Length effects on interactive buckling in thin-walled rectangular hollow section struts

Abstract

A variational model formulated using analytical techniques describing the nonlinear coupling between local and global buckling modes within an elastic thin-walled rectangular hollow section strut is presented. A system of nonlinear differential and integral equations subject to boundary conditions is derived and solved using numerical continuation techniques. The nonlinear behaviour of four representative lengths is investigated, which are characterized by the post-buckling equilibrium paths. The numerical results from the variational model are validated using a nonlinear finite element model and largely show excellent comparisons, particularly for the practically important ultimate load and the initial post-buckling behaviour. Boundaries for the four distinct length-dependent zones are identified and the most unstable zone is demonstrated to have a considerably narrower length range than previously determined for practical corner boundary conditions within the cross-section

Imperfection sensitivity of thin-walled rectangular hollow section struts susceptible to interactive buckling

“…The current work extends the previously developed variational models [36,37] to study the imperfection sensitivity of rectangular hollow section struts exhibiting local-global mode interaction. The developed system of nonlinear ordinary differential and integral equations subject to boundary conditions is solved using the well-known numerical continuation software Auto-07p [38].…”

“…A recent study [37] showed that in the transition from the pure local buckling mode, shown in Figure 3(a), to the global buckling induced interactive mode, shown in Figure 3(b), there is a redistribution of stiffness across the cross-section. Specifically, owing to the rigid connection between each individual plates, the less compressed web provides additional restraint to the more compressed side [48,49,50,37]. Hence, there is an effective increase in the axial stiffness of the more compressed web and flanges, thus leading to a higher resistance to compressive stresses.…”

“…The description of the global and local modal displacements adopts the same approach as in the recent study for the perfect system [37], as shown in Figure 2. The degrees of freedom known as 'sway' and 'tilt' [43,13], as shown in Figure 2(a), are introduced in combination to account for the effects of shear, since previous studies [13,14,16,44,45] have demonstrated that including the induced flexural shear strain in the total potential energy formulation is a way to preserve the terms necessary to model interactive buckling successfully.…”

“…The subscripts 'f' and 'w' represent the flanges and webs respectively; subscripts 'c' and 't' represent the more and less compressed webs respectively. The cross-section component of the local out-of-plane displacement field, as shown in Figure 3, is estimated by applying appropriate kinematic and static boundary conditions for each plate and their joints in conjunction with the Rayleigh-Ritz method, the detailed derivation of which can be found in previous work [36,37]:…”

“…α increasing β increasing flanges and webs due to local buckling, the membrane strain energy due to both global and local buckling, and the work done by the external load P E, where E is the total end-shortening. The formulation of the total potential energy functional follows a similar approach, as found in previous work [37], but currently accounts for the scenarios where both global and local geometric imperfections exist. The unloaded strut with initial global and local imperfections is assumed to be stress-relieved [53,22,23,24].…”