An analytical model for estimating restrainer design forces in bolted buckling-restrained braces

This article presents an analytical model to predict the normal thrust force for the design of the restraining system of all-steel buckling-restrained brace (BRB) members. The proper design of the restraining mechanism is key to obtaining a stable inelastic response from BRBs. Compared with existing models, the presented model accounts for the cyclic strain hardening behaviour of the BRB's steel core, the flexibility of the restraining system, the flow of frictional forces, the longitudinal variation of the core axial load and strain, and Poisson's effects on the core cross-section properties. The buckled shape of the core and the resulting normal thrust and frictional forces are evaluated along the core length using an iterative approach to satisfy the force equilibrium and geometric compatibility. The model predicts the maximum compressive and tensile loads resisted by the brace, buckling wavelengths, and the magnitude and distribution of the normal thrust and the frictional force along the core. Using a simplified stability analysis, the required restraining stiffness to achieve a stable inelastic response and avoid excessive gap opening is provided. A method to estimate the available restraining stiffness of a typical bolted all-steel BRB is presented and the internal actions in the restraining system resulting from the local buckling of the core are obtained through a simple and practical analysis. The analytical model is validated against the results of physical tests and finite element analyses for two different BRB members. The model was found to provide sufficiently accurate results for typical earthquake engineering applications.