Bracing stiffness requirements of members supported by discrete elastic supports

This study revisited the stability of members supported by discrete elastic supports, aiming to provide design recommendations with respect to bracing stiffness requirements. Analytical expressions for the critical load were derived by use of elastic stability theory for a series of configurations where bracing elements were modeled as linear-elastic springs. The configurations presented in this paper are: members with pinned ends and two, three or four spans (<i>i.e.</i> one, two and three springs respectively), members with two or three spans and laterally elastic ends and members with one or two spans and one pinned end. All analytical results are verified by buckling analysis performed by a finite element solver. The starting point for this paper is the design rules in the new generation of Eurocode 5, however the obtained expressions are applicable to any linear-elastic material. On the basis of the obtained results, a series of user-friendly design recommendations for the critical load and the effective buckling length are provided. Finally, Monte Carlo simulations were carried out to provide conservative design recommendations about the characteristic values of bracing stiffness which arguably should be used as input for safety design verifications. These simulations are timber-specific.