GATE CE 2018 Set 1 — Question 40
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Structural Engineering → Determinate Structures & Energy Methods → Determinate Structures
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Question
The figure shows a simply supported beam of uniform flexural rigidity carrying two moments and .
The slope at will be
Correct answer
(C) ML/(6EI)
Solution
We can use the conjugate beam method to find the slope at . First, find the reactions for the real beam.
Total clockwise moment . To balance this, the reactions must form a counter-clockwise couple of .
(downwards)
(upwards)The bending moment diagram () is:
, centroid from .
, centroid from .
, centroid from .Taking moments about in the conjugate beam:
Total clockwise moment . To balance this, the reactions must form a counter-clockwise couple of .
(downwards)
(upwards)The bending moment diagram () is:
- For :
- For :
- For :
, centroid from .
, centroid from .
, centroid from .Taking moments about in the conjugate beam:
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