A steel–concrete composite box girder has good anti-seismic energy dissipation capacity, absorbs seismic energy, and reduces seismic action. It is very suitable for high-rise and super high-rise mega composite structure systems, which is in accordance with the condition of capital construction. In order to accurately study the elastic–plastic seismic response of the composite structure, the restoring force model of the building structure is the primary problem that needs to be solved. Previous research shows that shear connection degree, force ratio, and web height–thickness ratio are the major factors that influence composite box girder bearing capacity and seismic behavior. In this paper, low cycle vertical load tests of four steel–concrete composite box girders were conducted with different shear connection degrees and ratios of web height to thickness. The seismic behavior of a steel–concrete composite box girder was analyzed in depth, such as the hysteresis law, skeleton curve, and stiffness degradation law, etc. The influence of the shear connection degree and ratio of web height to thickness on seismic performance of the steel–concrete composite box girder was investigated. A three-fold line model of the bending moment–curvature skeleton curve of composite box girders was established. On the basis of experimental data and theoretical analysis, the formula of positive and negative stiffness degradation of composite box girders was obtained. Furthermore, the maximum point orientation hysteresis model of the bending moment–curvature of steel–concrete composite box girders was established. The calculated results of the restoring force model agree well with the experimental results. The accuracy of the proposed method is verified. The calculation method of the model is simple and clear, convenient for hand calculation, and suitable for engineering applications.

In this paper, the low-cycle reciprocating load test was carried out on four-limb concrete-filled steel tubular (CFST) lattice columns with different slenderness ratios and axial compression ratios, and the seismic performance was studied. Two performance indicators, namely damage and hysteretic energy dissipation, were defined as the objective functions, and the axial compression ratio was used as an optimization variable to perform the multi-objective optimization analysis of four-limb CFST lattice columns. Optimization using the max–min problem approach aims to optimize the axial compression ratio to minimize damage and maximize the dissipation of hysteresis energy. The seismic performances before and after optimization were determined using a restoring force model and were evaluated by the finite element method under different axial compression ratios. The results show that, under low-cycle reciprocating loads, the load–displacement hysteresis curve is a bow shape (Members 1 and 2), inverse S-shape (Member 3), and approximate shuttle shape (Member 4). Through multi-objective optimization, the optimized axial compression ratio is 0.25 and the finite element analysis indicates that the optimal seismic performance is at an axial compression ratio of 0.25. Through the optimized design, the maximum horizontal load of lattice columns, the elastic stiffness, the dissipation capacity, and the seismic performance are all improved, under the premise of satisfying the structural safety.