American Society of Civil Engineers


Possible Ranges of End Slope for Cantilever Beams


by S. Navaee, A.M.ASCE, (Visit. Asst. Prof., Dept. of Civ. Engrg., Clemson Univ., Clemson, SC 29634) and R. E. Elling, M.ASCE, (Prof., Dept. of Civ. Engrg., Clemson Univ., Clemson, SC)

Journal of Engineering Mechanics, Vol. 119, No. 3, March 1993, pp. 630-635, (doi:  http://dx.doi.org/10.1061/(ASCE)0733-9399(1993)119:3(630))

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Document type: Technical Note
Abstract: The problem of large deflections of cantilever beams subjected to end loads has been studied by many researchers. In all these studies, only one equilibrium configuration was obtained for a specific beam and loading condition. In a study that was done previously by the writers, large deflections of cantilever beams subjected to inclined end loads were investigated. It was shown in this study that for each combination of the beam and loading condition, there are certain numbers of equilibrium configurations for the beam. In the technical note presented here, the writers discuss certain aspects regarding large deflections of cantilever beams. Specifically, they show that the possible values of the end slope of a beam for any particular angle of inclination of the load are limited to specific ranges. The derivation and discussion of these ranges are provided here. It should be mentioned that the cantilever beams studied by the writers are assumed to be initially straight and prismatic in addition to being homogeneous, elastic, and isotropic. Establishing the ranges of end slope of a beam is particularly important, because knowing these ranges, one is able to calculate the correct values of the end slope and therefore obtain the equilibrium configurations of the beam in an efficient manner.


ASCE Subject Headings:
Cantilevers
Beams
Deflection
Elasticity
Loads