Combination of modal responses: a new closed-form formulation for rigid response coefficient

Recently, US Nuclear Regulatory Commission (USNRC) conducted a study for combination of modal responses in response spectrum method of seismic analysis. Its outcome emphasized that each modal response quantity should be separated into damped-periodic and rigid parts using the 'rigid response coefficient'. The damped periodic parts of modal responses are combined using the double-sum equation and the rigid parts are combined algebraically. Existing methods for rigid response coefficient such as those given by Lindley-Yow (1980) and Gupta (1992) are either heuristic or based on numerical studies of free-field earthquake motions. Gupta's method works well for free-field earthquake motion within the frequency regions of interest. However, the earthquake input for secondary systems such as piping equipment is defined in terms of floor motion. The frequency characteristics of floor motions are very different from those of free field motion. In this paper, the validity of existing formulations is examined for the case of floor motions. A closed-form formulation based on time domain approach is developed to explain the nature of variation in rigid response coefficient. The results from this formulation gives identical results to numerically evaluated rigid response coefficient in the complete frequency region of interest. (authors)