A fixed beam AB of span 4 m is carrying a point load of 100 N at the centre. What is the fixed end moment at support A and B?
DSSSB JE - 2023,
Answer: C
For a fixed beam with a central point load W over a span L, the fixed-end moments are equal at both supports and equal to \(WL/8\), with a negative (hogging) sign:
\[ \begin{aligned} M_A = M_B = -\frac{WL}{8} \\ &= -\frac{100 \times 4}{8} = -50\ \text{N-m} \end{aligned} \]The values of 3, 12 and 6 N-m are not given by this formula. The formula \(WL/4 = 100\) N-m is the central bending moment of a simply supported beam, and the sagging moment at the centre of the fixed beam is also 50 N-m.
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