Dynamic Analysis of Frames With Material and Geometric Nonlinearities Based on the Semirigid Technique

This paper presents a method for nonlinear dynamic analysis of frames with material and geometric nonlinearities which is based on the semirigid technique. The plastic hinge that accounts for the material nonlinearity is modeled as a pseudo-semirigid connection with nonlinear hysteretic moment-curvature characteristics at the element ends. The stiffness matrix of a frame element with material and geometric nonlinearities is expressed as the sum of products of the standard stiffness matrix and the geometric stiffness matrix of the element, with their corresponding correction matrices based on the plasticity factors developed from the section flexural stiffness at the plastic hinge locations. The combined stress yield condition is used for the force state determination of plastic hinges, and force equilibrium iterations and geometry updating for frames are carried out in every time step. When the key parameters of a structure are updated in a time step, the time step is split up into substeps to ensure accuracy while keeping the computations to a reasonable amount. The plastic rotation history can be calculated directly or in an approximate indirect way. The method is computationally efficient and it needs no additional connection elements, which makes it convenient for incorporation into existing linear dynamic analysis programs. Besides, the method can handle accurately and efficiently the dynamic analysis of nonlinear frames using relatively large time steps in conjunction with time step subdivision to cope with key parameter changes. A portal frame is used to verify the correctness of the proposed method. A more complicated five-story frame is used to illustrate the applicability and performance of the proposed method.