12.6. Analysis and Solution Controls

The following analysis and solution-control topics are available:

 

12.6.1. Response-Spectrum Analysis Summary

Following is a summary of the response-spectrum analyses (RSAs) and corresponding solution controls:

Case Input Spectra Mode-Combination Method Missing-Mass Effect Rigid-Response Effect
A1X-direction inputSRSSNoNo
A2CQCNoNo
A3

Yes

(MMASS,ON, 0.54)1

No
A4

Yes

(RIGRESP,ON,LINDLEY,0.54)

A5

Yes

(RIGRESP,ON,GUPTA,2.80,11.90)2

A6

Yes

(RIGRESP,ON,GUPTA,2.80,6)2

A7X-, Y-, and Z-direction inputs

Yes

(RIGRESP,ON,LINDLEY,0.54)

  1. The input spectrum unit is g. To transform it into SI units, set FACT = 386.4 on the SVTYP command.

  2. The rigid-response effect initial frequency is 2.80 Hz (VAL1 on the RIGRESP command), and the final frequency is 6 Hz or 11.90 Hz (VAL2).

Fourteen modes exist below fZPA. All 14 modes are used in all seven spectrum analyses.

 

12.6.2. Full-Transient Analysis Summary

In the transient analysis, the damping coefficients α (proportional to the mass) and β (proportional to the stiffness) must be specified to reproduce the input spectrum's one-percent constant modal damping.

The equation ξi = α/2ωi + βωi/2 is used for the damping coefficients, where ωi is the natural circular frequency of mode i.

The coefficients are determined by specifying the target modal damping at the fundamental frequency (2.91 Hz) and at an intermediate frequency between this frequency and fZPA. A frequency of 14.32 Hz is chosen to achieve the best fit over the 2.91 Hz to 16.50 Hz range of interest.

The values obtained are α = 0.304 (ALPHAD) and β = 1.85e-4 (BETAD). Small variations of these coefficients have a negligible effect on the results.

Automatic time stepping ensures that the time step is small enough to accurately calculate the higher mode responses. The duration of the analysis is 14.99 seconds.

When performing the time history analysis with three-directional input motions, the individual responses for each input motion (X, Y, and Z directions) are combined using the SRSS method.