In this note we show that for a pinned half-sine arch under end couples snap-through buckling will occur unsymmetrically if the initial height of the shallow arch is greater than where r is the radius of gyration of the cross section. The closed-form expression for the critical couple can be obtained analytically.
Exact Critical Loads for a Pinned Half-Sine Arch Under End Couples
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, January 28, 2004; final revision, May 19, 2004. Associate Editor: R. C. Benson.
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Chen , J., and Lin , J. (February 1, 2005). "Exact Critical Loads for a Pinned Half-Sine Arch Under End Couples ." ASME. J. Appl. Mech. January 2005; 72(1): 147–148. https://doi.org/10.1115/1.1827244
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