Question

A mass of 500kg is suspended from a beam by two chains, 1,5m and 2,7m long respectively. The distance between the suspension points is 3,746m. Determine:
a) the load in each chain
b) the vertical and horizontal reactions at the suspension points

Answer 1

Answer on Question #64260-Engineering-Civil and Environmental Engineering

A mass of 500kg is suspended from a beam by two chains, 1,5m and 2,7m long respectively. The distance between the suspension points is 3,746m. Determine:

a) the load in each chain

b) the vertical and horizontal reactions at the suspension points

Solution

a) The angle between left chain (1) and horizontal direction is 19.46°.

The angle between right chain (2) and horizontal direction is 36.85°.

$$T _ {1} \cos 1 9. 4 6 ^ {\circ} = T _ {2} \cos 3 6. 8 5 ^ {\circ} \rightarrow T _ {2} = \frac {T _ {1} \cos 1 9 . 4 6 ^ {\circ}}{\cos 3 6 . 8 5 ^ {\circ}}$$ $$T _ {1} \sin 1 9. 4 6 ^ {\circ} + T _ {2} \sin 3 6. 8 5 ^ {\circ} = 5 0 0 (9. 8)$$ $$T _ {1} \sin 1 9. 4 6 ^ {\circ} + \frac {T _ {1} \cos 1 9 . 4 6 ^ {\circ}}{\cos 3 6 . 8 5 ^ {\circ}} \sin 3 6. 8 5 ^ {\circ} = 5 0 0 (9. 8)$$

The loads are:

$$T _ {1} = \frac {5 0 0 (9 . 8)}{\sin 1 9 . 4 6 ^ {\circ} + \frac {\cos 1 9 . 4 6 ^ {\circ}}{\cos 3 6 . 8 5 ^ {\circ}} \sin 3 6 . 8 5 ^ {\circ}} = 4 7 1 2 N.$$ $$T _ {2} = \frac {4 7 1 2 \cos 1 9 . 4 6 ^ {\circ}}{\cos 3 6 . 8 5 ^ {\circ}} = 5 5 5 2 N.$$

b) The vertical and horizontal reactions at the left point:

$$N _ {1 y} = T _ {1} \sin 1 9. 4 6 ^ {\circ} = 4 7 1 2 \sin 1 9. 4 6 ^ {\circ} = 1 5 7 0 N$$ $$N _ {1 x} = T _ {1} \cos 1 9. 4 6 ^ {\circ} = 4 7 1 2 \cos 1 9. 4 6 ^ {\circ} = 4 4 4 3 N$$

The vertical and horizontal reactions at the right point:

$$N _ {2 y} = T _ {2} \sin 3 6. 8 5 ^ {\circ} = 5 5 5 2 \sin 3 6. 8 5 ^ {\circ} = 3 3 3 0 N$$ $$N _ {2 x} = T _ {2} \cos 3 6. 8 5 ^ {\circ} = 5 5 5 2 \cos 3 6. 8 5 ^ {\circ} = 4 4 4 3 N$$

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