Combination rules and degree of correlation of the effects of individual components for moment resisting steel frames

For numerical evaluation purposes of the seismic response of structures, earthquakes motions are generally represented by three orthogonal components; two horizontal and one vertical. Most of design codes that address the issue specify that the total response can be obtained from the combination of the individual responses produced by each component. The commonly used ways of combining the individual effects are the 30% and the SRSS combination rules. Despite these rules seem to be simple to apply, there are many aspects of the problem that need clarification: a) How to select the critical orientation of the orthogonal components? b) Can the rules be applied for both, elastic and inelastic behavior? c) Are the effects of individual components uncorrelated for principal components as usually assumed? To meet the objectives of the study, the seismic responses of some structural models used in the SAC steel project are estimated as accurately as possible. The responses of moment resisting steel frames (MRSFs) are specifically studied. The results of this study indicate that the maximum response is obtained for principal components. In terms of mean values, the rules underestimate the total response by about 10% in the case of collinear individual response parameters. The COV significantly increases for inelastic behavior. For non-collinear response parameters the rules overestimate the combined response by about 10%. For the case of multiple response parameters the mean values increase but the COV decreases. The results of the numerical study clearly indicate that the accuracy of the rules depends on the type of parameter being considered and that the effects of individual components may be highly correlated even when principal components are considered. The codes should be more specific regarding applications of the mentioned commonly used combination rules.