GATE CE 2019 Set 2 — Question 46
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Structural Engineering → Indeterminate Analysis & Influence Lines → Influence Lines
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Question
A long uniformly distributed load of and a concentrated load of are moving together on the beam ABCD shown in the figure (not drawn to scale). The relative positions of the two loads are not fixed. The maximum shear force (in , round off to the nearest integer) caused at the internal hinge B due to the two loads is ______
Correct answer
70 to 70
Solution
1.Influence Line Diagram (ILD) for shear at B ():
- Segment AB is supported by a roller at A and an internal hinge at B. It acts like a simply supported beam for loads on AB.
- Segment BCD is supported by a pin at C and a roller at D, with a cantilever BC.
- When a unit load is on AB at distance from A, the reaction at B (which is the shear force transferred through the hinge) is . The ILD is linear from 0 at A to 1 at B.
- When a unit load is on BCD, segment AB remains in equilibrium with zero reactions because it is stable on its own for vertical loads. Thus, for any load on BCD.
- To maximize , place the concentrated load at the peak of the ILD (at B, ordinate = 1).
- Place the uniformly distributed load over the entire positive region of the ILD (segment AB).
- Max
- Max .
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