Flexural design of restraining panels in buckling-restrained steel plate shear walls considering high-order buckling modes

Buckling-restrained steel plate shear wall (BRSPSW) is one kind of excellent energy dissipating member. The inner steel plate in BRSPSW usually works with high-order buckling modes to resist lateral force under the buckling restrained effect of outer restraining panels. However, current design of the restraining panels is commonly based on simplified uniform-loaded plates without considering the effect of the high-order buckling modes, which may result in unsafe designs. In this paper, the high-order buckling modes in BRSPSW and their influence on the flexural design of the restraining panels were studied. Finite element (FE) models that can accurately simulate the out-of-plane interaction behavior of BRSPSW were developed and verified by existing test results. The numerical results show that the high-order buckling of the steel plate leads to a series of inclined strip-shaped stress regions on restraining panels. When the parameters of BRSPSW are varied in common range, the positive and negative bending moments of the restraining panel under the strip shaped force are 9.6 and 2.8 times those under the uniform force, respectively. The differences between the bending moment of the restraining panels under strip-shaped force and that under uniform force become larger as the spacings of the strip-shaped stress regions increase. Furthermore, the spacings of the strip-shaped stress regions increase with the decrease of the height-to-thickness ratio of the steel plate and the increase of the gap between the steel plate and the restraining panel. Two fitting formulas of the positive and negative moment amplification factors considering the effect of the high-order buckling modes are proposed to design the restraining panels safely. Additionally, a simplified model and bending moment equations of the restraining panels in BRSPSW are suggested. To avoid the excessive negative bending moments occurring at side supports of the restraining panel, the ratio of cantilever length to middle span is suggested to be not more than 0.4.