Sensitivity analysis and multi-criteria optimization of SMA cable restrainers for longitudinal seismic protection of isolated simply supported highway bridges

Abstract

Considering the flexibility of isolation bearings, isolated bridges are susceptible to unseating problems or even collapse due to excessive displacement under strong earthquakes. Shape memory alloy (SMA) wires can be utilized as seismic restrainers to confine this displacement. Recently, a design procedure for SMA restrainers has been proposed based on a linearized two degree-of-freedom analytical model. The key design parameters include three geometric factors (the ratio of the allowable displacement to the seat width, Δa/Lsw, horizontal angle, θ0, and normalized elongation parameter α), and three factors related to material properties of SMA (the maximum applied strain, εmax, the elastic modulus, E0, and the austenite to martensite start stress, fy,SMA). The objective of this study is to optimize the design procedure by evaluating the effect of each design factor on the seismic response of an isolated bridge which is retrofitted by SMA restrainers. After conducting a one-half fractional factorial analysis, it was found that the material factors have slight impact on the relative displacement between the pier and the girder, and the base shear of the pier, with percentage contributions smaller than 4% and 13%, respectively. Then, a full factorial analysis is followed through a multi-criteria decision making process in order to optimize the SMA restrainer. The results show that the optimal value of Δa/Lsw, which effectively reduces the relative displacement and simultaneously control the base shear of the piers, is 0.4; the optimum value of θ0 ranges from 0 to π/4; and the most effective value of α is 1.0.