Question

The value of slope at support B $\left({\theta }_B\right)$ for the continuous beam shown in the figure below is:

• A. $\frac{15}{EI}\text{(anti clockwise)}$
• B. $\frac{3}{EI}\text{(anti clockwise)}$
• C. $\frac{3}{EI}\text{(clockwise)}$
• D. $\frac{15}{EI}\text{(clockwise)}$

Answer 1

The correct option is B $\frac{3}{EI}\text{(anti clockwise)}$

Calculation of fixed end moments:

$M_{FAB}=-\frac{w{l}^2}{12}=\frac{-2\times 6^2}{12}=-6kN-m$

$M_{FBA}=\frac{+w{l}^2}{12}=\frac{2\times 6^2}{12}=+6kN-m$

$M_{BC}\text{(Final moment)}=-4kN-m$

$M_{BA}=M_{FBA}+\frac{2EI}{l}[2{\theta }_B+\text{/}{\theta }_A]=6+\frac{4EI{\theta }_B}{6}$

Equilibrium Equation:
$M_{BA}+M_{BC}=0$

$6+\frac{4EI{\theta }_B}{6}-4=0$

$\Rightarrow {\theta }_B=\frac{-2\times 6}{4EI}$

$=\frac{-3}{EI}\text{(Anti-clockwise)}$