Windmill Structure


When a new wind power generated was being constructed, the generator housing was offset 3 inches from the center line of the vertical support column. The design engineer is worried that the eccentric loading of the column will failure.

What is knows:

  • Column is a hollow round pipe with outer diameter of 6 in and thickness of 0.25 in.
  • The column height, L, is 30 ft.
  • The combined generator housing and blades weigh 5,000 lb.
  • Neglect the self-weight of the column and the wind acting on the column.
  • Assume the pipe is fixed at the base and free at the top.
  • The generator and blade weight is applied 3 in off the center line of the column.
  • The material is steel with a stiffness, E, of 29,000 ksi and an allowable strength of 36 ksi.
  • The required factor of safety is 3.


1. Does the actual stress exceed the allowable stress including the factor of safety?

2. What is the maximum weight the column can support assuming the weight is 3 in off center?


  • Determine the cross sectional area and the moment of inertia.
  • Apply the factor of safety to the allowable stress.
  • Using the secant formula, find the actual stress and then compare it to the allowable stress.
  • Using the allowable stress, solve for the maximum load P using the secant formula. This will involve using a trail and error method or numerical method to calculate P.
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