A 1100 kg steel beam is supported by two ropes. What is the tension in each?

Figure:

Login

0 votes

Weight = 1100 * 9.8 = 10,780 N

The sum of the vertical components of the two tension forces is equal to the weight of the beam. The horizontal components of the two tension forces are equal in magnitude.

T1 * cos 20 + T2 * cos 30 = 10,780

T1 * sin 20 = T2 * sin 30

T1 = T2 * 2 * sin 20

T2 * 2 * sin 20 * cos 20 + T2 * cos 30 = 10,780

T2 = 10,780 ÷ (2 * sin 20 * cos 20 + cos 30)

This is approximately 7144.7 N.

T1 = [10,780 ÷ (2 * sin 20 * cos 20 + cos 30)] * 2 * sin 20

This is approximately 4,887 N.