3D Tower View

Coordinate System Diagram

A coordinate system has been provided with the origin located at point O.

The top of the tower, point O, must be in static equilibrium, thus

     ΣF_o = F_wind + F_tower + F_A + F_B + F_C = 0

In order to sum all the vectors, it is easier to convert each force into Cartesian vector. Then each direction, i, j, and k, must equate to zero.

     F_W = -1.0k kN
     F_T = 5.2j kN

Substitute the forces into the equilibrium equation above gives,

     ΣF_o = -1.0k + 5.2j + 0.6095 T_Ai - 0.7928 T_Aj
               - 0.2387 T_Bi - 0.7850 T_Bj - 0.5717 T_Bk
               - 0.5760 T_Ci - 0.7327 T_Cj + 0.3625 T_Ck = 0

Sum each of its three components.

      0.6095 T_A - 0.2387 T_B - 0.5760 T_C = 0
     -0.7928 T_A - 0.7850 T_B - 0.7327 T_C = -5.2
                    - 0.5717 T_B + 0.3625 T_C = 1.0

The simultaneous solution of these three linear equations provides,

     T_A = 3.217 kN
     T_B = 0.3239 kN
     T_C = 3.270 kN

Since all tensions are positive and below 4 kN, the antenna will be safe. However, if the wind magnitude had caused tension T_B to act in a negative direction, the antenna could have become unstable, or one of the other cables could have broken.