Seismic behaviour of structures with plastic shear effects

Non-linear dynamics is generally recognized as the most reliable method to carry out analyses of structures subjected to earthquake actions. In general non-linear dynamics requires a great level of expertise, as well as cost and time necessary for calculation. The lack of suitable computational techniques has induced seismic analyses involving two classes of simplified procedures: modal approximations and constitutive and structural models with sufficient accuracy and low numerical complexities. The dynamic response of building structures subjected to seismic loads has been often examined using the single-degree-of-freedom model, that provides a good estimation of the fundamental response mode, which is normally responsible for overall structural failure. A SDOF analysis can give a preliminary assessment for a protective structure, even in cases in which the constitutive models are somewhat more complex. The rigid-plastic cantilever beam can be in fact a simple structural scheme to clarify the behaviour of more complex structures and to verify the accuracy of the numerical methods in a non-linear dynamic analysis. In general, significant differences exist between a complete building and uniform beams, nevertheless the continuum model provide useful results. This paper presents a general treatment to develop approximate solutions for rigid-plastic response of structures subjected to base harmonic pulse, that has been shown in literature as an appropriate approach to the seismic analysis. A numerical procedure has been on purpose developed, taking into account two different approaches: a step-by-step solution of the general non linear dynamic problem and the evaluation due to a modal approximate response, satisfying both kinematical admissibility requirements and boundary conditions. An estimation of the error due to the second approach is given. In order to assess the reliability of the approximate procedure it is shown that the approximation does not depend on the forcing accelerogram.