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STATICS - CASE STUDY

    Introduction


Problem Graphic

 

A painter is working from a ladder propped against an overhang. The unusual position places dangerous loads on the ladder and could cause it to fail.

What is known:

  • The ladder length L is 20 ft.
  • The ladder angle α is 70°.
  • The overhang height h is 12 ft.
  • The painter's weight W is 200 lb.
  • The painter is 3 ft from the top of the ladder.
     
    Questions


Problem DImensions
 
  1. If the ladder were to fail due to the shear force, where would it fail?
  2. If it were to fail due to the bending moment, where would it fail? Assume the ladder is pinned at its base.
   
  Approach

 
  • Solve for the external reactions.
  • Cut the ladder at an arbitrary point.
  • Form a free-body diagram with the appropriate sign convention.
  • Solve for the internal loads as a function of position along the length of the ladder.
  • Repeat steps 2-4 for each section of the ladder to get a complete shear force diagram and bending moment diagram.