Question

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 1

Answer:

the ratio of $W_1$ and $W_2$ is $2:1$

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 $2:1$