The cable ABCD of length L = 18m supports two street lights of weight W = 1kN ea

Question

The cable ABCD of length L = 18m supports two street lights of weight W = 1kN each.

Given L1 =5.5m, L2 =6.5mm, L3 =4.3m,d= 0.8m, we need to find the tensions in the three cable segments and the sags y1, y2. Neglect the weight of the cable.

Formulate the 5 equations (One equation for the total length of the cable plus two equilibrium equations at each node B, C) that contain the unknowns T1, T2, T3, y1, y2.

The cable ABCD of length L = 18m supports two street lights of weight W = 1kN each. Given L1 =5.5m, L2 =6.5mm, L3 =4.3m,d= 0.8m, we need to find the tensions in the three cable segments and the sags y1, y2. Neglect the weight of the cable. Formulate the 5 equations (One equation for the total length of the cable plus two equilibrium equations at each node B, C) that contain the unknowns T1, T2, T3, y1, y2.

Explanation / Answer

balancing vertical force at B

W = T1cosx1 + T2cosx2 ------------------------eqtn1

tanx1 = L1/y1

tanx2 = L2/(y1-y2)

tanx3 = L3/y3

L1+L2+L3 = 1.8

horizontal force

T1sinx1 = T2sinx2 ---------------------eqtn2

at C,

W + T2cosx2 = T3cosx3 ------------------------eqtn3

horizontal force

T2sinx2 = T3sinx3 -----------------------eqtn4

solve all equations.

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