An empirical transcendental hysteresis model for structural systems with pinching and degradation

Abstract

The authors present a novel transcendental hysteresis model based on the piecewise definition of arctangent functions. The definition of the shape parameters of the arctangent functions originates from the features of the experimental hysteresis curves directly. In the first step, the authors present this model's application to the experimental cyclic response of cross‐laminated timber (CLT), light‐timber frame (LTF) shear walls, and a steel angle bracket. Then, the response of a plywood‐coupled laminated‐veneer lumber (LVL) shear wall is used for validation purposes. The paper introduces the arctangent‐based model, labeled Atan model, by illustrating some possible shortcomings of hysteresis models with pinching. The paper concludes with a simple demonstration of these issues in the case of a Bouc‐Wen class hysteresis model, the extended energy‐dependent generalized Bouc‐Wen (eegbw) model. The numerical instabilities of the eegbw model are used to endorse the advantages of the proposed formulation in modeling complex structural arrangements, like wood joints and structural systems. The proposed model originates from the analysis of the experimental response of wood joints. However, it can be of more general application, and the particular reference to wood joints does not preclude other application fields.

Optimization of the Slip Force in a Novel Friction-Based Connection for the E-CLT Technology

“…The experimental data are used to simulate a frame's coupled response with masonry infill equipped with the AFC. The Atan model, which is an empirical hysteresis model proposed by [34], simulates the experimental cyclic response of an RC frame with masonry infill, tested by [31]. The authors tested the frame's response, represented by an SDOF oscillator with a lumped mass on the top, under a set of 41 earthquakes by varying the slip force in a given range.…”

“…6(a). by [34], which suits the simulation of mechanical systems with pinching, and both strength and stiffness degradation. It is a hysteresis model based on the arctangent function characterized by the following piece-wise definition:…”

Effect of pinching on structural resilience: performance of reinforced concrete and timber structures under repeated cycles

“…where m is the mass, x the displacement, € x the double derivative of x with respect to time, f s the resisting inelastic force, and € x g the ground acceleration. In this research, a modification of the Atan model, presented by Aloisio, Sejkot, Iqbal, and Fragiacomo (2021), reproduces the resisting inelastic force. Sengupta and Li (2016) reviewed the hysteresis models for RC and timber structures, and reported a significant variety of modelling choices.…”

“…The Appendix reports the model's mathematical details and the estimated parameters obtained from a least-squares optimisation. The proposed model has been validated on the experimental cyclic response of existing test specimens from the scientific literature in Aloisio, Sejkot, et al (2021). Figures 9 and 10 compare the experimental cyclic response with the outcomes of the empirical hysteresis model.…”

Assessment of the Seismic Response of CLT Shear Walls Using the EEGBW, a Bouc–Wen Class Predictive Model

“…Many of the recent research efforts in structural dynamics and earthquake engineering focus on predicting the inelastic response of real structures [1] or structural archetypes [2][3][4]. However, the analyses of rather elementary structures may require significant computational efforts.…”