Question

A rigid frame ABCD has AB member as overhang, with end 'A' being free. Support C and D are fixed. DB is vertical member and BC is horizontal member. DB = BC = 5m. If the moment equations are given by:

$M_{DB}=0.4EI{\theta }_B$ $M_{BD}=0.8EI{\theta }_B$
$M_{BA}=54$ $M_{BC}=-1.35+1.6EI{\theta }_B$

$M_{CB}=135+1.6EI{\theta }_{B}than{\theta }_{B}rotationatBisgivenby:$

• A. $\frac{33.75}{EI}$
• B. $\frac{-112.5}{EI}$
• C. $\text{None of the above}$
• D. $\text{Zero}$

Answer 1

The correct option is A $\frac{33.75}{EI}$



Equilibrium condition at B

$M_{BA}+M_{BC}+M_{BD}=0$
54 - 135 + 1.6 EI ${\theta }_B+0.8EI{\theta }_B=0$

-80 + 2.4 EI ${\theta }_B=0$

${\theta }_B=\frac{33.75}{EI}$