analysis for big systems. Only one load case in one ASE part (HEAD-END) allowed. No nonlinear effects are taken into account. The result loadcases can be superposed with MAXIMA. – SYST PROB NONL $ siehe Beispiel -> hase2_3d.dat STEX OPT ITER LC 1 Nichtlinear effects as bottom slab lifting on tension or nonlinear pile bedding are treated. A superposition with MAXIMA is usually not possible.
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ASE | Input Description
Halfspace examples via HASE: Task
Input file
Usage for big systems
hase2_3d.dat
Variable soil in ground view
hase5_profile_interpolation.dat
Halfspace with simple piles
hase8_slab_with_piles.dat
Pier with inclined piles
hase23_pier_foundation.dat
Bottomslab-pile interaction
kpp1.dat
-> Example overviews
-> Summary of example overviews
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Input Description | ASE
3.19
OBLI – Inclination
See also: GRP, SYST, LC
Item
Description
SX
OBLI Unit
Default
Inclination in X direction
−
0
SY
Inclination in Y direction
−
0
SZ
Inclination in Z direction
−
0
LC
Load case number of a available load case
−
-
FACV
Factor for displacements of LC
−
-
VMAX
Factor for imperfection
−
-
DIRE
Scaling direction of imperfection
−
-
XX,YY,ZZ
With OBLI it is possible to input a global inclination of the system. With the input of SX=1/200 for example all nodes get an inclination of u-x=1/200·height. The used height is the height above the node which is the lowest one in dead weight direction (see program SOFIMSHA/SOFIMSHC record SYST GDIR). The global inclination affects also the linear calculation according to first-order theory. It acts on all elements and also on mixed systems for example from beam and shell elements. In the same way a imperfection of the beam axes is considered due to the misalignment → lateral buckling. The input OBLI must occur before the definition of the load cases and acts then for all load cases of this ASE calculation. Imperfection With OBLI LC FACV an additional load case can be defined for imperfections, also if another primary load case is used with SYST PLC. The imperfection load case in OBLI is used always as a non-stressed one and the normally usual input GRP ... FACL is not necessary. Thus the input is easier and simultaneously more flexible. The input SYST ... FACV should be omitted in future. Alternatively (to FACL) a maximum imperfection can be scaled with OBLI VMAX. DIRE defines the scaling direction if necessary (without DIRE the maximum diplacementvector is scaled). For example OBLI LC 91 VMAX -0.050 DIRE YY describes an imperfection affin to load case 91 with a maximum value in global Y direction of - 50 mm.
SOFiSTiK 2014
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ASE | Input Description
An imperfection has here effects on the internal forces and moments of the first- and second-order theory. Note please, that an imperfection via OBLI does not generate local beam curvatures, however, a polyline-like continuous beam imperfection. The displacements always contain the sum of the displacement from the inclination plus additional deformation! So the inclination can be controlled graphically. If die additional deformation shall be printed separately, please first create a loadcase with pure inclination (DLZ=0.000001). Then calcualte a following loadcase, using the previous as PLC, apply the load and request storage of differential displacement with CTRL DIFF. Further possibilities for the input of imperfections: - affin imperfections from scaled primary load case - imperfections from buckling eigenvalue example ase9_quad_euler_beam.dat and: ase12_buckling_slab.dat - precurvature of beams for example with temperature load delta-t/h or local curvature TYPE KY or KZ see example ase11_girder_overturning.dat
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Input Description | ASE
3.20
SLIP – SLIP Cable
SLIP Item
Description
Unit
Default
NOSL
SLIP cable number
−
-
NOG
Group number of the cable elements
−
-
−
-
group 0 is not allowed NOEL
Element number of the cable element
SLIP Cable are a number of cable elements that get a forced common normal force. Thus they can slide so to speak at intermediate points. The common normal force is determined from the total strain of the corresponding cables divided by their total length. In WINGARF/GRAFIX the axial displacement shows the nodal deformation change. This can be used to visualize the slipping effect. Slip cable are calculated without an own inner cable lag. The definition of a SLIP Cable which is input in an ASE calculation is maintained in the database. It is used also in the following calculations. A new SLIP input in a further ASE calculation or a SLIP input without further parameters deletes the SLIP Cable definition in the database. Examples: SLIP NOSL 4 NOG 4 assigns all cables of the element group 4 to the SLIP Cable No 4. SLIP NOSL 5 NOEL 717,718,719 summarizes the cable elements to the SLIP Cable 5. The single cables 717+718+719 will have the same normal force in the final result. Example see slip_cable.dat
SOFiSTiK 2014
3-67
ASE | Input Description
3.21
VOLU – Air Volume Element
VOLU Item
Description
Unit
Default
NO
VOLU element number (without group)
−
-
GRP
associated QUAD-elements
−
-
POSI
QUAD element face (POSZ or NEGZ)
LT
POSZ
MNO
material number of the volume
−
0
default 0 = air under standard air pressure starting volume
P0
given pressure (without stiffness)
PLC
primary load case (default = SYST PLC)
V0
m3
1008
kN/ m2
1192
DV
volumen add-on
DT
temperature increase
[grd] 1215
MASS
mass participation
1008
−
*
−
m3
-
0.5
(0.5 = apply 50 % of air masse in eigenfrequency analysis) VOLU defines an air volume on a face of quad elements. VOLU distributes the air pressure uniformly onto the participated surfaces. It also generates a stiffness matrix that represents the compressibility of the enclosed air volume (stiffness bubble). VOLU is mainly used for membrane air cushions. An air pressure defined with VOLU-P0 is updated during the ASE-iterations and loads the rotated quad area. Also an increase of the quad area during formfinding updates the air pressure load! This is not done using SOFILOAD loads - see example air_volume_tennis.dat. An input VOLU without further data delets VOLU elements of a previous ASE run. Without VOLU-input all VOLU data is taken from the last run but without old load input P0, DV ir DT. With a VOLU input using only the VOLU number (without GRP, POSI, VO input) new loads for existing VOLU elements can be set. A VOLU analysis without P0 input creates a fully occupied stiffness matrix which causes high computation time. Therfore the number of contact nodes on the volume should not be greater than about 3000 betragen (maximum 5000)! Further explanations see:
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SOFiSTiK 2014
Input Description | ASE
Air pressure hall air_volume_tennis.dat Air cushion air_cushion.dat Please also ask for the corresponding SOFiSTiK paper contributed to the CIMNE Membranes 2011 conference.
SOFiSTiK 2014
3-69
ASE | Input Description
3.22
MOVS – Moving Spring
See also: V0, LAUN
MOVS
Item
Description
Unit
Default
NO
Spring number (GRP see below)
−
-
TYPE
Type
−
1
1
Use of the contact nodes
3
Use of QUAD elements
FROM
Start number of the nodes or elements
−
1
TO
End number of the nodes or elements
−
FROM+1
INC
Increment
−
1
LT/ m
-
−
-
AUTO L0
GRP
Automatical node chain search
Initial length for springs without end node N2 TRAN Consideration of the longitudinal and rotational effects instead of NO: all springs of group GRP
Examples to MOVS
Input file
Launching
csm40_incremental_launching_introduction.dat
Contact
movs_train_interaction.dat
Contact
movs_car_collision.dat
Kinematic
excavator.dat
-> Example overviews
-> Summary of example overviews
For the dynamic time step analysis it can be defined with the record MOVS (moving spring) that the wheel springs of a train which goes over the bridge search themselves for the current contact nodes of the bridge. Thus a train ride is implemented with all effects of the train-structure-interaction. The mass of the train is considered with the current train position. The contact nodes are determined from the particular relative displacement of the going train and the deformed bridge. Damper which are acted parallelly to the contact springs are converted also to the particular interpolated contact node. An input MOVS without further data delets MOVS elements of previous ASE
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SOFiSTiK 2014
Input Description | ASE
runs. A spring NO is defined as moving spring. Following types are possible:
TYPE=1
The spring searches for the contact nodes of the nodes FROM TO INC.
TYPE=2
The spring acts on one of the QUAD elements FROM TO INC.
With an input for L0 the definition of the springs is more simple, because only a direction has to be input and no node for kinematic constraint. In SOFIMSHA/SOFIMSHC or the graphical input only a normal spring without 2. node must be defined. The direction of the spring DX,DY+DZ then only defines the rough direction in which the spring will look for a contact. The length - important for first contact - will then be defined in ASE L0. The definition of MOVS in an ASE calculation is maintained in the database. It is used also in the following calculations. A new MOVS input in a further ASE calculation or a MOVS input without further parameters deletes the MOVS definition in the database.
SOFiSTiK 2014
3-71
ASE | Input Description
3.23
LAUN – Incremental Launching
See also: MOVS
Item
Description
GRP DX
LAUN Unit
Default
Group number (-1 for a new step)
−
-
Total displacement
m
0
DY
m
0
DZ
m
0
XM
Coordinates of a centre point for a
m
-
YM
rotation around a global axis
m
-
m
-
ZM NR1
Reference points for a rotation
−
-
NR2
around a free axis
−
-
PHI
Rotation (in radiant)
[rd] 3
-
Examples launching
Input file
Launching ASE
movs_incremental_launching_principle.dat
Launching CSM
csm41_launching_principle.dat
Launching training
csm40_launching_introduction.dat
Kinematic
kinematic_1.dat
Beam rotations
beam_rotation.dat
Excavator
excavator.dat
-> Example overviews
-> Summary of example overviews
A detailed description and training can be found in the CSM manual: Theoretical background - Incremental Launching Training. An input LAUN shifts the nodes of the element group GRP with DX,DY,DZ. An input of XM and YM rotates around the centre point with PHI [ rad] as arc length (around global Z axis). Starting on a PLC primary load case, the launching input is the new total displacement. A rotation around X- and Y- axis is possible with Input LAUN XM+YM : rotation around Z axis
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Input Description | ASE
Input LAUN YM+ZM : rotation around X axis Input LAUN XM+ZM : rotation around Y axis A rotation of systems around a free axis is possible with input LAUN NR1 NR2 by two reference nodes to defined the rotation axis. Also multiple rotations and displacements can be defined, separated by a LAUN -1 line: LAUN GRP 71 PHI 0.4 YM 3 ZM 3 $ rotation around the X axis LAUN -1 LAUN GRP 71,72 PHI 0.3 XM 0 YM 0 $ followed by a rotation around Z axis Problems may occur if two beams attach to a node and one beam rotates and the other not. Then the nodal LAUN nodal rotation is not clear and we assume: If the starting node of a beam rotates, the local coordinate system of the beam rotates. If the starting node of a beam does not rotate, the beam does not rotate (as shown in the animator beam coordinate system).
SOFiSTiK 2014
3-73
ASE | Input Description
3.24
SFIX – Fixing Stiffness
See also: GRP
Item
Description
LC PLC
SFIX Unit
Default
Load case number
−
*
Load case number of the normal force to be used
−
LC
Usage with one input line SFIX LC: With one input line SFIX LC (PLC is set to LC) for all elements (BEAM,QUAD,SPRI...) the geometric stiffness according to the normalforce of the PLC is added. So e.g. a set of loadcases can be analyzed with a unique geometric stiffness (TH2). This allows a later superposition with MAXIMA (linearization of the analysis). If a nonlinear material stiffness had been calculated with AQB in the PLC, this nonlinear stiffness is also used. Usage with multiple input lines for beam systems: Here the minimum of the AQB stiffness is determined from a series of load cases LC. With that and together with the geometrical stiffness from the normal force of a PLC a linear beam calculation is performed, so that the superposition principle is valid for following superposition. Example see sfix.dat Eigenfrequencies on cracked beam: aseaqb_1_column_cracked.dat
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SOFiSTiK 2014
Input Description | ASE
3.25
LC – Load Case and Masses
See also: LAG, LCC, MASS
Item
Description
NO
Load case number ALL
All load cases
TEST
Instability test
LC Unit
Default
−
!
FACT
Factor for all loads
−
1.0
DLX
Dead weight factor in global X direction
−
0.0
DLY
Dead weight factor in global Y direction
−
0.0
DLZ
Dead weight factor in global Z direction
−
0.0
BET2
Coefficient for crack width calculation
−
0.5
LT32
*
0.5
longtime loading
1.0
short-term loading
TITL
Load case designation
TYPE
Type/Action of load case
−
-
GAMU
Unfavourable safty factor
−
*
GAMF
Favourable safty factor
−
*
PSI0
Rare combination value rare
−
*
PSI1
Frequent combination value frequent
−
*
PSI2
Quasi-permanent combination value
−
*
PS1S
Non-frequent combination value
−
*
CRI1
−
0
CRI2
Criteria 1,2,3: Without input a nonlinear analysis stores: CRI1=iterations (0 = no convergencs found) CRI2=max. residual force, CRI3=energy Criteria 2
−
0
CRI3
Criteria 3
−
0
LC activates a load case. All loads which are input after the LC record are assigned to this load case. The factor FACT affects all loads, however, not the temperature, strain and prestressing loads! It does not affect DLX, DLY or DLZ dead loads. The loads are saved in the database without factor.
SOFiSTiK 2014
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ASE | Input Description
LC ALL calculates all load cases stored in the database from LC 1 to 9999. LC TEST activates the instability test. Comes aufomatically only for instable systems. For a negative dead load direction which is defined in the program SOFIMSHA/SOFIMSHC with SYST GDIR (e.g. SYST...GDIR=NEGZ) a positive value has to be input in LC DLx for a load in dead load direction (negative global direction). An error message follows for the input of a negative value (e.g. LC DLZ -1.00), because a double negation is misleading. A warning follows for a negative inputs unequal to -1.00 (e.g. for earthquake). Positive as well as negative values for DLZ are possible for SYST GDIR=POSZ in program SOFIMSHA/SOFIMSHC. During dynamic analysis ASE determines the dead weight of all elements according to its definition in the material records respective the cross section parameters. Additional masses can be defined with the record MASS. Therefore for eigenvalue determinations the dead load has not to be input in the record LC. For the dynamic time step method the mass inputs from ASE or DYNA are transformed to dead loads now with an input LC...DLZ, because these are used as masses and therefore they have to produce dead load. Vertical slab eigenvalues can be avoided with MASS FACT. If dead loads should be used from the program SOFiLOAD, then only the load case number NO has to be input for LC. If factors of the structural dead weight or other loading are defined after a LC record, all loading data for that load case will be deleted, to allow the redefinition of loading for a given load case. If no designation was input, the program generates automatically a title from the dead load factors as well as from the support sum. The action type and the corresponding safety factors and combination coefficients may be defined already here for a later superposition with program MAXIMA. Several literals which are described in detail in the record ACT of the program SOFILOAD are possible for TYPE. If safety factors and combination coefficients which are different from the default should be used, these can be input here. If the superposition factors are defined with the program SOFiLOAD or MAXIMA, nothing is to be input here for TYPE to PS1S. Values CRI1 to CRI3 are very general parameters of the load case. They may be used freely for postprocessing. You may specify them in advance or set them after the analysis by reading some results from the database. (e.g. a system dimension, a strength reduction etc.) TALPA uses CRI1 for the safety factor of the material needed by analysis according to Fellenius. The criteria are set
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Input Description | ASE
subsequently without further inputs with: LC TYPE PROP CRI1 ... CRI2 ... CRI3 ...
SOFiSTiK 2014
3-77
ASE | Input Description
3.26
TEMP – Temperature from HYDRA
See also: LC, GRP, GRP2
Item
Description
NO T1
Load case number of the temperature calculation Time of the interval beginning
T2
Time of the interval end
NOG
Element group which is to be loaded
TEMP Unit
Default
−
!
sec
0
sec
T1
−
*
−
1.0
LT
YES
LT
NO
−
1/2
Default: all groups FACT
Factor of the loading
EMOD
Stiffness modification of the elastic modulus for BRIC elements with HYDRA temperature fields, see also GRP2 ALP0 YES Consideration of the stiffness modification OFF No consideration of the stiffness modification value Development of elastic modulus according to Wesche Consideration of the relaxation via a reduced E modulus according to ’Technischen Empfehlungen Bautechnick BAW / Wesche’ YES Consideration
RELA
NO EXPO
No consideration
Exponent for the elastic modulus according to "Braunschweiger Stoffmodell"
After a transient temperature calculation with the program HYDRA the element group NOG with the temperature differences of the time T2-T1 from the HYDRA load case NO can be loaded with this record. With that changing material properties or support conditions can be examined in the course of the temperature development (e.g. variable elastic modulus during setting of the green concrete). The time values T1 and T2 are arbitrary. For missing exact time values from the program HYDRA the temperature is interpolated linearly between two available time values or an end temperature is used. For T1=T2 the temperature is used to this time.
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SOFiSTiK 2014
Input Description | ASE
If a stationary calculation occurred, the temperature is used fully in spite of an input for T1 and T2. The temperature loading is applied currently only to BRIC and QUAD elements. The input via GRP...FACT omits and is not anymore possible. For the hydration of volume elements the elastic modulus can be still modified according to the "Braunschweiger Stoffmodell" with an exponent:
E = E28 ·
α − α0
EXPO
1 − α0
(3.1)
The input is done with TEMP ... EMOD YES EXPO ... For BRIC elements the HYDRA temperature fields are implemented by varying material stiffness according to Wesche: With input TEMP ... EMOD=value the development of elastic modulus is activated according to Wesche. The value has to be be input as a·w/z , e.g. for Z25 value=7.1·0.4 = 2.84. The development of E-modulus can now be switched off per group with TEMP...EMOD OFF. Example see: bric_hydra_dt2h.dat BAW / Wesche: ripe_creep_comparision.dat
SOFiSTiK 2014
3-79
ASE | Input Description
3.27
LAG – Loads from Support Reactions
See also: LC, LCC
Item
Description
LCNO FACT
Number of the load case with the reaction forces Load factor
TYPE
Selection of transferred support reactions
Unit
Default
−
!
−
1.0
LT
PZ
m
-
m
0.1
LT
-
PZ
Z TOL PROJ
Only PZ support reactions are transferred. PP Only PP support reactions are transferred. FULL Forces and moments are transferred. Z coordinate
LAG
Tolerance for consideration of support forces Name of the project from which the support reactions should be used
Please use function SOFILOAD-COPY PSUP or SUPP AUFL to convert support forces to loads. ASE-LAG applies support nodes only on quad elements! With LAG the support reactions of a higher storey can be applied to the current lower storey. Thus the loads can be summarized from the roof up to the basement. The support reactions of the lowest storey can be used then for the dimensioning of the foundation. Wall loads have to be considered in each storey here. All support reactions which are farer outside the structure than TOL are ignored via an input for TOL (default 0.1 m). Without a definition of a project name all support loads of the load case LCNO in the current database are considered as nodal loads in the current load case which is specified with LC (the support loads are the support reactions multiplied by -1). If a project name is input, the support loads are applied as free loads with the coordinates of the support nodes of this external project database. The Z coordinate can be modified in this case e.g. in order to apply the support loads
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SOFiSTiK 2014
Input Description | ASE
of a plate which was analysed as SYST GIRD to a higher storey of a threedimensional structure.
SOFiSTiK 2014
3-81
ASE | Input Description
3.28
PEXT – Prestress of External Cables
PEXT Item
Description
Unit
Default
NOG
Group number or
−
-
NOEL
Number of a cable of the cable-chain
−
-
P0
Prestressing force at stressing anchorage
kN
-
SIDE
Prestressing side
−
-
BETA
deg/ m
-
MUE
POSX, POSY, POSZ, NEGX, NEGY, NEGZ Unintensional wobble angle (imperfect inclination) Friction coefficient
−
-
SS
Slip at stressing anchorage
mm
-
Cable groups or single cables can be selected with the record PEXT for prestressing. The cable side which is prestressed is defined with SIDE. For example POSX defines the cable side with the larger X coordinate. For external tendons see also CTRL QTYP V2.
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Input Description | ASE
Figure 3.3: Example: cable over two internal blocks
SOFiSTiK 2014
3-83
ASE | Input Description
3.29
LCC – Copy of Loads
See also: LC, LAG
Item
Description
NO
LCC Unit
Default
Number of an already defined load case
−
!
FACT
Load factor
−
1.0
ULTI
A Sofiload time function is applied see example step_sofiload_ase.dat Load factor increase at the ultimate load iteration YES
−
YES
−
NEW
OFF ALL see record ULTI
PLC
Prestress-, temperature loads and settlements will only be increased on ’ALL’ see record LC FACT Temperature and strain loads for primary load cases YES no use of temperature and strain loads automatically LC had been active in PLC NEW use of all loads (Load acts for the first time)
LCC can be used to copy loads from other load cases into the current load case. Inputs for prestress loads from the program TENDON are accepted as well. However, here the user must pay attention to the settings in the GRP -CS record. Dead weight loads DLX, DLY, DLZ are not transferred. If a load cases was already considered in the primary load case, only real loads have to be defined again when using the primary load case. Temperature or strain loads must not be defined again, because they act additive. These loads are extracted now automatically with PLC = YES. If for instance the load factor LC ... FACT is increased during a limit load iteration, the difference temperature is used additionally. Default is PLC NEW, all loads are used. In a dynamic time step analysis a SOFILOAD FUNC time funktion will be used.
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Input Description | ASE
The factor FACT will be multiplied with the time function using the time at the end of the actual time interval (time of PLC + dt/2). Base point accelerations from SOFILOAD (Effective force method und Large Mass Method) can also be used in LCC. Examples to LCC
Input file
Using PLC technique
ase6_two_span_girder_construction_stages.dat
LCC ULTI OFF load increase
push_over_quad_beam_frame.dat
Loadfunction SOFILOAD
a1_dynamic_overview.dat
Earthquake
a2_introduction_earthquake.dat
Large mass method
a3_introduction_base_acceleration.dat
Cinematic mashine loads
excavator.dat
-> Example overviews
-> Summary of example overviews
SOFiSTiK 2014
3-85
ASE | Input Description
3.30
EIGE – Eigenvalues and -vectors
See also: SYST, GRP, LC
Item
Description
NEIG ETYP
EIGE Unit
Default
Number of the sought eigenvalues
−
!
Method for eigenvalue calculation
LT
LANC
Buckling eigenvalue solver for large systems: BUSI Simultaneous vector iteration BULL
Method of Lanczos
BURA Method of Rayleigh BUCK uses the fastest solver for the current system. First positive with LMIN AUTO Dynamic eigenvalue solver: SIMU
Simultaneous vector iteration
LANC
Method of Lanczos
RAYL
Method of Rayleigh
REST
Eigenvalues already available
NITE
Number of iteration or Lanczos vectors
−
*
MITE
Maximum number of iterations
−
*
LMIN
Eigenvalue shift
− or 1/ sec
SAVE LC
LMIN AUTO to search the first positive buckling eigenvalue Number of the generated load cases Load case number of the smallest eigen mode shape
0 2
−
< 10
−
2001
The input of EIGE causes the use and possibly the determination of eigenvalues and eigenmode shapes. If eigenvectors have already been calculated, ETYP = REST as well as the load case number LC have to be input. This is planned for the subsequent calculation of modal damping values or loads. The masses from dead load γ are used always. All further masses (record
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Input Description | ASE
MASS) from the generation program and ASE are considered additionally. Vertical slab eigenvalues can be avoided with MASS FACT. If loads are defined additionally to EIGE, the modal loads are determined and saved in the database. A further analysis does not occur. The mode shapes are saved completely in the database in a compact form. This is sufficient for a regular dynamic analysis. They can be saved as regular load cases too. The latter form is to be selected, if a graphic representation of the eigenvectors with the program WinGRAF or evaluations of element stresses in the program DYNA should occur. Eigenvalue determinations are not possible with the basic program version. Explanations: Using the input LMIN (Unit 1/sec2 for dynamic eigenvalues, factor for buckling eigenvalues, taken from the result table Eigenfrequencies) the results can be shifted. The number of excluded Eigenvalues are shown in the printout. Example see ase4_eigenfrequency_shift.dat In a buckling eigenvalue analysis often only negative eigenvalues appear. They represent failure under a negative load factor. In this case with LMIN AUTO automatically an eigenvalueshift can be determined and applied to avoid the negative eigenvalues and find the first positive one. Example see buckling_eigenvalue_shift.dat The choice of method for the eigenvalue analysis depends on the number of the sought eigenvalues. The simultaneous vector iteration can be used in the case of few eigenvalues. The number of iterations may be reduced, if a somewhat expanded subspace for the eigenvalue iteration is used. Therefore the default value for NITE is here the minimum between NEIG+2 and the number of the unknowns. The iteration is interrupted, if the number of the maximum iterations (default max (15,2·NITE)) is reached or if the maximum eigenvalue has changed only by the factor less than 0.00001 opposite to the previous iteration. The method according to Lanczos is significantly quicker than the vector iteration, if a large number of eigenvalues is sought. A good accuracy is achieved, if the number of the vectors NITE is at least the double one of the sought eigenvalues (default). Unlike the vector iteration the larger eigenvalues are usually worthless for NITE=NEIG. The modal damping is calculated from the defined dampings of the groups after the determination of the eigenvalues.
SOFiSTiK 2014
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ASE | Input Description
The vibration mode shapes are stored as load cases with ascending load case numbers beginning with LC. Since the eigenvectors in certain cases may have large amplitudes, the output of element stresses or support reactions is not usually desirable. It should be turned off with the record ECHO. See also chapter theoretical orinciples eigenvalues (incl. examples).
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Input Description | ASE
3.31
MASS – Lumped Masses
MASS Item
Description
Unit
Default
NO
Node number
−
!
MX
Translational mass
t
0.
MY
Translational mass
t
MX
MZ
Translational mass
t
MX
MXX
Rotational mass
tm2
0.
MYY
Rotational mass
tm2
0.
MZZ
Rotational mass
tm2
0.
LC
Load case for mass conversion
-
-
PRZ
Factor in percent
%
*
LT
PG
PRZ=100: full conversion default: PSI2 value of the load case SELE
Selection of load direction PG or PXX or PYY or PZZ
Examples to MASS
Input file
LC mass conversion
ase4_eigenfrequencies.dat
Earthquake
a1_dynamic_overview.dat
-> Example overviews
-> Summary of example overviews
The masses are additional to those defined in the program SOFIMSH*. They are maintained over several input sets until they are redefined. Please notice that only SOFIMSH* masses also produce dead load in a static analysis! ASE additional masses don’t act as dead load e.g. dlz in a static load cases [ except in a time step analysis where they act as dead load and dynamic mass} ! MASS 0 can be used to delete all additional masses from ASE+DYNA. With MASS LC 0 additional masses defined in a previous run are applied. A mass acts usually the same in all three coordinate directions and thus, it need to be defined independently only for special cases. Rotational masses with inclined axis are not used in ASE.
SOFiSTiK 2014
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ASE | Input Description
The dead weight of the entire structure is always applied in the form of translational masses. If necessary, rotational masses must be defined separately with MASS. If the dead weight of a structure is not to be applied, the dead weight of the material or the cross section should be input as zero. MASS can be used also to import nodal loads from the database as masses to ASE. The load case number must be input in LC. The conversion factor has to be defined in PRZ. PRZ = 100 means full mass conversion. Other loads then loads in dead weight direction must be selected with SELE. Please check the sum of masses in the output! The input MASS LC 12 PRZ 100
creates translational masses from all loads of load case 12 in the direction of the dead weight. By default the masses are applied as X, Y and Z mass. If this is not desired, they can be factorized additionally with MX,MY and MZ, e.g. MASS LC 12 PRZ 100 MX 1.0 MY 0.2 MZ 1.0. With a negative node number MASS -NO the old input for a loadcase mass conversion can be used, but only up to 9999 → see DYNA manual. Masses can get also a factor with MASS. For this purpose the literal FACT has to be input for NO. This can be reasonable particularly for larger systems, where it is favourable to suppress many low frequencies which are not essential for the analysis. With the input MASS FACT MZ 0.01
The mass in global Z direction is reduced to one percent only. So vertical slab eigenvalues of big buildings can be avoided. MASS FACT works additive to MASS inputs and has an effect on the automatic element dead load mass. With MASS FACT 1 1 1 0 0 0 rotational masses can be suppressed. See also chapter theoretical orinciples masses (incl. examples).
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Input Description | ASE
3.32
V0 – Initial Velocity
See also: MOVS
Item
Description
NO
Node number
VX VY
V0 Unit
Default
−
-
Initial velocities in global
m/ sec
0
directions
m/ sec
0
m/sec
0
VZ
An initial velocity V0 in m/sec is defined for the node NO. To be used in a dynamic time step analysis. Example see: ase_nstr_pld_pile_crash.dat Car collision: movs_car_collision.dat Train interaction: movs_train_interaction.dat Glass impact: pendulum_impact_test.dat
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ASE | Input Description
3.33
REIN – Specification for Determining Reinforcement
See also: DESI
REIN
Item
Description
Unit
Default
MOD
Design mode
LT
SECT
LT
SING
−
1
SECT
Reinforcement in cut
BEAM Reinforcement in beam SPAN
Reinforcement in span
GLOB Reinforcement in all effective beams TOTL Reinforcement in all beams RMOD
Reinforcement mode SING
Single calculation
SAVE
Save as minimum reinforcement
SUPE
Superposition with minimum reinforcement ACCU Superposition with existing LCR reinforcement ACSA Comb. ACCU and SAVE ACSU
Comb. ACCU and SUPP
NEW
LCR
New definition of the reinforcement distribution (for special cases only) Number of reinforcement distribution a negative value reinitializes all
ZGRP
Grouping of prestressing tendons
−
0
SFAC
Factor for continuous reinforcement
−
1.0
P6
Parameter for determining
−
*
P7
reinforcement
−
*
P8
(See notes)
−
*
P9
−
*
P10
−
*
P11
−
0.20
Table continued on next page.
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Input Description | ASE
Item
Description
P12 TITL
Title of the design case
Unit
Default
−
*
LT24
-
Any number of types of reinforcement distribution can be stored in the database. Under number LCR, the most recently calculated reinforcement for graphic depictions and for determinations of strain is stored. LCR=0 is reserved 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 link reinforcement: SING
creates new LCR reinforcements using the given stored minimum reinforcement
SAVE
ignores the stored minimum reinforcement and overwrites it with the current reinforcement.
SUPE
uses the stored minimum reinforcement and overwrites it with the possibly higher values of this run.
ACCU
Superposition with existing LCR reinforcement
ACSA
Combination from ACCU and SAVE
ACSU
Combination from ACCU and SUPP
There is also a control flag CTRL REIN, defining if the reinforcements should be increased or not. The latter to be used for the analysis of existing structures. Mit BEW BMOD ACCU LFB nnn kann man bis zu 255 Bewehrungsfälle als vorhandene Bewehrung für die aktuelle Berechnung aktivieren, gespeichert wird unter der letzten angegeben LFB-Nummer. With REIN RMOD ACCU LCR nnn it is possible to add up to 255 reinforcement results as active reinforcement of this run. It will be saved with the last defined LCR entry SUPE cannot be used during an iteration, since then the maximum reinforcement for an iteration step will not be able to be reduced. STAR2 therefore ignores a specification of SUPE, as long as convergence has not been reached. AQB can update or superpose the reinforcements at a later time: with REIN RMOD SUPE but without any DESI input.
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ASE | Input Description
A specification of BEAM, SPAN, GLOB or TOTL under MOD refers to interpolated sections or sections with the same section number. For all connected ranges with the same section, the maximum for the range multiplied with SFAC is incorporated as the minimum reinforcement. The design is done separately in each case for each load, however, so that the user can recognize the relevant load cases.
1
2
Section 1
3
Sect. 2
4
Section 1
SECT
BEAM
SPAN
GLOB
Figure 3.4: Distribution of reinforcements
As the existing reinforcement has a considerable impact on the shear design, AQB will perform an intermediate superposition after the design for normal force and bending moments. However, use of minimum reinforcement in ultimate load design has also a detrimental effect 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 latter effect is especially strong with tendons, AQBS can give special effect to the latter in ultimate load design. This option is controlled with ZGRP: ZGRP = 0
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Tendons are considered with both their area and their prestressing. Normal reinforcement is specified at the minimum
SOFiSTiK 2014
Input Description | ASE
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 reinforcement if 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 non-prestressed 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 not to be changed by the user in general: Default
Typical
P7 Weighting factor, axial force
5
0.5 - 50
P8 Weighting factor moments
-2
-2
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. MN((N − N)2 + F1 · (MY − MY)2 + F2 · (MZ − MZ)2 )
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ASE | Input Description
F1 = P7 · (zm − zmn)P8 F2 = P7 · (ym − ymn)P8
The default value for P8 leads to the same dimensions for the errors. The value of P7 has been determined 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 reinforcement the value of P7 should be increased. Default
Typical
P9 Factor for reference point of strain
1.0
1.0
P10 Factor for reference point of moments
1.0
0.2-1.0
Lack of convergence in the design with biaxial loading can generally be attributed to the factors no longer shaping the problem convexly, 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 improper. P11 Factor for preference 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 control this. For biaxial bending P11=1.0, for uniaxial bending P11=0.0
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Input Description | ASE
3.34
DESI – Reinforced Concrete Design, Bending, Axial Force
See also: REIN, NSTR
DESI
Item
Description
Unit
Default
STAT
Load condition and code
LT
*
NO
Save reinforcement only
SERV
Serviceability loads
ULTI
Ultimate loads
NONL Non-linear analysis combin. ACCI
Accidental combination
KSV
Control for material of cross section
−
*
KSB
Control for material of reinforcements
−
*
AM1
Minimum reinforcement for beams
%
*
AM2
Minimum reinforcement for columns
%
*
AM3
Minimum reinforcement
%
*
%
*
%/ LT
*
SC1
the current reinforcements will be fixed as maximum Safety coefficient concrete bending
−
*
SC2
Safety coefficient concrete compression
−
*
SCS
Safety coefficient concrete shear
−
*
SS1
Safety coefficient reinforcing steel
−
*
SS2
Safety coefficient structural steel
−
*
C1
Maximum compression
o/ oo
*
C2
Maximum centric compression
o/ oo
*
S1
Optimum tensile strain, see below
o/ oo
*
o/ oo
*
statically required cross section AM4
Minimum reinforcement depending on normal force
AMAX
Maximum reinforcement FIX
(= limit for symmetric reinforcements) S2
Maximum tensile strain
Table continued on next page.
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3-97
ASE | Input Description
Item
Description
Unit
Default
Z1
Maximum effective compressive strain
o/ oo
*
o/ oo
*
LT
*
of prestressing steel Z2
Maximum effective tensional strain of prestressing steel
SMOD
Design mode shear NO
No shear design
TVS
Deductional shear stress / stress limit
N/ mm2
*
MSCD
Maximum tensile longitudinal stress
N/ mm2
*
KTAU
Shear design for plates
−/ LT
*
K1
K2S
not staggered for normal slabs (DIN 1045 17.5.5. equ. 14) not staggered for slabs with evenly distributed loading (DIN 1045 17.5.5. equ. 15) like K1, but staggered (DIN 1045 17.5.5. Table 13 1a) like K2, but staggered
num
coefficient k for equ. 4.18 EC2
0.0
no shear check
K2
K1S
TTOL
Tolerance for the limit values
−
0.02
TANA
Lower and upper limit for inclination of struts of shear design (tan Θ = 1/cot Θ)
−
*
−
*
−
3
TANB SCL
Plasticity control for steel and composite sections 1 No limits on steel stress 2 3 4
3-98
Outmost compressive yield stress is limited Compressive stress is limited to the yield value Yield stress will be applied as limit in the tensile and compressive region
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Input Description | ASE
Design may be performed for various safety concepts. 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. With KSV and KSB will be controlled the material law. As the correct default is taken from the INI-file selected with the design code NORM, it is only for very special cases that you may enter: EL
linear elastic, but without tension if concrete
ELD
linear elastic with added material safety factor from AQUA
SL
serviceability without safety factors
SLD
serviceability with added material safety factor from AQUA
UL
ultimate design without safety factors from AQUA
ULD
ultimate design with safety factors from AQUA
CAL
Calculatoric mean values
CALD
Calculatoric mean values with safety factors from AQUA
PL
plastic nominal without safety factors
PLD
plastic design with material safety factors from AQUA
The safety factors referenced above refer to the values defined with the material in AQUA. Without ”D” only the factors defined in the INI file or the explicitly defined values SC1 to SS2 of the DESI record are applied. However the additional safety factor γ’ for high strength concrete of DIN will be applied additionally. The printout will flag ”global safety factors” With Option ”D” we have to distinguish between two different cases: •
If the values defined in DESI are < 1.0 or negative or SC1 is not equal SC2 (e.g. ACI or odl DIN) or the design code has special provisions for that (SNIP), the safety factors are multiplicative. Printed stresses contain only the safety factors of the materials.
•
In all other cases the value from the material will be taken instead of the default value of DESI. However if the safety factor is explicitly defined with DESI with a value > 1 the option D will be deactivated with a warning. (Attention: has been changed Sept. 2008)
If a design without any safety factors is required, all saftey factors have to be specified as 1.0 which will then change the default for KSV/B to UL.
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ASE | Input Description
PL resp. PLD will modify for some design codes (DIN, EC, ACI) the stress strain law to a constant equivalent stress block, i.e. the stress value and the strain range will be modified according to the provisions of those codes. With the special definition of SS1 NRIL the safety factors of the reinforcements will be set to 1.05 and 1.10 according to the provisions of the German ”Nachrechnungsrichtlinie”, also the ordinates of those reinforcements will be reduced then by an offset of 20 resp. 10 mm. The minimum reinforcements AM1 to AM4 are preset according to the design code (INI file) and 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 statically required section
-
Minimum reinforcement defined in cross section program AQUA
-
Minimum reinforcement stored in the database
Note: The statically determined portion of the forces and moments of prestressing is always deducted when determining the external forces and moments. This contribution is found from the location of the tendons and their tensile force. AQB only: A specification of the bifurcation factor BETA in record BEAM is changed to additional moments according to DIN 1045 17.4.3 resp. Eurocode 4.3.5.6. resp. DIN 1045 neu 5.6.4. resp. OeNORM B 4700 2.4.3. or other design codes. The design will always generate both bending axis. The output of the extra moments is given with the forces of the combinations. Defaults for strain limits and safety coefficients depend on the selected design code and the type of load combination. They may be specified in the INI-file of the design code. If SC1 and SC2 are defined different (e.g. old DIN 1045, ACI), then the safety factors of the reinforcements will be also interpolated if SS1 is equal to SC1. The maximum strain depends on the stress-strain curve. The value of 2.2 is reduced for example at the old DIN or high strength concrete automatically. The EN and the DIN suggest to limit the strain also for the midpoint of compressive flanges. This option may be selected by defining a value of C2 as positive (select teh control) or negative (disable the control).
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Input Description | ASE
The values Z1 and Z2 do not limit the range of possible strains, but the maximum corresponding values are used as strain increments for the tension members in the section. This is necessary, for instance, when designing with partial prestressing under DIN 4227 Part 2. According to DIN 1045-1 8.2 (3) some bending structures should have a height of the compressive zone not larger than 0.45 d, or 0.35 d for high strength concrete. If this is not fulfilled a minimum shear link according to 13.1.1. (5) has to be provided. As the maximum compressive strain is fixed (3.5 per mille), this is equivalent to the request that the steel strain has at least a value of 4.278 or a higher value for C55 on. Thus the control of this paragraph is easily performed via the steel strain. An equivalent formulation is given in OENORM 4700, where it is requested that the steel should reach the yield strength. As the old DIN 1045 had the more general formulation for the same ductile request, that the compressive reinforcement is not allowed to be considered with a larger value than the tensile reinforcement Thus AQB provides symmetric reinforcements for all design codes when the steel strain does not exceed the value of S1, fulfilling the request for ductility in that way. This design operation is also suitable for non-reinforced sections. In that case the program produces internal forces and moments which are in the same proportion to each other as the external forces and moments. The safety factors SC1 and SC2 have to be defined dependent on the design code. The program then shows the relative load carrying capacity and prints a warning if this should fall below 1.0. The shear design finds the lever of internal forces for all load cases with compression and tension forces in the section, and finds the shear stress and shear reinforcement resulting from shearing force and torsion. The shear stress limits are set automatically depending on SMOD and the material. Deviating values for the shear stress limits can be defined within AQB with a record STRE (under 4227 only) or TVS. Since in case of excess of the shear stress limits no design more occurs, this can be exceeded onto own responsibility of the user with a tolerance. For the reduction of the shear capacity for tensile members the normal stress σpc is limited to the value MSCD. The default is selected with the mean tensile strength fctm . Consideration of the shift of the envelope line of the tensile force (shift rule) depends upon the CTRL option VM. The ratio Ved/Vrd,max and the value of the
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ASE | Input Description
shift will be saved to the database. If a section is to be considered as a plate has already been defined with the section itself. The definition of KTAU is thus only effective for those sections. For sections with tendons, the bond stress for every tendon will be evaluated according to DIN 4227 chapter 13 as the increment in tendon force divided by the periphery and the length given by BETA in record BEAM. (Use negative factors for bending members)
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Input Description | ASE
3.35
NSTR – Non-linear Stress and Strain
See also: REIN, DESI
NSTR
Item
Description
Unit
Default
KMOD
Nonlinearity for beam elements
LT
S0
LT
SL
LT
KSV
(and truss and cable elements) possible input - see manual AQB - or S0 = beam+truss+cables material linaer
KSV
S1,K1,KN... = beam+truss+cables nonlinear Selection of stress strain curve for quad, beam, truss, cable and springs
KSB
Stress strain curve for beam reinforcement (quad elements always use KSV inclusive tension stiffening)
...
further input for beam elements - see AQB manual
With NSTR the kind of investigated material limit state is specified, in particular, serviceability and ultimate limit state are distinguished, here. Depending on the choice, the appropriate material working law (cf. AQUA manual, input records SSLA and SFLA) is processed for evaluation of the material response. Possible specifications for KSV are: EL
linear elastic, but without tension if concrete
ELD
linear elastic with material safety factor
SL
service nominal without material safety factor
SLD
service design with material safety factor
UL
ultimate nominal without material safety factor
ULD
ultimate design with material safety factor
CAL
Calculatoric mean values
CALD
Calculatoric mean values with safety factors from AQUA
PL
plastic nominal without material safety factor
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ASE | Input Description
PLD
plastic design with material safety factor
Main usage without KMOD input (e.g. NSTR KSV SL) for: •
nonlinear quad elements (require additional SYST...NMAT YES)
•
nonlinear springs
•
beam elements with fullplastic interaction (KSV PL/PLD)
•
implicit beam hinges with spring work law (AQUA - SFLA)
Usage with KMOD input (e.g. NSTR KMOD K1 KSV ULD) for: •
nonlinear beam elements with internal AQB call
Detailed describtion of possibilities including example references see following chapter: ”Nonlinear Material Analysis in ASE”.
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Input Description | ASE
3.36
Non-linear Material Analysis in ASE
Examples see -> Summary of example overviews Non-linear material analyses can be activated or deactivated with different parameters: SYST PROB NONL activates a material non-linear analysis. Using SYST PROB TH2, TH3B, TH3 additional geometric non-linear effects are activated. SYST ... NMAT YES activates material non-linear effects for shell and volume elements: for shells: concrete rule (AQUA-CONC) steel yielding (AQUA-STEE) membranes (AQUA-NMAT-MEMB) for volume elements: soil mechanical yielding criteria (AQUA-NMAT-MOHR...) GRP ... LINE switches off non-linear effects of a group. NSTR Without input of a record NSTR: same as NSTR S0. NSTR S0 Beam, cable and truss elements are analyzed with a linear material behaviour. Spring elements are analyzed with a non-linear spring work law if defined. The non- linear spring effects GAP, CRAC, YIEL and MUE are taken into account in a nonlinear analysis. NSTR S1 or SN Beam elements are analyzed non-linear via an internal AQB calculation, Cables, truss and spring elements take into account all non linear effects. Material safety factors see following table *1). See example file aseaqb_1_column_cracked.dat NSTR S1 KSV PL (or PLD): For beam elements the internal forces and moments are limited in a simple way to the full plastic values of the program AQUA (without internal AQB calculation). See example file ase_nstr_pld.dat On the safe side a code independant interaktion with an exponent 1.70 is used (2.0 is too unsafe): ƒ = (M/ MPL)1.70 + (N/ NPL)1.70 + (V/ VPL)1.70 ...
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ASE | Input Description
Cable, truss and spring elements as described in NSTR S1”. The following table lists all possible material non-linear effects which are available in ASE. It shows also the essential inputs and possibilities for the activation or deactivation of different effects. In an input only with SYST PROB NONL without further definitions the behaviour ”=standard” is active! Elementtype NL effect
material input
activated in ASE:
deactivated:
Beam elements
AQUA-CONC
- NSTR S1/SN *1)
= standard
AQUA-STEE
(full-plastic:
- NSTR S0
AQUA-SSLA
NSTR S1 KSV PLD)
- GRP LINE
Cables + truss material stress-
= standard CONC/STEE/SSLA
- NSTR S1/SN
strain curves
- NSTR S0 - GRP LINE
Cables compress.failure
= standard *2)
- GRP LINE
= standard
- GRP LINE
= standard
- GRP LINE
Springelements gap,crac,yiel,mue
SPRI
Spring elements *3)
AQUA-SARB and
spring stress-
SPRI-MNO
strain curves implicit beam hing
AQUA-SARB
Spring elements *4)
AQUA-SSLA and
material stress
SPRI+AR
= standard
- GRP LINE
AQUA-BMAT-CRAC
= standard *5)
- GRP LINE
= standard *6)
or CRAC=9999 - GRP LINE
-strain curves QUAD bedding tension cut off
friction
AQUA-BMAT-MUE
QUAD elements
AQUA-CONC
of concrete/steel
AQUA-STEE
- SYST...NMAT YES
= standard *9)
*7)
AQUA-SSLA *8)
*9)
- GRP LINE
Membrane elements
AQUA-MAT-
- SYST...NMAT YES
= standard
NMAT MEMB *10)
- GRP LINE
Volume elements
AQUA-MAT...
- SYST...NMAT YES
= standard
BRIC
NMAT MOHR...
*11)
- GRP LINE
Halfspace contact
HASE-PLAS PMAX
= standard *12)
only SYST LINE
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Input Description | ASE
*1) Important is the input of the material safety factor with NSTR...KSV: Using NSTR always the stress-strain curves of the program AQUA are taken into account. In this case the material safety factors are not used for KSV SL, UL, CAL. On the other hand the AQUA material safety factors are multiplied for KSV SLD, ULD, CALD. In the first part of the ASE output the maximum stresses for the materials are printed. Due to different defaults in the programs AQB / STAR2 / ASE the items KSV and KSB should be input. The usage of material safety factors for the stiffness determination (NSTR) is interpreted differently by the specialists. For a ultimate limit check without further design the input ULD or CALD is reasonable (without modifications of the material stress-strain curve in the program AQUA). SL has to be used for calculations in the serviceability state. Default for the material safety factors of non-linear analyses: -
With an input of a record NSTR: default for KSV=ULD = stress-strain curve for the ultimate limit state with the material safety factor (SCM) of the program AQUA With that also the stiffness of linear elements is changed!
-
Without an input of a record NSTR all elements are analyzed with the linear E modulus. So a simple non-linear analysis will give the same displacements as a linear analysis (provided that non-linear effects do not occur).
At the end of a non-linear ASE calculation a statistics is printed with the available non-linear effects. *2) Cables which are loaded in the transverse direction (e.g. by dead load) never fail due to compression in a geometrical non-linear analysis TH3 with the default, because the inner cable sag produces always a tensile force (see CTRL CABL). For the input SYST PROB NONL or with CTRL CABL 0, cables cannot get an inner cable sag and fail due to pressure load! *3) Springs can be defined with a non-linear spring stress-strain curve in the program AQUA. Please refer to example a1_spring_overview.dat *4) For soil analysis (e.g. tunnel calculations) springs can be defined also via an effective area AR and a material number. Then ASE calculates a non-linear spring characteristic curve by using the material stress-strain curve SSLA of the program AQUA. *5) Without further input in program AQUA a QUAD bedding is preset with CRAC=0, i.e. QUAD elements can have a tension cut off. See example
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ASE | Input Description
ase_bed_uplift.dat *6) Without further input in program AQUA no friction coefficient MUE is preset, i.e. horizontal forces can be transferred without limitation, if the element is not cracked (no tension cut off). *7) QUAD elements with simple MAT input are analyzed linearly. Only QUAD elements of CONCRETE or STEEL can be analyzed non-linearly with the input SYST...NMAT YES . *8) Also for shell elements, ASE uses the concrete stress-strain curve of AQUA. The concrete tensile strength can be changed temporarily with CTRL CONC V3 V4. *9) Often only non-linear springs or bedding should be taken into account in a non-linear analysis. Therefore the material non-linear QUAD elements are deactivated in the default (default SYST ... NMAT=NO). If required, they have to be activated explicitly with SYST ... NMAT YES. *10) A membrane failure due to pressure must be activated via AQUA... NMAT MEMB and ASE...SYST NMAT YES. *11) For volume elements (BRIC) various soil-mechanical material rules can be defined in AQUA...NMAT MOHR.... Example see ase14_tunnel_3d.dat. BRIC elements with CONCRETE see bric_concrete.dat or STEEL see bric_steel_van_mise.dat *12) Details see program HASE.
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Input Description | ASE
3.37
ECHO – Output Control
See also: CTRL, SYST, GRP
ECHO
Item
Description
Unit
Default
OPT
A literal from the following list:
LT
*
NODE Nodal values GRP
Group parameters
MAT
Material parameters
ELEM
Element values
LOAD
Loads
DISP
Displacements
FORC Internal forces and moments SPRI
Spring and cable results (additiv)
NOST Internal forces and moments at the nodes BEDD Foundation stresses REAC
Support reactions
LINE
Distributed support reactions
PLAB
Statistics T-beam components
EIGE
Eigenvalues
RESI
ERIN
Residual forces during iteration. RESI=7 writes 90000...Iterationssteps Error estimates
STAT
Statistics + group + plots
NNR
Nodal displacement during iterations Element stresses during iteration
ENR
LSUM Sum of the loads + Statisticsk STRG Tendon group stresses BDEF
Local beam deformations
STOR
Database memory location Table continued on next page.
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ASE | Input Description
Item
Description
FULL
VAL
3-110
Unit
Default
−/ LT
*
All the above options
STRE, NSTR, DESI, REIN, SHEA, LC, BSEC, CRAC, B2T, USEP: See manual for the program AQB Output extent OFF
No calculation / output
NO
No output
YES
Regular output
FULL
Extensive output
EXTR
Extreme output
0-7
See output description for BRIC
SOFiSTiK 2014
Input Description | ASE
Default: ECHO LOAD ECHO DISP,FORC,REAC,NOST,BEDD,BDEF
YES NO
as well as NO for NODE and MAT and YES for all other for small beam systems < 1000 nodes additionally: ECHO LOAD ECHO DISP,FORC,NOST,BEDD ECHO REAC
FULL NO YES
for very small beam systems < 100 nodes additionally: ECHO DISP,FORC
YES
The record name ECHO should be repeated in every record to avoid confusion with similar record names. See chapter 4 for the effect of ECHO. ECHO SPRI activates only the result print of springs and cables. This is often useful in nonlinear analysis to focus on these elements. ECHO FORC also activates this print. For the check of the iteration ECHO NNR xxx prints the node displacements of the node xxx after each iteration (10 nodes maximum). Only the displacement component of the current analysis step is output (without primary load case component). ECHO ENR is implemented so far only for cables. With ECHO BDEF EXTR a storage of the local beam deformations can be enforced for primary load case processing. An outprint in ASE is not implemented, please use WINGRAF for this. The strain energy of the groups is only printed and stored with both input ECHO STAT FULL and ECHO GRP FULL.
SOFiSTiK 2014
3-111
ASE | Input Description
3-112
SOFiSTiK 2014
Output Description | ASE
4
Output Description
The results of the FE analysis are:
4.1
Check List of the Generated Structure
The table of nodal values is mostly identical to the table of the program SOFIMSHA/SOFIMSHC and is output with ECHO NODE YES. For evaluation of unstable systems the equation numbers may be printed with ECHO NODE FULL as well. ECHO MAT YES causes the output of the material parameters.
4.2
Check List of the Non-linear Parameters
These are output with SYST NMAT=YES for non-linear analyses with QUAD shell elements only (concrete or steel material rule).
4.3
Check List of the Analysis Control Parameters
ELEMENT GROUPS No
Group number
fac-S
Stiffness of the group
fac-L, fac-D, fac-P
Primary load case factors
Fak-B
Factor for bedding of QUAD elements
fac-T PLC
Factor for temperature load case from HYDRA Primary load case
HW
Ground water level
T1
Concrete age in days (GRP ... T1)
ANALYTICAL PRIMARY STRESS STATE Nr
Group number
Gam-P
Specific weight
Gam-P’
Specific weight under buoyancy
SOFiSTiK 2014
4-1
ASE | Output Description
H-P, K-P, sig-P, sig-H
Primary state parameters
Type of analysis Calculation with non-linear (SYST PROB NONL) material properties Geometrically analysis
non-linear (SYST PROB TH3)
Primary state for displace- (SYST PLC) ments of the total system is load case ...
4.4
Check Lists of the Loads
The check lists of the loads are taken over from the program SOFiLOAD. Or in the case of the load input in ASE they are generated in analog mode to the SOFiLOAD output. SUM OF LOADS CASE LC
Load case
PXX, PYY, PZZ,
Load sums
MXX, MYY, MZZ SUM OF MASSES TM-X(t), TM-Y(t)
Translatory masses TM-Z(t)
RM-X(tm2), RM-Y(tm2)
Rotational masses RM-Z(tm2)
total
Total mass
active
Active part
The loads are stored in the database without load case factor. However, they are output with this factor.
4.5
Process of the Analysis
For non-linear calculations the in each case maximum residual force is output with the corresponding energy norm (sum from nodal forces ·nodal displace-
4-2
SOFiSTiK 2014
Output Description | ASE
ments of all nodes) in the list of the iterations. The residual force is printed firmly in the dimension kN, the energy norm in kN·m, however, multiplied by the factor 10−6 , 10−3 , 103 or 103 according to the size. For linear systems without primary load case the system energy is equal to the printed energy norm/2. The e/f values indicate the correction factors of the Crisfield method (see chapter 3, record SYST). Example of a converging iteration: Iteration 1 Residual Iteration 2 Residual Iteration 3 Residual
5.578 energy 21.3532 e/f .000 1.000 2.478 energy 36.3192 e/f .000 1.701 .000 energy 48.2837 e/f .329 1.799
The user has to check for a non-linear calculation whether the residual forces are sufficiently small. In the case of calculations with non-linear material properties there is no error message, if the residual forces can not be counterbalanced fully. During ultimate load calculations the convergence is checked automatically and a new calculation is generated with a new load step. Example: ULS-iteration 1 loadcase 1 with loadfactor 1.000 was converged.
The residual forces can be checked with ECHO RESI: RESIDUAL FORCES ITERATION 1 nodeno
Node number
P-X,P-Y,P-Z,
Unbalanced residual force
M-X,M-Y,M-Z A graphic control can occur in program WING with NODE SV, because unbalanced residual forces are saved as support reactions.
4.6
Eigenvalues
Provided that eigenvalues are calculated, they are output in a table with the corresponding frequencies and error limits. The errors of the eigenvalues constitute a measure of the accuracy of the frequencies and, if their values are larger than 10−3 , they may indicate as well the presence of possible multiple eigenvalues which could be overlooked.
SOFiSTiK 2014
4-3
ASE | Output Description
EIGENFREQUENCIES Using Lanczos method or Using simultaneous vector iteration Iteration vectors
Input with EIGE record
Iterations
Required iterations for SIMU
No.
Number of natural frequency
LC
stored as load case LC
Eigenvalue (1/Sec2) Relative error
Error limits
omega (1/sec)
Circular frequency
frequency (Hertz) Period (sec) activated mass * modal damping
4.7
Element Results
BEAM FORCES AND MOMENTS Beam x(m)
Section identification
N, Vy, Vz, Mt, My, Mz,
Internal forces and moments
Mb, Mt2 PILE FORCES, MOMENTS AND REACTIONS Pile No. x(m)
Section identification
N, Vy, Vz, Mt, My, Mz
Internal forces and moments
Pa, Pt
Foundation forces long., transv.
Pty,Ptz
Components y and z of the pile pressure Pt
SHELL FORCES AND MOMENTS El-No.
4-4
Element number
SOFiSTiK 2014
Output Description | ASE
m-xx, m-yy, m-xy
Plate moments (kN/m)
m-I, m-II, alfa
Principal moments and their angle
v-x, v-y
Plate shear forces (kN/m)
n-xx, n-yy, n-xy
Membrane axial forces (kN/m)
n-I, n-II, alfa
Principal axial forces and their angle
The internal forces and moments are output in the centre of gravity of the element for every QUAD element. The principal moments and the principal axial forces are output with the option ECHO FORC FULL only. The input of ECHO FORC EXTR causes the output of the internal forces and moments at the integration points of the elements as well. The angles between the direction of m-I or n-I and the local x axis are output. Positive moments produce tensile stresses at the bottom side of the plate. ELASTIC SUPPORT OF QUADRILATERALS Number
Element number of the QUAD element
p(kN/m2)
Foundation stress perpendicularly to the element Tangential foundation stress
pt(kN/m2) P(kN)
Resultant perpendicular foundation force (element’s foundation force in kN)
Foundation stresses are output only with ECHO FORC FULL. ECHO FORC EXTR results in the output of the foundation values at the corners too. The value P represents the corner force resulting from the foundation stresses of this element. STRESSES IN 3D ELEMENTS Element Number
Element number
IP
Integration point 0=gravity centre
sig-x, sig-y, sig-z
Stresses in global system XYZ
tau-xy, tau-xz, tau-yz
Shear stresses
sig-I, sig-II, sig-III
Principal stresses
dx,dy,dz
Principal stress directions
Output control for volume elements BRIC: SOFiSTiK 2014
4-5
ASE | Output Description
ECHO FORC = 0
- no output (NO)
1
- internal forces in the centre of gravity (YES)
2
- additionally principal stresses σ -I, σ -II, σ -III (FULL)
3
- additionally principal stress directions (EXTR)
4 or 5
- internal forces in centre of gravity and integration points
6
- additionally principal stresses σ -I, σ -II, σ -III
7
- additionally principal stress directions
The same ECHO input values are also applicable in the case of ECHO NOST. Plastification mark: If an element is plasticized, a P is printed behind the stress values. TRUSS ELEMENTS Load case EL-NO
Element number
P (kN)
Axial force
u (mm)
Elongation Δ-l
FORCES AND DISPLACEMENTS OF SPRINGS Load case Number
Element number
P (kN)
Axial force
P-t (kN)
Lateral force
M (kNm)
Moment
u (mm)
Spring displacement, elongation
u-t (mm)
Lateral displacement
phi (mrad)
Rotation
FORCES IN CABLE ELEMENTS
4-6
Number
Element number
N (kN)
Max. cable force above
SOFiSTiK 2014
Output Description | ASE
u (mm)
Elongation Δ-l
u-t (m)
Cable sag perpendicularly to chord 1)
f0 (mm)
Cable sag in load direction
N-m (kN)
Cable force at midpoint
L_NO (mm)
Element length after normal force relaxation
1)
is calculated only for geometrically non-linear analysis and CTRL CABL >0. The program calculates the loading and the sag f0 in the direction of the load. These can be output for all iterations with ECHO ENR CableNo.
4.8
Non-linear Results
NON-LINEAR MATERIAL STEEL Elem. (-)
Element number
z (-)
ˆ = top side (neg-z) v bottom side
sigx,sigy,tau (MPa)
Stresses at side z
sig-I,sig-II (MPa)
Principal stresses at side z
sigv (MPa)
Equivalent stress at side z
sigvlin (MPa) depth (mm)
Equivalent stress calculated with eps*Elinear Depth of plastification
fy (-)
Plastification number sigvlin/sigzul-1 with sigzul = tensile strength (MPa)
NON-LINEAR MATERIAL CONCRETE Elem.
Element number
Rich
Observed direction w.r.t. x
eps-o (o/oo)
Upper strain (neg-z) in direction RICH
eps-u (o/oo)
Lower strain (pos-z)
x/d (-)
Depth of compressive zone
sigb-o (MPa)
Upper edge concrete stress
sigb-u (MPa)
Lower edge concrete stress
SOFiSTiK 2014
4-7
ASE | Output Description
sigs-o (MPa)
Upper steel stress, cracked condition
sigs-u (MPa)
Lower steel stress, cracked condition
wcalo (mm)
Upper crack width wk-cal
wcalu (mm)
According to Heft 400 DAfStb at the bottom side
ECHO FORC YES prints out both reinforcement directions, while ECHO FORC FULL prints also the values in principal stress directions at the top and the bottom side. Crack widths can be calculated only in the directions of the reinforcement. In the element centre of gravity the maximum of the non-linear effects of the four Gauss points of an element is stored in order to show the in each case most unfavourable value in the graphics. In the graphical representation (program WinGRAF) with ISOL YIEL (FLIU,FLIL) the plastification number is obtained as siglin/signl-1 (siglin = concrete stress computed linearly from the strain, signl = non-linear stress). The most unfavourable value from the tensile or the compressive zone is used. In the case of unreinforced concrete the crack width is set to 1 mm for the graphical representation of the crack pattern (a crack width can be computed only in context with reinforcement). Statistics of plastification: For non-linear calculations a statistics of the number and type of the plasticized Gauss points is printed in the result file. For area elements of concrete the compressive stresses which are larger than the linearity limit of 1/3·βr are output as a plastification, cracks as overflow of the tensile strength. For plates of massive steel an overflow of the linearity limit is calculated always as a plastification independently of tension/pressure.
4.9
Nodal Results and Support Reactions
ELIMINATED FORCES FROM CONSTRAINTS Node
Node number
P-X, P-Y, P-Z
Constraint forces
M-X, M-Y, M-Z, Mb The table of constraint forces is output only with ECHO REAC FULL.
4-8
SOFiSTiK 2014
Output Description | ASE
NODAL DISPLACEMENTS Node No
Node number
u-X, u-Y, u-Z
Displacement
phi-X, phi-Y, phi-Z
Rotation
Clockwise rotations are positive. NODAL REACTIONS AND RESIDUAL FORCES Node No
Node number
P-XX, P-YY, P-ZZ
Support reaction
M-XX, M-YY, M-ZZ
Restraint moment
Forces arise at all nodes with supports, kinematic constraints or elastic edges. The output is controlled with ECHO REAC: OFF Forces are not calculated. Thereby more main memory is available, what may be favourable for large systems. NO Forces are calculated and saved in the database. An output does not occur. YES Forces are output for all nodes, if they exceed a certain tolerance or if a support node is concerned. If forces appear at free nodes, then either a support has been defined by mistake or the available machine precision is not sufficient for the solution of the system. For non-linear analyses the residual forces are a direct measure of the quality of the iterative solution. FULL The constraint forces are output too. SUM OF REACTIONS AND LOADS Load case P-X, P-Y, P-Z, M-X, M-Y, M- 1st line= sum of the support reactions Z 2nd line= sum of the loads The output of the two lines serves as a check. The sum of the support reactions has to be equal to the sum of the loads.
SOFiSTiK 2014
4-9
ASE | Output Description
The sum of the support reactions and loads is an important index for the completeness of the loads and the accuracy of the entire analysis. In the case of linear analysis an error message is issued, if there is a noteworthy deviation of the two values.
4.10
Internal Forces and Moments at Nodes
SHELL FORCES IN NODES load case group
Element group
node
Node number
m-xx, m-yy, m-xy
Plate moments (kN/m)
m-I, m-II, alfa
Principal moments and their angle
v-x, v-y
Plate shear forces (kN/m)
n-xx, n-yy, n-xy
Membrane axial forces (kN/m)
n-I, n-II, alfa
Principal axial forces and their angle
STRESSES IN NODES OF 3D ELEMENTS Load case sum
Sum of the load
Group
Element group
Node
Node number
sig-x, sig-y, sig-z
Stresses in global system XYZ
tau-xy, tau-xz, tau-yz
Shear stresses
sig-I, sig-II, sig-III
Principal stresses
dx,dy,dz
Principal stress directions
The output is controlled with ECHO NOST, which has the same effect as ECHO FORC. Determination of the results at the nodes: The internal forces and moments and stresses of the adjacent elements are averaged in groups for each node and they are stored or output. The output is controlled with the ECHO option NOST.
4-10
SOFiSTiK 2014
Output Description | ASE
This averaging is not always allowed, e.g. in the case of jumps of the values between elements and especially for bends in folded structures, where shear forces change into axial forces. The program does not determinate the results in following cases: •
If at a node the thickness of the bordering elements jumps.
•
If at a node the material number changes.
•
If the direction of the local coordinate system jumps more than 5 degrees.
Two or more results are output then at the very same node. In program BEMESS the two results are calculated then with the relevant thickness and the relevant material number. At the group boundaries the results become also average provided that there no jump in the material number, the thickness or the local coordinate system is available. Kinematic constraints are ignored for the averaging (except for INTE). If needed, a known point of discontinuity can be described with double coupled (KF) nodes.
4.11
Error Estimates
ERROR ESTIMATES SHELL FORCES el-no.
Element number
m-xx, m-yy, m-xy
Error estimates for plate moments
v-x, v-y
Error estimates for plate shear forces
n-xx, n-yy, n-xy
Error estimates for membrane axial forces
ERROR ESTIMATES QUAD-ELEMENTS LC
Load case
type
Internal force or moment
dimension
Dimension of the internal force
maximum val
Maximum value of the internal force
maximum error
Maximum error of the internal force
element
Found in element ...
SOFiSTiK 2014
4-11
ASE | Output Description
ERROR ESTIMATES BRIC-STRESSES element number
Element number
sig-x, sig-y, sig-z
Error estimates for stresses
tau-xy, tau-xz, tau-yz
Error estimates for shear stresses
ERROR ESTIMATES BRIC-ELEMENTS LC
Load case
type
Internal force or moment
dimension
Dimension of the internal force
maximum val
Maximum value of the internal force
maximum error
Maximum error of the internal force
element
Found in element ...
The averaging of the results at the nodes allows the estimation of the error in individual elements. This error describes the average size of the jump in the results from one element to the other. The average values as well as the values at the element centre are usually considerably more precise. With ECHO ERIN YES the maximum magnitude of the internal forces and moments and the presumed maximum error for every load case are printed in the protocol file. With ECHO ERIN FULL the errors are output in all the elements. The error estimates are stored in the database and can be represented graphically. The user should take a closer look and possibly refine regions with high error estimates. Additional instructions are to be found in the manual of the program TALPA.
4.12
Distributed Support Reactions
The following result values are output for each boundary for which a designation has been input: DISTRIBUTED FORCES ALONG NODES LC
Load case
No.
Boundary number and designation
nodeno
Node number
4-12
SOFiSTiK 2014
Output Description | ASE
p-X, p-Y, p-Z
Distributed support reaction in kN/m
m-n
Distributed clamping moment in kNm/m about the axis of the boundary
m-n
2nd value, if boundary is a broken line
average
Average support reaction in kN/m
sum length
Total support reaction of the boundary in kN Length of the boundary
sum all boundaries
Total support reaction of all boundaries
The output can be controlled with ECHO LINE. With ECHO LINE YES only the sums of the boundaries appear, with ECHO LINE FULL the individual values are output too.
4.13
Strain Energy of Groups
The strain energy of the groups is only printed and stored with both input ECHO STAT FULL and ECHO GRP FULL: Strain energy of groups load case
Load case number
group
Group number
Energy
Energy in kNm
=% of sum
Percentage part
4.14
Wind Load Generation
With ECHO ELEM 4 an output of all QUAD elements with centre of gravity coordinates and normal direction can be requested. With that a further processing can occur for load generation with a spreadsheet program (wind load on a cooling tower).
SOFiSTiK 2014
4-13
