Question

Consider a beam which is fixed at end A and simply supported at end B of span \( L \). If the support B settles by an amount \( \delta \), then what is the fixed-end moment (FEM) developed at end A?

• A. \( 6 E I \frac{\delta}{L^2} \)
• B. \( 3 E I \frac{\delta}{L^2} \)
• C. \( 6 E I \frac{\delta}{4 L^2} \)
• D. \( 3 E I \frac{\delta}{4 L^2} \)

Hint:

In cases of support settlement, use the relationship between deflection and fixed-end moment for calculating the FEM at the fixed end.

Answer 1

The Correct Option is A

When the support B of a fixed beam settles by \( \delta \), the fixed-end moment at end A can be calculated using the deflection and bending stiffness of the beam. The formula for the fixed-end moment is \( 6 E I \frac{\delta}{L^2} \). Hence, the correct answer is \( 6 E I \frac{\delta}{L^2} \).