A novel algebraic hysteresis model based on the piece-wise definition of arctangent functions is presented. The paper introduces the arctangent-based model, labelled Atan model, by illustrating some possible shortcomings of hysteresis models with pinching. In some instances, algebraic hysteresis models may exhibit some advantages compared to differential hysteresis models. 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 response of a plywood-coupled Laminated-Veneer Lumber (LVL) shear wall is used for validation. Then application of this model to experimental cyclic response of Cross-Laminated Timber (CLT) and Light-Timber frame (CLT) shear walls, and a steel angle bracket is shown. A simple demonstration of issues with hysteresis models in the case of a Bouc-Wen class hysteresis model and the Extended Energy-dependent generalized Bouc-Wen model (EEGBW). The numerical instabilities of the EEGBW model are used to highlight the advantages of the proposed formulation in modelling wood joints and structural systems.