STAAD.Pro Instability And Zero Stiffness [FAQ]
| Applies To | |||
| Product(s): | STAAD.Pro | ||
| Version(s): | All | ||
| Environment: | N/A | ||
| Area: | Analysis | ||
| Subarea: | Instability and Zero Stiffness | ||
| Original Author: | Bentley Technical Support Group | ||
- Itriedtomodelaconcretefoundationusingsolidelements,basicallyfollowingtheapproachdescribedinexample24oftheexamplesmanual.However,Igotthiswarningstating"morethan12DOFwithzerostiffness".CananyonepleaseadvisemewhatarethetechnicalreasonsforthisandhowIcanpossiblyhandlethiswarning?
- Whenwegeneratethespringsupportsforaraftfoundationusingthecommand"list-of-jointsElasticmatDirYONLYSUB10000"wegetinstabilitywarningsinFX,FZandMYdirectionsatcertainjoints.Why?
- Ihaveanalyzedastructureandfindthatthereareinstabilitymessagesinthe.anl(output)file
- Ifthereareinstabilitymessages,doesitmeanmyanalysisresultsmaybeunsatisfactory?
- Ifthereareinstabilitymessages,arethereanysimplecheckstoverifywhethermyanalysisresultsaresatisfactory?
- WhatdoesazerostiffnesswarningmessageintheSTAADoutputfilemean?
1. I tried to model a concrete foundation using solid elements, basically following the approach described in example 24 of the examples manual. However, I got this warning stating "more than 12 DOF with zero stiffness". Can anyone please advise me what are the technical reasons for this and how I can possibly handle this warning?
A solid element by its basic nature does not have rotational degrees of freedom at its nodes. So, at all points on the structure where the only entities connected are solid elements, there is no rotational stiffness.
There is an explanation on the reasons behind zero stiffness messages at
http://www.reiworld.com/Search.asp?id=SP-1496
If you are using STAAD.Pro 2003 Build 1003.US or later, and the only entities in your structure are solids (no plates or beams), the program automatically applies restraints along those rotational degrees of freedom and the messages will hence not appear. However, if beams or plates are present in the structure in addition to solids, those messages will be present.
If you do not encounter instability warning messages in your output, and the applied loads are in equilibrium with support reactions, you may consider the zero stiffness warning messages harmless, and ignore them.
2. When we generate the spring supports for a raft foundation using the command "list-of-joints Elastic mat Dir YONLY SUB 10000" we get instability warnings in FX, FZ and MY directions at certain joints. Why?
The Elastic Mat instability messages have to do with the Y option versus the YONLY option. The Y option automatically fixes the FX and FZ directions at all mat joints whereas the YONLY option does not. Without any support in the FX and FZ directions, your structure is unstable in these directions and MY as well. You could switch to the Y option or perhaps fix FX, FZ and MY at one joint near the center. Since STAAD automatically applies very small springs at one joint to stabilize an unstable structure, you could ignore the messages if there are no FX, FZ, or MY loadings and if the displacements are small in those directions.
3. I have analyzed a structure and find that there are instability messages in the .anl (output) file, as follows :
***WARNING - INSTABILITY AT JOINT 26 DIRECTION = FX
PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING
K-MATRIX DIAG= 5.3274384E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 127
***NOTE - VERY WEAK SPRING ADDED FOR STABILITY
**NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS
DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE
BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL,
STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR
IS 1.000E-09
THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK
ELEMENTS AS WELL AS TRUE SINGULARITIES.
What is the significance of such messages?
An instability is a condition where a load applied on the structure is not able to make its way into the supports because no paths exist for the load to flow through, and may result in a lack of equilibrium between the applied load and the support reaction.
There is some explanation available in Section 1.18.1 of the STAAD.Pro Technical Reference Manual for the typical cause of instabilities. You will find it under the heading "Modeling and Numerical Instability Problems".
4. If there are instability messages, does it mean my analysis results may be unsatisfactory?
There are many situations where instabilities are unimportant and the STAAD approach of adding a weak spring is an ideal solution to the problem. For example, sometimes an engineer will release the MX torsion in a single beam or at the ends of a series of members such that technically the members are unstable in torsion. If there is no torque applied, this singularity can safely be "fixed" by STAAD with a weak torsional spring.
Similarly a column that is at a pinned support will sometimes be connected to members that all have releases such that they cannot transmit moments that cause torsion in the column. This column will be unstable in torsion but can be safely "fixed" by STAAD with a weak torsional spring.
Sometimes however, a section of a structure has members that are overly released to the point where that section can rotate with respect to the rest of the structure. In this case, if STAAD adds a weak spring, there may be large displacements because there are loads in the section that are in the direction of the extremely weak spring. Another way of saying it is, an applied load acts along an unstable degree of freedom, and causes excessive displacements at that degree of freedom.
5. If there are instability messages, are there any simple checks to verify whether my analysis results are satisfactory?
There are 2 important checks that should be carried out if instability messages are present.
a) A static equilibrium check. This check will tell us whether all the applied loading flowed through the model into the supports. A satisfactory result would require that the applied loading be in equilibrium with the support reactions.
b) The joint displacement check. This check will tell us whether the displacements in the model are within reasonable limits. If a load passes through a corresponding unstable degree of freedom, the structure will undergo excessive deflections at that degree of freedom.
One may use the PRINT STATICS CHECK option in conjunction with the PERFORM ANALYSIS command to obtain a report of both the results mentioned in the above checks. The STAAD output file will contain a report similar to the following, for every primary load case that has been solved for :
***TOTAL APPLIED LOAD ( KG METE ) SUMMARY (LOADING 1 )
SUMMATION FORCE-X = 0.00
SUMMATION FORCE-Y = -817.84
SUMMATION FORCE-Z = 0.00
SUMMATION OF MOMENTS AROUND THE ORIGIN-
MX= 291.23 MY= 0.00 MZ= -3598.50
***TOTAL REACTION LOAD( KG METE ) SUMMARY (LOADING 1 )
SUMMATION FORCE-X = 0.00
SUMMATION FORCE-Y = 817.84
SUMMATION FORCE-Z = 0.00
SUMMATION OF MOMENTS AROUND THE ORIGIN-
MX= -291.23 MY= 0.00 MZ= 3598.50
MAXIMUM DISPLACEMENTS ( CM /RADIANS) (LOADING 1)
MAXIMUMS AT NODE
X = 1.00499E-04 25
Y = -3.18980E-01 12
Z = 1.18670E-02 23
RX= 1.52966E-04 5
RY= 1.22373E-04 23
RZ= 1.07535E-03 8
Go through these numbers to ensure that
i) The "TOTAL APPLIED LOAD" values and "TOTAL REACTION LOAD" values are equal and opposite.
ii) The "MAXIMUM DISPLACEMENTS" are within reasonable limits.
6. What does a zero stiffness warning message in the STAAD output file mean?
The procedure used by STAAD in calculating displacements and forces in a structure is the stiffness method. One of the steps involved in this method is the assembly of the global stiffness matrix. During this process, STAAD verifies that no active degree of freedom (d.o.f) has a zero value, because a zero value could be a potential cause of instability in the model along that d.o.f. It means that the structural conditions which exist at that node and degree of freedom result in the structure having no ability to resist a load acting along that d.o.f.
A warning message is printed in the STAAD output file highlighting the node number and the d.o.f at which the zero stiffness condition exists.
Examples of cases which give rise to these conditions :
Consider a frame structure where some of the members are defined to be trusses. On this model, if a joint exists where the only structural components connected at that node are truss members, there is no rotational stiffness at that node along any of the global d.o.f. If the structure is defined as STAAD PLANE, it will result in a warning along the MZ d.o.f at that node. If it were declared as STAAD SPACE, there will be at least 3 warnings, one for each of MX, MY and MZ, and perhaps additional warnings for the translational d.o.f.
These warnings can also appear when other structural conditions such as member releases and element releases deprive the structure of stiffness at the associated nodes along the global translational or rotational directions. A tower held down by cables, defined as a PLANE or SPACE frame, where cable members are pinned supported at their base will also generate these warnings for the rotational d.o.f. at the supported nodes of the cables.
Solid elements have no rotational stiffness at their nodes. So, at all nodes where you have only solids, these zero stiffness warning messages will appear.
These are warnings and not errors because :
The reason why these conditions are reported as warnings and not errors is due to the fact that they may not necessarily be detrimental to the proper transfer of loads from the structure to the supports. If no load acts at and along the d.o.f where the stiffness is zero, that point may not be a trouble-spot.
What is the usefulness of these messages :
A zero stiffness message can be a tool for investigating the cause of instabilities in the model. An instability is a condition where a load applied on the structure is not able to make its way into the supports because no paths exist for the load to flow through, and may result in a lack of equilibrium between the applied load and the support reaction. A zero stiffness message can tell us whether any of those d.o.f are obstacles to the flow of the load.
See Also
Structural Product TechNotes And FAQs
External Links
Bentley Technical Support KnowledgeBase
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