A beam of length L is pinned at both ends and is subjected to a concentrated bending couple of moment M at its centre. The maximum bending moment in the beam is

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BPSC AE Paper 5 (Civil) 14 Oct 2022 Official Paper
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  1. M
  2. M/2
  3. ML
  4. ML/2

Answer (Detailed Solution Below)

Option 2 : M/2
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Detailed Solution

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Explanation:

The beam under the given loading is

F3 Vilas Engineering 24.11.2022 D1

Taking moment about the point A, we get

M0 - RB × L = 0

RB = M0/L (↑)

Taking, Σ V = 0

RA + RB = 0 (As there is no vertical loading)

RA =  M0/L (↓ )

So, the FBD of the above beam can be drawn as

F3 Vilas Engineering 24.11.2022 D2

So, the SFD will be

F3 Vilas Engineering 24.11.2022 D3

From, the SFD we can say that the maximum shear force will be M0/L throughout the beam, including the midsection.

BMD

F3 Vinanti Engineering 29.12.22 D1

The maximum bending moment in the beam is

= M/2 or Mo/2

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