As a classic issue, structural seismic bearing capacity could not be accurately predicted since it was based on a structural ultimate state with inherent uncertainty. This result led to rare research efforts to discover structures’ general and definite working laws from their experimental data. This study is to reveal the seismic working law of a bottom frame structure from its shaking table strain data by applying structural stressing state theory: (1) The tested strains are transformed into generalized strain energy density (GSED) values. (2) The method is proposed to express the stressing state mode and the corresponding characteristic parameter. (3) According to the natural law of quantitative and qualitative change, the Mann–Kendall criterion detects the mutation feature in the evolution of characteristic parameters versus seismic intensity. Moreover, it is verified that the stressing state mode also presents the corresponding mutation feature, which reveals the starting point in the seismic failure process of the bottom frame structure. (4) The Mann–Kendall criterion distinguishes the elastic–plastic branch (EPB) feature in the bottom frame structure’s normal working process, which could be taken as the design reference. This study presents a new theoretical basis to determine the bottom frame structure’s seismic working law and update the design code. Meanwhile, this study opens up the application of seismic strain data in structural analysis.

This study develops a modified multi-support response spectrum (MSRS) method, in order to efficiently and accurately calculate the response of multi-support structures under incoherent ground motions. The modified MSRS method adopts three ancillary processes, constructing structural displacement vectors or constructing infinite stiffness members or increasing the degrees of freedom at structural supports. Then, the modified MSRS method is verified in a comparison with the existing MSRS method through a model of a five-span reinforced concrete continuous rigid frame bridge. Finally, the collective structural response spectrum, the structural power spectrum, and the simplified structural power spectrum are deduced from the equation of the motion taking ground motion displacements as the input, and validated through the same bridge model.