1) Rough Surface Contact (no slip)

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.

3) Smooth and Rough Surface Contact

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

• 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.