Analysis of Large Deflections in Spring-Hinged Cantilever Beam under Inclined Tip Load.

Abstract

A flexible cantilever beam subjected to a rotational load is commonly encountered in mechanical elements, for example, a flat spring under a spring limit test, a leaf spring in a vibrating conveyor or a paper machine, a jib ( : boom) of a jib crane or a luffing crane, an arm of an industrial robot or a manipulator, and an aircraft wing. In such elastic elements, a large deflection is produced without exceeding the elastic limit of the materials. This property is of both analytical and technological interest. It is necessary to analyze the large deflection behavior to achieve high reliability of the structural components. The purpose of this report is to clarify the large deflection problem, namely elastica problem, of a cantilever beam. As an analytical example, an inclined concentrated load at the free end of a spring-hinged cantilever beam was solved in terms of elliptic integrals as well as by carrying out a large flexural-bending test. Experimental data agree very closely with the theoretical results.