The shape of the seismic response interaction diagram: The effect of combination rules in response spectrum analysis

Abstract

This paper deals with the construction of seismic response interaction diagrams that show the correlation of multiple responses and are important to determine the critical combination of modal responses. Many design problems, such as column design under combined axial force and bending moments, fall into this category. We address general modal and multicomponent combination rules and study their effect on the shape of the response interaction diagrams, thus extending previous work done for quadratic combination rules. Special attention is given to multilinear combination rules which lead to polyhedral shapes. Having developed efficient methods to deal with polyhedral shapes, we explore the idea of adopting a multilinear modal combination rule to compose with a multicomponent percentage rule.