GATE CE 2017 Set 1 — Question 40
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Structural Engineering → Indeterminate Analysis & Influence Lines → Analysis of Beams
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Question
The value of in the beam shown in the figure is such that the joint does not rotate.
The value of support reaction (in kN) at should be equal to ___________
Correct answer
59 to 61
Solution
1.Identify the condition: The joint does not rotate, which means the slope at is zero ().
2.Analyze Span AB: Support is fixed (as per the standard symbol in the diagram) and . Thus, span behaves like a fixed-fixed beam.
3.Calculate Reaction from AB at B: For a fixed-fixed beam of length with a uniformly distributed load , the vertical reaction at each support is .
4.Analyze Span BC: Span has no external load. Since and support is a roller with no settlement, there is no bending moment or shear force generated in this span due to the condition at .
5.Total Reaction at B: The total support reaction at is the sum of the shear forces from the adjacent spans.
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