Subject : Structural Analysis 1

Topic : Deflection in Beams

Difficulty : Low

$1. Reaction: $

$\sum M_A=0$

$15*2+10*4-V_B*6=0$

$V_B=11.67KN$

$\sum F_Y=0$

$V_A-15-10+11.67=0$

$V_A=13.33KN$

$2. By \hspace{1mm} Macaulay's \int\int integration \hspace{1mm} method:$

$Consider \hspace{1mm} part \hspace{1mm} (xA)$

$B.M_x=EI \frac{d^2y}{dx^2}=13.33*x- 15(x-2)- 10(x-4)\hspace{1mm} eqn.1$

$Integrating \hspace{1mm}wrt \hspace{1mm}x,$

$EI\frac{dy}{dx}=13.33*\frac{x^2}{6}- \frac{15(x-2)^2}{2}-\frac{10(x-4)^2}{2}+C_1 \hspace{1mm} eqn.2$

$Again \hspace{1mm} integrating \hspace{1mm} wrt \hspace{1mm} x,$

$EIy=13.33*\frac{x^3}{6}-\frac{15(x-2)^3}{6}-\frac{10(x-4)^3}{6}+C_1x+C_2 \hspace{1mm} eqn.3$

$3. To \hspace{1mm} find …