Question 3.30: Determine reactions of hinge and roller bearing for the give...

R_{A}+R_{B}= U.D.L. on A C + U.V.L. on A D + U.V.L . on D B portion

=(15 \times 2)+\left(\frac{1}{2} \times 3 \times 20\right)+\left(\frac{1}{2} \times 6 \times 20\right)

= 30 + 30 + 60

R_{A}+R_{B}= 120                                                    ….. (1)

R_{B} \times 9+(15 \times 2) \times 1+50=80+\left(\frac{1}{2} \times 6 \times 20\right) \times\left(3+\frac{1}{3} \times 6\right)+\left(\frac{1}{2} \times 3 \times 20\right)\left(\frac{2}{3} \times 3\right)

9 R_{B}+80=80+60 \times 5+30 \times 2

9 R_{B}=300+60=360

R_{B}=40  KN

Substituting value of R_{B} in equation (1) R_{A}=80  KN