Improved Method for the Calculation of Plastic Rotation of Moment-Resisting Framed Structures for Nonlinear Static and Dynamic Analysis

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.