Search
 
 

STATICS - CASE STUDY

    Introduction


Radio Tower

 

The radio antenna for station WEML sits on a nearby hill for better transmission. The support cables have been pre-tensioned to keep the antenna stable, which causes a known force on the antenna. In addition, a storm with high winds is adding a significant lateral load on the antenna. The storm could cause problems because the cable anchors were not placed to provide maximum support.

What is known:

  • The locations of the cable anchors on the ground (in reference to point O) are
         A(x,y,z) = (66.5 m, -86.5 m, 0 m)
         B(x,y,z) = (-26.3 m, -86.5 m, -63.0 m)
         C(x,y,z) = (-68.0 m, -86.5 m, 42.8 m)
  • The wind exerts a 1 kN force, Fwind, on the antenna in the negative z direction, Fwind.
  • The antenna experiences a 5.2 kN compression force, Ftower, due to the pre-tensioning in the cables.
  • The cables will fail at tensions greater than 4 kN.
     


Force Diagram

  Questions

 

Will any of the cables break due to the force of the wind on the antenna?

   
  Approach

 
  • Use Cartesian coordinates to define cable forces.
  • Apply the equilibrium equations to solve for the cable tensions. (This will involve 3 equations and 3 unknowns.)
  • Remember, cables experience only tension forces.