| Applies To | |||
| Product(s): | STAAD.Pro | ||
| Version(s): | All | ||
| Environment: | N/A | ||
| Area: | Analysis | ||
| Subarea: | Response Spectrum Analysis | ||
| Original Author: | Bentley Technical Support Group | ||
As I understand The Rayleigh method is used for natural Frequency calculations (first mode only) in the command CALCULATE NATURAL FREQUENCY & also in the command DEFINE UBC LOAD or 1893 load. Whereas the matrix method of iteration (like Staddola method) is used in the Response Spectrum method of analysis . Does this mean the values which we got by define 1893 load or Calculate natural frequency are wrong?
It is not true that the lowest frequency is the one which is associated with significant amount of participation of the masses of the model. That may be true of structures which look like a cantilever. But if the spatial distribution of masses is extensive, there is no guarantee that the fundamental mode is the most critical mode.
The statement that the Rayleigh frequency is associated with the first mode of the structure too is not correct.
A structure has several modes of vibration. If the structure were free to vibrate, the modes of vibration will follow the ascending order of strain energy. Consequently, if Y is the weakest direction of the structure, a Y direction mode will be the first mode. If the next weakest direction is Z, then the second mode will be a Z direction mode. Structures have local modes, where a small region within the model vibrates while the rest of the model remains stationary. It is entirely possible that a local mode is the lowest energy mode.
In many cases, torsional modes happen to be the lowest modes. Local and torsional modes are associated with negligible mass participation. You should look at the mode shapes of all the modes to get a sense of all the major vibration modes.
Since when using the Rayleigh method, one tends to load the structure in a manner which generally resembles a large mass participation mode, there is no sense in comparing the Rayleigh frequency with the lowest frequency from the eigensolution. Instead, you have to try to compare the displaced shape of the model used in the Rayleigh calculations with the various modes from eigensolution until you find a mode shape which resembles the displaced shape. When you do find a match, you will find that the Rayleigh frequency will be similar in value to the frequency of the matching mode.
If you do not like the frequency being used in the IS 1893 load generation, which is Rayleigh based, there is an option in STAAD for the user to provide his/her own value of the frequency. This is done using the PX and PZ options, as in the following example.
ZONE 0.05 K 1.0 I 1.0 B 1.0 PX 0.4 PZ 0.8
The values you provide for PX and PZ will be used in place of the one calculated by the Rayleigh method.