Building codes in the U.S. require at least two horizontal ground motion components for three-dimensional (3D) response history analysis (RHA) of structures. For sites within 5 km of an active fault, these records should be rotated to fault-normal/fault-parallel (FN/FP) directions, and two RHA analyses should be performed separately (when FN and then FP are aligned with transverse direction of the structural axes). It is assumed that this approach will lead to two sets of responses that envelope the range of possible responses over all non-redundant rotation angles. This assumption is examined here using 3D computer models of a single-story structure having symmetric (that is, torsionally-stiff) and asymmetric (that is, torsionally flexible) layouts subjected to an ensemble of bi-directional near-fault strong ground motions with and without apparent velocity pulses. In this parametric study, the elastic vibration period of the structures is varied from 0.2 to 5 seconds, and yield strength reduction factors R is varied from a value that leads to linear-elastic design to 3 and 5. The influence that the rotation angle of the ground motion has on several engineering demand parameters (EDPs) is examined in linear-elastic and nonlinear-inelastic domains to form a benchmark for evaluating the use of the FN/FP directions as well as the maximum-direction (MD) ground motion, a new definition of horizontal ground motions for use in the seismic design of structures according to the 2009 NEHRP Provisions and Commentary.