Ultimate Seismic Resistance Capacity for Long Span Lattice Structures under Vertical Ground Motions

Seismic resistance capacities of frame structures have been discussed with equilibrium of energies among many researchers. The early one is the limit design presented by Housner, 1956; that is, frame structures should possess the plastic deformation ability equivalent to an earthquake input energy given by a velocity response spectrum. On such studies of response estimation by the energy equilibrium, the potential energy has been generally abandoned, since the effect of self-weight or fixed loads on the potential energy is negligible, while ordinary buildings usually sway in the horizontal direction. However, it could be said that the effect of gravity has to be considered for long span structures since the mass might be concerned with the vertical response. In this paper, as for ultimate seismic resistance capacity of long span structures, an estimation method considering the potential energy is discussed as for plane lattice beams and double-layer cylindrical lattice roofs. The method presented can be done with the information of static nonlinear behavior, natural periods, and velocity response spectrum of seismic motions; that is, any complicated nonlinear time history analysis is not required. The value estimated can be modified with the properties of strain energy absorption and the safety static factor. 1. Introduction Long span and spatial structures have been utilized as a roof structure of buildings including large space. They are often used as a place of refuge or stronghold of rescue in a disaster area. Then it is important for government or caretaker to grasp ultimate seismic resistance capacity of such buildings without regard to new or existing buildings in advance. They might wish to know concretely the seismic motion level at which structures reach a limit state if it would be subjected to over design loads. The information would be just an ultimate seismic resistance capacity of structures. Seismic resistant capacities for long span structures have been studied by many researchers all over the world. Among them early on, Kato et al. [1] studied the static and dynamic behaviors of long span beams against vertical loads to express the quantitative earthquake resistant capacity in terms of the first natural period and the slenderness ratio of upper chord members. The selected measure was peak ground acceleration (PGA) at dynamic collapse. Ishikawa and Kato [2] studied the resistance capacity of double-layer lattice domes under static loading and vertical earthquake motions to present an estimation method for PGA at collapse. The method was