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MECHANICS - CASE STUDY

    Introduction


Canopy Diagram

 

A building owner has decided to build a canopy over a small alley next to his building that he owns. However, the adjacent building owner does not want any bolts or anchors into his building. Therefore, the joint at the owners building (point A) is a simple vertical plate that can freely move up and down, but cannot rotate. The roof beam is also supported by a pin joint at its center (point B). Finally, the roof beam is fixed into the owner's building at point C.

What is known:

  • The canopy roof beams are standard 2x4 structural steel tubes. The 4 inch dimension is in the vertical direction.
  • The roof load produces 50 lb/in on a typical beam.
  • Assume the steel stiffness, E, is 29,000 ksi.
  • The total length of the canopy roof beam is 120 inches.
     
    Question

   

What is the deflection of the roof canopy at the neighbor's building (point A)?

     
    Approach

   
  • The beam is indeterminate and compatibility conditions are required.
  • Release two of the four support reactions and solve for those support reactions using the principal of superposition.
  • Use basic equilibrium equations to solve for the other two support reactions.
     
   
 
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