Elastic stability of pony-truss bridges - Seng-Lip Lee
A series of catastrophic failure at the end of the nineteenth century first brought the attention of the structural engineering profession to the lateral stability of the top chord of pony-truss bridges. Since then, numerous methods of analysis based on various simplifying assumptions have been advanced. The few experimental investigations of the subject, however, were confined to the fundamental problem of the elasticity supported beam-column. In this dissertation, a general method of analysis which takes into consideration many secondary effects neglected in the various simplified solutions is presented. The method lends itself not only to the solution of the buckling problem, but also to the determination of the secondary stresses developed in the members under loads less than the critical load. The procedure consists of the formulation of a system of simultaneous linear equations derived by consideration of the equilibrium conditions at the joints along the top chord. The solution of these equations yields the displacement components of the joints from which the secondary stresses can be calculated. The buckling condition is obtained by equating to zero the determinant of the system equations. The proposed theory was substantiated by experimental verification. Test results obtained by subjecting a pony-truss bridge model to different loading conditions showed that, for the same total load, the critical loading condition is that which produces maximum stress in the center portion of the top chord and not that which causes the absolute maximum stress. This is an agreement with the analytical results. Although the investigation was directed primarily to the problem of elastic stability, the proposed method was extended to cover the case of inelastic buckling. It was found that in the inelastic range, a few of the satisfactory simplified analyses gave results with reasonably small errors. Their validity, however, cannot be generalized and their application in the elastic range is not advisable. While the problem of local failure due to the combined action of axial and secondary stresses is beyond the scope of this dissertation, the proposed method provides a rational approach to the study of this problem.