Question 3.27: Two rollers C and D produce vertical forces P and Q on the h...
Two rollers C and D produce vertical forces P and Q on the horizontal beam AB as shown in the Fig. 3.38. Determine the distance ‘x’ of the load P from support A if the reaction at A is twice as great as the reaction at B. The weight of beam is to be neglected.
(UPTU 2008–09 II Sem)
Given:
P = 18 kN, Q = 9 kN, l = 3.6 m and C = 0.9 m
Consider FBD of beam AB, as shown in Fig. 3.38 (a)
\sum Y=0, \qquad R_{A}+R_{ B }=18+9= 27 KN …(1) and given that R_{A}=2R_{ B }
thus 2 R_{B}+R_{B}=27, R_{B}=9 kN , R_{A}=18 kN
\sum M_{A}=0, \qquad R_{B} \times 3.6=18 \times x+9(x+0.9)9 \times 3.6=18 x+9 x+8.1
32.4=18 x+9 x+8.1
27 x=24.3
x=0.9 m
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