Modification of Substitute Frame for steel moment frames with irregular bay lengths

Mass nonlinear dynamic analysis is unavoidable in many fields of earthquake and structural engineering, such as incremental dynamic analysis, probabilistic performance-based design, and optimization approaches. Using simplified models with fewer degrees of freedom instead of detailed original models to a great extent reduces the computational cost and prevents extremely time-consuming analysis. Among different simplified models for steel moment frames, stick models (such as shear beam models) only use the global story stiffness to estimate the original model responses, which do not consider the structural configuration. The stick models are only suitable for obtaining the general responses of the structure, such as global and interstory drift. However, simplified frame models are the more accurate simplified models that consider the details of the original frame, such as beam and column elements, nonlinear plastic hinge springs, and joint rotations. Substitute Frame is one of these models, which is a one-bay frame that predicts the structural responses for concrete and steel moment frames with very high accuracy. The purpose of this research is to develop a substitute frame model for steel moment frames with unequal bay lengths. For this purpose, the beam stiffness and nonlinear behavior of rotational springs were modified based on linear and nonlinear structural analysis approaches and the proposed model is called Modified Substitute Frame. In the following, to evaluate the accuracy of the proposed model, three types of 12-story buildings with unequal bay lengths were designed using ASCE7-16 and AISC 341-16 criteria and subjected to three different ground motion data sets, i.e., far field, near field with pulse and without pulse ground motions. The nonlinear time history analysis results showed that the Modified Substitute Frame predicts the original frame responses with very high accuracy. Moreover, the Modified Substitute Frame prediction was more precise than the Improved FishBone model which was recently presented for moment frames with unequal bay lengths.