Question

For the fixed beam shown in the figure, the influence line diagram for the bending moment at the mid-span of the beam is best represented as

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The ILD for BM at mid span can be obtained by introducing a pinned connection at mid point and giving unit rotation at that point. The deflected shape of beam will give the ILD.



${\theta }_{BA}=\frac{M_B\left(L/2\right)}{EI}$

$\text{and}{\theta }_{BC}=\frac{M_B\left(L/2\right)}{EI}$

${\theta }_{BA}+{\theta }_{BC}=1.0$

$M_B=EI$

$\text{Deflection at B}=\frac{M_B(L/2{)}^2}{2EI}=\frac{1}{8}$

Slope at end A and end C will be zero. Therefore (a) will be the correct answer.