RAM Structural System Help

Response Spectra Analysis

Last updated: January 20, 2021

In a response spectra analysis, the program evaluates modal story and joint displacements and member forces for a given digitized acceleration vs. period response spectrum. RAM Frame has a library of common response spectra such as El Centro (1940), discretized UBC and NEHRP. Users can also create response spectra tables (See the RAM Manager manual for details). For IBC 2006, 2003, 2000, UBC 1997, China GB50011-2001 and AS 1170.4-2007 specifications for dynamic analysis, RAM Frame allows users to enter the parameters that define the spectrum curve to be used.

A response spectra analysis is always preceded by an Eigen value extraction. The modal responses associated with each direction of excitation are then calculated. The modal responses (story displacements, nodal displacements, member forces etc.) are then combined using any of the two common methods, namely CQC (complete quadratic combination) and SRSS (square root of the sum-of-squares). Users can select the desired method while specifying the lateral load cases.

The SRSS method, as its name implies, takes the square root of the sum of the squares of the modal responses. The CQC method, on the other hand, is based on random vibration theory and combines modal responses by taking the complete quadratic terms and cross-modal coefficients. The cross-modal coefficients are evaluated as functions of modal frequencies and damping ratios of the structure.

It should be mentioned that research has shown that the SRSS method may give errors in three-dimensional buildings [Wilson, et al., 1981]. As a result, the CQC method is recommended for use for three-dimensional building structures where the frequencies are often close and the mode shapes coupled. For two-dimensional structures, the SRSS scheme gives results as good as CQC.