Threshold stiffness of lateral bracing in systems of parallel compression members. (November 2021) - Ziemian, C.W.; Ziemian, R.D.
Abstract: This paper explores the stiffness requirements for bracing components used in systems of parallel compression members or sub-assemblages. While rudimentary closed form equations are available to compute the threshold brace stiffness for single column systems, determining the stiffness of bracing components in multi-member systems is more complex. With the goal of developing useful multi-member stiffness models, the presented formulation is based on an equilibrium analysis of a single arbitrary column within a braced n -member system of interest. The resulting recursive relationship associated with tie-brace deformation is expanded, together with the brace-to-column shear connections and boundary conditions representing the anchor bracing, to generate a system of brace stiffness equations. Reformulating the equations as an eigenvalue problem, the minimum eigenvalue is the basis for subsequent equations derived to compute the required tie-brace stiffness in terms of the number of parallel members, and the stiffness of the shear connectors and the components of the system anchorage. Two approximations of the theoretically exact solution are also developed, providing useful alternatives for estimating system bracing requirements. Error analysis indicates that both approximate expressions sufficiently determine threshold bracing stiffness for structural systems with multiple parallel members with one or more brace points. An illustrative example is presented to demonstrate the use of the approximate expressions, and subsequent results are compared with both the derived theoretical solutions and results from finite element analyses. Graphical abstract: Unlabelled Image Highlights: System formulation supports computationally efficient eigen-solving algorithms. Solution accuracy confirmed by 2D eigenvalue analyses using finite element software. Tie-brace stiffness is a nonlinear function of connector and anchorage stiffnesses. Tie-brace stiffness is inversely proportional to stiffness of connectors and anchors. Approximate expressions for system brace stiffness are also developed and provided.