An effective geometric nonlinear analysis approach of framed structures with local material nonlinearities based on the reduced-order Newton-Raphson method

The P-Δ effect is essential to be considered in the quasi-static pushover or horizontal seismic analysis of high-rise framed structures. Owing to the presence of the P-Δ effect, however, the geometric stiffness varies with the members’ internal variables (such as axial force and relative lateral displacement). Using a conventional nonlinear analytical process, each iteration has to update the structural effective stiffness even though the material remains elastic. Consequently, it requires a tremendous amount of computational effort in the material and geometric (double) nonlinear analysis of large-scale frames. To alleviate this disadvantage, this study presents an efficient and accurate nonlinear analysis approach for the high-rise framed structure considering the P-Δ effect. Assuming an invariant (time-independent) vertical load of each storey after the gravity analysis, the structural geometric stiffness induced by the P-Δ effect is then constant. Accordingly, the conventional double nonlinear system could be converted into an equivalent material nonlinear one whose effective stiffness contains material and geometric components. After that, a reduced-order Newton-Raphson method is employed to simplify the iterative analysis of the global system into that of a reduced subsystem comprised by yielding elements. Four application cases demonstrated the accuracy and reliability of the presented geometric nonlinear analysis approach. Predictably, the presented strategy will considerably improve the efficiency of double nonlinear analysis of the tall framed structure with local material nonlinearities. •An effective approach is presented for material and geometric (double) nonlinear analyses of frames.•Double nonlinear analyses of a frame can be changed to material nonlinear analysis of an equivalent system.•Only displacements of yielding elements are solved in double nonlinear analyses of frames.•The presented approach is efficient in double nonlinear analysis of high-rise frames with nonlinear localization.