Applies To
	Product(s):	STAAD.Pro
	Version(s):	All
	Environment:	N/A
	Area:	Analysis Solutions
	Subarea:	Response Spectrum Analysis
	Original Author:	Bentley Technical Support Group

The natural frequencies obtained during a Response Spectrum Analysis do not match the values calculated using the CALCULATE RAYLEIGH FREQUENCY command. Why is that?

In STAAD, there are 2 methods for obtaining the frequencies of a structure.

1. The Rayleigh method using the CALCULATE RAYLEIGH FREQUENCY command
2. The elaborate method which involves extracting eigenvalues from a matrix based on the structure stiffness and lumped masses in the model.

The Rayleigh method in STAAD is a one-iteration approximate method from which a single frequency is obtained. It uses the displaced shape of the model to obtain the frequency. Needless to say, it is extremely important that the displaced shape that the calculation is based on, resemble one of the vibration modes. If one is interested in the fundamental mode, the loading on the model should cause it to displace in a manner which resembles the fundamental mode. For example, the fundamental mode of vibration of a tall building would be a cantilever style mode, where the building sways from side to side with the base remaining stationary. The type of loading which creates a displaced shape which resembles this mode is a lateral force such as a wind force. Hence, if one were to use the Rayleigh method, the loads which should be applied are lateral loads, not vertical loads.

For the eigensolution method, the user is required to specify all the masses in the model along with the directions they are capable of vibrating in. If this data is correctly provided, the program extracts as many modes as the user requests (default value is 6) in ascending order of strain energy. The mode shapes can be viewed graphically to verify that they make sense.

Thus, the answer to the question is : If you want to use the Rayleigh method, make sure you provide the right type of loading. If the load you apply causes an arbitrary displaced shape which has no resemblance to the vibration mode you are interested in, the frequency value you get will be wrong.