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A uniform simply supported beam is subjected to a clockwise moment M at the left end. What is the moment required at the right end so that rotation of the right end is zero?
  • a)
    2M
  • b)
    M
  • c)
    M/2
  • d)
    M/3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A uniform simply supported beam is subjected to a clockwise moment M a...

at left end
To keep rotation at right and zero a moment should be applied in anticlockwise direction. Let the moment in M'
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Most Upvoted Answer
A uniform simply supported beam is subjected to a clockwise moment M a...
Given:

- A uniform simply supported beam
- Clockwise moment M at the left end

To find:

- Moment required at the right end so that rotation of the right end is zero

Solution:

- Let the length of the beam be L
- Let the cross-sectional area and the modulus of elasticity of the beam be A and E, respectively
- Let θ1 and θ2 be the rotations at the left and right ends of the beam, respectively
- The rotation θ1 at the left end due to the moment M is given by:

θ1 = M / (EI)

where I = (1/12)AL^2 is the second moment of area of the beam

- The rotation θ2 at the right end due to the moment required (say M') is given by:

θ2 = M' / (EI)

- For the rotation of the right end to be zero, we need θ2 = 0
- Therefore, we have:

M' / (EI) = 0

- Solving for M', we get:

M' = 0

- Therefore, the moment required at the right end so that rotation of the right end is zero is M/2, i.e., option C.

Final Answer:

- Moment required at the right end so that rotation of the right end is zero is M/2.
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