Probabilistic evaluation of combination rules for seismic force demands from orthogonal ground motion components

A probabilistic approach to assessing the effectiveness of the rules used to combine demands from orthogonal ground motion components is developed. Full probability distributions of the ratio between the force demands obtained from nonlinear response history analyses using bidirectional loading, which are taken as the "true" demands, and rule-based combinations of the demands from unidirectional loading, are developed. For the percentage combination rules (100-p), a relationship is established between the value of p (e.g. p = 30% for 100-30 rule) and the probability that the bidirectional loading demands exceed the rule-based combination of the unidirectional loading demands. Using this relationship, an appropriate value of p based on an acceptable exceedance probability is determined. The proposed framework is demonstrated using special concentric braced frames with biaxially loaded columns, which are shared by orthogonal braced frames. The combinatorial effect of the orthogonal responses is found to be influenced by several factors including the type of demand parameter (e.g. column axial forces versus stresses), demand level and building height.