Question

The bent beam ABC is attached to a pin at C and rests against a roller support at B. Neglecting the weight of the beam, find the reactions at B and C caused by the 150- kg load. 

Answer 1

$M_C=0:$

$$-mg(3m+2m)+R_B(\dfrac{4}{\sqrt{3^2+4^2}})(2m)$$

$$+R_B(\dfrac{3}{\sqrt{3^2+4^2}})(1.5m)=0$$

$$R_B=2mg$$

$$R_B=2(150kg)(9.81m/s^2)=2943N$$

$$\sum_iF_{ix}=0$$

$$C_x-R_B(\dfrac{3}{5})=0$$

$$C_x=0.6(2941N)=1765.8N$$

$$\sum_iF_{iy}=0$$

$$C_y+R_B(\dfrac{4}{5})-mg=0$$

$$C_y=150kg(9.81m/s^2)-0.8(2941N)=-881.3N$$

$$R_B=2943N, C_x=1765.8N,C_y=-881.3N$$