Lateral-torsional buckling of butterfly-shaped beams with rectangular cross section

This paper analyzes lateral-torsional buckling (LTB) of elastic beams with rectangular cross section having constant thickness, and depth symmetric with respect to the midpoint and tapered linearly in each half with smallest depth at the midpoint. This type of butterfly-shaped beam is used as a shear link in steel plates that serve as structural fuses to reduce the seismic response of buildings. LTB has been observed in previous quasi-static tests and found to be a critical limit state. The ends of the beam are prevented from twisting and can be assumed to be pinned with respect to bending in the weak direction. Numerical results are obtained for LTB of butterfly-shaped beams with the use of a shooting method assuming uniform torsion. Pure bending, reversed moments, and end moments with unequal magnitudes are investigated first. A compressive load is included next, and interaction curves for combinations of critical moment (squared) versus axial load are determined. Finally, the effect of in-plane shear deformation on LTB is examined. Plots showing the influence of various parameters are presented, along with some analytical approximations for the critical moment in terms of geometric and material quantities.