GATE ME 2023 Set 1 — Question 39
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Strength of Materials → Beams & Columns → Shear Force & Bending Moment
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Question
A beam of length is loaded in the -plane by a uniformly distributed load, and by a concentrated tip load parallel to the -axis, as shown in the figure. The resulting bending moment distributions about the and the axes are denoted by and , respectively.Which one of the options given depicts qualitatively CORRECT variations of and along the length of the beam?
Correct answer
(B) [figure]
Solution
1.Identify the loads and their planes:
- The uniformly distributed load acts in the -plane (downwards in the direction). This load creates a bending moment about the -axis ().
- The concentrated tip load acts parallel to the -axis (in the direction). This load creates a bending moment about the -axis ().
- For a cantilever beam with a UDL , the bending moment at a distance from the fixed end is given by .
- This is a second-order (parabolic) variation.
- At , . At , . The curve is concave downwards.
- For a cantilever beam with a tip load in the -direction, the bending moment at a distance from the fixed end is given by (using standard sign conventions for internal moments).
- This is a first-order (linear) variation.
- At , . At , .
- must be linear and must be parabolic. This matches the qualitative shapes in Option B, where is a triangle (linear) and is a parabola.
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