Ricerc@Sapienza

This paper presents a force-based equivalent frame procedure applied to analyse masonry walls structural response under cyclic loadings. The presented macroelement formulation, consisting in the arrangement in series of a central elastic beam, two nonlinear flexural hinges at the ends and a nonlinear shear link, adopts a smooth hysteresis model for these latter, where a scalar damage variable is introduced to reproduce strength and stiffness degradation.

Masonry structures subjected to seismic actions exhibit a complex nonlinear behaviour. To obtain a comprehensive representation of all the occurring nonlinear mechanisms, constitutive models including damage and plasticity are required and nonlinear dynamic analyses are considered the most reliable. Hence, models considering both degrading effects and hereditary nature of restoring forces are needed. Different approaches can be adopted, relying on microscopic, macroscopic, multi-scale and macroelement formulations.

Hysteresis is a well-known phenomenon involving history-dependent response of many structural (and non-structural) materials. Among the various models that can be adopted to describe it, the Bouc-Wen model is certainly one of the most widely used, and it is considered the forefather of an entire class of hysteresis models. During the last decades, the original formulation was modified to take into account the effects of strength and stiffness degradation, pinching and non symmetric response. Moreover, issues related to its thermodynamic admissibility were tackled.

The response of single and two-degree-of-freedom mechanical systems with elements exhibiting a hysteretic restoring force is studied under harmonic imposed motion to characterize the nonlinear dynamic properties of the system. The hysteretic behavior of the element is described by the Bouc-Wen model, which is simple but able to represent different hysteretic behaviors. Since for a given restoring force the nonlinear response is affected by the oscillation amplitude, frequency-response curves for various excitation levels are constructed.