Postcritical Imperfection-sensitive Buckling and Optimal Bracing of Large Regular Frames

ABS!RA~T: Periodic i.nterior buckling of regular multistory and multibay rectangular elastic frames with elastic bracmg IS analyzed. It IS shown that there exists a certain critical bracing stiffness for which the critical loads f~r the nonsw~y (symmetric) ~d sway (antisymme~c) buckling modes coincide. Simple formulae for the critical stIffness .are .glven .. For the. c~.tica~ and soft~r bracI~~, ~e type of postcritical buckling behavior is the unstable ~ymmetrtc. blfur~atlOn, eX~lblting !J?~erfectlOn ~:nsltlVlty. according to Koiter's 2/3-power law. For stiffer bracmg, there IS n? ImperfectIOn se.nsItlVlty. !he cn~~al. br~cmg, however, represents a naive optimal design which sho~ld be aVOIded ~ca~se the Im~rfection SenSItivIty IS t~e strongest. It is recommended that the truly optimal bracm~. sho.uld be sl~rufican!lr .stl~er .(p:rhaps 1.1 to 2 times as stiff). The buckling behavior, including the postcntlcall~perfect1on sensItivIty, IS slmtlar to that of a portal frame analyzed before. The solution also provides a demons~ation ~f ~ simple method for t~e. i~tia~ postcritical analysis of frames recently proposed by Bafant ~d Cedohn, whIch IS based on energy mmuruzatlOn. In this method, the distribution of cross section rotations IS assumed to be the same as in the classical linearized theory. The curvatures and deflections are obtained from the rotations by integration with at least a second-order accuracy (in terms of the rotations) and the axial shortening with at least a fourth-order accuracy. '