Q1: Can Staad calculate Rayleigh frequency for a model with tension member only?
Q2: Can I use mode shape command to determine frequency with a model having tension member only? Thank you in advance.
The answer is yes for both questions.
PS: Please refer to Kris's detailed answer below which explains the approximations involved in such calculation.
Answer Verified By: Staad123
To add to what Sye has written, here is some information that you may find helpful.
Your question:
Can Staad calculate Rayleigh frequency for a model with tension only members?
Answer:
Yes. The program first performs an iterative static analysis to calculate the joint displacements. Using the displacements of the converged solution (final iteration), it calculates the Rayleigh frequency. If member tension is specified, some of those members are likely to be switched off and the frequency will be for the full structure minus those members.
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Q2: Can I use mode shape command to determine frequency with a model having tension member only?
Apologies for the long-drawn answer. There is no simple way to answer this.
The frequency calculation methods in STAAD are designed for small deformation linear entities. By that we mean:
(a) transverse deformations are small enough that they do not induce axial effects. A cable strung between two points sags under its own weight which in turn causes axial tension. Hence, it is not a small deformation entity.
(b) entities that are active in tension as well as in compression. This is what we meant when we wrote earlier that "In a dynamic analysis, the axial force in a member changes sign over and over again since vibration causes the structure to deflect in opposing directions periodically." The eigensolution is based on a single stiffness matrix, and, all entities whose contribution is in that matrix are active throughout the oscillations of the structure.
So, the consequences of these assumptions are:
1) When you model a cable as a tension-only member, its non-linear characteristics (axial force induced by transverse deformation) are not being considered in the frequency calculation. The true behavior of a non-linear cable is not being captured.
2) If you have members that are active in tension, but not in compression, or vice-versa, that behavior cannot be captured in a single stiffness matrix. For conventional beams columns and braces, the state of the axial force when the oscillations are at one extremity are likely to be opposite to the axial force when the oscillations are at the other extremity. If the member is to be treated as active at one extremity and inactive at the other, it is not possible to do that correctly with a single stiffness matrix.
This is why the program displays the message ("**Possible Error - Dynamic case solved while Tension/Compression is active."
You have rightly stated "But following the warning and error, STAAD gives a solution of calculated frequencies.........)
This is because, instead of ignoring the request to calculate frequencies or terminating the analysis, it is computing them based on some approximations. In cases like MODAL CALCULATION REQUESTED, it first uses the weights of that load case as static loads and does an iterative static analysis to find which members to keep and which ones to inactivate. The residual structure is then used for forming the stiffness matrix.
In other cases like SPRING TENSION/COMPRESSION, it ignores the specification altogether.
In our opinion, it is best not to use MEMBER TENSION/COMPRESSION or SPRING TENSION/COMPRESSION for frequency calculation, response spectrum or time history analysis. By definition, frequency calculation involves a free vibration problem that is based on just masses and stiffnesses. What should be the basis for determining which of those tension-only members or springs are to be treated as active and which ones must be switched off?
If you have a reasonable assessment of which among the tension-only members you want to include in the frequency analysis, use the INACTIVE MEMBER command for switching off the members that you don't want to be included in the [K] matrix. If the model also contains static load cases with MEMBER TENSION, use the following sequence
LOAD NNN (last static load case)
..
PERFORM ANALYSIS
CHANGE
MEMBER TENSION 0 (This removes the tension/compression attribute as well as the SPRING TENSION/COMPRESSION attribute from all members)
INACTIVE MEMBER member-list (This list contains members that you do not want to be used in the frequency calculation or dynamic analysis)
LOAD PPPP (Dynamic load case - frequency extraction, response spectrum, time histiry, etc.)
...
LOAD COMBINATION QQ
LOAD LIST ALL
Answer Verified By: Sye
Hi Kris and Sye, four years later from when these questions were raised, is STAAD now capable of determining the fundamental frequency based on TENSION/COMPRESSION only members or member with CABLE specification and Pretension?These are very important considerations for dynamic analysis of bridges.