Hong, HKHKHongLI-WEI LIUShiao, YPYPShiaoChang, CJCJChang2023-02-042023-02-0420221727-7191https://scholars.lib.ntu.edu.tw/handle/123456789/627637Developed herein is an analysis procedure based on closed-form solutions to elastoplastic bilinear model of building structures accounted for different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels due to the layout of buildings and the complexity of structural members. The seismic design often considers earthquake forces on multiple floor levels but usually only in a single direction. However, in reality, the direction of the earthquake is not limited to one particular direction. Therefore, studying the influence of a two-way, furthermore multi-dimensional, earthquake on buildings is of great value. To estimate the total seismic demand on inelastic building structures subjected to multi-dimensional loading, this paper aims to find closed-form solution responses to an input rectilinear force path for the elastoplastic bilinear model of Hong and Liu (1999) which already has available closed-form solution responses to an input rectilinear displacement path. In this paper the elastoplastic bilinear model of building structures and Minkowski spacetime are adapted to accommodate such situations as different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels.elastoplastic bilinear model; closed-form formulae; multi-dimensional earthquake forces; rotated yield ellipse; Minkowski spacetime; DISTRIBUTED-ELEMENT MODELS; MINKOWSKI SPACETIME; INTERNAL SYMMETRY; CYCLIC PLASTICITY; LORENTZ GROUP; BEHAVIORjournal article10.1093/jom/ufac0452-s2.0-85145356541WOS:000893405800001https://api.elsevier.com/content/abstract/scopus_id/85145356541