A beam AB 5m long is supported at it's ends A and B. two point loads w

1.	A beam AB 5m long is supported at it's ends A and B. two point loads w1 and w2 are placed at C and D , 1m and 3m respectively from the end A. if the reaction at A is twice the reaction at B , find the ratio of the loads w1 and w2?
Answer» Answer: the ratio of $W_1$ and $W_2$ is $2:<klux>1</klux>$ Explanation: Let the REACTION at B = R Then Reaction at A = 2R In vertical direction, the forces will be equal Thus $W_1+W_2=2R+R$ $\implies W_1+W_2=3R$ ..............(1) Again Moment with RESPECT to any point will be zero Taking moment w.r.t. A $W_1\times 1+W_2\times 3=R\times 5$ $\implies W_1+3W_2=5R$ $\implies W_1+3W_2=5(\frac{W_1+W_2}{3})$ $\implies 3W_1+9W_2=5W_1+5W_2$ $\implies 2W_1=4W_2$ $\implies \frac{W_1}{W_2}=\frac{2}{1}$ $\implies W_1:W_2=2:1$ Therefore, the ratio of $W_1$ and $W_2$ is $2:1$