Question

The moment required to rotate the near end of a prismatic beam through unit angle, without translation, the far end being fixed, is given by ........

• A. \( \dfrac{EI}{L} \)
• B. \( \dfrac{2EI}{L} \)
• C. \( \dfrac{3EI}{L} \)
• D. \( \dfrac{4EI}{L} \)

Hint:

When dealing with prismatic beams, remember the moment required for unit rotation at the fixed end is proportional to the flexural rigidity (\(EI\)) and inversely proportional to the length of the beam.

Answer 1

The Correct Option is D

For a prismatic beam with the far end fixed and the near end subjected to a moment causing rotation, the required moment for unit rotation (without translation) can be calculated using the following equation: \[ M = \dfrac{4EI}{L} \] where:
- \( E \) is the Young's modulus of the material,
- \( I \) is the moment of inertia of the beam section,
- \( L \) is the length of the beam.
This equation represents the moment required to rotate the near end through a unit angle while the far end remains fixed.