An extended modal pushover procedure for estimating the in-plane seismic responses of latticed arches

The vertical displacements induced by the in-plane vibrating modes of an arch formed structure are as important as the lateral ones. Therefore, the vertical response components should be considered in the modal pushover load patterns for the in-plane seismic performance evaluation of latticed arches. Since the equivalent force of the modal equivalent single-degree-of-freedom (ESDF) system is determined by the base shear in conventional modal pushover procedures, which could not reflect the vertical part of the pushover load, an extended modal pushover analysis (MPA) procedure is proposed in this paper. In the extended MPA, the modal ESDF system of the in-plane vibrating mode of a latticed arch is established by the aid of an energy-based structural stiffness parameter, and the equivalent load of theESDF system is obtained according to the static pushover load factor, instead of using the base shear or other kinds of support reactions. The extended MPA approach not only takes the vertical components of the pushover load patterns into consideration, but also maintains the conceptual understandability and simplicity exhibited by conventional MPA procedures. Numerical examples carried out on two latticed arches demonstrate that the proposed extended MPA is more accurate than the conventional MPA, because in the former, the displacement coupling between horizontal and vertical directions are reflected when the arches are excited by in-plane earthquake actions.