Question

A continuous beam ABCD is shown in figure. The magnitude of rotation at joint 'B' for the given system of loading in radians is ____ $(TakeEI=3000kN-m^2)$

• A. $4\times {10}^{-4}$
• B. $4\times {10}^{-3}$
• C. $2\times {10}^{-3}$
• D. $2\times {10}^{-4}$

Answer 1

The correct option is A $4\times {10}^{-4}$

$\because$ It is a case of symmetric beam with symmetric loading, we will consider half of the structure only.

Thus,

$K_{BA}=\frac{8EI}{3}$ & $K_{BC}=\frac{2EI}{3}$

$D{F}_{BA}=0.8$ & $D{F}_{BC}=0.2$

$M_{BA}=\frac{8EI}{3}\left[2{\theta }_B\right]+12=18.4$

$\Rightarrow {\theta }_B=4\times {10}^{-4}radians$