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STATICS - CASE STUDY


Problem Description
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1) Rough Surface Contact (no slip)

  Introduction

 

In the lesser-known tale of the Trojan Cow, the would-be invaders of a castle attempt to cross the moat while hidden in the belly of a giant, wooden gift-cow. To cross the moat, an engineer wedges a wooden bridge between the walls of the moat.

What is known:

  • The cow exerts a resultant vertical force at a distance d from the left edge of the bridge.
  • There are three ways the bridge can be wedged against the walls of the moat:
    1) The bridge is in contact with the rough surface of the walls on each end.
    2) The bridge has smooth surface on both ends which allows slipping (similar to a roller).
    3) The bridge is in contact with the rough surface of the walls on one end, and has a smooth surface on the other.

 

     

2) Smooth Surface Contact (slip)


3) Smooth and Rough Surface Contact

  Question

 

Which method of laying the bridge will enable the engineer to determine the reactions at the supports?

   
  Approach

 
  • When the bridge is in contact with the rough surface of the moat wall, a support force is exerted with components parallel and perpendicular to the surface of the wall.
  • When the bridge has a smooth surface (similar to a roller) on the end, a support force is exerted only perpendicular to the wall.
  • Evaluate the problem in 2-D.