Question

$\text{The given figure shows a portal frame with one end}$ $\text{fixed and other hinged. The ratio of the fixed end moments}$$\frac{M_{BA}}{M_{CD}}\text{due to side sway will be}$

• A. 1.0
• B. 2.0
• C. 2.5
• D. 1.0

Answer 1

The correct option is A 1.0

Due to sway, the deflection of point B will be equal to that of point C.

$M_{BA}=\frac{6EI\Delta }{L^2}$

$M_{CD}=\frac{3E\left(0.5I\right)\Delta }{{\left(\frac{L}{2}\right)}^2}=\frac{6EI\Delta }{L^2}$

$\therefore \frac{M_{BA}}{M_{CD}}=1.0$

Note: This question is not 100% correct. If member BC is not rigid then rotation at B and C is different then equation of $M_{BA}$ is not correct.