Question

For the frame as shown in figure. The value of a is

• A. 0.67
• B. 0.61
• C. 0.55
• D. 0.47

Answer 1

The correct option is A 0.67

$\left[\begin{array}{c}{M}_{AB}\\ M_{BA}\\ M_{CD}\\ M_{DC}\end{array}\right]=EI\left[\begin{array}{cccc}a& b& c& d\\ e& f& g& h\\ i& j& k& l\\ m& n& o& p\end{array}\right]\left[\begin{array}{c}{\theta }_B\\ {\Delta }_B\\ {\theta }_C\\ {\Delta }_C\end{array}\right]$
By slope deflection equations,
$M_{AB}=\frac{2EI}{3}({\theta }_B+{\Delta }_B)=EI[\frac{2}{3}{\theta }_B+\frac{2}{3}{\Delta }_B]$
From the matrix given,
$M_{AB}=EI[a{\theta }_B+b{\Delta }_B+c{\theta }_C+d{\Delta }_C]$
On comparing equation (i) and (ii), we get
$\therefore a=\frac{2}{3}=0.67$