Elastica Supported at Midpoint by a Spring

by George E. Sliter,
Arthur P. Boresi,

Serial Information: Journal of the Engineering Mechanics Division, 1964, Vol. 90, Issue 2, Pg. 1-16

Document Type: Journal Paper


A thin strut or elastica is transversely supported at its midpoint by a linearly elastic spring. A comprehensive force is directed along the undeformed axis of the strut, and the hinged supports are restrained to move along this axis. The effect of the spring on the character of buckling and the deformed shape of the elastic strut are investigated. The exact moment-curvature relationship for the elastica leads to a nonlinear differential equation. Solutions in terms of elliptic functions are found for two cases that differ as to the assumed shape of the buckled strut. Graphs of the deflection of the midpoint and the distance between the supports vs. the comprehensive force are presented. With a lateral spring support, a snap-through type of buckling occurs.

Subject Headings: Struts | Buckling | Elastic analysis | Linear functions | Hinges | Deformation (mechanics) | Curvature | Differential equations

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