Ase 1
Ase 1
Ase 1
ASE
ASE
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Task Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Theoretical Principles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Implemented Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3. Beam Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1. SOFiSTiK TBeam Philosophy . . . . . . . . . . . . . . . . . . . . . . .
2.4. Pile Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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. Nonconforming Formulation . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9. Volume Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10. Primary Load Cases of Element Groups. . . . . . . . . . . . . . . . . . . .
2.11. Primary States of Single Elements for Creep Analyses . . . . . . . .
2.12. Nonlinear Analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13. Nonlinear Analysis of Plates and Shells. . . . . . . . . . . . . . . . . . .
2.13.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13.2. Input of the Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13.3. Analysis Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13.4. Output of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13.5. Miscellaneous Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14. Membrane Structures: Formfinding and Static Analysis . . . . . . .
2.14.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14.2. The Membrane Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14.3. Formfinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14.4. Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14.5. Unstable Membrane Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14.6. Calculations of Cable Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.14.7. Check List Notes Problem Solutions . . . . . . . . . . . . . . . . .
2.14.8. Overview about the Used Examples . . . . . . . . . . . . . . . . . . . . . .
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Input Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1. Input Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Input Records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3. CTRL Control of the Calculation . . . . . . . . . . . . . . . . . . . . . . .
3.4. SYST Global Control Parameters . . . . . . . . . . . . . . . . . . . . . . .
3.5. STEP Time Step Method Dynamics . . . . . . . . . . . . . . . . . . . . .
3.6. ULTI Limit Load Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7. PLOT Plot of a Limit Load Iteration . . . . . . . . . . . . . . . . . . . . .
3.8. CREP Creep and Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9. GRP Group Selection Elements . . . . . . . . . . . . . . . . . . . . . . . .
3.10. GRP2 Expanded Group Selection . . . . . . . . . . . . . . . . . . . . . . .
3.11. HIGH Membrane High Points . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12. PSEL Selection of Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13. TBEA Reduction of the Width for TBeams . . . . . . . . . . . . .
3.14. MAT General Material Properties . . . . . . . . . . . . . . . . . . . . . . .
3.15. NMAT Nonlinear Material . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.1. Invariants of the Stress Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.2. Material Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.3. Nonlinear state variables (hardening parameters) . . . . . . . . .
3.15.4. Material Law MISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.5. Material Law VMIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.6. Material Law DRUC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.7. Material Law MOHR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.8. Material Law GRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.9. Material law SWEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.10. Material Law FAUL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.11. Material Law ROCK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.12. Material Law GUDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.13. Material Law LADE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.14. Material Law DUNC (obsolete) . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.15. Material Law HYPO (obsolete) . . . . . . . . . . . . . . . . . . . . . . . . .
3.15.16. Material law MEMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3102
3104
3106
3107
3109
3110
3112
3113
3114
3117
3118
3120
3122
3127
3128
3129
3132
3135
3139
3141
3143
3145
3147
3150
3152
3153
3158
3163
3166
3167
3168
3169
3171
3176
4
4.1.
4.2.
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Output Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Check List of the Generated Structure . . . . . . . . . . . . . . . . . . . . .
Check List of the Nonlinear Parameters . . . . . . . . . . . . . . . . . .
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4.3.
4.4.
4.5.
4.6.
4.7.
4.8.
4.9.
4.10.
4.11.
4.12.
4.13.
4.14.
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411
412
412
5
5.1.
5.2.
5.3.
5.4.
5.5.
5.6.
5.7.
5.8.
5.9.
5.10.
5.11.
5.12.
5.13.
5.14.
5.15.
5.16.
5.17.
5.18.
5.19.
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spherical Shell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tbeam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Eigenvalue Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wind Frame with Cable Diagonals. . . . . . . . . . . . . . . . . . . . . . . . .
Single Span Girder with Auxiliary Support. . . . . . . . . . . . . . . . . .
Internal Force Redistribution Due to Creep. . . . . . . . . . . . . . . . .
Sunshades. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
QUADEuler Beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beam with Cable Action According to ThirdOrder Theory. . .
Girder Lateral Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plate Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Buckling Mode Shapes in Supercritical Region. . . . . . . . . . . . . . .
3D Tunnel Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Elastoplastic Analyses with Shell Elements. . . . . . . . . . . . . . . . . .
Prestressed Plane Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reinforced Concrete Slab in the Cracked Condition (State II). .
Displacement Controlled Bearing Load Iteration . . . . . . . . . . . .
Examples in the Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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518
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527
531
539
543
546
549
555
561
567
567
568
570
571
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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.
Nonlinear 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.
Nonlinear materials are available for threedimensional and shell elements. Geometrical nonlinear computations allow the investigation of 2nd
and 3rd order theory effects by cable, beam and shell structures.
In case of beam structures, the program can calculate warping torsion with
up to 7 degrees of freedom per node.
The analysis of folded structures or shells with finite elements requires considerable experience. 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.
Extended versions of ASE offer calculations of:
Influence surfaces
Nonlinear analyses
Pile elements with linear/parabolic soil coefficient distribution
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Theoretical Principles.
2.1.
General
ASE
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 socalled nodes. Displacements can be obtained with an elementwise 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 socalled 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 elementwise interpolation.
The complete method is divided into four main parts:
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2.2.
Implemented Elements.
The elements shown in the following table are available in ASE. A nonlinear
analysis can occur also for some types of elements. A detailed list of the implemented nonlinear effects is written in part NSTR_1
Nonlinear
Material
Element
SPRI
TRUS
CABL
BEAM
PILE
QUAD
BRIC
BOUN
FLEX
Halfspace
2.3.
yes
no compressive forces
yes
elastic support only
yes
yes
yes
Geometrical
Nonlinearity
yes
yes
yes + cable sag
yes
yes
yes
Beam Elements
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2.3.1.
A plate analysis is usually sufficient and desirable for beams with effective
cross section widths which are positioned in plates. Only in a plate analysis
normal forces are not determined in the plate or in the beam! The advantage
is that the plate 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 Tbeam cross section.
Procedure: The user or the graphical input program positions the beam in the
node plane (with the Tbeam cross section), therefore in the centre of gravity
plane of the QUAD elements (see picture c). Because the beam is also positioned in its centre of gravity, the upper edge of the Tbeam looks seeming out
of the plate this is also visible in WinGRAF. The ANIMATOR displaces the
cross section a little bit downwards, so that the upper edges beam+plate appear at the same position for a better visualization. The web has to be defined
here with the corresponding effective plate width as beam cross section.
As shown in the upper picture the plate would be now twice available in the
area of the effective cross section width of the beam. Therefore these plate
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parts (Iplate = bVd3/12 with b=effective width = width of the cross section)
are diverted automatically from the stiffness of the beam ITbeam. An equivalent beam is used:
Iequivalent beam = ITbeam Iplate
The program determines then at first a bending moment of this equivalent
beam in a FE analysis. The internal forces parts of the plate (Mplate = m
plate V b) are added immediately automatically. Thus the complete Tbeam
internal forces are available for the following beam design:
MTbeam = Mequivalent beam + Mplate
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 plate are already available in the printout of the beam
internal forces.
A statistic of the plate parts follows after the beam internal forces. The
maximum plate parts are compared with the maximum beam internal
forces:
Statistic Beam Additional Forces from a Slab
Loadcase
2
The printed beamforces include max. additional forces of a slab:
max. beamforce without slabaddition |
max. slabaddition
cnr
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 forces. This method can be uneconomical for smaller beam heights.
Beams which are connected with kinematic constraints at the plate are also
processed, if the beams are positioned in the plate plane.
Defaults for the addition of the plate internal forces to the beam internal
forces:
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changeable acting about the whole width. The internal forces and moments are therefore not exactly integrated about the effective width!
The plate stiffness Iplate (without the part of Steiner) is diverted from
the total cross section stiffness Icross. If the subtrahend Iplate is
bigger than 0.8Icross, a warning is printed and the minimum stiffness of 0.2Icross is used.
For threedimensional systems the subtrahend is maximal 0.9A
cross for the area Aplate. At least 0.1Across 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
CTRL PLAB 0
added plate parts
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:
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Also with the above describes method, the normal forces occur in the compression zone (plate) first during the design of the Tbeam. Normal forces are not
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:
1st 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 Tbeam. The method is therefore
only reasonable for composite slabs with eccentrically defined steel
beams (see ASE example 5.3).
kinematic constraint
2nd 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 plateweb is not
defined twice:
3rd 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
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plate is here necessary in the input. All elements can be defined eccentrically below the node 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 Tbeam 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 2.5plate 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.
eccenticity
plane of the
node points
underside of the
QUAD elements
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
Literature:
C. Katz J. Stieda, Praktische FEBerechnungen mit
Plattenbalken
Bauinformatik 1/92
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2.4.
ASE
Pile Elements
2.5.
Truss and cable elements can transfer only axial forces. In the case of nonlinear analysis the cable elements can not sustain compressive forces.
An internal cable sag is considered for geometrically nonlinear analysis. In
this case the transverse loading of the cable is calculated for the cable geometry (extensible plane prestressed cable). For an extremely large cable sag,
the cable must 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.
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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@u
(1)
A spring is defined with a direction (dX, dY, dZ) and three spring constants.
The here implemented element allows the following nonlinear effects which
are of course only usefully during a nonlinear analysis:
prestress (linear effect)
failure
yield
friction with cohesion
slip
spring nonlinear work laws, please refer to chapter NSTR_1
springs with a reference area AR and a nonlinear material work law
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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 boundaries without number and also at the record FLEX. The effect
of the elements appears directly in the form of support reactions at the corresponding nodes.
Distributed support reactions are determined for boundary elements with
number (compare program SOFIMSHA/SOFIMSHB). 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 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 @ CLCR ) CL
CR ) CLCL ) 3 @ CR
with
CR + CA @ L12CL + CB @ L12
CA,CB
L
2.8.
Shell Elements.
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The consideration of each structural behaviour can be specified in the program SOFIMSHA/SOFIMSHB for each particular element. The defaulted
values are:
SYST FRAM
SYST GIRD
SYST SPAC
The elements defined in SOFIMSHA/SOFIMSHB 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 secondbest shape and the general quadrilateral
the thirdbest. General quadrilaterals with reentrant 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/SOFIMSHB 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
Kirchhoffs theory. The ratio of the thicknesses of two adjacent elements
should not be smaller than 1:10 due to its cubic effect.
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2.8.1.
The ASE element for the plate structural behaviour is based on Mindlins
plate theory, as described in the implementations of Hughes, Tessler and
Crisfield (2,3,4), with an extension of a nonconforming formulation.
The cross sections remain plane also according to Mindlins 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.
q x + dw ) qS x
dx
(2)
with
w
q
qS
d.../dx
=
=
=
=
deflection
total rotation
shear rotation
derivative w.r.t. x (similarly for y)
For the curvature and the shear angle one receives then
kx + dq x
dx
(3)
dq y
dy
(4)
dq
kxy + dq x ) y
dy
dx
(5)
qS x + q x * dw
dx
(6)
qS y + q y * dw
dy
(7)
ky +
(8)
(9)
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(10)
and
vx + Sx @ qS x
(11)
vy + Sy @ qS y
(12)
By +
Ex @ t x3
12 @
Ey @ t y3
12 @
Sx + 5 G @ t x
6
(13)
Sy + 5 G @ t y
6
(14)
1 * m2
1 * m2
3
Ex @ t xy
12 @ 1 * m2
(15)
torsional stiffness
G @ td3
Bd +
12
(16)
with
Ex,Ey
G
m
tx,ty,txy,td
= elastic moduli
= shear modulus
= Poissons ratio
= plate thicknesses
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(17)
To reach this the mathematical thickness for txy and td must be input
in addition to the orthotropic input of Ex and Ey.
t xy + t d + t x @ 3ByBx
(18)
pf
z + f @ sin p @ x ; a +1 )
2l
l
(19)
1
E @ t3
@
a 12 @ 1 * m2
(20)
@ E @ t @ f2
0.81
By +1 *
2
2
1
)
2.5
2l
(21)
Bxy [ 0
(22)
E @ t3
Bd + a @
2 12 @ 1 * m 2
(23)
Bx +
b @ t 3o
t y + t x @1 )
a @ t 3x
(24)
t xy + t x
(25)
(26)
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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. An anisotropic Poissons ratio is not considered:
nxx + S x @ x * m @ S xy @ y
(27)
nyy + S y @ y * m @ S xy @ x
(28)
nxy + G @ t xy @ g xy
(29)
(30)
Ey @ t y
1 * m2
(31)
E x @ t xy
1 * m2
(32)
S y +
S xy +
2.8.3.
Elastic Foundation
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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 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
1 * m
C + E @
+ Es
1 ) m @ 1 * 2m
h
h
(33)
In analog mode one can obtain Winkler coefficients for multilayered 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 twodimensional 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
Cf + 3 @ EI
h
(34)
(35)
(36)
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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
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
CTRL BTYP < 0
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.
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 Inplanerotation of the nodes is coupled
via a weak torsional spring at the displacements of the corner nodes in an intern way.
2.8.5.
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. Threedimensional curved structures may be analysed in this way with sufficient
accuracy.
In the case of twisted shell elements as well as geometrically nonlinear
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 threedimensional curved
structures.
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2.8.6.
In the case of Tbeams, 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 Tbeam effect is realized correctly.
The position of the elements is input in the program SOFIMSHA/SOFIMSHB (e.g. QUAD ... POSI=BELO).
Additional explanations can be found in the school example "Prestressed
Skewed Tbeam Bridge".
2.8.7.
Prestressed cables defined with the program GEOS 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 and ELLO
CS.
Prestressing cables in the QUAD elements can be used only in a geometrically linear analysis.
2.8.8.
Nonconforming Formulation
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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.
A corresponding nonconforming 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 manuals of
the programs SEPP and TALPA.
2.9.
Volume Elements.
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For the analysis of construction stages in tunnel structure or for the definition of load steps in geometrical nonlinear analyses it is possible to use a
previous load case. The parameters of the primary stress state are defined
groupwise for this purpose. A detailed description of the method is given in
the TALPA manual.
2.11.
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Nonlinear Analyses.
Nonlinear effects can be analysed only with iterations. This is done in ASE
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.
Following nonlinear material effects are implemented currently: please also
refer to chapter NSTR_1:
Spring elements (failure, yield, slip, friction, work laws)
QUAD foundation elements (failure, yield, slip, friction)
Cable elements (material work laws, compression failure)
Truss elements (material work laws)
Nonlinear bedding for PILE elements
Nonlinear beam elements
Nonlinear material laws for QUAD and BRIC elements
Geometrically nonlinear analyses with truss, spring, cable, beam
and QUAD elements, for cable elements with internal cable sag
BRIC elements (geometric stiffness)
Tendons defined in the QUAD elements with the program GEOS can be used
only in geometrically linear analysis.
For TRUS, SPRI, CABL, BEAM and QUAD and for geometrically nonlinear
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/SOFIMSHB is used for this purpose see CTRL CABL). Thereby the iterations are markedly more stable
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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 increases or decreases the load
stepbystep 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. The initial deformation is saved with the results for displacements, thus it does not need
to be redefined in additional subsequent load cases. Deformations from a
modal analysis can be prescribed also as initial deformations via scaling with
FACV, see chapter 5, example Buckling Shapes in Supercritical Region.
The iteration process in ASE with SYST PROB TH2/TH3 is done well, however, a lot CPU time is necessary due to the iterations. Following procedure
is recommended for big BRIC systems in order to economize the CPU time:
In dependence to PLC stresses, a TH2 stiffness can be used with SFIX PLC.
This procedure works quick and accurate, if normal forces dont change much
in TH2. Example: see ase9_all.dat.
Nonlinear analyses are not possible with the basic version.
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2.13.1. Overview
The LayerModel 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 nonlinear calculation of elements consisting of a homogeneous material. In this case it is used to establish the positions of the individual layers. This method is especially suited for the nonlinear calculation
of plates and shells consisting of steel and reinforced concrete. Up to now the
nonlinear construction material models, steel and concrete, have been implemented for the shellelements.
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 shellelement (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.
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the stressstrain curves which are represented below for the desired concrete. Here are according to chapter 9.1.5 of DIN 10451 (02.07):
sigu (red)
sigr (blue)
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ULTI
UL / ULD
CALC
CAL / CALD
SERV
SL / SLD
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525
525
$
$
$
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tensile zone
The stressstrain curves which are input in this way can be seen and checked
as modified serviceability stressstrain curve (sigm / green) in the AQUA
output of the material values and in the plot of the stressstrain curves:
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CTRL CONC ..V3 temporary FCT = fctm => tensile strength for tension
stiffening
CTRL CONC ..V4 temporary FCTK = fctk0.05 => tensile strength for
pure concrete
Selection of a StressStrain Curve for an ASE Calculation
The selection of a preset or manually defined stressstrain 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.
Check of the Material Values in ASE
In order to increase the transparency of the calculation the material values
and further definitions for the nonlinear 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 stressstrain curves of the materials as well as a detailed plot
of the concrete stressstrain curve in tensile zone are printed in the URSULA
output.
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PROG AQUA
MATE 11 E
60e3
MATE 12 E
0.8e3
$ glassplasticglass
MLAY NO 1 T0 0.006 11
T1 0.003 12
T2 0.003 12
T3 0.003 12
T4 0.006 11
END
MUE 0.2
MUE 0.3
$ glass
$ plastic
$$
$$
$$
$$
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.
Note: The analysis is according to plate theory, i.e. assuming that the cross
section 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 crosssections is very important. At these points one could evaluate a spatial stressstate, which can only be depicted by volume elements.
Any arbitrary material can be used basically also orthotropic as layer for non
linear analyses.
At the moment only layers from the material concrete or steel are processed
nonlinearly. The loading and unloading curve is generated independent on
each other (hysteresis).
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xiLOAD
v
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.
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.
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q @ S *xi
I @ b
For homogenous material definitions, in the linear domain, this would result
in a parableshaped shear stress distribution over the height of the element,
with the maximum value of max = 1.5 q / h. For sandwich elements, with
thick (strong) toplayers, it would mean that a nearly constant shear stress
is present in the middle of the element; given by max = 1.0 q / h (h=element
thickness).
Nonlinear Analysis STEEL
Examples see ase.dat\...\ase12_plattenbeulen.dat or
ase15_stahlfliessen_quad.dat in sofistikase.datenglish
For a nonlinear 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:
s *xi + s *xi*PLC ) D *xi @ de *xi
and
t *xi + t *xi*PLC ) dt *xi
(simplified)
The total stress xi is therefore not just put together by the total strain
multiplied with the stiffness, instead it might be that the nonlinear eigen
stresses of the individual layers of xiPLC 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 Gausspoints. This information is needed
for the next load case as xiPLC.
From these initial linear stresses a new linear comparison stress is calculated:
For QUAD elements the following applies:
s v + s 2x ) s 2y * s x @ s y ) 3t 2xy ) 3t 2x ) 3t 2y
(where xy = disc shear and x, y = plate shear perpendicular to the plate)
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If the so calculated linear comparison stress vxi is above the allowed stress
(by considering the hardening, which is calculated by summing up the plastic
strains, by entering a trilinear stressstrain curve); then first of all the linear
component is established (Breakthrough point through the plastic area).
Then the remaining strain increment dxi with the elastoplastic material
matrix DP is applied incrementally, with the consideration of possible
hardening. The nonlinear 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 nonlinear material behaviour is according to
the elastoplastic plasticlaw, described in TALPA, which is according to van
MISE and includes hardening. For more information on this topic you are referred to Zienkiewicz"Methode der finiten Elemente".
The following diagram results from uniaxial stress:
In the case of combined stress, which is made up of normal stress (N/A M/w)
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 parableshaped 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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[2]
[3]
[5]
[6]
[7]
DIN 10451 Ausgabe Juli 2001 (mit Berichtigung 1, Juli 2002) z.B.
in [2]
[8]
The material behaviour of reinforced concrete can be described by the following properties:
Nonlinear stressstrain curve in tension and compressive zone
Contribution of the concrete between cracks (tension stiffening)
Nonlinear material behaviour of the steel inserts
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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 5epslin see CTRL CONC VAL.
If a stressstrain 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 > ase.dat\...\nonlinear_quad\stahlfaserbeton.dat.
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Simplified method of the tensile stiffening acc. to Heft 525 (Bild H 84)
As are mentioned the methods according to Heft 400 DAfStb are used always
for calculation in serviceability limit state, because e.g. the bar diameter is
not practical for the nonlinear method according to DIN 10451. At first the
strains are determined here in the steel layers in reinforcement direction.
These strains are equal to the mean steel strains sm according to [3] Schiel
Heft 400 DAfStb. Thus the steel stress s in the cracked cross section in
cracked condition (state II) can be determined with equation (6) according to
[3], page 162 after the determination of the crack initiation stress sr which
is calculated in dependence on the corresponding strain state.
The analytical value of the crack width is determined according to Heft 400
for old DIN 1045 or for explicit input CTRL CONC V5 400.
w k,cal + 1.7 @ a m @ e sm
For the new design codes (and without the input of CTRL CONC V5 400) the
crack width is calculated according to DIN 10451 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) s with the
reinforced concrete area. This value can now be added to the concretes internal forces and moments.
The crack widths are always calculated in the direction of the reinforcement!
For nonreinforced elements it is only possible to calculate one crack direction, but the crack width can not be established. It is recommended to input
a minimum reinforcement therefore also for nonreinforced concrete in order
to get more attractive crack pictures.
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The calculated steel stress is checked with a uniaxial material law for the reinforced concrete.
The coefficient describing the connection properties is to be defined in
AQUASTEE. The factor for the influence of the load period is input in
ASELC.
For ultimate limit state the calculation is done according to Heft 525, if DIN
10451, DIN FB 102 or new EC 2 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
= q/z = q/(0.8 h)
If the linear calculated shear stress rises over the input value 02, then the
shear force is reduced accordingly and the element undergoes plastic shear
deformation. The value 02 is input with ASECTRL FRIC in N/mm2 and
the default value is set to 2.4 N/mm2.
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 nonlinear ASE
calculation, then a check of the shear stresses in ASE is not done in the areas
of the punching point.
If this is not the case or if the permissible shear stress is exceeded at other
singular points, this not desired effect can be switched off via an increase of
TAU02 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 threedimensional system, this is because the crack opening will cause horizontal node displacements, even in the
plate analysis. For the special case of a reinforcedconcrete plate analysis the
system can also be entered as a girder grid SYST ROST the program SEPP
will then automatically introduce a horizontal statically determinate support.
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The first step would involve a linear analysis of the individual load cases, a
superposition 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
CTRLLCR).
Subsequently a state load case has to be put together for the nonlinear
analysis. For the calculation of longterm 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 nonlinear 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 ASEBEWQ).
The convergence of this nonlinear 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 nonlinear analysis is usually calculated by excluding creep and shrinkage. Subsequently another nonlinear 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
nonlinear analysis without creep and shrinkage
nonlinear analysis with creep and shrinkage
The entire procedure for the calculation of a floor slab, in the cracked condition (state II), can be found in example betobeme_edin.dat in sofistik
ase.datenglish
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
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The next picture shows the nonlinear 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.
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The visualization of the nonlinear 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 nonlinear results, like the crack widths or stresses in the cracked
condition (state II), can only be released by an ASE or SEPP calculation. For
this the ECHO FORC record is used. The internal forces and moments can
be released subsequently with DBVIEW, DBPRIN or MAXIMA.
Statistics of Nonlinear Effects
The available nonlinear effects are logged at the end of a nonlinear calculation in ASE:
Statistic nichtlinear effects:
==============================
Statistic plasticity: number of checked QUADgausspoints:
number of plastified gausspoints:
number of cracked gausspoints
:
Maximum concrete compression strain ............
Minimum averaged reinforcement strain ..........
Maximum averaged reinforcement strain ..........
Maximum reinforcement tension strain in crack ..
Maximum concrete compression stress ............
Maximum concrete tension in the concrete layers
Minimum reinforcement stress ...................
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:
:
:
:
:
:
:
3960
3481
2333
0.55
0.27
0.71
1.01
16.79
1.93
54.69
[o/oo]
[o/oo]
[o/oo]
[o/oo]
[MPa]
[MPa]
[MPa]
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201.11
0.12
0.000
0.115
0.115
0.000
[MPa]
[mm]
[m]
[m]
[m]
[m]
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2.14.1. 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.
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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 threenoded or fournoded 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 (linearelastic approximation).
K + K 0 ) K s
Input of the Membrane element
Membrane elements are input like normal shell elements as element type
QUAD. If the element formulation NRA=2 (see SOFiMSHAQUAD) is set
immediately, the element is marked as membrane. Otherwise a normal
QUAD element can be defined as membrane with a nonlinear material input
NMAT.
Nonlinear properties can be activated in AQUA with NMAT MEMB P1 P2.
P1
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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 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:
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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.
The strain stiffness disappears here in the mathematical model. The equilibrium results only from the threedimensional equilibrium of the isotropic
stresses. The stiffness of the membrane results to:
K + K s
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.
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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.
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P=nr
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.
cable 2
cable 1
cable 3
2.14.3. Formfinding
System Definition Two Options
The initial structure can be defined with two options for the formfinding:
Definition of a threedimensional initial system with at first plane partial areas:
The boundary points of the structure are input threedimensionally.
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 twodimensionally. At arbitrary points the
structure is hoisted" then at support nodes.
Threedimensional Initial System
Threedimensional initial system without cable edges
Example angle, example file mwinkel.dat.
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A load case with real 1.0times 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
SYST PROB TH3 PLC
GRP 0 FACS 1
$
$
LC 2
END
The iterations are necessary due to the effects from thirdorder theory. The
vertical force parts (sinus() ) change due to the large displacements. In
addition the element geometries change also in part considerably. The first
ASE calculations ends successfully after 9 iterations:
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1.889 energy
22.6089
Step
11 f=
1.000
0.239 energy
0.222 energy
30.7733
32.4090
Step
Step
21 f=
31 f=
1.487
1.814
0.134 energy
0.017 energy
0.008 energy
32.7557
32.6185
32.6450
Step
Step
Step
41 f=
42 f=
51 f=
1.838
0.604
0.607
0.003 energy
32.6701
Step
61 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.
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Vlong/Vlat=1:5
Vlong/Vlat=1:2
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Stand roofing initial system plane left and angular picture right
Group classification:
group 1:
group 2:
group 3:
membrane
edge cable left
edge cable right
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 1E10:
PROG ASE
HEAD Formfinding
CTRL CABL 0
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SYST PROB TH3
GRP
1
FACS 1E10 PREX 10 PREY
GRP
2
FACS 1
PREX 160
3
FACS 1
PREX 460
GRP
LC 1 DLZ 1 TITL Formfinding with DL
END
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:
PROG ASE
HEAD Compensation of Possible Residual Forces with FACS=1.0
$ uses primary load case 1
SYST PROB TH3 PLC 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:
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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
mwinkel.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
or
P=nr
r = P / n = 8 kN / 2 kN/m = 4 m
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Formfinding in global Z direction with CTRL FIXZ 3
CABL 0 $ without inner cable sag
PROB TH3
0 FACS 1E10 PREX
2 PREY
2 $ membrane 2 kN/m
2 FACS 1E10 PREX 20*2
DLZ 1 TITL Formfinding
NO
P1 type=wz
3
8.40
127
6.06
285
3.28
399
7.76
398
8.40
355
3.98
61
3.28
1
12.18
END
PROG ASE M4
KOPF Compensation with FACS=1.0
CTRL PROB TH3 PLC 1
GRP (0 99 1) FACS 1
LC 2 DLZ 1 TITL Compensation with FACS=1.0
END
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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 socalled mesh control during formfinding.
If this automatic mesh control does not function, further variants can be activated with the manual control CTRL ... FIXZ:
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.E10). 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.
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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
CTRL FIXZ=5
CTRL FIXZ=4
or
5
CTRL FIXZ=2
CTRL FIXZ=3
CTRL FIXZ=4
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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:
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FACS 1.0
LC 13 TITL Compensation with FACS=1.0
ELLO 1 9999 1 TYPE PZ P 2.0
END
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load case 11
Angle with internal pressure
load case 12
Because the local coordinate systems are directed inwards, the internal pressure was input negatively in ELLO.
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.
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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
ELNo
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 |
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System update for calculation of new displacements
from formfinding state LC 2
PLC 2 STOR YES
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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. Because the full wind loading of 0.8 kN/m2 does not converge
in a step, only 0.3 kN/m2 are used at first:
PROG
HEAD
CTRL
NMAT
SYST
GRP
GRP
GRP
ASE
Wind pressure from below 0.3 kN/m2
CABL 0
1 MEMB P2 0 $ membrane without compressive stresses
PROB TH3 NMAT YES PLC 2 $ NMAT=YES due to switch off of compression
1
FACS 1
FACL 1 PREX 0 $ prestress due to FACL 1.0
2
FACS 1
FACL 1 PREX 0 $ uses from PLC, PREX is not input
3
FACS 1
FACL 1 PREX 0 $ anymore, therefore
$ all group factors should be now FACS+FACL=1.0,
$ because stress modifiction is now reasonable and necessary
LC 13 DLZ 1.0 TITL Wind pressure from below 0.3
ELLO 1000 1999 1 TYPE PZ P 0.3
END
A further load increase of the wind load till 0.4 kN/m2 is done then in load case
14 by using the convergent primary load case 13:
PROG ASE
HEAD Wind pressure from below
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CTRL CABL 0
NMAT 1 MEMB P2 0.1 $ A possible smaller compression admission should be
$ allowed in intermediate steps!
SYST PROB TH3 NMAT YES PLC 13
LC 14 DLZ 1.0 TITL Windpressure from below 0.4
ELLO 1000 1999 1 TYPE PZ P 0.4
END
In the same manner the load is increased in further partial steps till 0.8
kN/m2 in load case 18. The input control for the processing of the compressive
stresses NMAT ... MEMB ... P2=0.1 has following meaning:
If a compressive stress is available in an element, this stress is used only
0.1times. That means, that the elastic modulus for the compression zone is
decreased about this factor. The tensile stresses remain as before. In the case
of a repeated setting up onto the in each case last state the stresses are reduced here again and again, so that no compressive stresses are remaining
practically for small load step width.
It is also possible to input immediately P2 equal to 0.0. It can happen, however, that the system converges only very bad or it does not converge at all.
An attempt with P2=0.0 can be done in any case (see example membdruc.dat).
In the following picture the stresses in the centre are actually only uniaxial
for the load case 18. The stress is omitted biaxially even in four elements:
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The file membdruc.dat is recommended as a further example with compression switching off.
Textile Material Laws
Especially textile material laws were not implemented up to now. Essential
membrane properties can be described with an orthotrop but otherwise linearelastic material according to an article in Bauingenieur 70, 1995 on page
271 by R. Mnsch and H. W. Reinhardt. Such a material can be defined at SOFiSTiK with the record MAT. It means here:
record MAT:
E
EY
MUE
G
e *x
s * x
m
*
E
EY
0
e
*
y
1
s
*
y
+
*
*
2
1*m
0
g * xy
t * xy
0 G * 1 * m2
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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 set in the material
input NMAT MEMB with P2.
Examples for material input see innenhof.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.
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PROG ASE
HEAD Bottleneck
HEAD ASE prints divergence nevertheless look at load case 1 with ANIMATOR
SYST PROB TH3
GRUP
0
FACS 1E10
HIGH 0 0 PR1 10 PTPR 1.0 $ is soap skin but not possible!
LC 1 DLZ 1 TITL Bottleneck
NL 481 WZ 6
$ lifting of the central node 481 about 6 m
END
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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:
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.
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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 pointwise 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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For insistent problems, mail the input file to the SOFiSTiK hotline
Special feature
mwinkel.dat
mdach.dat
Further examples:
membran5.dat
plane initial system with 4 high reference points and
a deep point
tennis.dat
plane initial system formfinding due to load
use of a constant internal pressure compressed air hall
sechseck.dat
plane initial system formfinding with constant internal
pressure
mzelt2.dat
plane initial system and two high reference points defined
as rings, unstable formfinding soap skin,
comparison with elastic skin calculation
mwinkel2.dat
formfinding with at first straight boundary cable
comparison fournoded and threenoded elements
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Modal Analysis.
The program is able to calculate, instead of a static analysis, the mode shapes
and natural frequencies of the examined structure. The analysis of eigenvalues is more extensive than a static analysis. Therefore the user should begin
such a task with special considerations. Two analysis methods are available:
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.
The eigenvalues can be calculated in relation to a reference point. The so
forced decomposition of a modified equation system leads to the output of the
number of eigenvalues below the reference point for an estimate or a check
with the Sturm sequence. A small negative value can be used, if the structure
is not supported.
The algorithm finds only new eigenvectors above the reference point, if the
eigenvectors below the reference point are known and if it can filter them out
of the solution area. If these are not given, then one compulsorily gets the harmonic oscillations of the lower eigenvalues.
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, unless a displacement
of the subarea takes place. Indeed this is possible in ASE, but it requires extensive CPU time and should not be used therefore.
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.
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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.
2.16.
Masses.
2.17.
Damping Elements
Damping elements from the program SOFIMSHA/SOFIMSHB are considered for the timestep method.
2.18.
The modal damping dij 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.
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Also loads can be defined additionally. ASE calculates then the generalised
loads and saves them in the database for a further use with the program
DYNA.
2.19.
Literature
(1)
O.C.Zienkiewicz (1984)
Methode der finiten Elemente
2. Auflage , Hanser Verlag Mnchen
(2)
T.J.R.Hughes,T.E.Tezduyar (1981)
Finite Elements Based Upon Mindlin Plate Theory With Particular
Reference to the FourNode Bilinear Isoparametric Element.
Journal of Applied Mechanics,48/3, 587596
(3)
A.Tessler,T.J.R.Hughes (1983)
An improved Treatment of Transverse Shear in the MindlinType
FourNode Quadrilateral Element.
Computer Methods in Applied Mechanics and Engineering 39,
311335
(4)
M.A.Crisfield (1984)
A Quadratic Mindlin Element Using Shear Constraints
Computers & Structures, Vol. 18, 833852
(5)
K.J.Bathe,E.N.Dvorkin (1985)
A FourNode Plate Bending Element Based on Mindlin/Reissner
Plate Theory and a Mixed Interpolation.
Int.Journal.f.Numerical Meth. Engineering Vol.21 367383
(6)
T.J.R.Hughes,E.Hinton (1986)
Finite Elements for Plate and Shell Structures
Pineridge Press International, Swansea
(7)
Timoshenko/WoinowskyKrieger (1959)
Theory of Plates and Shells, MacGrawHill, NewYork
(8)
Taylor,Beresford,Wilson (1976)
A NonConforming Element for Stress Analysis
Int.Journal.f.Numerical Meth. Engineering Vol.10 12111219
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Input Description.
3.1.
Input Language
The input is made in the CADINP language (see general manual SOFiSTiK:
FEA / STRUCTURAL Installation and Basics).
3.2.
Input Records
The statical system is input with a graphic input program or with the program SOFIMSHA/SOFIMSHB. 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:
Records
Items
CTRL
SYST
OPT
TYPE
FACV
VAL
PROB
NMAT
ITER
STOR
TOL
CHAM
FMAX
FMIN
EMAX
EMIN
STEP
ULTI
PLOT
CREP
N
STEP
LC
NCRE
DT
FAK1
TO
RO
INT
FAKE
NNO
T
ALF
DFAK
DIRE
RH
DEL
PRO
TYPE
TEMP
THE
DL
LCST
PRIM
SELE
DMIN
GRP
NO
FACL
CS
HING
NO
GEOM
VAL
FACD
PREX
FACB
STEA
FACS
FACP
PREY
CSDL
QUEA
PLC
FACT
PHI
MNO
QUEX
GAM
HW
EPS
H
GAMA
RELZ
K
RADA
PHIF
SIGN
RADB
PHIS
SIGH
MODD
T1
QUEY
ALP0
ULUS
QEMX
EXPO
XM
FROM
NC
YM
TO
b
ZM
INC
NX
REDP
NY
REDA
NZ
REDT
PR1
PTPR
NOG
GRP2
HIGH
*PSEL
TBEA
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31
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Records
Items
MAT
E
OAL
TYPE
P9
NOEL
ASB
ABT
FACT
MUE
OAF
P1
P10
TOP
ASBT
REIQ
NO
MXY
NO
P8
NOG
ASTT
AB
LCB
STEX
OBLI
SLIP
MOVS
LAUN
SFIX
NAME
SX
NOSL
NO
GRP
LC
SY
NOG
TYPE
DX
PLC
LC
NO
GAMF
NNO
NO
FROM
FROM
NO
NMAT
REI2
LOAD
NL
BOLO
ELLO
*PILO
POLO
LILO
BLLO
TEMP
LAG
PEXT
LCC
EIGE
MASS
V0
32
G
SPM
P2
P11
BOTO
BST
K
TITL
P3
P12
HT
BSTT
GAM
GAMA
ALFA
EY
P4
P5
P6
P7
DHT
BSB
HB
BSBT
DHB
AT
AST
ATT
SZ
NOEL
FROM
DY
LC
FACV
VMAX
DIRE
STOR
TO
DZ
INC
XM
L0
YM
FACT
PSI0
PX
TYPE
TO
TO
TYPE
DLX
PSI1
PY
P1
INC
INC
PA
DLY
PSI2
PZ
P2
TYPE
TYPE
PE
DLZ
PS1S
MX
P3
PA
P
A
BET2
CRI1
MY
PF
PE
DPZ
L
TITL
CRI2
MZ
TYPE
CRI3
REF
ETYP
PCS
NNR
NNR
PE
NNR
DZS
SEL
X
XA
NOG
XA
DXT
PROJ
Y
YA
SEL
YA
DYT
Z
ZA
PROJ
ZA
DZT
TYPE
DX
P
DY
N=G
DZ
SEL
TYPE
PROJ
PA
DX
TYPE
DY
P1
DZ
P2
DXS
P3
DYS
NOG
NO
LCNO
NOG
NO
NEIG
NO
NO
T1
FACT
NOEL
FACT
ETYP
MX
VX
T2
TYPE
P0
NOG
NITE
MY
VY
NOG
Z
SIDE
NFRO
MITE
MZ
VZ
FACT
TOL
BETA
NTO
LMIN
MXX
EMOD
PROJ
MUE
NINC
SAVE
MYY
RELA
EXPO
LCRS
SS
ULTI
LC
MZZ
GAMU
PLC
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Items
REIN
MOD
P10
STAT
SC2
SMOD
KMOD
BB
TANS
RMOD
P11
KSV
SS1
TSV
KSV
HMIN
TANC
OPT
VAL
DESI
NSTR
ECHO
LCR
P12
KSB
SS2
MSCD
KSB
HMAX
ZGRP
TITL
AM1
C1
KTAU
KMIN
CW
SFAC
P6
P7
P8
P9
AM2
C2
TTOL
KMAX
CHKC
AM3
S1
TANA
ALPH
CHKT
AM4
S2
TANB
FMAX
CHKS
AMAX
Z1
SCL
CRAC
FAT
SC1
Z2
CW
SIGS
The records PSEL and PILO are only available in the ASE version which was
expanded by the pile element.
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The records HEAD, END and PAGE are described in the general manual SOFiSTiK: FEA / STRUCTURAL Installation and Basics.
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3.3.
Item
Description
OPT
Control option
SOLV Solution of the system
ITER Iteration method
BTYP Formulation beam elements
QTYP Formulation of QUAD ele
ments
AFIX Handling of movable degrees
of freedom
VKNO Shear forces at nodes
MSTE Number of the RungeKutta
steps
NHPM Number of the Hardening rule
parameters
TOLP Tolerance of the pile elements
CUT
Spring handling for geometri
cally nonlinear calculation
CABL Cable handling for geometri
cally nonlinear calculation
PRES Factor of the prestressing
stiffness (not prestressfactor)
DRIL Calculation of twisted shell
elements
NLAY Number of disks for QUAD
concrete rule
FRIC Maximum allowable shear
stress for QUAD concrete rule
SHEA Shear stresses for QUAD
steel rule
PLAB Tbeam components
FORM Yield process cross section
reduction
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Dimension
Default
LIT
35
ASE
Item
Description
FIXZ
WARP
STII
MFIX
RMAP
UNRE
SFIX
INPL
CONC
STEA
QUEA
DIFF
BRIC
CANT
BEAM
SOFT
SPRI
MCON
GIT
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Dimension
Default
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Description
Dimension
Default
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
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standard element
nonconforming formulation
use of rotational masses (dynamic only)
Default (1)
Any input for QTYP forces a new calculation of the stiffness matrix.
AFIX
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stiffness. An input unequal to 1 for CTRL AFIX turns off this instability check.
0 =
1 =
2 =
3 =
4 =
5 =
6 =
7 =
Default: 1
VKNO Control of the averaging of the shear forces at nodes
VKNO = +1: The shear forces are calculated always positive at
nodes. The shear force in elements at intermediate supports is
positive at a side and negative at the other one. If these results are
averaged maintaining their sign, the resultant shear force is approximately 0 at the node. If, however, the absolute values are averaged, realistic shear forces are generated for the support nodes.
Pictures in the program WING show only positive values, if nodal
values are used, whereas they represent both positive and negative values, if element values are used in the program WING
(STYP ELEM).
The superposition of absolute values at a node has a negative effect: If the shear force is positive for a load case and negative for
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Default: (1)
CABL Cable handling
CABL = 0 No consideration of the internal cable sag
CABL = 1 Consideration of the internal cable sag
The consideration is not done for cables with FACS not
equal 1.0 (formfinding)
CABL = 2 Calculation of cables with FACS not equal 1.0
(formfinding) with inner cable deflection
(Default: 1)
PRES Factor for prestressing stiffness (not factor of prestress!)
PRES = x The initial stress matrix of elements is calculated
with the prestress multiplied by |x| from the program SOFIMSHA/SOFIMSHB or with PREX PREY from the record
GRP. The factor does not act, if a primary load case is considered.
The prestress of the primary load case multiplied by 1.0 is used
always here. Structures with a small initial prestress from the
program SOFIMSHA/SOFIMSHB can be analysed in this way too
(for example CTRL PRES 100). For cable systems without a prestress from the program SOFIMSHA/SOFIMSHB or PREX (record GRP) PRES is used as cable prestress in N/mm2.
Attention: PRES does not change the prestress value but only the
stiffness for the first iteration step!
(Default: 1.0)
DRIL
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FIXZ = 3
FIXZ = 4
FIXZ = 5
FIXZ = 0
iteration steps
fixes generally all nodes in global XY
= formfinding in global Z
can be used also for a cable nets
fixes the local z coordinate in the first iteration
step, in further steps the transverse direction
(as for FIXZ 2)
fixes the local z coordinate in all iteration steps
no such effects
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SFIX
INPL
Inplane stiffnesses
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.
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CONC V2 = 1
ASE
CAL, CALD
The parameter NMAT...LADE...P6 is
interpreted a length of decresing tension
stress.
CONC V3
CONC V4
With CTRL DIFF the difference internal forces (and displacements) between a load case and the primary load case are saved
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BRIC
CANT 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. This can be controlled with
CTRL CANT. Usage see program CSM Construction Stage Manager.
CANT = 0
CANT = 1
CANT = 2
CANT = +4
no action
only consideration of displacements
consideration of displacements and rotations
= tangential cantilevering construction
retention of the XY position
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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 nonlinear analysis with corners which
are displaced upwards (see SYST PROB LIFT).
default: 5E7
SPRI
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There are several equation solvers available. They will be updated and enhanced from time to time. The user may select the optimum of them only with
some knowledge or experience depending on many system parameters. He
has the following choices:
Direct Skyline Solver (Gauss/Cholesky)
This is the classical solver of the FEMethod, it uses a skyline, i.e. the
storage needed depends on an internal numbering of the nodes and
may become quite large for 3D structures. That is why the original version uses a block mechanism to segment the equation system on disk.
Direct Sparse Solver
This types of solvers are the latest technology but still subject of research and under development. A highly efficient version is available
based on the work of Timothy A. Davis (http://www.cise.ufl.edu/research/sparse/ldl)
Iterative Solver (Conjugate Gradients)
The advantage of the iterative solver is mainly the reduced requirements for strorage, but it may also reduce the computing time especially for 3D systems.
The advantage of the direct solver is especially given for multiple right hand
sides, as the effort for this step is very small compared to the decomposition
step. Thus they are the first choice for any dynamic analysis or many load
cases, because all the benefits of the iterative solvers will vanish for those
cases.
Computing times from 1996 (90 MHz) may show some of the properties of the
two solvers. The third example did not fit at all on the 500 MByte Harddisk
at these days:
System
Unknowns
Plate
42724
1739
1124
129
12
3.6
Shell
37452
1097
737
149
20
1.6
Cube
63504
12485
469
30
29.3
Computing time
(sec)
Direct
Iterativ
Storage (MByte)
equation system
Direct
Iterativ
Element
file
MByte
The selection of equation solver is done via CTRL SOLV. The first value defines the type of the solver, while the other may contain additional para-
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V5
V6
The iterative Solvers require a preconditioning in any case to scale the matrices We have available the following variants:
Diagonal scaling (W4=0)
Although this is the fastest method with the least memory requirements, it will need a considerable high amount of iterations and is
therefore of little use in most cases.
Incomplete Cholesky (W4=1)
This type of preconditioning suppresses the FillIn of a normal Cholseky solution of the equation system. If one has a fully populated matrix, it will however solve the total system during the preconditioning
step which lets vanish any computing time advantages.
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For any preconditioning one may restrict the numbers of entries to the preconditioning matrix either by a relative threshhold value of W5, or via a maximum number of entries via W6. The optimum choice may depend on the individual type of structure and may be found only by some tests.
The internal numbering of the nodes is not important for the iterative solver
itself, thus it would be also possible to specify CTRL OPTI 0. However the preconditioning is sensitive to the numbering scheme. We found best to use
CTRL OPTI 1.
CTRL SOLV 3
Direct Sparse Solver.
The program will use automatically allocated memory special parameters
are not foreseen. However it is mandatory to select in SOFIMSHA /SOFIMSHB with CTRL OPTI 50 a minimisation of the fill in to achieve good timings and storage requirements.
CTRL SOLV 4 to 7
Experimental solvers to be tested.
Please do not apply without contacting SOFiSTiK before and read the current
state in the HTMFile! These solvers are not released.
CTRL SOLV 9
Direct Solver (Gauss/Cholesky).
This solver is intended for rather large systems with limited memory space.
It is not available for DYNA. The program will use only the explicit allocated
memory. As a rule of thumb this memory should be large enough to allow a
block size which contains more equations than the maximum band width of
the system. If we have smaller blocks, excessive IO may occur as the blocks
have to be reused several times. However selecting a block size to large may
degrade the overall system performance due to swapping without gaining any
advantage for the solver itself.
The block size to be used may be also specified directly:
CTRL SOLV 9 W2
W2
Block size
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one may have one CDB with the total system and all loads subdivided into
groups. From this master one may then create identical copies for any substructure. As an alternate way one may define the connecting surface with
elements of group zero which are deactivated when building the substructure. Then there are the following general steps:
Creating the substructureMatrices
Input: CTRL SOLV 11 + Group selection
A Substructure is defined by the selected groups and will be save in an
external file "projectname.ZDS".
The Interface nodes are defined as belonging to the activated and to the
deactivated groups. When creating the substructure one has to specify
all load cases with loads within the substructure at the same time as
these will be saved into the ZDS file.
The total system will be analysed by selecting the substructures with
record STEX. The node numbers of the substructure may be shifted by
a constant value, but to use a substructure several times, one has to
make a copy of the ZDSfile for each instance. If the total system consists only of substructures a definition of CTRL SOLV 10 will achieve
this without defining any groups or loads.
Computing the internal displacements and stresses of a substructure
Input: CTRL SOLV 12 + Group selection
The interface displacements from the ZDSfile will be taken and used
to solve for the rest of the unknowns in the interior of the substructure.
One should work on the different child CDBs as the results will be overwritten otherwise.
CTRL SOLV 999 (ASE only)
The old stiffnesses of the last calculation are reused.
CTRL SOLV 998: Build stiffness matrix one time in one ASE run and use it.
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Parallel Solvers
Since some time the clock frequency of the processors are stuck at about 3 Gigahertz, Moores Gesetz however is still valid if we consider parallel processing. Unfortunately the most lengthy part of FE analysis the solution of the
equation system is rather difficult to be treated with that approach. After
some experiments with workstation clusters (PVM / MPI) we have decided
to use a shared memoryarchitecture with OpenMP.
So you need a computer with several processors or cores to make use of this
features. A so called hyperthreading" only computer does not provide any
benefit at all.
SolverTypes 1 to 3 are available for that technique if you have such a computer an a license for the HighPerformance Solver ISOL". Following remarks are given:
SOLV 1
SOLV 2
The Iteration itself is best for parallelization, but the convergence is strongly dependant on the preconditioning step and
the best method for this (incomplete cholesky) is not suitable
for parallel processing. The second best method (incomplete
inverse) may be parallelized perfectly, so the slightly higher
effort may be overcome if we have more than 2 processors.
SOLV 3
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Profile Loadbalance
Skyline serial
2 Threads parallel
direct sparse
2 Threads parallel
5456223
1600478
1585372
Iterative Solver
diagonal scaling
2 Threads
incomp. cholesky
2 Threads
incomp. inverse
2 Threads
303549
OPTI 17
LB 70/30 %
OPTI 50
LB 48/52 %
Iterations
3492
774
882
CPU 1st LC
CPU 2nd LC
24.52
15.89
7.11
5.88
5.58
4.70
0.39
0.39
0.23
312.03
179.60
85.17
58.76
132.95
82.59
312.00
179.52
84.17
57.75
132.00
81.78
0.19
The next table shows the values obtained for different solvers on a 4 Processor
Opteron with 2.4 Gigahertz for a compact spatial structure with 52788 equations for 64 bit Linux. Here the CPUTimes have been summed up for all
threads.
Solver
Profile
WallClock
CPU 1st LC
CPU 2nd LC
Skyline serial
106517384
2 Threads parallel
4 Threads parallel
Direct Sparse
15983191
2 Threads parallel
55.7/44.3
4 Threads parallel 21/37/11/31
Iterativ cholesky
871399
2 Threads parallel
(253 Iter.)
4 Threads parallel
Iterativ inverse
871399
2 Threads parallel
(265 Iter.)
4 Threads parallel
454
272
279
40
39
38
27
16
12
40
24
15
453.99
544.68
995.80
39.66
77.55
151.61
26.93
33.36
34.23
40.39
47.34
56.38
0.74
0.42
26.60
23.70
For OpenMP there are some user environment variables to control the behaviour. For a single processor with hyperthreading or a computer to be used for
many other tasks it might be useful to set the number of processors to 1, for
other compilers (PGI) however it is requested to specify numbers > 1 explicitly.:
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OMP_NUM_THREADS
OMP_OMP_DYNAMIC
OMP_NESTED
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3.4.
Item
Description
TYPE
Control option
* This input is not analyzed, the value
is taken over from generation pro
gram.
Type of the analysis
LINE Linear analysis
NONL Nonlinear analysis
TH2
Analysis according to second
order theory
TH3
Analysis according to third
order theory
TH3b Limited TH3
THII
Equal to TH3
LIFT Analysis of plates with
corners which are displaced
upwards
PROB
SYST
Dimension
Default
LIT
LIT
LINE
ITER
TOL
Number of iterations
Iteration tolerance
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
40
0.001
FMAX
4.00
0.25
0.60
0.40
FMIN
EMAX
EMIN
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Item
Description
Dimension
Default
PLC
FACV
NMAT
LIT
NO
STOR
Geometry update
LIT
NO
CHAM
no magnification
1.0
magnification calculation
VMAX
Nonlinear analyses are not possible with the basic version of program.
Further explanations to PROB:
LINE
linear analysis
NONL
TH2
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TH3b
THII
LIFT
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 nonlinear analysis the stiffness is
calculated for the deformed structure.
A predeformation with PLC and FACV effects the internal forces moments
only for PROB THII, see Chapter 2: Nonlinear Analyses and Chapter 5:
example Buckling Shapes in Supercritical Region. The application of a non
stressed predeformation is explained in the school example ase9.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).
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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 nonlinear 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 secondorder
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 iterations 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
nonlinear calculations according to the firstorder 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
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
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SYST PLC 101 FACV 1 VMAX 0.5 defines the primary load case 101 with
a maximum imperfection uX 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.
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 secondorder
and thirdorder 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 90019009.
$ 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
LOAD ...
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.dat
GeometryUpdate
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
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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/SOFIMSHB. 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
update. 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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3.5.
SYST GRP
Item
Description
N
DT
INT
ALF
DEL
THE
LCST
SELE
STEP
Dimension
Default
/LIT
1/4
1/2
1.
*
*
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=
=
=
=
=
=
=
=
=
displacements
support reactions
velocities
accelerations
beam internal forces and moments
local beam deformations
spring results
truss+cable+boundary results
QUAD results
QUAD results in nodes
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STEP 1 LCST ... SELE +1024
STEP 1 LCST ... SELE +2048
STEP 1 LCST ... SELE +4096
STEP 1 LCST ... SELE +8192
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3.6.
Item
Description
STEP
FAK1
FAKE
DFAK
PRO
ULTI
Dimension
Default
9999
1
2
DL
LIT
YES
PRIM
LIT
YES
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 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 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. Either the dead weight is increased or it keeps the old factor depending on the input for DL.
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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 + DFAKPRO and
so on.
The default values FAK1=1, DFAK=1 and PRO=2 result in the following load
steps:
Load case
Load case
Load case
Load case
Load case
1
2
3
4
5
Factor
Factor
Factor
Factor
Factor
1.00
2.00
4.00
8.00
16.00
1
2
3
4
5
Factor
Factor
Factor
Factor
Factor
1.00
2.00
3.00
4.00
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 may be eliminated. The user has to convince himself of the accuracy of
the final solution because also nonconvergent results may be saved!
The limit load iteration ends, if FAKE or the maximum number STEP are reached.
If a new stable primary load case is used, the program generates always the
new tangential geometry stiffness matrix.
Nonlinear analyses are not possible with the basic program version.
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3.7.
ULTI
Item
Description
LC
TO
PLOT
Dimension
Default
NNO
Node number
DIRE
Direction
TYPE
Plot type
FACT loaddisplacement plot
TIME displacement plot on time axis
LCNO displacement plot on load case
number
LIT4
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 dircetions can be input for DIRE:
X,Y,Z
PHIX,PHIY,PHIZ
global directions
rotation directions
VX,VY,VZ,
VPHX,VPHY,VPHZ
nodal velocities
AX,AY,AZ
APHX,APHY,APHZ
nodal accelerations
PX,PY,PZ
MX,MY,MZ
support reactions
The definition for PLOT can be done also in a separate ASE input, e.g.
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PORG ASE
HEAD
PLOT 101 NNO 200 DIRE Y
END
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3.8.
Item
Description
NCRE
CREP
Dimension
Default
RO
T
RH
TEMP
days
%
degrees
0.0
40
20
BEAM
Control for takeover 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
Calculation in ASE
ASE
Additional inputs are necessary in the record GRP ... PHI EPS RELZ PHIF:
PHI
EPS
RELZ
PHIF
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at plates. At the cracked tensile side shrinkage acts only on the cracked
width. The creep and shrinkage values affect all materials and elements,
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
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. 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 d/(1 + ROd))
ZKF = Z( 1 df/(1 + ROd))
(shrinkage)
with d=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 (1relz), in all further
creep steps with the factor 1.0.
At shrinkage the partial shrinkage coefficient which was reduced according
to Trost is used: loadstrain = dZKF = 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
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small way or more creep steps have to be input. For a prestress from the program GEOS only RO=0 is possible generally in order to avoid an unintentional reduction of 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 d=0.2 the importance of RO comes in the
background.
Creep and shrinkage are effective for all elements from the type BEAM,
TRUS, CABL, QUAD + BRIC. BOUN + pile elements are not incorporated!
PHIF acts only on spring and QUAD foundations. Thereby the QUAD foundation can get another creep coefficient (settlement) independently of the
QUAD element. RELZ acts only on tendons of the plate prestress.
The program extension ASE1 is necessary for creep calculations.
Creep and shrinkage for time input
If nothing is input for GRP...PHI + EPS, the creep functions are calculated
according to the time duration of the creep step from:
CREP T RH TEMP BEAM
T, RH and TEMP correspond to the record EIGE in program AQB. With
CREP BEAM 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!
If a time duration T and GRP...PHI+EPS values are input, at first the creep
increments are determined described as above, but they are scaled then to the
input final creep value PHI. Without an input for the time duration T the
creep increment which is only necessary in this ASE calculation is to be defined.
No record CREP is necessary, if only beams are used and all creep curvatures
are taken over from AQB. Then only the load case of the creep curvatures
from AQB is to be used.
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3.9.
Item
Description
NO
Group number
default ALL = all groups
VAL
Selection
OLD
Only damping values are
changed.
OFF
The group is not used.
YES
The group is used.
FULL Use of group + result output
LIN
YES, but material linear
LINE FULL, but material linear
(TH2, TH3 not affected)
FACS
GRP
Dimension
Default
ALL
LIT
FULL
PLC
GAM
H
K
SIGN
SIGH
Parameter of an additional
analytical primary state
kN/m
m
kN/m
kN/m
0
0
1
0
0
1
0
FACL
FACL
FACD
FACP
(FACT
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Description
Dimension
Default
HW
GAMA
m
kN/m
999.
10
RADA
1/sec
0.
sec
0.
MODD
CS
PREX
PREY
kN,m
kN,m
0
0
RADB
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Item
Description
Dimension
Default
PHI
EPS
RELZ
0
0
0
PHIF
T1
days
HING
ACTI
FACB
FACS
PHIS
CSDL
MNO
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.
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/SOFIMSHB manual
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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 groups are selected, the stiffness matrix must be reconstructed again. If,
however, only new damping values should be determined with already calculated eigenvalues, the literal OLD has to be input for VAL .
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
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With GRP ... PREX PREY a real prestress can be defined in addition
to TRUSCABLSPRI 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 thirdorder theory. A membrane high 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/SOFIMSHB for the GRP prestress:
PRE acts in all load cases as long as a primary load case
(PLC) is not used.
GRPPREX acts only in ASE calculations in which it is input, how
ever, 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 EPSPHIS/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
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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
Temporary BEAM pinjoints can be fixed with GRP HING FIX. Thus a construction stage can be calculated with pinjoint and a final stage without pin
joint. The results can be superpositioned and designed. All pinjoints are active with the default GRP HING ACTI.
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).
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3.10.
GRP TEMP
Item
Description
NO
STEA
GRP2
Dimension
Default
Group number
Orthotropic slabs:
reduction of the QUAD axial force
stiffness only in local x
Orthotropic slabs:
reduction of the QUAD axial force
stiffness only in local y
ALP0
Lower threshold for stiffness development for BRIC elements HYDRA temperature field
0.001
ULUS
QEMX
EXPO
Exponent for the elastic modulus according to Braunschweiger Stoffmodell" separated according to groups
1/2
GEOM
Groupwise control of the geometric stiffness from primary load case for buckling
eigenvalues
QUEA
QUEX
QUEY
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STEA With STEA the normal force stiffness component of beams can be
increased. The bending stiffness remains unchangeable.
QUEA With QUEA the EA part of the QUAD elements can be modified.
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
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cables
1 dont use geometric stiffness at all (also in static analysis
and natural frequencies)
dont 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
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See also:
3.11.
Item
Description
XM
HIGH
Dimension
Default
m/LIT
m/
m
*
0
0
0
1
kN/m
YM
ZM
NX
NY
NZ
PR1
PTPR
NOG
shows:
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See also:
3.12.
Item
Description
FROM
TO
INC
REDP
REDA
REDT
PSEL
Dimension
Default
1
FROM
1
1.0
1.0
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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Item
Description
NC
b
TBEA
Dimension
Default
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3.14.
Item
Description
NO
Material number
E
MUE
G
K
GAM
GAMA
ALFA
EY
MXY
OAL
MAT
Dimension
Default
Elastic modulus
Poissons ratio (between 0 and 0.49)
Shear modulus
Bulk modulus
Specific weight
Specific weight under buoyancy
Thermal expansion coefficient
kN/m2
kN/m2
kN/m2
kN/m3
kN/m3
1/K
*
0.2
*
*
25
*
E5
kN/m2
deg
E
MUE
0
deg
SPM
1.0
TITL
Material name
Lit32
OAF
Materials which can be used for SVAL or QUAD and BRIC elements may be
defined with the record MAT and MATE. The number of the material must
not be used for other materials.
The differences between the two records are mainly the used dimensions.
MATE is analogue to CONC,STEE etc. (MPa) and has additional strength values, while MAT uses (kN/m2) analogue to NMAT. MAT has older item names
for the orthotropic parameters.
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3.15.
Item
Description
NO
TYPE
Material number
Kind of material law
LINE Linear material
MISE Mise / Drucker Prager law
VMIS von Mise law, optional
viscoplastic extension
DRUC DruckerPrager law, optional
viscoplastic extension
MOHR Mohr Coulomb law
GRAN Granular hardening
SWEL Swelling
FAUL Faults in rock material
ROCK Rock material
GUDE Gudehus law
LADE Lade law
DUNC DuncanChang law
HYPO Schad law
MEMB Textile membrane
USP1 to USP8 and USD1 to USD8
reserved for user defined material
models
P1
P2
P3
P4
...
P12
NMAT
Dimension
Default
LIT
1
!
*
*
*
*
The types of the implemented material laws and the meaning of their parameters can be found in the following pages.
In a linear analysis the yield function for the nonlinear material is merely
evaluated and output. This enables an estimation of the nonlinear regions
for a subsequent nonlinear analysis.
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I1
3
s y + s y *
I1
3
s z + s z *
I1
3
J2 + 1 (s x2 ) s y 2 ) s z 2) ) t xy 2 ) t yz 2 ) t xz 2
2
J3 + s xs ys z ) 2t xyt yzt xz * s xt yz 2 * s yt xz 2 * s zt xy 2
3 3 J 3
q + 1 sin *1*
3
3
2J22
362
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6
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Characteristic values:
DIN 1054100 Appendix A gives characteristic values for soils as follows:
Soil type
Designation Density
DIN 18196
Weight
wet
Weight
buoan.
[kN/m 3]
[kN/m 3]
cal
SE as well
as SU with
U<6
loose
mid.dense
dense
17.0
18.0
19.0
9.0
10.0
11.0
30.0
32.5
35.0
GE
loose
mid.dense
dense
17.0
18.0
19.0
9.0
10.0
11.0
32.0
36.0
40.0
18.0
19.0
20.0
18.0
20.0
22.0
10.0
11.0
12.0
10.0
12.0
14.0
30.0
34.0
38.0
30.0
34.0
38.0
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Soil type
Weight cal
ck
cuk
[kN/m 2] [kN/m 2]
18.0
19.0
20.0
*
*
*
*
*
*
*
*
*
19.0
19.5
20.5
20
20
20
0
5
10
5
25
60
20.0
20.5
21.0
27
27
27
0
5
10
5
25
60
14.0
17.0
11.0
5
15
5
13.0
20
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e p,dev +
23 e
.
p,xx
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p1
v0
3
Application range:
Metals and other materials without friction
Parameters:
P1
P2
P3
P4
P5
=
=
=
=
=
Comparison stress
Friction parameter
Hardening module
Tensile strength z
Compressive strength (cap) c
[kN/m2]
[]
[kN/m2]
[kN/m2]
[kN/m2]
Several substitutes for P1 and P2 can be used for the calculation of common
parameters in soil mechanics. Commonly used e.g. is the compression cone:
P1 +
6c cos
3 * sin
P2 +
2 sin
3 (3 * sin )
The values for the internal cone are better suited for plane strain conditions:
P1 +
6c cos
3 ) sin
P2 +
2 sin
3 (3 ) sin )
P1 + 2 @
f c @ f t
f c ) f t
f * f t
P2 + 1 @ c
3 f c ) f t
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Reference:
M.A.Chrisfield
Nonlinear Finite Element Analysis of Solids and Structures. Vol. I.
Essentials. Chapter 14. Wiley & Sons (1991)
M.A.Chrisfield
Nonlinear Finite Element Analysis of Solids and Structures. Advanced Topics. Vol. II. Chapter 6. Wiley & Sons (1997)
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Unit
Default
P1 Yield stress
[kN/m2]
[kN/m2]
0.0
[]
[]
1.0
[kNs/m2]
0.0
dt
g s,
dt
+ l@
s
Ff s, g s,
@
dt
+
h
s
t
. vp
Dvp +
t0
t0
t0
In case of an associative flowrule (e.g. von Mise material) the plastic potential g equals the yield function. The overstress function F reads
m
f(s, ) , f w 0
F +
, f t 0
0
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2 sin
6c cos
@ I 1 ) J 2 *
v0
3 3 " sin
3 3 " sin
g +
2 sinn
@ I ) J 2
3 3 " sin n 1
This formulation describes a cone in principal stress space that either embraces the MOHR yield surface ( sign) or is inlying and tangent to it (+ sign).
For description of the materials viscoplastic extension see NMAT VMIS.
Application range:
Soil and rock with friction and cohesion. Modelling of timedependent
effects (consolidation, short term strength...)
Parameters:
Description
Unit
Default
P1 Friction angle
(< 0 inner cone, > 0 outer cone)
P2 Cohesion c
[]
0.0
[kN/m2]
0.0
P3 Tensile strength t
[kN/m2]
0.0
[]
0.0
[kN/m2]
[0/00]
0.0
[]
P1
[kN/m2]
P2
[]
[]
1.0
[kNs/m2]
0.0
P4 Dilatancy angle
P5 Cap parameter (compressive strength) c
(at the time, not used)
P6 Plastic ultimate strain u
P7 Ultimate friction angle u
P8 Ultimate cohesion cu
P10 Type of creep law (overstress function)
(0=no viscous effects, pure elasto
plastic)
P11 Creep parameter, exponent m >= 1.0
P12 Viskosity >= 0.0
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Reference:
M.A.Chrisfield
Nonlinear Finite Element Analysis of Solids and Structures. Advanced Topics. Vol. II. Chapter 14. Wiley & Sons (1997)
O.C.Zienkiewicz,G.N.Pande
Some Useful Forms of Isotropic Yield Surfaces for Soil and Rock
Mechanics. Chapter 5 in Finite Elements in Geomechanics
(G.Gudehus ed.) Wiley & Sons (1977)
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sin q sin
) * c cos v 0
3
Unit
Default
[]
0.0
P2 Cohesion c
[kN/m2]
0.0
P3 Tensile strength t
[kN/m2]
0.0
[]
0.0
[kN/m2]
[0/00]
0.0
[]
P1
[kN/m2]
P2
[]
[]
1.0
[kNs/m2]
0.0
P1 Friction angle
P4 Dilatancy angle
P5 obsolete
P8 Ultimate cohesion cu
P10 Type of creep law (overstress function)
(0=no viscous effects, pure elasto
plastic)
P11 Creep parameter, exponent m >= 1.0
P12 Viskosity >= 0.0
Special comments:
The following expressions are better suited for checking the yield criterion:
f + sI *
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2c cos
@ s III *
1 ) sin
1 ) sin
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Unit
Default
[]
0.0
P2 Cohesion c
[kN/m2]
0.0
P3 Tensile strength ft
[kN/m2]
0.0
[]
0.0
[kN/m2]
[]
1sin
[kN/m2]
[]
0.7
[]
0.9
[kN/m2]
100.0
P1 Friction angle
P4 Dilatancy angle
P5 Stiffness modulus Es,ref (GRANextended)
P6 lateral earth pressure coefficient k0
(GRANextended)
P9 Modulus for primary loading E50,ref
The extended version of the GRANmodel (twosurface model, double hardening) is activated by specification of the oedometric stiffness modulus Es,ref
(P5) only in this case the lateral earth pressure coefficient k0 (P6) takes effect. In case no input of Es,ref is provided, the basis version of the GRAN material model (singlesurface model, single hardening) is adopted.
The hardening rule is based on the hyperbolic stressstrain relationship proposed by KONDNER/ZELASKO, which was derived from triaxial testing.
Hardening is limited by the materials strength, represented by the classic
MOHR/COULOMB failure criterion. Additionally, the model accounts for the
stress dependent stiffness according to equations (46). A further essential
feature is the models ability to capture the loading state and can therefore
automatically account for the different stiffness in primary loading and un/
reloading paths.
In the subsequent notation, compression and contraction are defined as negative; for the principal stresses the relation s 1 w s 2 w s 3 holds. Accordingly,
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for the triaxial state index 3 denotes the axial and index 1 the lateral direction.
Summary of essential features:
deviatoric hardening based on the hyperbolic stressstrain relationship according to KONDNDER/ZELASKO
=> plastic straining prior to reaching shear strength
parameter:
E50,ref; Rf
; c
m; pref
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s
k 0 + slateral, e.g. according to Jaky as k 0 + 1 * sin
axial
parameter:
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q + s1 * s3 +
* 3
b * a @ 3
(1)
where
1 +E ] 2@E
i
50
b
q
1 + qa + f
a
Rf
(2)
(3)
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p
@
sin
)
c
@
cos
ref
(4)
p
@
sin
)
c
@
cos
ref
(5)
p
@
sin
)
c
@
cos
ref
(6)
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(7)
sin y m +
sin m * sin cs
1 * sin m sin cs
(8)
(since TALPA v23.36 / ASE v14.57). Therein, the critical state friction angle
cs marks the transition between contractive (small stress ratios with
m t cs) and dilatant (higher stress ratios with m u cs) plastic flow.
The mobilized friction angle m in equation (8) is computed according to
sin m +
s 1 * s 3
2c cot * s 1 * s 3
(9)
At failure, when m 5 , also the dilatancy angle reaches its final value
y m 5 y. Accordingly, from equation (8) the critical state friction angle can
be derived as
sin cs +
sin * sin y
1 * sin sin y
(10)
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p ref + 100kPa
m ] 0.4AAA 0.7
R f ] 0.7AAA 0.9
E 50,ref [ Es,ref
E ur,ref ] 3 @ E 50,ref
Reference:
Kondner, R.L.: Zelasko, J.S. (1963): A hyperbolic stress strain
relation for sands, Proc. 2nd Pan. Am. ICOSFE Brazil 1, 289394
Schanz, T. (1998): Zur Modellierung des mechanischen Verhaltens
von Reibungsmaterialien, Habilitationsschrift, Institut fr
Geotechnik der Universitt Stuttgart
Duncan, J.M.: Chang, C.Y. (1970): Nonlinear analysis of stress and
strain in soil, J. Soil Mech. Found. Div. ASCE 96, 16291653
Desai, C.S.: Christian, J.T. (1973): Numerical Methods in
Geotechnical Engineering, Chapter 2, McGrawHill Book Company
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0s i t s 0i
log s i s v s v * p
q
i
0i
2
iR + * p1 @ 10 s 0i
log 10 s c * p 2 t s i
s 0i
i + 1..3
si =
s 0i =
Parameters:
Description
Unit
Default
P1 Swelling modulus Kq
[o/oo]
3.3
[kN/m2]
10.0
[kN/m2]
2000.0
[h]
0.0
Special comments:
Swelling of soils is a complex phemomena that is influenced by various factors. There are two swelling mechanisms of practical importance that can be
distinguished for both processes the presence of (pore) water is a common
prerequisite. The first mechanism is termed as the osmotic swelling" of clay
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course of construction work are only due to unloading related to the new primary state for swelling" s 0 :
D q + q * q
iR
i,tot
i,hist
s
+ * p1 @ log s i
0,hist
* * p @ logss
1
0i
0,hist
s
+ * p1 @ log s i
0i
qRs * q
+
h
.q
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W.Wittke
Grundlagen fr die Bemessung und Ausfhrung von Tunnels in
quellendem Gebirge und ihre Anwendung beim Bau der
Wendeschleife der SBahn Stuttgart.
Verffentlichungen des Institutes fr Grundbau, Bodenmechanik,
Felsmechanik und Verkehrswasserbau der RWTHAachen 1978
W.Wittke, P.Rissler
Bemessung der Auskleidung von Hohlrumen in quellendem
Gebirge nach der Finite Element Methode.
Verffentlichungen des Institutes fr Grundbau, Bodenmechanik,
Felsmechanik und Verkehrswasserbau der RWTHAachen 1976,
Heft 2, 746
Nichtlineare Stoffgleichungen fr Bden und ihre Verwendung bei
der numerischen Analyse von Grundbauaufgaben. Mitteilungen
Heft 10 des BaugrundInstituts Stuttgart (1979)
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Unit
Default
[]
0.0
P2 Crevice cohesion c
[kN/m2]
0.0
[kN/m2]
0.0
[]
0.0
[]
(*)
[]
(*)
[kNm/m2]
0.0
This material law may be specified up to three times in addition to any other
nonlinear material law, allowing the consideration of different multiple
fault directions.
Specification of meridian angle OAL and descent angle OAF follows the instructions given in the descriptions for input records MAT /MATE. For planar systems the value OAL directly defines the slope of the stratification, i.e.
the angle between the local x direction and the global X direction. Input for
OAF is not evaluated for the plane case.
For P9>0 a scalar damage model with exponential softening of the tensile
strength is applied. The softening obeys
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ft + f tu @ exp* w @
ASE
f tu
G f
where w denotes the crack opening. In this context, the tensile fracture energy G f represents an objective material parameter. In order to minimize discretization dependent spurious side effects, a characteristic element size is
incorporated into the softening formulation. This requires, however, a sufficiently fine finite element discretization in the corresponding system domains.
In case of P9=0 a tension cutoff with respect to ftu without consideration of
softening is executed.
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(Kluftflche/Fault)
(Felsmaterial/Rock)
Application range:
Plane strain conditions and anisotropic material
Parameters:
P1
P2
P3
P4
P5
=
=
=
=
=
P6
P7
P8
P9
=
=
=
=
Default values:
[degrees]
c [kN/m2]
z [kN/m2]
[degrees]
[degrees]
(0.)
(0.)
(0.)
(0.)
(*)
[degrees]
c [kN/m2]
z [kN/m2]
[degrees]
(0.)
(0.)
(0.)
(0.)
Special comments:
This law ignores the effect of the third principal stress acting perpendicularly
to the model. One can, however, specify the strength of the rock as well as the
strength of the sliding surfaces, which are defined by the angle P5 (default
value is that of an anisotropic material). The flow rule of the shear failure is
nonassociated if P4 is different from P1.
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3 3 @ J3
q + 1 g ) 1 @ J 2 * g * 1 @
2 @ J2
2g
c5 = (12c2cos2)/A ; A = (3sin )2
c6 = (24c cos sin)/A
c7 = (12 sin2)/A
c8 = (24c cos sin)/B ;
B = (3sin )(3sin)
c9 = (12 sinsin)/B
Application range: soil and rock with friction and cohesion
Parameters:
P1
P2
P3
P4
P5
P6
P7
P8
=
=
=
=
=
=
=
=
Default values:
friction angle
cohesion
tensile strength
dilatatancy angle
compressive strength (cap)
plastic ultimate strain
ultimate friction angle
ultimate cohesion
[degrees]
c [kN/m2]
z [kN/m2]
[degrees]
c [kN/m2]
u [o/oo]
u [grad]
cu [kN/m2]
(0.)
(0.)
(0.)
(0.)
()
(0.)
(P1)
(P2)
Special comments:
This law is capable of describing a multitude of plane or curved yield surfaces.
For =1 a circle in the deviatoric plane is obtained. The dilatation angle is
usually set either to zero or equal to the friction angle.
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Reference:
W.Wunderlich, H.Cramer, H.K.Kutter, W.Rahn
Finite Element Modelle fr die Beschreibung von Fels Mitteilung
8110 des Instituts fr konstr.Ingenieurbau der Ruhr Universitt
Bochum, 1981
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*27 ) p1 @
3
g + I1 *27 ) p4 @
f + I1
@ I v 0
m
p
a
I1
@ I
p
a
I1
with
pa = 103.32 kN/m2 = atmospheric air pressure
I1 + * s 1 * P 3 * s 2 * P 3 * s 3 * P 3
I3 + * s 1 * P 3 @ s 2 * P 3 @ s 3 * P 3
Application range: all materials with friction including rock and concrete
Parameters:
P1
P2
P3
P4
P5
P6
P7
P8
=
=
=
=
=
=
=
=
Default values:
Parameter ""
Exponent "m"
Uniaxial tensile strength
Parameter "" for flow rule
Compressive strength (cap)
Plastic ultimate strain
Ultimate Parameter ""
Ultimate Exponent "m"
[kN/m2]
c [kN/m2]
u [o/oo]
()
()
(0.)
()
()
(0.)
(P1)
(P2)
Special comments:
Material LADE has shown very good compliance between analytical and experimental results. In practice therefore, the parameters can be taken from
experiments on the materials strength. The law at hand can also describe
concrete or ceramics. A simple comparison with the material parameters of
the MohrCoulomb law can be made only if the invariant I1 is known.
Due to the nonphysical parameters the calibration of the LADE yield function might not seem straight forward at first sight. For this reason, the basic
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I31
I1
P 1 + * 27@p
I3
a
I3 + s I @ s II @ s III
Where ft+ P 3 and fc are the magnitudes of the uniaxial tensile and compressive strength, respectively, I1 and I3 the required invariants for this
stress state. Substituing into the rewritten yield function yields the yet unknown parameter P1.
The following table contains exemplary parameters for selected concrete
types, derived from the procedure described above (classification according
to EC2, Ultimate Limit State).
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Strength
class
C20/25
C30/37
C40/50
C50/60
fcd
[kN/m2]
13333
20000
26667
33333
P3 (fctk;0.05)
[kN/m2]
1500
2000
2500
2900
P2
[]
1.0
P1
[]
24669.11
1.5
324095.87
1.0
43466.02
1.5
689515.99
1.0
63426.77
1.5
1153410.57
1.0
88162.15
1.5
1778218.62
Reference:
P.V.Lade
Failure Criterion for Frictional Materials in Mechanics of
Engineering Materials, Chap 20 (C.s.Desai,R.H.Gallagher ed.)
Wiley & Sons (1984)
394
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maxp3 * s I, 0
p7 @ 1 * sinp1 @ s I * s III
Et +1 *
@ p 4 @
pa
2 @ p2 @ cosp1 * 2 @ s I @ sinp 1
maxp3 * s I, 0
Et + p 5 @
pa
=
=
=
=
P5 =
P6 =
P7 =
Friction angle
Cohesion
Tensile strength
Reference elastic modulus
during loading
Reference elastic modulus
during unloading
Exponent (w 0)
Calibration factor (w 0)
Default values:
[degrees]
c [kN/m2]
z [kN/m2]
[kN/m2]
(0.)
(0.)
(0.)
()
[kN/m2]
()
[]
[]
()
()
Special comments:
The model distinguishes between primary loading, unloading and reloading
different moduli for loading and un/reloading can be specified.
Loading is defined as an increase of the stress level S:
1 * sinp1 @ s I * s III
S +
2 @ p @ cosp * 2 @ s @ sinp
I
2
1
1
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The initial state should be calculated linearly in doing so, parameters defining the loading history are initialized and the resulting stress state is interpreted as loading".
After having passed a deviatoric stress minimum in case of unloading, a primary loading branch is traced again, thus the simulation of cyclic loading behaviour is possible.
The original law according to DUNCAN/CHANG has been modified in order
to allow for a better simulation of the plastic flow in soil materials. Poissons
ratio is not kept constant but is defined as a function of the tangential modulus of elasticity and the bulk modulus. The bulk modulus is kept constant in
this case.
With P6=P7=0 one can define a law having a constant elastic modulus for
loading and unloading respectively.
In order to avoid numerical difficulties, the elastic modulus in the MAT record
should not be chosen smaller than the initial elastic modulus.
Anisotropic materials are not possible with this model.
Reference:
J.M.Duncan, C.Y.Chang
Nonlinear Analysis of Stress and Strains in Soils
J.Soil.Mech.Found.Div. ASCE Vol 96 SM 5 (1970) ,16291653
C.S.Desai, J.T.Christian
Numerical Methods in Geotechnical Engineering, 8188
McGrawHill Book Company
396
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=
=
=
=
=
=
=
=
=
Default values:
[kN/m2]
[kN/m2]
[kN/m2]
[kN/m2]
[]
[]
[]
[]
[kN/m2]
()
()
()
()
()
()
()
()
(0)
Special comments:
According to MohrCoulomb, this law must have a vanishing shear modulus
at failure, thus the following expressions are obtained:
p2 = p6 2 c cos
p5 = p6 sin
Anisotropic Material constants are not possible with this model.
Version 14.66
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Reference:
H.Schad
Nichtlineare Stoffgleichungen fr Bden und ihre Verwendung bei
der numerischen Analyse von Grundbauaufgaben. Mitteilungen
Heft 10 des BaugrundInstituts Stuttgart (1979)
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P2
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Dim
Type
Description
Ss
Double
SsPrim
Double
deltaSn
Double
SnIe
Double
StateV
10
Double
State variables
Mtype
ParMat
12
ElcMat
16
Double
(6,6)
Double
(6,6)
Double
Elastic compliance
Ctrl
Single
deltaTime
Double
not used
NrEl
iGP
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Return values:
Parameter
Dim
Type
Description
Ss
Double
SnIe
Double
not used
StateV
10
Double
(6,6)
Double
iNonl
iUpd
iErr
3102
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3.16.
Item
Description
NOG
NOEL
Group number
Element number
TOP
BOTO
REI2
Dimension
Default
degree
degree
HT
DHT
HB
DHB
m
m
m
m
0.06
0.01
0.06
0.01
AST
ASTT
ASB
ASBT
cm/m
cm/m
cm/m
cm/m
BST
BSTT
BSB
BSBT
cm/m
cm/m
cm/m
cm/m
AT
ATT
AB
ABT
m
m
m
m
0.010
0.010
0.010
0.010
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If NOEL is not given, the reinforcement input is valid for all QUAD elements
of the group NOG. With an input for NOEL, only for this element the inputs
are considered despite an input for NOG.
An input for BST, BSTT, BSB, BSBT limits a reinforcement read from the
program BEMESS see REIQ.
TOP, BOTO = Angle between local x axis and 1st reinforcement direction
Only symmetrical bilinear or trilinear stressstrain curves are accepted from
the program AQUA. For example BST 500/550 with trilinear stressstrain
curve in the ultimate limit state with loads multiplied by 1.75:
PROG AQUA
CONC 1 B 25 FC 17.5 QC 0.2 FCT 3.21 FCTK 1.00
STEE 2 BST 500
SSLA EPS
SIG TYPE=POL
10
550 ; 4.62 550 ; 2.38 500
2.38
500 ;
4.62
550 ; 10
550
0 0 ;
FCT is the concrete tensile strength for tensionstiffening, FCTK is the tensile strength of the bare concrete. For the checks in the ultimate limit state
FCTK should be input in a maximally small way (e.g. 0.04 N/mm2).
The input reinforcements are saved in the database (see REIQ) and can be
represented graphically with the program WinGRAF or WING for control
purposes.
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3.17.
Item
Description
LCR
REIQ
Dimension
Default
FACT
Multiplication factor
1.0
LCRS
99
With REIQ a reinforcement can be used from the program BEMESS for a
nonlinear calculation of plates and shells according to cracked condition.
LCR is the reinforcement of the design load case LCR from the program BEMESS (without an input for CTRL LCR in the program BEMESS it is the
number 1).
The compiled reinforcement considering an input for REI2 (or corresponding
dates in the data base, for example from SOFiPLUS) is saved then in the design load case LCRS.
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 not used from the program BEMESS. They are
used:
either from the database (SOFiPLUSDefinition)
or from input of the record REI2 in ASE
or as default with 6 cm.
Bar diameter: same procedure as for centre of gravity distance:
default 10 mm
Reinforcement directions:
They are:
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3.18.
GRP SYST
Item
Description
NAME
STEX
Dimension
Default
LIT24
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See also:
3.19.
OBLI Inclination
Item
Description
SX
SY
SZ
LC
FACV
VMAX
DIRE
STOR
OBLI
Dimension
Default
Inclination in X direction
Inclination in Y direction
Inclination in Z direction
0
0
0
LIT
SUM
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
ux=1/200height. The used height is the height above the node which is the
lowest one in dead weight direction (see program SOFIMSHA/SOFIMSHB
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 nonstressed one and the normally
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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.
An imperfection has here effects on the internal forces and moments of the
first and secondorder theory. Note please, that an imperfection via OBLI
does not generate local beam curvatures, however, a polylinelike continuous
beam imperfection.
For usage see example ase9.dat.
The sum of the displacement from the inclination plus additional deformation
is output with the default STOR=SUM. The inclination can be controlled then
graphically.
Only the additional deformations are output and saved as inclinations with
STOR=DIFF. However, the use of such a load case as primary load case is then
not anymore possible.
Further possibilities for the input of imperfections:
affin imperfections from scaled primary load case
imperfections from eigenvalues described in the Chapter 5
example: Buckling Shapes in Supercritical Region (file ase13.dat)
precurvature of beams for example with temperature load
deltat/h or local curvature ELLO .. TYPE KY or KZ
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3.20.
Item
Description
NOSL
NOG
NOEL
SLIP
Dimension
Default
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.
The function is only permissible for nonlinear analysis. 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.
If you have interest, please request the example slip.dat.
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3.21.
V0 LAUN
Item
Description
NO
TYPE
MOVS
Dimension
Default
Spring number
Type
1 Use of the contact nodes
3 Use of QUAD elements
FROM
TO
INC
1
FROM+1
1
L0
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 trainstructureinteraction. 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.
A spring NO is defined as moving spring. Following types are possible:
TYPE=1
TYPE=2
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/SOFIMSHB 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
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rough direction in which the spring will look for a contact. The length important for first contact will then be defined in ASE L0.
If you have interest, please request the examples moving_springs.
Example
with
moving
superstructure
on
fixed
ase.dat\deutsch\bridge\movs_incremental_launching_2.dat
3112
piers:
Version 14.66
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3.22.
MOVS
Item
Description
GRP
Group number
DX
DY
DZ
Total displacement
XM
YM
LAUN
Dimension
Default
ds/r
m
m
0
0
0
m
m
The record MOVS (moving supports) is extended here to linear analysis for
incremental launching. An input shifts the nodes of the element group GRP
with DX,DY,DZ. An input of XM and YM rotates around the centre point with
DX [rad] as arc length. Starting on a PLC primary load case, the launching
input is the new total displacement.
Example see movs_incremental_launching_principle.dat
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See also:
3.23.
Item
Description
LC
PLC
SFIX
Dimension
Default
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3.24.
Item
Description
NO
LC
Dimension
Default
FACT
1.0
DLX
DLY
DLZ
0.0
0.0
0.0
BET2
0.5
TITL
LIT24
TYPE
GAMU
GAMF
PSI0
PSI1
PSI2
PS1S
*
*
*
*
*
*
CRI1
CRI2
CRI3
Criteria I
Criteria II
Criteria III
0
0
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 of the type BOLO,
LOAD and ELLO as well as POLO, LILO and BLLO, 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.
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for the safety factor of the material needed by analysis according to Fellenius.
The criterias are set subsequently without further inputs with:
LC TYPE PROP CRI1 ... CRI2 ... CRI3 ...
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See also:
3.25.
Item
Description
NNO
PX
PY
PZ
Load in X direction
Load in Y direction
Load in Z direction
MX
MY
MZ
LOAD
Dimension
Default
kN
kN
kN
0
0
0
kNm
kNm
kNm
0
0
0
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3.26.
NL Nodal Load
Item
Description
NO
Node number
TYPE
P1
P2
P3
PF
Factor for P1 to P3
NL
Dimension
Default
LIT
kN,m
kN,m
kN,m
0
0
0
=
=
=
=
M
MX
MY
MZ
=
=
=
=
WX
WY
WZ
DX
DY
DZ
This input can be used also in order to consider a restraint displacement for
elastically supported nodes. The following case differentiation is planned for
an exemplary input NL 318 WZ=0.01:
Case 1:
Node 318 is fixed in z direction:
Node 318 has a restraint displacement of uz = 1 cm
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Case 2:
Node 318 is supported with a stiff spring with a spring stiffness
of cp=1E20 kN/m:
Node 318 has a restraint displacement of uz = 1 cm
Case 3:
Node 318 is supported elastically via a spring with the spring stiffness of e.g. cp=1E6 kN/m:
The base point of the spring is displaced by uz = 1 cm. The node
318 may get a little smaller displacement due to statically indeterminate support condition. The spring gets a tensile force corresponding to the restraint displacement. (Case 3 is processed differently than in the program STAR2!)
Case 4:
Node 318 is a free node:
Node 318 has a restraint displacement of uz = 1 cm and gets a
corresponding support reaction.
Support displacements with NL
If a primary load case is used and support displacements are input, the input
support displacement is used then as the new total displacement (no addition
to the primary displacement).
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3.27.
Item
Description
FROM
TO
INC
TYPE
PA
PE
REF
BOLO
Dimension
Default
1
FROM+1
1
LIT
PZ
kN,m
kN,m
PA
LIT
or
or
or
MX
MY
Version 14.66
PXS
PYS
PZS
3121
ASE
MZ
M
The loads PXP, PYP and PZP are loads per projected length (e.g. wind or
snow). The other loads refer always to the actual length (e.g. dead weight or
water pressure).
The input of REF is required only for PE which is unequal to PA and for a discontinuous load distribution (broken boundary).
Edge loads:
An edge defined in the program SOFIMSHA/SOFIMSHB can be loaded with
BOLO also without node input. For BOLO FROM the edge number of the program SOFIMSHA/SOFIMSHB has to be defined. The input TO must be
omitted then. A free load input with LILO is in general simpler for plane
structures.
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3.28.
LC BLLO PILO
Item
Description
FROM
TO
INC
TYPE
Load value
DPZ
ELLO
Dimension
Default
ALL
FROM
1
LIT
PZ
*,m
ETYP
Element type
BEAM Load acts only on BEAM
elements
QUAD Load acts only on QUAD
elements
BRIC Load acts only at BRIC
elements
TRUS Load acts only on TRUS
elements
CABL Load acts only on CABL
elements
LIT
QUAD
(BEAM)
PCS
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elements with another type than the default must be defined explicitly with
ETYP. Only elements which are active according to the current combination
of groups and element formulations can be loaded.
DPZ can be used to define loads which are variable with the depth (e.g. earth
or water pressure), but only for QUAD elements. In such case P describes the
pressure acting on Z = 0 and DPZ is the increase with the depth. Thus the
loading results for a point according to the formula:
P(Z) + P ) Z @ DPZ
The following load types are available:
Value
Meaning
Dimension
PX
PY
PZ
PXP
PYP
PZP
PXS
PYS
PZS
Local x loading
Local y loading
Local z loading
Global X loading
Global Yloading
Global Z loading
Global X loading
Global Y loading
Global Z loading
kN/m*
kN/m*
kN/m*
kN/m*
kN/m*
kN/m*
kN/m*
kN/m*
kN/m*
*
*
*
*
*
*
*
*
*
TEMP
DT
Temperature increase
Temperature difference
(topbottom)
Temperature increase
(rightleft)
Temperature increase
(bottomtop)
degrees
degrees
*
*
DTY
DTZ
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
degrees
degrees
m*: The dimension of the load depends on the loaded element type. At beams,
cables and trusses the dimension is kN/m, at QUAD elements kN/m, at
BRIC elements kN/m.
It is marked in this table, which load type acts on which element type
(Q=Quad, B=BRIC, S=BEAM, F=TRUS, CABL).
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The difference between PXP and PXS is that PXS is determined as a load referring to the actual element surface (e.g. dead weight) while PXP refers to
the projection of the element surface to the YZ plane (e.g. snow).
Loads DTY and DTZ are only reasonable for beams with geometrically defined cross sections.
The following additional load types are available:
Version 14.66
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Value
Meaning
Dimension
EX
EY
EZ
Strain local x
Strain local y
Strain local z
0/00
0/00
0/00
*
*
*
*
*
KX
KY
KZ
Curvature local x
Curvature local y
Curvature local z
1/km
1/km
1/km
*
*
PMX
PMY
PMXY
PVX
PVY
PNX
PNY
PNXY
PVZ
PMZ
Prestress mxx
Prestress myy
Prestress mxy
Prestress vx
Prestress vy
Prestress nx
Prestress ny
Prestress nxy
(not implemented yet)
Prestress Mz
kNm/m,kNm
kNm/m,kNm
kNm/m
kN/m
kN/m,kN
kN/m,kN
kN/m
kN/m
*
*
*
*
*
*
*
*
PRE
IMX
IMY
IMXY
IQX
IQY
INX
INY
INXY
Influence area mx
Influence area my
Influence area mxy
Influence area vx
Influence area vy
Influence area nx
Influence area ny
Influence area nxy
*
*
*
*
*
*
*
*
kNm
*
*
The prestress load types generate an appropriate stress state and the corresponding strain and curvature loads for the analysis of statically indetermi-
3126
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nate parts. The prestress of the ELLO input has no influence to the initial stiffness of the elements (see record GRP).
Unlike the program STAR2 also the BEAM element does not get any loading
due to the shortening for a statically determined support in ASE. No internal
forces and moments remain then in the beam (in the program STAR2 the
prestress remains in spite of shortening).
In the case of load type PRE prestress from the program GEOS, the prestressing forces of the GEOS tendon groups with the construction stage
number CS are are used for the defined QUAD elements. The load value P has
to be then 1.0. However, a value which is unequal to 1.0 can be input, if the
required prestressing steel area is sought in the design procedure. Nevertheless the prestressing steel areas which are multiplied by 1.0 remain saved
then in the database! A construction stage number CS must be input in the
record GRP. The example GRP ... CS 0 ; ELLO 1 9999 1 TYPE PRE P 1.0 CS
1 applies the prestressing loads of the 1st construction stage to the net cross
sections. Thus the calculated deformations cause no stresses in the prestressing steel.
With the types IMX to IQY singularities are installed in the element and a
loading is generated. With that the influences area is determined for a corresponding internal force. The load value is usually then 1.0. Only an element
is should be loaded per load case.
After output of the deformation uz of the influence area load case in isoline
representation (program WING ISOL VZ) the influence area can be evaluated easily by hand for single loads for example for a SLW. For other loads
(block load) the isoline representation supplies the areas to be loaded which
must be input then in a further ASE calculation.
Influence areas can be calculated only with the expanded version ASE1.
Version 14.66
3127
ASE
See also:
3.29.
Item
Description
NO
Pile number
TYPE
Type of loading
PX
Local x loading
PY
Local y loading
PZ
Local z loading
PXP
Global X loading
PYP
Global Y loading
PZP
Global Z loading
PXS
Global X loading
PYS
Global Y loading
PZS
Global Z loading
PA
PE
A
L
PILO
Dimension
Default
LIT
PZ
kN/m
kN/m
!
PA
m
m
0
*
The difference between PXP and PXS is that PXS is determined as a load referring to the pile length while PXP refers to the YZ plane.
Further explanations are to be taken from the PFAHL manual.
Only one load case per input block can be analysed for a nonlinear analysis.
3128
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Free Loads.
Free loads are a possibility, which is very friendly for the users to put the loads
at an arbitrary position of the structure. The loads are converted into equivalent nodal loads. Moments are not converted into forces couples, however, in
analog mode into nodal moments. All QUAD elements are examined for loading, even the ones which are without element stiffness.
All loads can be an input in absolute global coordinates or in reference to any
arbitrary node of the structure.
The problem of ambiguous loading may arise, if the user defines some elements which lie upon each other or if coupled nodes with identical coordinates exist in the system. For point and line loads the least extensive solution
is to define each load a single time only. Here the program uses the very first
found element. This is not generally possible for block loads, therefore all
found elements are loaded. In the default with PROJ=ELEM the program
uses only loaded elements, which lie in the plane of the load (storey). Besides
other inputs of PROJ the user can control the load accretion via the specification of group numbers and normal directions for the elements and the loading.
An additional FRA number which describes the ratio of the loaded area to the
defined load area is calculated and output for all loads. Any value other than
1.0 causes a warning in the output.
ECHO LOAD can be used in order to output and check the generated nodal
loads.
Version 14.66
3129
ASE
See also:
3.31.
Item
Description
NNR
POLO
Dimension
Default
Reference node
X
Y
Z
m
m
m
0.
0.
0.
TYPE
P
LIT
kN
PZP
0.
NOG
SEL
Selection of elements
ALL
no further selection
POS
only elements with local z in
the direction of global Z
NEG
only elements with local z
against the global Z direction
LIT
ALL
PROJ
LIT
ELEM
3130
Version 14.66
ASE
Meaning
Dimension
PX
PY
PZ
PXP
PYP
PZP
Local x loading
Local y loading
Local z loading
Global X loading
Global Y loading
Global Z loading
kN
kN
kN
kN
kN
kN
MX
MY
MZ
MXX
MYY
MZZ
kNm
kNm
kNm
kNm
kNm
kNm
During evaluation the program examines for all QUAD elements whether the
load lies inside the elements plane (PROJ=ELEM). For buildings only the
storeys with the correct Z coordinate are loaded here.
Version 14.66
3131
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3132
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3.32.
Item
Description
NNR
LILO
Dimension
Default
Reference node
XA
YA
ZA
m
m
m
0.
0.
0.
DX
DY
DZ
Load dimensions
m
m
m
0.
0.
0.
TYPE
LIT
PZP
PA
PE
kN/m
kN/m
0.
PA
NOG
SEL
Selection of elements
ALL
no further selection
POS
only elements with local z in
the direction of global Z
NEG
only elements with local z
against the global Z direction
LIT
ALL
PROJ
LIT
ELEM
Version 14.66
3133
ASE
Meaning
PX
PY
PZ
PXP
PYP
PZP
PXS
PYS
PZS
Local x loading
Local y loading
Local z loading
Global X loading
Global Y loading
Global Z loading
Global X loading
Global Y loading
Global Z loading
kN/m
kN/m
kN/m
kN/m
kN/m
kN/m
kN/m
kN/m
kN/m
MX
MY
MZ
MXX
MYY
MZZ
kNm/m
kNm/m
kNm/m
kNm/m
kNm/m
kNm/m
3134
Dimension
Version 14.66
ASE
The difference between PXP and PXS is that PXS is determined as a load referring to the actual load length in element plane (e.g. dead weight) while PXP
refers to the projection of the load length to the YZ plane (e.g. snow).
The selection of loaded elements occurs with NOG, SEL and PROJ as in the
record POLO. Only the first found element is loaded.
Version 14.66
3135
ASE
See also:
3.33.
Item
Description
NNR
BLLO
Dimension
Default
Reference node
XA
YA
ZA
m
m
m
0.
0.
0.
DX
DY
DZ
m
m
m
!
!
0.
DXS
DYS
DZS
m
m
m
DX
0.
0.
DXT
DYT
DZT
m
m
m
0.
DY
0.
TYPE
LIT
PZP
P1
P2
P3
kN/m
kN/m
kN/m
0.
P1
P1
NOG
3136
Version 14.66
ASE
Description
Dimension
Default
SEL
Selection of elements
ALL
no further selection
POS
only elements with local z in
the direction of global Z
NEG
only elements with local z
against the global Z direction
LIT
ALL
PROJ
LIT
ELEM
AL
degree
BLLO describes general block loads which are applied independently of the
element mesh. The program transforms the load into nodal loads acting on
the neighbouring nodes.
The selection of loaded elements occurs NOG, SEL and PROJ as in the record
POLO. If several elements are possible, all these elements are loaded with
BLLO. The value PERC becomes then larger than 1.
The input of loads acting on the element mesh can occur effectively with
ELLO.
The load area may not have any reentrant corners. Only the values DX and
DY has to be defined for rectangular load areas. The relations DY=DYS+DYT
and DX=DXS+DXT have to be fulfilled for a parallelogram. For threedimensional load areas all three values DX, DY and DZ must be input always, even
if they are zero.
The sequence of the load values can be selected freely. However, the 2nd load
value is always valid for the load corner specified with DXS, DYS and DZS.
For different load values P1, P2 and P3 the load value at the 4th load corner
is extrapolated linearly, i.e. the load area remains plane. Thus the load value
at the 4th corner depends on the geometry of the load area.
Version 14.66
3137
ASE
Block load
The following load types are available:
3138
Version 14.66
ASE
Meaning
Dimension
PX
PY
PZ
PXP
PYP
PZP
PXS
PYS
PZS
Local x loading
Local y loading
Local z loading
Global X loading
Global Y loading
Global Z loading
Global X loading
Global Y loading
Global Z loading
kN/m
kN/m
kN/m
kN/m
kN/m
kN/m
kN/m
kN/m
kN/m
MX
MY
MZ
MXX
MYY
MZZ
kNm/m
kNm/m
kNm/m
kNm/m
kNm/m
kNm/m
The difference between PXP and PXS is that PXS is determined as a load referring to the actual element area (e.g. dead weight) while PXP refers to the
projection of the elements area to the YZ plane (e.g. snow). In the case of plane
structures (FRAM, GIRD, PLAN) the loads refer always to the elements
area.
1)
Version 14.66
3139
ASE
See also:
3.34.
Item
Description
NO
T1
T2
NOG
TEMP
Dimension
Default
sec
sec
0
T1
FACT
1.0
EMOD
LIT
YES
RELA
LIT
NO
EXPO
1/2
After a transient temperature calculation with the program HYDRA the element group NOG with the temperature differences of the time T2T1 from
the HYDRA load case NO can be loaded with this record. With that changing
3140
Version 14.66
ASE
a * a0
E + E28 @
1 * a0
EXPO
The input is done with TEMP ... EMOD YES EXPO ...
Version 14.66
3141
ASE
See also:
3.35.
Item
Description
LCNO
LAG
Dimension
Default
FACT
Load factor
1.0
TYPE
LIT
PZ
TOL
0.1
PROJ
Name of the project from which the support reactions should be used
LIT
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).
3142
Version 14.66
ASE
If a project name is input, the support loads are applied as free POLO 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 of a plate which was analysed as SYST GIRD to a higher storey of a
threedimensional structure.
Version 14.66
3143
ASE
3.36.
Item
Description
NOG
NOEL
Group number or
Number of a cable of the cablechain
P0
SIDE
BETA
MUE
SS
PEXT
Dimension
Default
kN
degree/m
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.
3144
Version 14.66
ASE
Version 14.66
3145
ASE
See also:
3.37.
Item
Description
NO
LCC
Dimension
Default
FACT
Load factor
1.0
NOG
NFRO
NTO
NINC
NFRO
1
ULTI
YES
PLC
NEW
LCC can be used to copy loads from other load cases into the current load case.
All loads of the types LOAD, NL, BOLO, ELLO, PILO, POLO, LILO, BLLO and
LAG are transferred. ELLO inputs for prestress loads from the program
GEOS 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 of the LC
record are not transferred.
3146
Version 14.66
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The load case NO may have been defined already during a previous analysis
or it may appear in the same input block for the first time. In the second case,
however, it must have been defined before the current load case. All loads can
be multiplied by a factor during copy. The loads were saved in the database
in each case without the load case factor.
Moreover, in the case of nodal loads (record LOAD, BOLO) only specific loads
can be copied purposely through the selection of a region NFRO to NTO in
steps of NINC. For loads upon elements (record ELLO) NOG can be used to
assort loads groupwisely. This is also valid for the free loads (record POLO,
LILO, BLLO).
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.
Version 14.66
3147
ASE
See also:
3.38.
Item
Description
NEIG
ETYP
EIGE
Dimension
Default
LIT
LANC
NITE
MITE
LMIN
1/sec
*
*
0
SAVE
LC
<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 are used always. All further masses (record
MASS) from the generation program and ASE are considered additionally.
Vertical slab eigenvalues can be avoided with MASS FACT.
3148
Version 14.66
ASE
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:
The eigenvalue problem can be displaced by one value. This is applied for
structures that are not supported (eigenvalue of zero as the smallest value)
as well as for the check of the numbers of eigenvalues via a Sturm sequence.
During the displacement the number of the ignored eigenvalues are recognizable in the number of the sign change in the determinant.
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 (15,2NITE)) 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.
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.
Version 14.66
3149
ASE
3150
Version 14.66
ASE
3.39.
Item
Description
NO
MASS
Dimension
Default
Node number
MX
MY
MZ
Translational mass
Translational mass
Translational mass
t
t
t
0.
MX
MX
MXX
MYY
MZZ
Rotational mass
Rotational mass
Rotational mass
tm2
tm2
tm2
0.
0.
0.
LC
PRZ
LIT
PG
SELE
Example see ase4.dat. The masses are additional to those defined in the program SOFIMSHA/SOFIMSHB. They are maintained over several input sets
until they are redefined. Please notice that only SOFIMSHA/SOFIMSHB
masses also produce dead load in a static analysis! ASE additional masses
dont 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 masses. With MASS LC 0 masses defined in a previous run can be
taken.
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.
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
Version 14.66
3151
ASE
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.
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.
The use of the record MASS is explained in the example ase4.dat "Natural
Frequencies of a Cylindrical Shell".
3152
Version 14.66
ASE
3.40.
MOVS
V0 Initial Velocity
Item
Description
NO
Node number
VX
VY
VZ
V0
Dimension
Default
m/sec
m/sec
m/sec
0
0
0
Version 14.66
3153
ASE
See also:
3.41.
Item
Description
MOD
REIN
Dimension
Default
Design mode
SECT Reinforcement in cut
BEAM Reinforcement in beam
SPAN Reinforcement in span
GLOB Reinforcement in all
effective beams
TOTL Reinforcement in all beams
LIT
SECT
RMOD
Reinforcement mode
SING Single calculation
SAVE Save as minimum reinforcem.
SUPE Superposition with minimum
reinforcement
ACCU Superposition with existing
LCR reinforcement
ACSA Comb. ACCU and SAVE
ACSU Comb. ACCU and SUPP
NEW New definition of the reinfor
cement distribution (for
special cases only)
LIT
SING
LCR
0
1.0
P6
P7
P8
P9
P10
P11
P12
*
*
*
*
*
0.20
*
TITL
LIT24
ZGRP
SFAC
3154
Version 14.66
ASE
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
SAVE
SUPE
ACCU
ACSA
ACSU
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.
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.
Version 14.66
3155
ASE
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:
3156
Version 14.66
ASE
ZGRP > 0
ZGRP < 0
If ZGRP < > 0 has been specified, the tendons are grouped into tendon groups.
The group is a whole number proportion which comes from dividing the
identification number of the tendon by ZGRP. Group 0 is specified with its
whole area, the upper group as needed. Any group higher than 4 is assigned
group 4. The group number of the tendons is independent of the group number
of the nonprestressed reinforcement.
Assume that tendons with the numbers 1, 21, 22 and 101 have been defined.
With the appropriate inputs for ZGRP, the following division is obtained:
ZGRP
ZGRP
0
10
Default
5
2
Typical
0.5 50
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.
Version 14.66
3157
ASE
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
P9 Factor for reference point of strain
1.0
P10 Factor for reference point of moments
1.0
Typical
1.0
0.21.0
3158
Version 14.66
ASE
3.42.
REIN NSTR
Item
Description
STAT
KSV
KSB
AM1
AM2
AM3
AM4
AMAX
SC1
SC2
SCS
SS1
SS2
C1
C2
S1
S2
Z1
Z2
Version 14.66
DESI
Dimension
Default
LIT
*
*
%
%
%
0
*
*
o/oo
o/oo
o/oo
*
*
*
*
*
*
*
*
o/oo
o/oo
*
*
o/oo
3159
ASE
Item
Description
Dimension
Default
SMOD
LIT
TVS
MSCD
N/mm2
N/mm2
*
*
KTAU
/LIT
TTOL
TANA
TANB
0.02
*
*
SCL
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.
3160
Version 14.66
ASE
With KSV and KSB will be controlled the material law. As the correct default
is taken from the INIfile selected with the design code NORM, it is only for
very special cases that you may enter:
EL
ELD
SL
SLD
UL
ULD
CAL
CALD
PL
PLD
The safety factors referenced above refer to the values defined with the material in AQUA. Without D" only the factors SC1 to SS2 of the DESI record
are applied, which are all preset to 1.0 however. With Option D" we have to
distinguish between two different cases:
If the values defined in DESI are < 1.0 or SC1 is not equal SC2 or the
design code has special provisions for that (ACI, SNIP), the safety factors are multiplicative. Printed stresses contain only the safety factors
of the materials.
In all other cases the given value will replace that of the material. The
additional safety factor for high strength concrete will be applied
additionally. Fibre materials (e.g. Carbon fibres) keep their safety factor.
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.
The minimum reinforcements AM1 to AM4 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
Version 14.66
3161
ASE
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 INIfile
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 stressstrain curve. The value of 2.2 is
reduced for example at the old DIN or high strength concrete automatically.
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 10451 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.
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This design operation is also suitable for nonreinforced 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
pc 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 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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See also:
3.43.
Item
Description
KMOD
NSTR
Dimension
Default
Determining stiffness
S0
State definition without
change of stiffnesses
S1
Secant stiffness from given
curvatures
SN
Secant stiffness from given
moments
K0
Plastic strains without itera
tion
K1
Plastic strains from given
curvatures
KN
Plastic strains from given
moments
T0
Tangent stiffness without
iteration
T1
Tangent stiffness from given
curvatures
TN
Tangent stiffness from given
moments
S0/S1
KSV
KSB
*
*
KMIN
KMAX
Minimum stiffness
Maximum stiffness
0.01
4.00
ALPH
FMAX
Damping factor
Acceleration factor
0.4
5.0
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Description
CRAC
CW
BB
HMIN
HMAX
CW
CHKC
CHKT
CHKS
Dimension
Default
LIT
mm/
0.2/1
0.5
mm
m
mm/
0.0
0.8
CW
/MPa
/MPa
/MPa
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Item
Description
FAT
SIGS
TANS
TANC
DUMP
Dimension
Default
LIT
N/mm2
*
0.756
0.571
Lit96
TS0
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The default values are dependant on the input to DESI according to the selected design codes (INIfiles), Without a DESI the following values are appropriate:
without crack width (Ultimate load)
with crack width (Serviceability)
KSV=KSB=CALD or SLD
KSV=KSB=SL
Very large (fully plastic) strains will be created. Internal forces should
have the same ratio as given moment and shear force, a relative bearing capacity will be printed. Clause 755 will be applied directly unless
KMIN > 0 is given explicitly.
Design plasticplastic
When iterating between STAR2 and AQB a calculation according to the
yield zone theory is allowed. A limit on the plastic moment as requested
for the plastic hinge method is not necessary.
The design check of the b/tratio has differences for the elastic region and the
fully plastic region. As an interpolation is not foreseen, AQB will use the more
restrictive formulas whenever the maximum stress is within 1 o/oo of the
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yield limit. With NSTR DEHN S0 table 15 of DIN 18800 is used, for all other
cases table 18.
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The more recent design check according to Appendix A1 is selectable via record STRE. NSTR calculates the obsoleted original form where CW is the factor for environmental conditions. The following values can be used:
Environment 1
Environment 2
Environment 3
CW = 1.0
CW = 0.75
CW = 0.50
(default)
BS 5400 / IS 456:
These design codes classify three possible crack width values (0.30, 0.20 and
0.10 mm). For the analysis we need the nominal cover Cnom of table 13 (BS
54004) resp. table 16 of IS 456 to be specified at item HMIN. The tension
stiffening effect is introduced by a stress of BB at the height of the centroid
of the reinforcement.
SNIP 2.03.01:
For the design you have to select a crack width. The calculation of the crack
width is done for the completed crack pattern according to equation 144. The
input value BB is used for an explicit parameter l, which is in general preset
by the concrete class.
EHE:
This Spanish design code is rather similar to the Eurocode (BB is factor k2).
It classifies four possible crack width values (0.40, 0.30, 0.20 and 0.10 mm).
But then then formulas for the effective height and the crack distance and the
mean strain quite different. Thus there is no dependency on the bond properties of the reinforcements. The distance of the longitudinal bars is always
taken as 15 , because we have not enough information available for more
details. Tension stiffening is treated as with EC 2.
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Selection of the optimum iteration method is difficult. The user should start
with SN for lightly loaded systems and with S1 for more heavily loaded systems, and should then shift to K1 or K0 if necessary. When there are many
similar systems, it pays to find the optimum method by experimentation.
To prevent endangering the iteration procedure, only changes of stiffness of
a certain magnitude are permitted. A value of 0.4 for ALPH means that in
each step the stiffness can decrease at most to 0.4 times its last value, or increase at most to 1/0.4 times its last value. ALPH is preset to 0.4 in STAR",
but to 0.01 in AQB itself. Independently of that, the stiffnesses remain limited to the range between KMIN and KMAX, referenced to the elastic stiffness.
With critical systems, which exceed their loading capacity in the course of the
iteration, it may be necessary to limit the maximum acceleration factor with
FMAX. A value of less than 1.0 damps the iteration procedure. A value of 0.0
turns the procedure off. The default of FMAX is 2.0 at a calculation with
NSTR KMOD SN and CTRL INTE 4.
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It might be helpful to increase the volume of print out via ECHO NSTR EXTR
in such cases.
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3.44.
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ase_dehn_pld.dat.
Cable, truss and spring elements as described in NSTR S1".
The following table lists all possible material nonlinear 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!
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Elementtype
NL effect
Beam elements
Cables + truss
material stress
strain curves
Cables
compress.failure
Springelements
gap,crac,yiel,mue
Spring elements
*3) spring stress
strain curves
Spring elements
*4) material stress
strain curves
QUAD bedding
tension cut off
material
input
AQUACONC
AQUASTEE
AQUASSLA
SPRI
AQUASARB and
SPRIMNO
AQUASSLA and
SPRI+AR
3174
= standard *2)
GRP LINE
= standard
GRP LINE
= standard
GRP LINE
= standard
GRP LINE
AQUABMATMUE
AQUACONC
AQUASTEE
AQUASSLA *8)
AQUAMAT
NMAT MEMB *10)
Volume elements
AQUAMAT...
BRIC
NMAT MOHR...
Halfspace contact HASEPLAS PMAX
friction
QUAD elements
of concrete/steel
*7)
Membrane elements
= standard *6)
GRP LINE
or CRAC=9999
GRP LINE
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*1) Important is the input of the material safety factor with NSTR...KSV:
Using NSTR always the stressstrain 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 stressstrain curve in the program AQUA). SL has to be used for calculations in the serviceability state.
Default for the material safety factors of nonlinear analyses:
With an input of a record NSTR:
default for KSV=ULD = stressstrain 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 nonlinear analysis will give the same displacements as a linear analysis (provided that nonlinear effects do not occur).
At the end of a nonlinear ASE calculation a statistics is printed with the
available nonlinear effects.
*2) Cables which are loaded in the transverse direction (e.g. by dead load)
never fail due to compression in a geometrical nonlinear 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 nonlinear spring stressstrain curve in the
program AQUA. Please refer to example ase_feder_arbeitslinie.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 nonlinear spring characteristic curve by using the material stressstrain curve
SSLA of the program AQUA.
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*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
ase_bettnl.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 nonlinearly with
the input SYST...NMAT YES .
*8) Also for shell elements, ASE uses the concrete stressstrain curve of
AQUA. The concrete tensile strength can be changed temporarily with CTRL
CONC V3 V4.
*9) Often only nonlinear springs or bedding should be taken into account in
a nonlinear analysis. Therefore the material nonlinear 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 P2=0 and ASE...SYST NMAT YES.
*11) For volume elements (BRIC) various soilmechanical material rules can
be defined in AQUA...NMAT MOHR.... Example see ase14.dat. BRIC elements which are defined with CONCRETE or STEEL are analyzed linear.
*12) Details see program HASE. Example see hase9.dat.
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3.45.
Item
Description
OPT
Version 14.66
ECHO
Dimension
Default
LIT
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Item
Description
Dimension
Default
/LIT
Output extent
OFF
No calculation / output
NO
No output
YES
Regular output
FULL Extensive output
EXTR Extreme output
07
See output description for
BRIC
Default:
ECHO LOAD
ECHO DISP,FORC,REAC,NOST,BEDD
as well as NO for NODE and MAT and YES for all other
YES
NO
FULL
NO
YES
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.
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 BDEV 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 DBVIEW, DBPRIN or WINGRAF for this.
The printout of the saved norm of the energy of the groups is done with ECHO
STAT, REAC or GRP FULL.
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With ECHO FORC OFF the calculation of eigenvalues can be done without
saving of the element internal forces and moments.
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Settings for reduction of database memory size with ECHO STOR ... (Bit pattern):
ECHO STOR 0
ECHO STOR +1
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Output Description.
4.1.
The table of nodal values is mostly identical to the table of the program SOFIMSHA/SOFIMSHB 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.
These are output with SYST NMAT=YES for nonlinear analyses with QUAD
shell elements only (concrete or steel material rule).
4.3.
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Primary state for displacements of the total system is load case ...
(SYST PLC)
4.4.
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
TMX(t) TMY(t)
Translatory masses
TMZ(t)
RMX(tm2) RMY(tm2)
Rotational masses
RMZ(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.
For nonlinear calculations the in each case maximum residual force is output with the corresponding energy norm (sum from nodal forces nodal displacements of all nodes) in the list of the iterations. The residual force is
printed firmly in the dimension kN, the energy norm in kNm, however,
multiplied by the factor 106, 103, 10 or 10 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
Iteration
Iteration
42
1 Residual
2 Residual
3 Residual
5.578 energy
2.478 energy
.000 energy
21.3532 e/f
36.3192 e/f
48.2837 e/f
.000
.000
.329
1.000
1.701
1.799
Version 14.66
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The user has to check for a nonlinear calculation whether the residual forces
are sufficiently small. In the case of calculations with nonlinear 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:
ULSiteration 1 loadcase 1 with loadfactor 1.000 was converged.
F O R C E S ITERATION
1
Node number
Unbalanced residual force
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 103, they may indicate as well the presence of possible multiple
eigenvalues which could be overlooked.
EIGENFREQUENCIES
Using Lanczos method
or
Using simultaneous vector iteration
Iteration vectors
Input with EIGE record
Iterations
Required iterations for SIMU
No.
LC
Eigenvalue (1/Sec2)
Relative error
omega (1/sec)
frequency (Hertz)
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Period (sec)
activated mass *
modal damping
4.7.
Element Results
BEAM FORCES
Beam x(m)
N, Vy, Vz, Mt, My, Mz,
Mb, Mt2
AND MOMENTS
Section identification
Internal forces and moments
AND MOMENTS
Element number
Plate moments (kN/m)
Principal moments and their angle
Plate shear forces (kN/m)
Membrane axial forces (kN/m)
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 mI or nI 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
pt(kN/m2)
Tangential foundation stress
P(kN)
Resultant perpendicular foundation
force (elements foundation force in kN)
44
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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
Element Number
IP
sigx, sigy, sigz
tauxy, tauxz, tauyz
sigI, sigII, sigIII
dx,dy,dz
3D
ELEMENTS
Element number
Integration point 0=gravity centre
Stresses in global system XYZ
Shear stresses
Principal stresses
Principal stress directions
no output
(NO)
internal forces in the centre of
gravity
(YES)
additionally principal stresses I,
II, III
(FULL)
additionally principal stress
directions
(EXTR)
internal forces in centre of gravity
and integration points
additionally principal stresses I,
II, III
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
Load case
ELNO
P (kN)
u (mm)
ELEMENTS
FORCES AND
SPRINGS
Version 14.66
Element number
Axial force
Elongation l
DISPLACEMENTS
OF
45
ASE
Load case
Number
P (kN)
Pt (kN)
M (kNm)
u (mm)
ut (mm)
phi (mrad)
FORCES
Number
N (kN)
u (mm)
ut (m)
f0 (mm)
Nm (kN)
L_NO (mm)
Element number
Axial force
Lateral force
Moment
Spring displacement, elongation
Lateral displacement
Rotation
IN
CABLE ELEMENTS
Element number
Max. cable force above
Elongation l
Cable sag perpendicularly to chord 1)
Cable sag in load direction
Cable force at midpoint
Element length after normal force
relaxation
1)
4.8.
Nonlinear Results
N O N L I N E A R
Elem. ()
z ()
sigx,sigy,tau (MPa)
sigI,sigII (MPa)
sigv (MPa)
sigvlin (MPa)
depth (mm)
fy ()
N O N L I N E A R
Elem.
Rich
46
MATERIAL STEEL
Element number
^ = top side (negz) v bottom side
Stresses at side z
Principal stresses at side z
Equivalent stress at side z
Equivalent stress calculated with
eps*Elinear
Depth of plastification
Plastification number
sigvlin/sigzul1
with sigzul = tensile strength (MPa)
MATERIAL CONCRETE
Element number
Observed direction w.r.t. x
Version 14.66
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ECHO FORC YES prints out both reinforcement directions which were input
with REI2, 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 nonlinear 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/signl1 (siglin =
concrete stress computed linearly from the strain, signl = nonlinear 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 nonlinear 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 1/3r 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.
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PX, PY, PZ
MX, MY, MZ, Mb
Constraint forces
The table of constraint forces is output only with ECHO REAC FULL.
NODAL DISPLACEMENTS
Node No
Node number
uX, uY, uZ
Displacement
phiX, phiY, phiZ
Rotation
Clockwise rotations are positive.
NODAL REACTIONS AND RESIDUAL
FORCES
Node No
Node number
PXX, PYY, PZZ
Support reaction
MXX, MYY, MZZ
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
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 nonlinear analyses the residual forces are a direct measure
of the quality of the iterative solution.
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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.
SHELL FORCES
load case
group
node
mxx, myy, mxy
mI, mII, alfa
vx, vy
nxx, nyy, nxy
nI, nII, alfa
STRESSES IN
Load case
sum
Group
Node
sigx, sigy, sigz
tauxy, tauxz, tauyz
sigI, sigII, sigIII
dx,dy,dz
IN
NODES
Element group
Node number
Plate moments (kN/m)
Principal moments and their angle
Plate shear forces (kN/m)
Membrane axial forces (kN/m)
Principal axial forces and their angle
NODES OF
3D E L E M E N T S
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.
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.
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4.11.
Error Estimates
410
ESTIMATES BRICELEMENTS
Load case
Internal force or moment
Version 14.66
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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 manuals of the programs SEPP
and TALPA.
4.12.
The following result values are output for each boundary for which a designation has been input:
DISTRIBUTED
LC
No.
nodeno
pX, pY, pZ
mn
mn
average
sum
length
sum 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.
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4.13.
For primary load cases the strain energy of the groups is printed with the
input ECHO STAT, FORC or GRP FULL:
Strain energy of groups
load case
group
Energy
=% of sum
Group number
Energy in kNm
Percentage part
4.14.
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).
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Examples
5.1.
General Information
ASE
ASE has essentially the same elements as the programs SEPP or TALPA. Except for the nonlinear and axialsymmetrical possibilities of the program
TALPA, most of the examples from the manuals SEPP and TALPA can be
analysed with ASE as well.
Particularly the basic properties of the elements are documented extensively
in both other manuals.
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5.2.
The following example of a spherical shell with uniform loading is characterized by an available theoretical solution.
Spherical Shell
The ratio of thickness to radius amounts only to 1/1000. Thus the system behaves essentially as a membrane. Serious disturbances occur at the boundaries.
An effective model is constructed practically with the symmetrical properties
of the structure. Thus it is sufficient to examine a sector of 10 degrees for instance.
A refinement at the boundary is suggested due to the disturbances.
52
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be used as boundary conditions of the nodes of the first boundary, if the edge
is one of the global coordinate axes. If the coordinate axis, however, is placed
along the bisecting line of the angle, the boundary has to be defined with polar
coordinates.
The constraints of the nodes along the boundary can be described with PRMT,
if the horizontal normal of the boundary is selected as direction of the support.
The constraint of the simply supported node, however, requires special considerations. An additional input of PZ is possible here, but it is not permitted
generally because it may contradict to the coupling condition. It is best therefore to define the moment boundary condition similarly to the other nodes and
subsequently define a constraint PT (= two directions restrained) in a 90 degrees rotated direction.
The constraints of the nodes of the second boundary can be defined either with
the same method or with symmetric conditions. In the case of a symmetric
condition each node of one boundary has to be coupled with FIX SYM at its
partner node with the same radius at the opposite boundary.
The choice between the various methods is to a certain degree a matter of
taste. Considerations relating to the local coordinate systems may affect the
decision to certain degree.
In the following input the Y axis was placed on the bisecting line of the angle:
PROG
HEAD
NORM
STEE
END
AQUA
SPHERICAL SHELL UNDER OUTSIDE PRESSURE SECTOR 10 DEG RADIAL Y
DIN 18800
1 S 235
PROG GENF
HEAD SPHERICAL SHELL UNDER OUTSIDE PRESSURE SECTOR 10 DEG RADIAL Y
HEAD REFINEMENT TOWARD BOUNDARY
SYST SPAC
NODE
1 35. 0
0 ZPMM COOR SP
( 3 13 2) 35. 85 ( 4 4) PRMT DX COS(5) SIN(5)
( 4 14 2) 35. 95 ( 4 4) PRMT DX COS(5) SIN(5)
(15 23 2) 35. 85 (25 1) PRMT DX COS(5) SIN(5)
(16 24 2) 35. 95 (25 1) PRMT DX COS(5) SIN(5)
25 35. 85
30 MT
DX COS(5) SIN(5)
25
FIX PT
DX SIN(5) COS(5)
26 35. 95
30 MT
DX COS(5) SIN(5)
26
FIX PT
DX SIN(5) COS(5)
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GRP 0 T 0.035
QUAD 1 1 3 4 ; 2 3 5 6 4 DNO 1 ENO 12 NNO 2
END
Load
val.
14.50
PXX[kN]
0.0
Dimension
Variation
dP/dX
dP/dY
dP/dZ
[kN/m2]
PYY[kN]
139.7
PZZ[kN]
385.6
Afterwards the internal forces and moments at the gravity centres of the elements and the displacements and forces at the nodes which are presented
here in an abbreviated form are printed.
Shell Forces and Moments
Loadcase
1
SPHERICAL SHELL OUTSIDE
elno.
mxx
myy
mxy
vx
vy
nxx
nyy
[kNm/m] [kNm/m] [kNm/m] [kN/m] [kN/m] [kN/m] [kN/m]
1
0.14
0.14
0.00
0.00
1.57 257.59 290.86
2
0.02
0.15
0.00
0.00
0.33 241.19 264.04
3
0.01
0.05
0.00
0.00
0.08 243.97 254.55
4
0.02
0.05
0.00
0.00
0.01 256.47 253.31
5
0.06
0.18
0.00
0.00
0.19 242.65 253.31
6
0.21
0.63
0.00
0.00
0.79 241.49 250.48
7
0.53
1.48
0.00
0.00
0.03 379.43 251.94
8
0.12
0.04
0.00
0.00
4.61 669.94 261.64
9
1.66
5.67
0.00
0.00 14.15 887.75 280.31
10
5.33
16.88
0.00
0.00 23.21 480.75 296.45
11
9.09
27.45
0.00
0.00 13.08 1489.84 276.04
12
6.05
15.34
0.00
0.00
50.34 5633.58 163.44
54
nxy
[kN/m]
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
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phiY
[mrad]
0.000
0.029
0.029
0.011
phiZ
[mrad]
0.000
0.000
0.000
0.000
14.138
34.236
34.236
45.231
45.231
1.237
2.995
2.995
3.957
3.957
0.000
0.000
0.000
0.000
0.000
MX
[kNm]
0.44
MY
[kNm]
0.00
0.16
0.16
0.02
MZ
[kNm]
0.00
0.01
0.01
0.00
4.89
3.57
3.57
0.15
0.15
2.61
1.95
1.95
0.09
0.09
. . .
22
23
24
25
26
0.010
0.612
0.612
1.710
1.710
0.118
6.996
6.996
19.548
19.548
35.153
22.408
22.408
0.000
0.000
198.4
2050.7
2050.7
1975.5
1975.5
17.4
179.4
179.4
172.8
172.8
192.8
192.8
PXX[kN]
0.0
0.0
Version 14.66
PYY[kN]
139.7
139.7
group
vy
[kN/m]
1.57
0.95
0.95
0.20
PZZ[kN]
385.6
385.6
0
nxx
[kN/m]
257.59
252.65
252.65
235.72
nyy
[kN/m]
290.86
277.45
277.45
259.30
nxy
[kN/m]
0.00
0.00
0.00
0.00
55
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22
23
24
25
26
7.59
10.54
10.54
1.72
1.72
23.68
31.08
31.08
0.09
0.09
0.58
0.53
0.53
0.35
0.35
0.00
0.00
0.00
0.00
0.00
18.14
31.71
31.71
50.34
50.34
21.11
2998.50
2998.50
8219.55
8219.55
286.25
219.74
219.74
163.44
163.44
0.00
0.00
0.00
0.00
0.00
The values are in excellent agreement with those of the theoretical solution
as indicated in the following table. A uniformly partitioned element mesh
with 8 elements and a mesh with regular elements without nonconforming
formulation were examined for comparison too.
Value
theoret.
solution
myy
mxx
30.3
10.6
31.1
10.7
11.6
4.1
23.5
7.9
8.2
3.3
nxx ()
nxx (+)
nyy
813
271
937
8220
288
360
5706
356
560
7576
261
693
5230
536
vy ()
vy (+)
22
19
+50
9
+26
12
+19
9
+13
56
refined mesh
QART 1
QART 0
uniform mesh
QART 1
QART 0
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Tbeam.
Beams which are available in the building construction are calculated in general without consideration of normal forces in the plate therefore without
eccentrically connected beams with equivalent Tbeams.
If nevertheless this problem should be analysed more exactly, the system of
the Tbeam can be described as a plate and an eccentric underhanging beam
with the area of web. The nodes of the beam have to be coupled with KF at
those of the plate. An error concerning the shear transmission is made with
this formulation, so that the normal subdivision of the span into some elements is necessary even in the case of pure beam structures.
For plate structures with crossing girders and in general for Tbeams with
slim webs an analysis with eccentrically connected QUAD shell elements is
in practice significantly easier in the input and more practical for the result
evaluation. The example presented here illustrates only a comparative
analysis with eccentrically connected beam.
System beamplate
A simply supported singlespan girder with a large span is described in order
to show the differences between a pure Tbeam and a mixed plate girder
structure.
A distinction is made subsequently between a beam structure (a continuous
beam with Tbeam cross section SVAL 1) and a FEBEAM structure
(QUAD elements as a top plate and an eccentrically placed continuous beam
with web cross section SREC 2).
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Tbeam
The structure with uniform load is input as follows:
PROG AQUA
HEAD SINGLE SPAN TBEAM
NORM DIN 10451
CONC 1 C 30
$ C 30 =
C30/37 !
STEE 2 BST 500SA titl bar reinforcement
STEE 3 BST 500MA titl mesh reinforcement
$ TBEAM B/D/BO/DO = 30/100/150/20
SREC 1 B 0.30 H 1.00 HO 0.20 BO 1.50 MNO 1
SREC 2 B 0.30 H 0.80 MNO 1
END
PROG GENF
HEAD SINGLE SPAN TBEAM
SYST SPAC FIXS MZ OPTI NO GDIV 50000
GRP 0 0.20
$ BEAM STRUCTURE
NODE 1 FIX PPYM ; 2 8.0 ; 3 16.0 FIX XPMZ
BEAM 1001 1 2 ; 1002 2 3
$ TBEAM STRUCTURE
NODE 11 0.0 0.75 ; 15 = 0.75 ; 13 FIX PPYM
171 16.0 0.75 ; 175 = 0.75 ; 173 FIX XPMZ
MESH 11 171 175 15 M 16 N 4 MNO 1
NODE (16 176 10) 0. 0. 0.50 FIX KF (13 10)
BEAM (201 216 1) (16 10) (26 10) NCS 2
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Stresses in Tbeam
By contrast, the analysis of the FEBEAM structure produces the following
values with a subdivision of the span into 16 elements:
Beam structure
FEBeam str.
Displacement
Nweb
Mweb
Nplate
Mplate
9.59 mm
9.55 mm
679.0
672.7
130.36
133.6
679.0
675.
10.18
9.75
Version 14.66
phiX
[mrad]
0.000
phiY
[mrad]
0.000
phiZ
[mrad]
0.000
0.092
0.361
0.000
59
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Eigenvalue Analysis.
Cylindrical shell
The input is in a parametric form in order to consider simply different mesh
refinements.
PROG
HEAD
NORM
STEE
END
AQUA
NATURAL FREQUENCIES OF A CYLINDRIC SHELL
DIN 18800
1 S 235
PROG GENF
HEAD NATURAL FREQUENCIES OF A CYLINDRIC SHELL
SYST SPAC
LET#1 8
$ NUMBER OF SEGMENTS VARIABLE 1 TO 9
LET#2 28.64/#1
$ ELEMENT FLARE ANGLE
LET#3 3.048/#1
$ ELEMENT LENGTH
NODE (1 #1+1 1) 6.096 (0 #2) 0 F COOR CY
TRAN 1 #1+1 1 DZ (#3 #3) DNO (10 #1*10 10)
TRAN 1 9999 1 ALPH 90 BETA 9014.32 THET 90 DNO 0
GRP 0 T 0.03048
QUAD (1 #1 1) (1 1) (11 1) (12 1) (2 1) $$
DNO 10 ENO (10*(#11)+1 1) NNO 10
END
The eigenvalues are computed now according to both methods, first according
to the Lanczos method.
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PROG ASE
HEAD
MASS 0 $ to delete possible additional masses in database
EIGE 7 LANC
END
The output begins with the sum of the masses and the eigenvalues:
Sum of Masses
TMX[t]
total
2.222
activ
2.083
TMY[t]
2.222
2.083
Eigenfrequencies
Using Lanczos Method
Iteration vectors
No.
LC
Eigenvalue
[1/Sec2]
1
1 2.82862E+03
2
2 7.43345E+03
3
3 2.26713E+04
4
4 4.32428E+04
5
5 5.27588E+04
6
6 9.51546E+04
7
7 1.81121E+05
8
2.24765E+05
9
2.77531E+05
10
4.00794E+05
11
5.89990E+05
12
1.25812E+06
13
5.87842E+06
14
4.74006E+07
* activated mass in %
sum of active mass,
TMZ[t]
2.222
2.083
RMX[tm2]
0.000
0.000
RMY[tm2]
0.000
0.000
RMZ[tm2]
0.000
0.000
14
Relativ frequency
Period aktivated
modal
error
[Hertz]
[sec] mass [%]*
damping
1.22E19
8.465 0.118139
24.63219
0.00000
2.35E18
13.722 0.072876
27.18657
0.00000
5.78E13
23.964 0.041729
31.00171
0.00000
1.18E07
33.096 0.030215
25.38651
0.00000
4.27E08
36.557 0.027355
18.14918
0.00000
3.05E05
49.095 0.020369
24.47535
0.00000
8.72E03
67.734 0.014764
20.61970
0.00000
1.94E02
75.454 0.013253
2.89E01
83.845 0.011927
4.26E01
100.758 0.009925
3.99E01
122.248 0.008180
2.11E01
178.518 0.005602
1.03E+00
385.878 0.002591
5.35E+00
1095.751 0.000913
= product |u|*M = displacement*mass, in relation to the
u scaled on a maximum displacement or rotation of 1.00.
Also the eigenvalues of the higher vectors are output for the information. It
can be seen that the seventh eigenvalue is already a little more inaccurate,
therefore the number of 14 vectors is absolutely required.
The in comparison performed analysis according to the method of the simultaneous vector iteration gives the following eigenvalues:
Eigenfrequencies
Using simultan vectoriteration
Iteration vectors
Iterations
No.
LC
Eigenvalue
Relativ
512
9
18
frequency
Period
aktivated
modal
Version 14.66
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error
[Hertz]
[sec] mass [%]*
damping
3.47E08
8.465 0.118139
24.63219
0.00000
8.74E09
13.722 0.072876
27.18657
0.00000
5.35E09
23.964 0.041729
31.00171
0.00000
1.09E08
33.096 0.030215
25.38650
0.00000
1.65E08
36.557 0.027355
18.14918
0.00000
3.75E08
49.095 0.020369
24.47430
0.00000
4.79E04
67.119 0.014899
21.19257
0.00000
2.59E07
67.738 0.014763
2.55E06
75.574 0.013232
= product |u|*M = displacement*mass, in relation to the
u scaled on a maximum displacement or rotation of 1.00.
The values and the printed error limits confirm the results of both methods.
Comparing both methods the simultaneous vector iteration method is the
better one, if only the first eigenvalue is sought with a tolerance of 0.0001
(three vectors). The Lanczos algorithm achieved in the case of three vectors
an accuracy of 0.01, in the case of 6 vectors an accuracy of 0.000001.
The rest of the output includes by default only the modal shape displacements. The element stresses, however, are calculated and stored for the program DYNA.
Stresses, internal forces and moments or support reactions are calculated
from the displacement vectors as static load cases. Support reactions which
represent the maximum accelerating forces at the nodes arise thus at all
nodes with masses.
The representation of the vibration mode shapes occurs as a deformed structure with the program WING with following input:
PROG
HEAD
SIZE
VIEW
LC 1
LC 2
LC 3
LC 4
END
WING
4 0 ; STRU 0 0
ANGL 110 120 20
; DEFO YES 1. ; STRU
; DEFO YES 1. ; STRU
; DEFO YES 1. ; STRU
; DEFO YES 1. ; STRU
0
0
0
0
0
0
0
0
;
;
;
;
AND
AND
AND
AND
;
;
;
;
DEFO
DEFO
DEFO
DEFO
NO
NO
NO
NO
;
;
;
;
STRU
STRU
STRU
STRU
CONT
CONT
CONT
CONT
Version 14.66
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514
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Modal shapes 1 to 3
For a dynamic analysis with the program DYNA it is possible to define additionally a load configuration to the eigenvalue calculation or for the post processing of existing eigenvalues. ASE multiplies the load vector with the eigenvectors and stores the modal loads in the database.
Version 14.66
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1.000
0.000
0.000
0.000
Sum of Loads
LC Title
92 ADDITIONAL_MASSES
Sum of Reactions and Loads
LC Title
92 ADDITIONAL_MASSES
Load
val.
2.00
Dimension
Variation
dP/dX
dP/dY
dP/dZ
[kN/m2]
PXX[kN]
0.0
PYY[kN]
0.0
PZZ[kN]
2.3
PXX[kN]
0.0
0.0
PYY[kN]
0.0
0.0
PZZ[kN]
2.3
2.3
In the next ASE calculation the additional masses of the load case 92 are used
and the total masses and the eigenfrequencies are determined:
PROG ASE
HEAD
MASS 92
$ (can be
$ of load
EIGE 7 LC
END
516
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TMY[t]
2.454
2.315
Eigenfrequencies
Using Lanczos Method
Iteration vectors
No.
LC
Eigenvalue
[1/Sec2]
1 101 2.16234E+03
2 102 5.66126E+03
3 103 1.77307E+04
4 104 3.67825E+04
5 105 4.38873E+04
6 106 7.22422E+04
7 107 1.56277E+05
8
1.91636E+05
9
2.03138E+05
10
4.29945E+05
11
6.67785E+05
12
1.00814E+06
13
5.05524E+06
14
4.81389E+07
* activated mass in %
sum of active mass,
TMZ[t]
2.454
2.315
RMX[tm2]
0.000
0.000
RMY[tm2]
0.000
0.000
RMZ[tm2]
0.000
0.000
14
Relativ frequency
Period aktivated
modal
error
[Hertz]
[sec] mass [%]*
damping
8.76E20
7.401 0.135119
26.56052
0.00000
8.00E19
11.975 0.083507
28.96872
0.00000
1.13E13
21.193 0.047186
31.93917
0.00000
1.46E07
30.524 0.032761
26.30272
0.00000
3.39E08
33.342 0.029992
23.11740
0.00000
3.85E06
42.778 0.023377
21.43210
0.00000
8.40E03
62.917 0.015894
21.16607
0.00000
3.63E02
69.672 0.014353
1.62E01
71.732 0.013941
1.53E01
104.358 0.009582
6.19E01
130.058 0.007689
2.63E01
159.802 0.006258
8.03E01
357.842 0.002795
5.32E+00
1104.252 0.000906
= product |u|*M = displacement*mass, in relation to the
u scaled on a maximum displacement or rotation of 1.00.
Sum of Masses
TMX[t]
total
2.454
TMY[t]
2.454
TMZ[t]
2.454
RMX[tm2]
0.000
2.222 T
0.232 T
2.454 T
=========
RMY[tm2]
0.000
RMZ[tm2]
0.000
Version 14.66
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ASE
5.5.
Wind frame
The input for the programs AQUA and GENF read as follows:
PROG
HEAD
NORM
CONC
STEE
STEE
SVAL
END
AQUA
CABLE ELEMENT WIND FRAME FROM STAR2 MANUAL
DIN 10451
1 C 30
$ C 30 =
C30/37 !
2 BST 500SA titl bar reinforcement
3 BST 500MA titl mesh reinforcement
1 1 A 0.001
PROG
HEAD
SYST
NODE
TRUS
END
GENF
CABLE ELEMENT WIND FRAME FROM STAR2 MANUAL
FRAM GDIR NEGY
1 0 0 F ; 2 0 3 ; 3 3 3 ; 4 3 0 F
(1 3 1) (1 1) (2 1) ; CABL 11 1 3 ; 12 2 4
For the input of ASE it has to be considered that the load cases are analysed
in separate blocks. This is in general mandatory for nonlinear load cases. A
maximum of 5 iterations is allowed in the SYST record. The input of the first
load case reads:
PROG ASE
HEAD Failure cable 2
518
Version 14.66
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Load Case
1
Factor forces and moments
Factor dead weight
DLXX
Factor dead weight
DLYY
Loads acting on Nodes
Node
PX[kN]
PY[kN]
MB[kNm2]
2
10.0
1.000
0.000
0.000
PZ[kN]
Sum of Loads
LC Title
1
Iteration sequence
Iteration 1 Residual
Iteration 2 Residual
Iteration 3 Residual
Iteration 4 Residual
Forces in TrussElements
Loadcase
1
Number
N[kN]
u[mm]
1
0.0
0.000
2
10.0
1.060
Version 14.66
PXX[kN]
10.0
5.578
2.478
0.000
0.000
energy
energy
energy
energy
MX[kNm]
MY[kNm]
PYY[kN]
0.0
22.6267
38.4868
51.1633
51.1633
MZ[kNm]
PZZ[kN]
0.0
e/f
e/f
e/f
e/f
0.000
0.000
0.329
0.000
1.000
1.701
1.799
1.000
L_N0[mm]
519
ASE
3
1.060
Forces in CableElements
Loadcase
1
Number
N[kN]
u[mm]
ut[mm]
f0[mm]
Nm[kN] L_N0[mm]
11
14.1
2.119
4242.639
12
0.0
3.618
failed
L_N0 = elementlength after normal force relaxation
Nodal Displacements and Reactions
Loadcase
1
Node
uX
uY
phiZ
No
[mm]
[mm]
[mrad]
1
0.000
0.000
0.000
2
5.116
0.000
0.000
3
4.057
1.060
0.000
4
0.000
0.000
0.000
Sum of Reactions and Loads
LC Title
1 sum_PX= 10.00 kN
PY
[kN]
10.0
0.0
10.0
PXX[kN]
10.0
10.0
PX
[kN]
10.0
PYY[kN]
0.0
0.0
MZ
[kNm]
PZZ[kN]
0.0
0.0
2
1
The load is reduced to 9 kN in a second input block. The load case 1 is considered as primary load case PLC 1 in record SYST.
PROG
HEAD
HEAD
SYST
LC 2
END
ASE
Smaller load, however, furthermore failure cable 2
Displacements have to be reinitialized at first!
NONL ITER 25 PLC 1
; LOAD 2 9.0
The table of the element groups with the information of the used primary load
case is printed additionally in the output. The cable 2 fails still.
Primary state for displacements of total system is load case
520
Version 14.66
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facL
1.000
facD
0.000
facP
1.000
facB
1.000
PLC
1
HW [m]
Forces in CableElements
Loadcase
2
Number
N[kN]
u[mm]
ut[mm]
f0[mm]
Nm[kN] L_N0[mm]
11
12.7
1.907
4242.640
12
0.0
3.256
failed
L_N0 = elementlength after normal force relaxation
The cable 2 gets a tensile force of 1 kN in the third input block. The load case
2 is here the primary load case.
PROG
HEAD
HEAD
SYST
LC 3
END
ASE
Now negative load, cable 2 with a little tensile force
Failure cable 1
NONL ITER 25 PLC 2
; LOAD 2 1.0
The number of the necessary iterations increases to 10. Now a failure of the
cable 1 is to be seen.
Iteration sequence
Iteration 1 Residual
5.578
energy
22.6280 e/f
Iteration 2
Iteration 3
Iteration 4
Iteration 5
Iteration 6
Iteration 7
Iteration 8
Iteration 9
Iteration 10
2.478
1.707
0.984
0.309
0.206
0.127
0.017
0.003
0.002
energy
energy
energy
energy
energy
energy
energy
energy
energy
38.4899
51.1688
47.5597
49.1081
49.4929
49.9666
50.0760
50.1005
50.1063
Residual
Residual
Residual
Residual
Residual
Residual
Residual
Residual
Residual
Forces in TrussElements
Loadcase
3
Number
N[kN]
u[mm]
1
1.0
0.106
2
0.0
0.000
3
0.0
0.000
Forces in CableElements
Loadcase
3
Number
N[kN]
u[mm]
11
0.0
0.286
Version 14.66
e/f
e/f
e/f
e/f
e/f
e/f
e/f
e/f
e/f
0.000
1.000
0.000
0.329
0.204
0.177
0.069
0.131
0.013
0.023
0.051
1.701
1.799
0.670
0.600
1.026
2.764
0.849
1.148
1.088
L_N0[mm]
ut[mm]
f0[mm]
Nm[kN]
L_N0[mm]
failed
521
ASE
12
1.4
0.212
L_N0 = elementlength after normal force relaxation
522
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Version 14.66
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A 60 m long girder which is fixed at both ends is assembled from two precast
parts by using an auxiliary support. The loading consists of the dead weight
only. The auxiliary support is removed after establishing a monolithic connection.
Singlespan girder
At first the materials, the cross section and the static system are defined as
two single span girders with the programs AQUA and GENF. A spring which
is allocated to the group 9 is input for the auxiliary support.
The input for AQUA and GENF is:
PROG
HEAD
NORM
CONC
STEE
STEE
SREC
END
AQUA
TWO SPAN GIRDER WITH CONSTRUCTION STAGES
DIN 10451
1 C
25
$ = C25/30
2 BST 500MA TITL mesh reinforcement
3 BST 500SA TITL bar reinforcement
1 B 1.0 H 1.5 MNO 1 MRF 3
PROG GENF
HEAD TWO SPAN GIRDER WITH CONSTRUCTION STAGES
$ ASEMANUAL
SYST FRAME GDIV 1000 GDIR POSY
NODE 1 0 0 F ; 2 30. 0 ; 4 60 0 F
GRP 1
BEAM 1 1 2 AHIN MY
2 2 4 AHIN MY EHIN MY
GRP 9 $ auxiliary support
Version 14.66
523
ASE
The calculation for the load case 1 dead load is done with ASE. All groups inclusive the auxiliary support are activated with the record GRP. HING ACTI
defines here the articulated joints of the beams.
The input for ASE reads:
PROG ASE
HEAD Construction Stage Articulated System with Auxiliary Support
HEAD Effect like two singlespan beams
GRP (0 99 1) HING ACTI
LC 1 ; ELLO 1001 1002 1 PYS 10.0
END
Vy
[kN]
0.00
0.00
0.00
0.00
Vz
[kN]
150.00
150.00
150.00
150.00
Mt
[kNm]
0.00
0.00
0.00
0.00
My
[kNm]
0.00
0.00
0.00
0.00
Mz
[kNm]
0.00
0.00
0.00
0.00
The moments of the two single span girders are not visible here, since the results are given at the two ends only. A graphic representation with the program WinGRAF shows the actual moment distribution.
Then the program ASE is used once more in order to change the static system
and calculate it simultaneously:
and ASE is started with:
PROG ASE
HEAD Final Stage without Hinges
SYST PLC 1
GRP (0 99 1) HING FIX
GRP
9 OFF $ delete auxiliary support!
LC 2 ; ELLO 1001 1002 1 PYS 10.0
END
The record ELLO is used to apply all the loads which acts to this time. The
input data for SYST have the effect that the load case 1 is used as primary load
524
Version 14.66
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case. The beam joints are removed and replaced through fixed connections
with HING FIX in the first record GRP. The auxiliary support is deleted via
switching off of the group 9.
Primary state for displacements of total system is load case
Elementgroups
No
facS
1
1.000
facL
1.000
facD
0.000
facP
1.000
facB
1.000
PLC
1
HW [m]
Load Case
2
Factor forces and moments
Factor dead weight
DLXX
Factor dead weight
DLYY
Primary load case
1.000
0.000
0.000
1
Loadval Dimens.
PXX[kN]
0.0
ya[m]
za[m]
ye[m]
[kN/m]
[kN/m]
PYY[kN]
600.0
PZZ[kN]
0.0
If the middle support still existed, the external load (ELLO) would be in equilibrium with the primary stresses. No additional deformations or stresses
would arise.
Due to the removal of the middle support the missing support reaction acts
now as a downward point load and the middle node settles by 45 mm. Using
SYST PLC 1 these additional deformations are added to the old deformations
of the load case 1 (phiZ=1.5 mrad) and they are output as total deformations of the load case 2: (uY=45 mm, phiZ= 1.5 mrad).
Version 14.66
525
ASE
PX
[kN]
PX
[kN]
PY
[kN]
150.0
300.0
150.0
MZ
[kNm]
0.00
PY
[kN]
300.0
MZ
[kNm]
2250.00
300.0
2250.00
0.00
Vy
[kN]
0.00
0.00
0.00
0.00
Vz
[kN]
300.00
0.00
0.00
300.00
Mt
[kNm]
0.00
0.00
0.00
0.00
My
[kNm]
2250.00
2250.00
2250.00
2250.00
Mz
[kNm]
0.00
0.00
0.00
0.00
526
Version 14.66
ASE
It is not the task of this manual to offer a complete overview of the different
creep theories. More explanations can be found e.g. in the manuals of the programs STAR2 and AQB. The method implemented in ASE, which convert the
stresses of an arbitrary load case to creep deformations, allows a generalised
procedure.
The creep law describes the relationship between creep deformations and acting stress:
+ f @ sEb
However, it is of little importance how one takes the variable creep coefficients and elastic moduli into consideration. More important is the relation
that defines the creep deformations as a function of the stresses of one or several load cases. Such creep laws are generally valid only for constant acting
stress. This is given only for statically determinate structures according to
firstorder theory. The structure deforms free of forces in this case.
For statically indeterminate structures, however, the stress changes due to
constraints. This results in a relatively complicated differential equation
which of course can not be solved exactly by ASE. The alternative solutions
are either the use of creep coefficients which take this effect into consideration or a numerical integration of the differential equation.
An acceptable solution is offered by the Trost method with a relaxation coefficient. Instead of a complicated differential equation, an algebraic relation
with a relaxation coefficient, which can be defined usually with = 0.8 without significant loss of accuracy, results from an introductory analysis.
t + 01 ) f ) DsE @ 1 ) f
The resultant decrease of the internal forces and moments from constraint
for progressively applied constraint is
Z + Z R
1
1 ) f
Z + Z 0 1 *
Version 14.66
f
1 ) f
527
ASE
Twospan girder
The structure is defined with two groups in program GENF:
PROG
HEAD
ECHO
NORM
CONC
STEE
STEE
SREC
END
AQUA
CREEP REDISTRIBUTION FOR CONTINUOUS BEAM WITH CONSTRUCTION STAGES
MAT,SECT EXTR
DIN 10451
1 C
25
$ = C25/30
2 BST 500MA TITL mesh reinforcement
3 BST 500SA TITL bar reinforcement
1 B 1.0 H 1.5 MNO 1 MRF 3
PROG GENF
HEAD CREEP REDISTRIBUTION FOR CONTINUOUS BEAM WITH CONSTRUCTION STAGES
SYST GDIV 1000
NODE 1 0 0 PP ; 2 20. 0 PP ; 3 40 0 PP
GRP 1 ; BEAM 1001 1 2
GRP 2 ; BEAM 2001 2 3
END
The first construction stage (left singlespan beam) as well as the second one
are defined in ASE as described in the previous chapter. The socalled single
casting stage can be analysed as a third load case. This is the case, if the structure is constructed monolithically in one stage.
PROG ASE
HEAD CONSTRUCTION STAGE 1
GRP 1
LC 1 ; ELLO 1001 TYPE PYS 30.0
END
528
Version 14.66
ASE
PROG ASE
HEAD CONSTRUCTION STAGE 2
SYST PLC 1
GRP 1,2 FACL 1 FACP 1 FACD 0
LC 2 TITL WITH CONSTRAINT T=0
ELLO 1001 2001 TYPE PYS 30.0
END
The resultant internal forces and moments in load case 2 show a support moment with the half regular value of a twospan girder.
Beam Forces and Moments
Loadcase
2
WITH CONSTRAINT T=0
beam
x
N
Vy
Vz
Number
[m]
[kN]
[kN]
[kN]
1001
0.000
0.0
0.00
262.50
20.000
0.0
0.00 337.50
2001
0.000
0.0
0.00
337.50
20.000
0.0
0.00 262.50
Mt
[kNm]
0.00
0.00
0.00
0.00
My
[kNm]
0.00
750.00
750.00
0.00
Mz
[kNm]
0.00
0.00
0.00
0.00
The internal forces and moments from constraint have been produced exactly
by means of the GRP loading. In a third step one can provide this stage of the
sudden constraint with the appropriate Trost coefficient instead of 1.0. The
result is for group 1 (beam 1001) with PHI=2.18:
FAKL + 1 *
2.18
+ 1.0 * 0.794
1 ) 0.8 @ 2.18
The input
PROG ASE
HEAD CREEP OF THE IMMEDIATE CONSTRAINT
SYST PLC 2
GRP 1 FACL 1.00.794
$ PHI = 2.18
GRP 2 FACL 1.00.849
$ PHI = 2.62
LC 4 TITL WITH CONSTRAINT T=INFINITE
ELLO 1001 2001 TYPE PYS 30.0
END
Version 14.66
Mt
[kNm]
0.00
My
[kNm]
0.00
Mz
[kNm]
0.00
529
ASE
2001
0.0
0.0
0.0
0.00
0.00
0.00
368.31
368.31
231.69
0.00
0.00
0.00
1366.12
1366.12
0.00
0.00
0.00
0.00
Rsch indicates a value of 1380 kNm. The value My = 1500 kNm of the
singlecasting stage is given for comparison.
530
Version 14.66
ASE
Sunshades.
Sunshades
The analysis which was carried out for a roof in a camel race track in Near
East is shown here as a real life example. The umbrellalike structure consists of precast reinforced concrete plates which are anchored with struts at
four steel composite columns. The joints between plates are poured subsequently. A reinforced concrete beam which is used as stiffening and as support
for the plates is placed in the longitudinal direction along the roof ridge. The
structure is 10 m high and has plan dimensions of 4515 meters. Due to symmetry only one half of the structure was discretised.
The following input for the program AQUA defines as cross sections 1 and 2
the composite cross sections with standard steel profile and concrete materials, as cross section 3 the pure steel cross section of the struts and as cross
section 4 the reinforced concrete tie.
PROG
NORM
CONC
STEE
STEE
SECT
CIRC
SECT
CIRC
SECT
CIRC
AQUA
DIN 10451
1 C 30
$ C 30 =
C30/37 !
2 BST 500SA TITL bar reinforcement
3 S 235
1 ; SV AY 0 0
1 R .3365 ; CIRC 2 R .3187 ; CIRC 3 R .3187 3
2 ; SV AY 0 0
1 R .2665 ; CIRC 2 R .2487 ; CIRC 3 R .2487 3
3 ; SV AY 0 0
1 R .09685 ; CIRC 2 R .08435
Version 14.66
531
ASE
In order to avoid unnecessary work, first the nodes of a plate were defined
easily with the help of cylindrical coordinates. All other nodes were generated
then easily by means of rotation and displacement with the record TRAN.
Small corrections were required additionally at the symmetry plane. The
joints between the precast components were modelled as kinematic constraints. So one obtains the forces which are required for the dimensioning
of the joint seals.
The definition of the elements is a diligence task which can be made easier
with the copying function of the text editor. It is noted that the example comes
from a time when graphical input capabilities as those of MONET or SOFiPLUS were not yet available. One would probably choose graphical input
today. The figures depict the structure in plan and in elevation.
Due to limited space only the first page of the GENF input is reproduced here.
The complete input can be found in the enclosed files.
PROG GENF
HEAD CONCRETE UMBRELLAS
SYST SPAC GDIV 50000
NODE 1 0
0
0
2 2
203.245 0 1 COOR CY ; 3 = 156.755 ==
38 9.402 203.245 == ; 43 = 156.765 ==
8 3.234 203.245 == ; 13 = 156.755 ==
44 11.402 203.245 == ; 49 = 156.755 ==
6 2.6
185
== ; 7 = 175 ==
45 10.2
195
== ; 48 = 165 ==
46 9.5
185
== ; 47 = 175 ==
MESH 2 6 M 2 ; 3 7 M 2
38 43 13 8 5 5
NODE 20 5.701 203.245 0 1 ; 25 = 156.755 ==
MAT 1
GRP 0 T .22
$
TRAN 1 49 1 DY 4.5 ALPH 90 90 41.926 50
51 99 1 7.794 4.5 7 90 90 180 50
51 99 1 0 9 DNO 100
101 149 1 0 9 DNO 100
51 99 1 3.897 11.25 BETA 60 DNO 150
51 99 1 3.897 15.75 BETA 120 DNO 200
51 99 1 0
9
BETA 180 DNO 350
51 99 1 0
18
BETA 180 DNO 250
1 49 1
BETA 180 DNO 450
532
Version 14.66
ASE
2
2
10
46
10
453
453
461
497
461
MESH
$
NODE 38
45
15
27
8
20
... ...
... ...
49 1
6.427
6
5.583
.753
40
6.427
457
5.583
.753
491
DY
0
M
0
0
M
0
M
0
0
M
9
5.772
2
5.015
.677
5
5.772
2
5.015
.677
5
0 4.5 11 F ;
0 13.5
6
0 6.36 0.417
0 9.828 0.677
0 0
0.677
0 2.64 0.417
Version 14.66
CA
5.867
40
1.367
1.228
457
5.867
5.269
491
39 0
4.5
;
;
;
21
33
14
0
0
0
1.367
5.269
1.228
6 ; 44 0 13.5 11 F
8.172
11.640
0.828
0.677
0.417
0.677
533
ASE
248
295
288
243
242
289
296
247
237
282
290
236
283
297
241
246
231
276
291
298
344
299
292
225
270
278
338
293
272
326
281
345
339
333
268
321
263
308
315
346
340
334
217
322
316
323
317
232
187
181
226
221
198
216
212
260
211
261 256254
207 210
252
203205
206 209
262 257
255
204
253
302
304
310306
175
220
215
192
186
169
214
180
174
208
163
168
202
153
162
155
161
157
309
328
227
222
258
213
259
314
269
327
218
266
267
238
193
223
219
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265
274
320
275
233
228
273
244
199
239
224
279
280
332
287
234
229
271
286
245
230
277
285
240
235
284
191
197
185
173
179
167
166
172
178
184
190
196
45
151
44
301
201
394
149
251
347
341
335
329
156
160
154
159
143
152
311307
305
312
303
388
318
313
382
324
330
158
137
319
376
336
342
165
389
364
331
377
195
119
176
130
124
365
343
352
359
354
360
356
189
136
371
337
358
183
170
125
142
383
348
177
131
164
395 33 148
325
370
171
182
113
118
366
372
378
367
373
379
384
390
396
27
147
141
135
188
103
105
111
107
112
129
123
117
122
116
349
444
351
101
99
194
357
361
355
362
438
353
385
391
397
21
146
140
134
128
368
432
363
115
374
127
433
139
392
421
440
387
408
434
422
416
80
74
132
63
68
393
402
404
410406
138
53
55
409
428
92
86
126
69
415
446
98
120
75
398 15 145
414
381
427
114
81
133
386
375
420
439
108
87
121
380
369
426
445
106
110
104
109
93
102
91
97
85
73
79
67
66
72
78
84
90
96
62
57 61
51
399
38
494
49
39
401
144
447
441
435
429
423
417
411407
405
412
488
403
56 60
54
52
43
59
418
482
413
424
430
65
37
58
419
476
442
470
425
448
83
489
36
477
24
465
451
449
443
452
459
454
460
456
453
455
457
461
95
19
76
30
471
458
437
89
25
70
42
483
464
431
77
31
64
495 20 48
436
71
13
82
18
478
466
472
467
473
479
484
485
490
491
496
497
14
47
46
41
40
35
34
3
88
5
11 7
106 4 2
12
29
28
23
17
22
16
1
94
Plan view
534
Version 14.66
ASE
248
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242
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276
284
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234
285
292
239
230
277
225
270
229
278
298
245
344
299
199
244
271
224
219
264
223
272
265
218
273
222
266
217
258
213
259
212
260
211
256
207
210
254
205 261
252
203
257
206
262
209
308
163
208
255
204 263
253
202
302
153
309
162
155
304
310
161
157
306
274
221
279
228
286
233
280
227
332
287
187
232
338
293
193
238
326
281
181
226
345
198
267
216
268
215
320
275
220
175
339
192
333
186
269
314
214
169
327
180
321
174
315
168
334
185
322
173
328
179
316
167
317
166
323
172
329
178
335
184
197
340
191 346
45
151
301
201
394
149
251
156
307
311
160
154
305
312
159
143
388
303
152
44
341 347
190
196
318
165
137
382
158
313
324
171
330
177
376
131
319
164
148
395
33
336
183
189
342
325
170
370
125
142
389
383
136
195
348
119
364
331
176
130
377
124
371
113
358
182
337
118
365
147 390
396
27
141
135
384
343
188
352
103
354
105
360
111
356
107
359
112
129
378
123
372
366
117
122
373
116
367
349
101
194
351
444
99
140
21
146 391
397
385
134
379
128
106
357
361
110
355
104
362
109
102
438
353
93
368
115
363
87
108
432
121
374
127
380
81
426
114
369
133
386
139
392
98
445
120
375
75
420
15
145
398
439
92
433
86
126
381
69
414
80
427
74
421
132
387
63
408
415
68
393
138
53
402
409
62
404
55
410
61
406
57
434
85
73
422
428
79
416
67
417
66
72
423
429
78
84
435
144
399
494
49
401
51
97
91 446
440
39
407
56
411
60
54
405
59
412
52
43
488
403
38
441
90 447
96
65
418
58
37
482
413
71
424
77
430
64
419
31
476
20
48
495
436
83
442
89
25
470
425
70
42
489
36
483
448
95
19
464
76
431
30
477
24
471
13
458
82
437
18
465
14
47 490
496
41
46 491
497
8
40
35
484
34
485
3
452
88
443
5
454
460
11
7
456
106
461
457
4 4
455
253
12
459
29
478
28
479
23
472
17
466
22
473
467
16
1
449
451
94
Elevation
The dead weight (LC 4), wind (LC 5 and 6) and 3 temperature load cases were
analysed subsequently. Snow load was not anticipated!
PROG
HEAD
HEAD
LC 1
ASE
CONCRETE UMBRELLAS
TEMPERATURE DIFFERENCE: TBELOW TABOVE = 40 K
TYPE T
Version 14.66
535
ASE
ELLO 1 499 1 DT 40
END
PROG
HEAD
HEAD
LC 2
ELLO
END
ASE
CONCRETE UMBRELLAS
TEMPERATURE DIFFERENCE : 40 K
TYPE T
1 499 1 TEMP 40
PROG
HEAD
HEAD
LC 3
ELLO
ELLO
END
ASE
CONCRETE UMBRELLAS
TEMPERATURE DIFFERENCE : T = 40 K BETWEEN RIGHT AND LEFT SIDE
TYPE T
1 249 1 TEMP +5
251 499 1 TEMP 5
PROG
HEAD
HEAD
LC 4
END
ASE
CONCRETE UMBRELLAS
DEAD LOAD
TYPE G1 DLZ 1.0
PROG
HEAD
HEAD
ECHO
LC 5
ELLO
ELLO
END
ASE
CONCRETE UMBRELLAS
WIND PARALLEL TO XAXIS
FULL NO
TYPE W
1 249 1 PZ
1.25
251 499 1 PZ 1.25
PROG
HEAD
HEAD
ECHO
LC 6
ELLO
ELLO
END
ASE
CONCRETE UMBRELLAS
WIND PARALLEL TO XAXIS FROM BELOW
FULL NO
TYPE W
1 249 1 PZ
1.56
251 499 1 PZ
1.56
The two following pictures show the distribution of moments and membrane
forces for load case 1 ( DT = Tbottom Ttop= 40 degrees K). Any attempt to reproduce here even parts only of the alphanumeric output would largely increase the size of this manual.
536
Version 14.66
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Version 14.66
537
ASE
538
Version 14.66
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QUADEuler Beam.
A simple Euler beam fixed at its bottom is used as an example of the analysis
of shells according to secondorder theory. The geometrically nonlinear
analysis gets started with CTRL THII.
The small horizontal load at the top is necessary in order to induce an initial
horizontal displacement. Any load or imperfection can be used in principle.
On the one hand it should be sufficiently large to cause a nonlinear iteration,
but on the other hand it should not affect unintentionally the result. The application of horizontal loads is usually the most practical. Additional initial
imperfections can be omitted then.
Structure data:
Height 4 m, Width 20 cm, Thickness 10 cm
Version 14.66
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PROG
HEAD
NORM
STEE
END
PROG GENF
HEAD QUAD EULER BEAM
SYST SPAC
NODE NO
X
(1
5
1) 0
(11 15
1) 0
GRP 0 T 0.1
MESH N1
N2
N3
N4
1
5
15
11
NODE NO FIX
1,11 F
END
Y
0
0.2
M
4
N
1
Z
(0 1)
(0 1)
MNO
1
PROG ASE
HEAD Limit Load Iteration geometrically nonlinear
ECHO DISP,REAC,FORC,NOST NO
ULTI 18 FAK1 1.0 DFAK 1.0 PRO 1
SYST PROB THII ITER 20 TOL 0.0001
LC 1 ; LOAD 5,15 PX 0.01
LOAD 5,15 PZ 50
END
An ultimate limit load iteration is started with the input ULTI 18 FAK1 1.0
DFAK 1.0 PRO 1. It begins with a load factor of 1.0 (FAK1). The load is increased then by a factor of 1.0 each time, if the previous step is recognized as
a stable one. A load step is considered as stable, if the residual force iteration
achieves the accuracy TOL within the 20 iterations specified by SYST. When
the above tolerance is not satisfied after the 20 iterations, the last load step
is halved.
The following load steps were processed automatically in the present
example (summary at the end of the results file):
Summary of the
ULSiteration
ULSiteration
ULSiteration
ULSiteration
ULSiteration
ULSiteration
ULSiteration
540
1.000
2.000
3.000
4.000
5.000
6.000
5.500
was
was
was
was
was
was
was
convergent.
convergent.
convergent.
convergent.
convergent.
instabil.
instabil.
Version 14.66
ASE
8
9
10
11
12
13
14
15
16
17
18
loadcase
loadcase
loadcase
loadcase
loadcase
loadcase
loadcase
loadcase
loadcase
loadcase
loadcase
6
7
8
8
8
8
9
10
10
11
12
with
with
with
with
with
with
with
with
with
with
with
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
5.250
5.375
5.562
5.469
5.422
5.398
5.410
5.428
5.419
5.423
5.423
was
was
was
was
was
was
was
was
was
was
was
convergent.
convergent.
instabil.
instabil.
instabil.
convergent.
convergent.
instabil.
convergent.
convergent.
convergent.
The buckling load according to the theory of elasticity without horizontal load
amounts to
+ 540kN ,
P ki + p 2 @ EI
s 2k
The program calculates with the small horizontal load a value of 542 kN
(5.422250).
The displacements and the internal forces and moments increase sharply and
at a load of 300 kN they are already twice as big as those of the firstorder
theory.
Loaddeformation curve
A buckling eigenvalue determination as well as a concurrent eigenvalue
analysis are available in the complete example ase9.dat (SOFiSTiKCD).
Version 14.66
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542
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Beam series
Input:
PROG
HEAD
NORM
STEE
SVAL
END
AQUA
BEAM DEVELOPING CABLE ACTION BY THIRDORDER THEORY
DIN 18800
1 S 235
1 A 0.01 IY 0.0001/12
PROG GENF
HEAD BEAM DEVELOPING CABLE ACTION BY THIRDORDER THEORY
SYST SPAC
NODE NO X FIX ; 1 0 PPMX
11 10 PXXM ; (2 10 1) (1 1)
BEAM (1 10 1) (1 1) (2 1) NR YY
END
PROG ASE
ECHO FULL NO; ECHO DISP YES
ULTI 9 FAK1 1.0 DFAK 2.0 PRO 2
SYST PROB TH3 ITER 40 TOL 0.0001
LC 1 FACT 1.0 ; ELLO 1 10 1 PZS 0.01
END
PROG ASE
ECHO FULL NO ; ECHO DISP YES
SYST PROB LINE
LC 99 FACT 511 ; ELLO 1 10 1 PZS 0.01
END
Version 14.66
543
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A summary of the displacements shows the strong influence of the cable action. Although the load factor in load case 9 already amounts to 511 the displacements are only 23 times bigger than those of load case 1 with load factor
1. Load case 99 with load factor 511 was analysed linearly for comparison. It
is evident that the combined stiffness in load case 9 is about 23 times bigger
than the pure bending stiffness of the linear analysis.
NODAL DISPLACEMENTS
Node
uX
No
[mm]
LC1
11
0.000
LC2
11
0.000
LC3
11
0.000
LC4
11
0.000
LC5
11
0.000
LC6
11
0.000
LC7
11
0.000
LC8
11
0.000
LC9
11
0.000
LC99
11
0.000
uY
[mm]
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
uZ
[mm]
11.451
28.616
48.542
70.640
95.973
125.959
162.247
206.828
262.170
6083.333
phiX
[mrad]
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
phiY
[mrad]
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
phiZ
[mrad]
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Load case 99 can not reproduce the actual loadbearing behaviour due to the
missing cable action in linear analysis.
544
Version 14.66
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Graphical representation results in the following figure (10times magnified): The linearly analysed load case 99 can not be plotted due to its large deformation (LC 99, beam axis directed steeply downwards, immense deformation).
In order to assess the loadbearing action load case 99 was plotted scaled
down (LC 99b), so that the midspan deflection is equal to that of load case 9.
One can recognise the hyperbolic cable line (LC9, rather circular, thick solid
line) in comparison to the linear bending line (parabolic shape with stronger
curvature at midspan, LC 99b, thin line, about 2 mm above line of LC 9 in figure).
A prestress has to be specified in program GENF, if cable structures are to
analysed fully without the bending components. This prescribes an initial
stress stiffness that makes the structure stable at the beginning even in the
cases of articulated chains.
Version 14.66
545
ASE
5.11.
A solid cross section 20 cm wide, 100 cm high is examined with a span width
of 20 m and simple torsional restraint. A small torsional loading at midspan
serves as initial imperfection:
AQUA
GIRDER OVERTURNING
DIN 10451
1 C 30
$ C 30 =
C30/37 !
2 BST 500SA TITL bar reinforcement
1 H 1 B 0.20 MNO 1
PROG GENF
HEAD GIRDER OVERTURNING
SYST SPAC
NODE NO X FIX ; 1 0 XPMX
11 10 PXXM ; (2 10 1) (1 1)
BEAM (1 10 1) (1 1) (2 1) NR YY
END
PROG
ECHO
ULTI
SYST
LC 1
546
ASE
FULL NO ; ECHO DISP YES
20 FAK1 1.0 DFAK 1.0 PRO 2
PROB TH3 ITER 35 TOL 0.00001
FACT 1.0 ; ELLO 1 10 1 PZS 1.0
Version 14.66
ASE
A rotation of the beam and thus of its principal axes may cause a lateral movement of the beam since a part of the vertical load acts on the weak axis. It is
important for working with primary load cases to define the load as global,
because in the case of local load definition the load direction would rotate
along with the girder (not within an ASE iteration analysis, since only the
rotation of a primary load case causes a load rotation!).
The critical load results analytically to:
pki + 28.32 @
EIz @ GIt
l3
Version 14.66
uY
uZ
phiX
phiY
phiZ
547
ASE
LC1
LC2
LC3
LC4
LC5
LC6
LC7
LC8
LC9
LC10
LC11
LC12
LC99
No
11
11
11
11
11
11
11
11
11
11
11
11
11
[mm]
0.000
0.001
0.002
0.009
0.038
0.171
1.474
3.295
6.697
8.727
9.485
9.485
0.000
[mm]
4.416
8.831
17.662
35.323
70.644
141.261
282.314
317.521
335.119
339.520
340.620
340.620
375.318
[mrad]
0.002
0.004
0.007
0.015
0.030
0.067
0.274
0.529
0.998
1.275
1.379
1.379
0.062
[mrad]
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
[mrad]
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
The loss of stability is evident, since the rotation phiX at midspan increases
rapidly with only a small load increase starting from load case 7. Load case
99 with load factor 85.00 is linearly analysed for comparative purposes and
results in a rotation of only a part of the nonlinear value (0.062 opposite
0.274). There is no lateral movement uY for LC 99.
The ultimate load result of 77.25 kN/m is in very good agreement with the
theoretical solution.
The convergence is a little worse for standard steel profiles which are weak
in torsion, because the large difference between the high bending stiffness
and the small torsional stiffness may lead to numerical problems. A convergent result is always smaller than the actual ultimate load, however, always
at the safe side (a high accuracy is required as shown during an analysis with
primary load cases)! Rapidly increasing displacements or rotations are an indication here for the beginning of an instability. Possible warping forcetorsional stiffnesses are to be added by hand to the torsional stiffness according
to SaintVenant! The method works with additional axial forces as well and
can model thus lateral torsional buckling effects too.
548
Version 14.66
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Plate Buckling.
A 1 cm thick steel plate with 1.200 x 2.400 m dimensions has articulated supports at its edges and is subjected to a compressive force in the direction of
its long dimension. A small point load at node 202 is applied as initial imperfection. Notice that this imperfection has little to do with the resultant
buckling shape. It should be only asymmetric.
Plate buckling
Input:
N=8
$ GLOBAL VARIABLE N = MESH PARTITION
PROG AQUA
HEAD PLATE BUCKLING
NORM DIN 18800
ECHO MAT VOLL
STEE 1 S 235
SSLA ULTI 1.10
$ Material Safety Coefficient 1.10
SSLA EPS SIG TYPE=POL $ Trilinear Stressstrain Curve
10
370
5
370
1.039 240
0
0
1.039
240
5
370
10
370
END
PROG GENF
HEAD PLATE BUCKLING
ECHO NO
SYST SPAC GDIV 50000
LET#1 101
Version 14.66
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ASE
LET#2 101+$(N)*100
LET#3 101+$(N)*100+$(N)*2
LET#4 101+$(N)*2
GRP 0 T 0.01
NODE NO X Y
#1 0
0
; #2 0 1.2
#3 2.4 1.2 ; #4 2.4 0
MESH #1 #2 #3 #4 M $(N) N $(N)*2 MNO 1
NODE NO FIX
(#1 #2 100) PZ ; (#1 #4 1)
PZ
(#2 #3 1)
PZ ; (#4 #3 100) PZ
#1 PP ;
#2 YP
END
PROG ASE
LET#1 101 ; LET#2 101+$(N)*100
LET#3 101+$(N)*100+$(N)*2
LET#4 101+$(N)*2
ECHO REAC,FORC,NOST,BEDD NO
ULTI 25 FAK1 100 DFAK 100 PRO 2
SYST PROB TH3 TOL 0.0001
LC 1 FACT 1.0 ; LOAD 202 PZ 1E3
BOLO #1 #2 100 PXS 1
BOLO #4 #3 100 PXS 1
END
The ultimate load iteration exhibits serious convergence problems for factor
500:
Summary of the load step iterationen:
ULSiteration 1 loadcase
1 with loadfactor
ULSiteration 2 loadcase
2 with loadfactor
ULSiteration 3 loadcase
3 with loadfactor
ULSiteration 4 loadcase
4 with loadfactor
ULSiteration 5 loadcase
4 with loadfactor
ULSiteration 6 loadcase
4 with loadfactor
ULSiteration 7 loadcase
5 with loadfactor
ULSiteration 8 loadcase
6 with loadfactor
ULSiteration 9 loadcase
7 with loadfactor
ULSiteration 10 loadcase
8 with loadfactor
ULSiteration 11 loadcase
8 with loadfactor
ULSiteration 12 loadcase
9 with loadfactor
ULSiteration 13 loadcase 10 with loadfactor
ULSiteration 14 loadcase 10 with loadfactor
ULSiteration 15 loadcase 10 with loadfactor
ULSiteration 16 loadcase 10 with loadfactor
ULSiteration 17 loadcase 11 with loadfactor
ULSiteration 18 loadcase 12 with loadfactor
550
100.000
200.000
400.000
800.000
600.000
500.000
550.000
650.000
850.000
1250.00
1050.00
1150.00
1350.00
1250.00
1200.00
1175.00
1187.50
1212.50
was
was
was
was
was
was
was
was
was
was
was
was
was
was
was
was
was
was
convergent.
convergent.
convergent.
instabil.
instabil.
convergent.
convergent.
convergent.
convergent.
instabil.
convergent.
convergent.
instabil.
instabil.
instabil.
convergent.
convergent.
convergent.
Version 14.66
ASE
19
20
21
22
23
24
25
loadcase
loadcase
loadcase
loadcase
loadcase
loadcase
loadcase
13
14
15
16
16
16
16
with
with
with
with
with
with
with
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
loadfactor
1262.50
1362.50
1562.50
1962.50
1762.50
1662.50
1562.50
was
was
was
was
was
was
was
convergent.
convergent.
convergent.
instabil.
instabil.
instabil.
convergent.
After processing the critical load range by factor 500, the load can be increased again. The displacements at point 505 (= midspan, first buckling)
show at load factors 500550 a strong increase of the uZ deviation:
Nodal Displacements
Node
uX
No
[mm]
LC1
505
0.029
LC2
505
0.057
LC3
505
0.114
LC4
505
0.143
LC5
505
0.168
LC6
505
0.224
LC7
505
0.343
LC8
505
0.473
LC9
505
0.548
LC10 505
0.573
LC11 505
0.593
LC12 505
0.649
LC13 505
0.736
LC14 505
0.882
LC15 505
1.132
LC16 505
1.132
uY
[mm]
0.008
0.017
0.034
0.042
0.033
0.001
0.107
0.283
0.400
0.432
0.449
0.480
0.550
0.716
1.130
1.130
uZ
[mm]
0.014
0.036
0.164
1.045
6.305
12.175
19.962
26.399
29.498
30.373
30.943
32.326
34.572
38.412
45.049
45.049
phiX
[mrad]
0.013
0.026
0.055
0.071
0.076
0.079
0.079
0.072
0.069
0.069
0.069
0.071
0.073
0.075
0.078
0.078
phiY
[mrad]
0.011
0.029
0.117
0.274
0.599
2.166
6.786
11.945
14.126
14.225
13.776
12.098
10.989
10.994
13.080
13.080
phiZ
[mrad]
0.000
0.000
0.000
0.000
0.000
0.001
0.004
0.011
0.023
0.034
0.045
0.057
0.075
0.107
0.157
0.157
4 @ p 2 @ E @ h 2
pkr +
@ t + 527kNm
12 @ b21 * m3
A comparison of the first analysis LC 1 (load factor 100) with load case 5 (load
factor 550) shows additionally that the buckling shape is relatively independent of the starting imperfection. In fact, the latter ones are not be recognized
in load case 5.
Version 14.66
551
ASE
552
Version 14.66
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Version 14.66
553
ASE
0.255
0.111
0.474
0.0557
0.0279
0.446
0.118
0.0279
0.116
0.272
0.307
0.362
0.388
0.334
0.418
0.139
0.111
0.0836
0.0557
0.0279
0.0557
0.502
0.530
0.0836
0.0279
0.167
0.139
0.111
0.0836
0.0557
0.557
0.279
0.251
0.223
0.390
0.362
0.334
0.307
The stable calculations end now at about 870 kN/m. A contour line presentation of the plastified zones leads to the following picture:
0.195
0.167
0.279
0.251
0.223
0.195
0.307
0.485
0.374
0.859
0.369
0.518
0.195
0.223
0.251
0.279
0.307
0.223
0.251
0.279
0.0279
0.0557
0.0836
0.111
0.139
0.111
0.0836
0.272
0.362
0.474
0.116
0.334
0.502
0.118
0.0279
0.307
0.334
0.362
0.522
0.257
0.0557
0.390
0.0279
0.0557
0.0836
0.111
0.139
0.167
0.446
0.418
0.0279
0.0557
0.167
0.195
0.388
554
Version 14.66
ASE
ASE
FULL NO ; ECHO STAT FULL
10 FAK1 0.10 DFAK 0.20 PRO 1.5
PROB THII PLC 0 ITER 25 FMAX 3 TOL 0.001
; ELLO 1 9999 1 TYPE PZ 1000
0.100
0.300
0.600
1.050
1.725
1.388
1.219
1.303
1.261
1.219
was
was
was
was
was
was
was
was
was
was
convergent.
convergent.
convergent.
convergent.
instabil.
instabil.
convergent.
instabil.
instabil.
convergent.
Version 14.66
555
ASE
PROG
HEAD
ECHO
ECHO
ECHO
131
132
133
556
3.43974E+04
3.93786E+04
4.25738E+04
Relativ
error
1.70E05
2.01E04
1.80E04
14
frequency
[Hertz]
37.841
39.453
42.853
Period
[sec]
0.026426
0.025346
0.023336
aktivated
mass [%]*
25.34235
23.05468
48.02222
modal
damping
0.00000
0.00000
0.00000
2.10E07
3.89E06
2.27E05
29.518
31.583
32.839
0.033878
0.031663
0.030452
22.66512
26.19929
20.53174
0.00000
0.00000
0.00000
Version 14.66
ASE
161
162
163
2.13418E+03
2.13419E+03
4.85068E+03
4.57E11
3.71E11
5.42E07
7.353
7.353
11.085
0.136008
0.136008
0.090215
20.05050
20.05058
22.81404
0.00000
0.00000
0.00000
The three buckling mode shapes are supposed to be applied now scaled as
nonstressed imperfection (In the test example ase9.dat also the use of a non
stressed imperfection is explained).
At first the maximum deflections of the vibration mode shapes are printed
here:
PROG DBPRIN
HEAD MAX. DISPLACEMENTS OF THE EIGENVALUES FOR SCALING:
ECHO SELE NO
ITEM NODE DISP
LC 161 ; PRIN MAMI
LC 162 ; PRIN MAMI
LC 163 ; PRIN MAMI
END
Loadcasenumber name
161 Eigenform
7.35 Hz
Nodal Displacements
name
Maximum
Minimum
ux
uy
uz
Phix
Phiy
Phiz
[mm]
[mm]
[mm] [mrad] [mrad] [mrad]
145.174 160.972 337.178 393.349 440.006 347.662
151.79 129.02 337.18 470.86 437.81 347.66
Loadcasenumber name
162 Eigenform
7.35 Hz
Nodal Displacements
name
Maximum
Minimum
ux
uy
uz
Phix
Phiy
Phiz
[mm]
[mm]
[mm] [mrad] [mrad] [mrad]
160.971 151.785 337.176 440.006 470.860 347.664
129.02 145.17 337.18 437.81 393.35 347.66
Loadcasenumber name
163 Eigenform
11.08 Hz
Nodal Displacements
name
Maximum
Minimum
ux
uy
uz
Phix
Phiy
Phiz
[mm]
[mm]
[mm] [mrad] [mrad] [mrad]
147.528 147.528 315.044 395.196 395.197 273.735
147.53 147.53 315.04 395.20 395.20 273.74
Version 14.66
557
ASE
maxuz. Thus the third vibration mode shape LC 163 is added with the factor 5mm/616.9mm to the other ones. At first an empty load case which includes the displacements from the program MAXIMA and which can be used
for the following load case as a primary load case has to be generated:
PROG ASE
HEAD GENERATION OF AN EMPTY LOAD CASE LOAD ALMOST 0
ECHO FULL NO
LC 201 FACT 0.001 ; ELLO 1 9999 1 TYPE PZ 1000
END
PROG MAXIMA
HEAD DISPLACEMENTS FROM VIBRATION MODE SHAPES COPY SCALED TO LC 201
ECHO FULL NO ; ECHO TABS YES
COMB 1 STAN
$ superpostion without coefficients!
LC 161 G FACT 5/337.2
$ RESULT IS MAX. IMPERFECTION OF 20 MM FOR VIBRATION MODE SHAPE 1
LC 162 G FACT 5/337.2
$ RESULT IS MAX. IMPERFECTION OF 20 MM FOR VIBRATION MODE SHAPE 2
LC 163 G FACT 5/315.0
$ RESULT IS MAX. IMPERFECTION OF 20 MM FOR VIBRATION MODE SHAPE 3
$
^ 315.0 MM = MAX. DISPLACEMENT uz LC 163 (FROM DBPRINOUTPUT)
SUPP 1 EXTR MAX ETYP NODE TYPE UZ LC 201 $ ADDS THE DISPLACEMENTS INTO LC 201
END
The load case 201 contains now the superpositioned deformations and (almost) no internal forces and moments. An ultimate load iteration follows with
consideration of this load case 201. It ends now already with the load factor
1.022:
PROG ASE
HEAD new ultimate load
ECHO FULL NO
ULTI 10 FAK1 0.10 DFAK
SYST PROB THII ITER 25
LC 202 ; ELLO 1 9999 1
END
Summary of the
ULSiteration
ULSiteration
ULSiteration
ULSiteration
ULSiteration
ULSiteration
ULSiteration
ULSiteration
558
0.100
0.300
0.600
1.050
0.825
0.938
1.106
1.022
was
was
was
was
was
was
was
was
convergent.
convergent.
convergent.
instabil.
convergent.
convergent.
instabil.
convergent.
Version 14.66
ASE
UZ
U0
Version 14.66
1.1353
Step
11 f=
1.000
559
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Curve B (load cases 201208) shows the load deformation curve with the imperfection from the first three scaled vibration mode shapes. The ultimate
load is smaller now, what on one hand results from the scheduled deformation
(u0) and on the other hand, however, the load deformation curve of a shell
has in general a reducing curve after the ramification point, that one can imagine form point A to the point B. The reducing curve can not be processed
currently with the program ASE.
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3D Tunnel Analysis.
3D tunnel
A tunnel excavation according to NATM (New Austrian Tunnelling Method)
is examined as an example of a threedimensional analysis with volume elements. The input of the program GENF has a parametric form and it is very
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extensive despite the use of input loops. An alternative input option consists
in the generation of a node disk with a graphical generator and then in the
copying several times along the direction of the tunnel. An accurate consideration of the partitioning in group numbers is required a priori, because the
groups have to be controlled separately during the various construction
stages. The following subdivision was chosen in the present case:
Group numbering:
Disks in tunnels direction
Element:
BRIC
Ground
BRIC
Calotte
BRIC
Base
QUAD Calotte
QUAD Base
QUAD Outer layer
1 2 3 4
Group number:
1 2 3 4
11 12 13 14
16 17 18 19
21 22 23 24
26 27 28 29
6
5
5
15
20
25
30
The ground elements of groups 15 describe the soil outside the tunnel shell.
Groups 2130 model the shotcrete shells.
Group 6 is only necessary for the graphic representation of contour lines at
the structures overlay. It is not used in the analysis, it is only activated in program WING (without QUADshell overlays BRIC results can be represented
as principal stress crosses only).
The input for ASE is not as extensive as the input for GENF and it is reproduced here. The input block 1 is used several times:
PROG ASE
HEAD CONSTRUCTION STAGE I RELAXATION CALOTTE 1
LET#4 1
$ LOAD CASE
$BLOCK BEG1
LET#5 #41
$ PRIMARY LOAD CASE
ECHO FULL NO
CTRL MSTE 105
SYST PROB NONL ITER 20 FMAX 3 NMAT YES
LET#1 5 $ NUMBER OF DISKS IN LONGITUDINAL TUNNEL DIRECTION
LET#2 0.25
$ LOOSENING FACTOR
LET#3 0.50
$ STIFFNESS FACTOR FRESH CONCRETE
MAT NR E
MUE D
GAM
GAMA
1,2 125000 0.35 1.00 22.0 12.0
3 30E6
0.20 0.15 25.0 15.0
NMAT 1 GUDE 20.000 1.000 9999 20.000 P10 0.80
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FACS
1.0
#2
1.0
1.0
FACP
1.0
#2
1.0
1.0
PLC
#5
#5
#5
#5
FACL
1.0
#2
1.0
1.0
FACD
1.0
#2
1.0
1.0
GAM
22.0
22.0
22.0
22.0
H
12
12
12
12
K
0.5
0.5
0.5
0.5
SIGN
0 $ BRIC OUTSIDE
0 $ BRIC INSIDE UPSIDE
0 $ BRIC INSIDE UPSIDE
0 $ BRIC INSIDE
$ DOWNSIDE
END
PROG ASE
HEAD CONSTRUCTION STAGE II
LET#4 2
$ LOAD
$BLOCK SET1
GRP
NO
FACS FACP
( 1 0+#1 1) 1.0
1.0
(12 10+#1 1) 1.0
1.0
16
#2
#2
(17 15+#1 1) 1.0
1.0
21
#3
1.0
END
FACL
1.0
1.0
#2
1.0
1.0
FACD
1.0
1.0
#2
1.0
1.0
$
$
$
$
$
BRIC
BRIC
BRIC
BRIC
QUAD
PROG ASE
HEAD CONSTRUCTION STAGE III RELAXATION CALOTTE 2 /
LET#4 3
$ LOAD CASE
$BLOCK SET1
GRP
NO
FACS FACP PLC FACL FACD
( 1 0+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
12
#2
#2
#5
#2
#2
$ BRIC
(13 10+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
(17 15+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
21
1.0
1.0
#5
1.0
1.0
$ QUAD
26
#3
1.0
0
1.0
1.0
$ QUAD
END
PROG ASE
HEAD CONSTRUCTION STAGE 4 EXCAVATION CALOTTE 2 /
LET#4 4
$ LOAD CASE
$BLOCK SET1
GRP
NO
FACS FACP PLC FACL FACD
( 1 0+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
(13 10+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
17
#2
#2
#5
#2
#2
$ BRIC
(18 15+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
21
1.0
1.0
#5
1.0
1.0
$ QUAD
22
#3
1.0
0
1.0
1.0
$ QUAD
26
1.0
1.0
#5
1.0
1.0
$ QUAD
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OUTSIDE
OUTSIDE UP
INSIDE DOWN
INSIDE DOWN
UP
EXCAVATION BASE 1
OUTSIDE
INSIDE UPSIDE
INSIDE UPSIDE
INDSIDE DOWNSIDE
UPSIDE
DOWNSIDE
RELAXATION BASE 2
OUTSIDE
INSIDE UPSIDE
INSIDE DOWNSIDE
INSIDE DOWNSIDE
UPSIDE
UPSIDE
DOWNSIDE
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END
PROG ASE
HEAD CONSTRUCTION STAGE 5 RELAXATION CALOTTE 3 /
LET#4 5
$ LOAD CASE
$BLOCK SET1
GRP
NO
FACS FACP PLC FACL FACD
( 1 0+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
13
#2
#2
#5
#2
#2
$ BRIC
(14 10+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
(18 15+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
21,22
1.0
1.0
#5
1.0
1.0
$ QUAD
26
1.0
1.0
#5
1.0
1.0
$ QUAD
27
#3
1.0
0
1.0
1.0
$ QUAD
END
PROG ASE
HEAD CONSTRUCTION STAGE 6 EXVACATION CALOTTE 3 /
LET#4 6
$ LOAD CASE
$BLOCK SET1
NO
FACS FACP PLC FACL FACD
GRP
( 1 0+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
(14 10+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
18
#2
#2
#5
#2
#2
$ BRIC
(19 15+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC
21,22
1.0
1.0
#5
1.0
1.0
$ QUAD
23
#3
1.0
0
1.0
1.0
$ QUAD
26,27
1.0
1.0
#5
1.0
1.0
$ QUAD
END
EXVACATION BASE 2
OUTSIDE
INSIDE UPSIDE
INSIDE UPSIDE
INSIDE DOWNSIDE
UPSIDE
DOWNSIDE
DOWNSIDE
RELAXATION BASE 3
OUTSIDE
INSIDE UPSIDE
INSIDE DOWNSIDE
INSIDE DOWNSIDE
UPSIDE
UPSIDE
DOWNSIDE
PROG ASE
HEAD CONSTRUCTION STAGE 7 RELAXATION CALOTTE ROOF 4 / EXVACATION BASE 3
LET#4 7
$ LOAD CASE
$BLOCK SET1
GRP NO
FACS FACP PLC FACL FACD
( 1 0+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC OUTSIDE
14
#2
#2
#5
#2
#2
$ BRIC INSIDE UPSIDE
(15 10+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC INSIDE UPSIDE
(19 15+#1 1) 1.0
1.0
#5
1.0
1.0
$ BRIC INSIDE DOWNSIDE
21,22,23
1.0
1.0
#5
1.0
1.0
$ QUAD UPSIDE
26,27
1.0
1.0
#5
1.0
1.0
$ QUAD DOWNSIDE
28
#3
1.0
0
1.0
1.0
$ QUAD DOWNSIDE
END
The elements of the surrounding soil are secured sufficiently with the shotcrete shell. By contrast, the elements of the excavation region are analysed
linearly, because the local front can not stand alone numerically with the
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given material parameters (20 degrees friction angle and 1 kN/m2 cohesion).
More accurate investigations could be necessary for the local front, if necessary. The nonlinear iteration leads to results with good convergence:
for load case
Iteration sequence
Iteration 1 Residual
Iteration 2 Residual
Iteration 3 Residual
Iteration 4 Residual
Iteration 5 Residual
Iteration 6 Residual
Iteration 7 Residual
22.140
14.367
3.294
1.028
0.266
0.121
0.063
energy
energy
energy
energy
energy
energy
energy
4.3019
4.4802
4.7338
4.7624
4.7670
4.7677
4.7678
e/f
e/f
e/f
e/f
e/f
e/f
e/f
0.000
0.000
0.106
0.085
0.163
0.110
0.136
1.000
1.041
2.462
1.118
1.359
1.118
1.402
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5.16.
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5.17.
The calculation is done here with ASE, however, it can occur also with PROG
SEPP, if SEP4 is set in the authorization file name.nam. The input SYST ...
NMAT YES is important, because the QUAD elements are processed only
then nonlinearly with the concrete law. The actually used material parameters should be checked in the calculation output!
The convergence of the nonlinear calculation has to be checked in any case.
A look in the file .prt or .erg shows, that a sufficient convergence of the residual forces was reached with the used concrete tensile strength:
Iteration
Iteration
Iteration
Iteration
568
1
2
3
4
Residual
Residual
Residual
Residual
72.887
66.342
45.552
57.400
energy
energy
energy
energy
4.0596
4.3677
5.1877
5.6622
e/f
e/f
e/f
e/f
0.000
0.000
0.365
0.523
1.000
1.076
3.640
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5 Residual
56.359
energy
6.0344 e/f
0.811
2.018
4.285
4.343
4.447
4.457
4.468
4.479
energy
energy
energy
energy
energy
energy
7.8341
7.8344
7.8348
7.8349
7.8349
7.8350
0.000
0.591
0.583
0.000
0.000
0.000
0.297
1.182
1.166
0.297
0.297
0.297
...
...
Iteration
Iteration
Iteration
Iteration
Iteration
Iteration
67
68
69
70
71
72
Residual
Residual
Residual
Residual
Residual
Residual
e/f
e/f
e/f
e/f
e/f
e/f
Especially the energy as product from load vector deformation vector converges very well. It is also seen the file .prt, that the number of the equations
increases to 5031 unknowns in opposite to the linear calculation with 2517
unknowns, because the horizontal deformations must be used here.
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90 TOL 0.002 NMAT YES
1) PHI 2.0 EPS 22E5
LCRS 99 $ reinforcement from BEMESS incl. min reinf.
1.00 BET2 0.5 TITL SLS+CS
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The results of another calculation clarifies once more the influence of the concrete tensile strength to the maximum displacement:
The underside of the plate does not cracked at the calculation of the load case
203. The deformation is therefore only about the factor 1+PHI = 1+2.0 = 3.0
higher in opposite to the linear calculation of the load case 200. The plate
cracks below, however, with a large surface at the calculation of the load case
202. The crack widths are here clearly larger as for load case 201 due to the
creep and shrinkage effects of the concrete.
5.18.
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Internal forces and moments for two elements during the displacement
controlled loading
X = the two middle elements 5+6
= the two adjacent elements 4+7
Further examples for creep and shrinkage:
ase.dat\...\nonlinear_quad\ betokri2.dat = statically determined supported
single span girder
for "nonlinear methods" in connection with beams see also
ase.dat\...\nonlinear_beam\aseaqb_1.dat
5.19.
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