TR.34.1 Rayleigh Frequency Calculation
This command may be used to calculate the Rayleigh method approximate frequency of the structure for vibration corresponding to the general direction of deflection generated by the load case that precedes this command. Thus, this command typically follows a load case.
Description
This command is specified after all other load specifications of any primary load case for which the Rayleigh frequency is calculated. This Rayleigh frequency calculation is based on the Rayleigh iteration method using 1 iteration. If a more accurate, full-scale eigensolution is required, the MODAL CALCULATION command (see next section) may be used. A full eigensolution is automatically performed if a RESPONSE SPECTRUM or TIME HISTORY is specified in any load case.
Example
LOADING 1 SELFWEIGHT X 1.0 CALCULATE RAYLEIGH FREQUENCY LOADING 2 SELFWEIGHT Z 1.0 CALCULATE RAYLEIGH FREQUENCY LOADING 3 WIND LOAD
In this example, the Rayleigh frequency is calculated for the X direction mode of vibration in load case 1, and the Z direction in case 2.
In case 1, the structure is being displaced by SELFWEIGHT applied statically along global X. For most frames which are supported only at their base, this produces a deflected shape resembling the lowest mode shape along global X. Hence, this frequency will resemble that for the lowest X direction mode.
Similarly, the frequency calculated for load case 2 ought to be similar to that for the lowest Z direction mode because the selfweight is applied statically along global Z.
The output will consist of the value of the frequency in cycles per second (cps), the maximum deflection along with that global direction and the joint number where that maximum occurs.
Notes
This command is based on the Rayleigh method of iteration using a single iteration. The frequency calculated estimates the frequency as if the structure were constrained to vibrate in the static deflected shape generated by the loads in the load case.
In many instances, the forces should be in one global direction to get the mode and frequency associated with that direction.
As the Rayleigh method is force-dependant, the inverse of the frequency (period, T = 1/f) may not match the Tb value calculated for a static seismic load by STAAD.Pro. This is because the approximate fundamental period using the Rayleigh method is initially calculated using the vertical mass weights as a horizontal force to obtain deflections.