Question

The guy wires AB and AC are attached to the top of the transmission tower. The tension in cable AB is 9.1 kN. Determine the required tension T in cable AC such that the net effect of the two cables is a downward force at point A. Determine the magnitude R of this downward force.

Answer 1

Answer:

 T_ac = 6.586 KN

R = 10.51 KN

Explanation:

Given:

- Tension in cable T_ab = 9.1 KN

Find:

- Determine the required tension T in cable AC such that the net effect of the two cables is a downward force at point A

- Determine the magnitude R of this downward force.

Solution:

- Compute the three angles as shown in figure attached, a, B , y:

                                 a = arctan (40/50) = 38.36 degrees

                                 B = arctan (50/30) = 59.04 degrees

                                 y = 180 - 38.36 = 82.6 degrees

- Use cosine rule to calculate R and F_ac as follows:

                                 sin(a) / T_ac = sin(B) / T_ab = sin(y) / R

                                 sin(38.36) / T_ac = sin(59.04) / 9.1 = sin(82.06) / R

                                 T_ac = 9.1 * ( sin(38.36) / sin(59.04) )

                                T_ac = 6.586 KN

                                 R = 9.1 * ( sin(82.06) / sin(59.04) )

                                 R = 10.51 KN