GATE CE 2020 Set 2 — Question 17
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Structural Engineering → Stress, Strain & Beams → Flexural Stresses
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Question
A weightless cantilever beam of span is loaded as shown in the figure. For the entire span of the beam, the material properties are identical and the cross section is rectangular with constant width.
From the flexure-critical perspective, the most economical longitudinal profile of the beam to carry the given loads amongst the options given below, is
Correct answer
(C) [figure]
Solution
The bending moment at any section from the free end is given by . At the free end (), . At the fixed end (), . The bending moment diagram is a trapezoid. For a rectangular section with constant width , the required depth is determined by the section modulus . Since , we have . The required depth profile is parabolic, starting from a non-zero value at the free end. Among the given options, (C) provides the most economical linear approximation of this profile, as it accounts for the non-zero moment at the free end and the increase towards the support.
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