Hysteretic modelling of x-braced shear walls

We present a differential model of the hysteretic behavior of unsheathed x-braced frames. The model includes all the relevant aspects (perfect or hardening plasticity of diagonal straps under tension, buckling of diagonal straps under compression). The frame is treated as a single-degree-of-freedom system, and the hysteretic model is written as a small system of ordinary differential equations. In spite of this simplified modelling approach, the proposed model captures the key features of hysteretic cycles of x-braced frames (extreme pinching and slackness) and can be used to obtain the q-factor for simplified seismic design based on the reduction of elastic spectra. The model also allows to couple several x-braced frames to obtain the response of more complex structures such as complete façades. In fact, the agreement with a more sophisticated approach, such as a finite element model of the frame, is excellent, but the computational cost is considerably lower. This point is illustrated by various numerical examples.