POSTCRITICAL IMPERFECTION-SENSITIVE BUCKLING AND OPTIMAL BRACING OF LARGE REGULAR FRAMES

Periodic interior buckling of regular multistory and multibay rectangu lar elastic frames with elastic bracing is analyzed. It is shown that there exists a certain critical bracing stiffness for which the critic al loads for the nonsway (symmetric) and sway (antisymmetric) buckling modes coincide. Simple formulae for the critical stiffness are given. For the critical and softer bracing, the type of postcritical bucklin g behavior is the unstable symmetric bifurcation, exhibiting imperfect ion sensitivity according to Koiter's 2/3-power law. For stiffer braci ng, there is no imperfection sensitivity. The critical bracing, howeve r, represents a naive optimal design which should be avoided because t he imperfection sensitivity is the strongest. It is recommended that t he truly optimal bracing should be significantly stiffer (perhaps 1.1 to 2 times as stiff). The buckling behavior, including the postcritica l imperfection sensitivity, is similar to that of a portal frame analy zed before. The solution also provides a demonstration of a simple met hod for the initial postcritical analysis of frames recently proposed by Bazant and Cedolin, which is based on energy minimization. In this method, the distribution of cross section rotations is assumed to be t he same as in the classical linearized theory. The curvatures and defl ections are obtained from the rotations by integration with at least a second-order accuracy (in terms of the rotations), and the axial shor tening with at least a fourth-order accuracy.