Tapered Cantilevers with Varying Distributed Loads

by Tung-Ming Wang, (M.ASCE), Assoc. Prof. of Civ. Engrg.; Univ. of New Hampshire, Durham, NH,
Chun-Hsiung Lee, Engr.; De Leuw, Cather Int. Inc., Consulting Engrs., Taipei, Taiwan,

Serial Information: Journal of the Engineering Mechanics Division, 1973, Vol. 99, Issue 4, Pg. 919-925

Document Type: Journal Paper


Many investigators have considered the problems of cantilever beams undergoing large deflections. Barton and Bisshopp and Drucker solved exactly a cantilever carrying a concentrated load at its free end. Hummell and Morton, Bickley, and Rhode presented an approximate treatment of a cantilever beam under uniformly distributed load. All of the above cases were for beams of constant section. Recently, Kemper solved the problems of tapered cantilevers subjected to a concentrated load at the free end by computer methods, considering both rectangular and round cross sections, and the results were checked by experimental verification. In the present note, a slender cantilever beam with a uniform taper of the rectangular cross section, carrying varying distributed loads, is considered, and the solution is obtained by the use of power series method. A general load distribution function is introduced and a set of coefficients are provide for various kinds of load distribution. Numerical results of load-deflection relationships are also presented for a cantilever with a uniformly distributed load.

Subject Headings: Concentrated loads | Beams | Cantilevers | Load distribution | Load factors | Displacement (mechanics) | Cross sections | Distribution functions

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