Question 3.31: Determine the reactions at A, B and D of the system as shown...
Determine the reactions at A, B and D of the system as shown in Fig. 3.42.
(UPTU 2001–02 Ist sem)
First draw the F.B.D. of both beams and apply equilibrium equations to beam CD and AB respectively as shown in Fig. 3.42 (a).
Load acting on beam CD is a combination of U.D.L and U.V.L.
thus, \sum Y=0,
R_{C}+R_{D}=(3 \times 6)+\left(\frac{1}{2} \times 6 \times(12-3)\right)
=18+\frac{1}{2} \times 6 \times 9
= 45
\sum M_{C}=0, R_{D} \times 8=(3 \times 6) \times\left(\frac{6}{2}\right)+\left(\frac{1}{2} \times 6 \times 9\right) \times\left(\frac{2}{3} \times 6\right)
R_{D}=20.25 kN
Substituting value of R_{D} in equation (1),
R_{C} = 45 – 20.25
R_{C} = 24.75 KN
Considering FBD of beam AB,
\sum Y=0, \qquad R_{A}+R_{B}=R_{C}
R_{A}+R_{B}=24.75 ….. (2)
\sum M_{A}=0, \qquad R_{B} \times 5=24.75 \times 2
R_{B}=9.9 kN
Substituting value of R_{B} in equation (2),
R_{A}=14.85 kN
