Question

A beam 5m long is supported at it's ends A and B point load W1&W2 were placed at C and D, 1m and 3m respectively from A. If the reaction at A is twice the reaction at B, find the ration of the loadss W1&W2...

Answer 1

Answer on Question #48058, Physics, Mechanics | Kinematics | Dynamics

A beam 5m long is supported at it's ends A and B point load W1&W2 were placed at C and D, 1m and 3m respectively from A. If the reaction at A is twice the reaction at B, find the ration of the loadss W1&W2...

Let $N_A$ and $N_B$ be the reaction forces at the left and right supports.

Taking moments of all forces about the point of contact of the left support,

$$W _ {1} * A C + W _ {2} * A D - N _ {B} * A B = 0$$ $$W _ {1} + 3 W _ {2} - 5 N _ {B} = 0$$

Thus,

$$N _ {B} = \frac {W _ {1} + 3 W _ {2}}{5}$$

Taking moments of forces about the point of contact of the right support,

$$N _ {A} * A B - W _ {1} * C B - W _ {2} * D B = 0$$ $$5 N _ {A} - 4 W _ {1} - 2 W _ {2} = 0$$

Thus,

$$N _ {A} = \frac {4 W _ {1} + 2 W _ {2}}{5}$$

From given

$$\frac {N _ {A}}{N _ {B}} = 2$$ $$\frac {N _ {A}}{N _ {B}} = \frac {4 W _ {1} + 2 W _ {2}}{W _ {1} + 3 W _ {2}} = 2$$ $$4 W _ {1} + 2 W _ {2} = 2 \left(W _ {1} + 3 W _ {2}\right)$$ $$4 W _ {1} + 2 W _ {2} = 2 W _ {1} + 6 W _ {2}$$ $$2 W _ {1} = 4 W _ {2}$$

Thus,

$$\frac {W _ {1}}{W _ {2}} = 2$$

Answer: $\frac{W_1}{W_2} = 2$

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