A cantilever of length L is designed to resist bending from a point load at its
ID: 1885624 • Letter: A
Question
A cantilever of length L is designed to resist bending from a point load at its end. If the maximum stress should not exceed the tensile strength of the material, what is the ‘parameter’ that should be maximized to give a minimum weight design? (tips: 1. for the design, you can assume the maximum stress to reach the strength of the material. 2. When comparing different materials, we can assume the geometry of the section to be the same. For simplicity, we can simply take the section to be a square.)
Explanation / Answer
If a load P is applied at the end of the cantilever, then the maximum bending moment = M =PL
This bending moment cause flexural stres = M/S = PL/S, where S is the section modulus.
There are two ways:
(a) Maximise the stiffness (Section Modulus) of the section.
(b) Select the material with the highest possible yield strength.
Section modulus is the dimensional property of the section. It can be maximized by finding out the optimum width and depth of the section. The section must not be a square one until the bending moment is applied along both the axes.
Yield strength is the material property and it does not depend upon the section dimensions. Sor example Steel has a higher yield strength than the wood. If dimensions are same, then a steel section will resist higher bending moment than that of a wood.
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