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MECHANICS - CASE STUDY

    Introduction


Cross Section of Test System


Specimen Testing Set Up

 

The warehouse is filling up fast, and it has been decided that a new storage rack needs to be placed over an elevated portion of the warehouse. This is the only open place remaining.

The new rack will straddle a change in floor elevation as illustrated. One side will be made from a single 1/2" aluminum pipe and the other side from a single 1/2" steel pipe. Two pieces of equipment will be placed on the rack weighing 200 and 300 lb, respectively. The equipment must remain horizontal (within 0.5 degrees from level).

The rack was constructed in the middle of winter when the temperature was only 20o F. Before any equipment or packages are placed on the rack, it was perfectly level. During the summer, the warehouse can reach 125o F. The two pieces of equipment are located on the rack as shown in the diagram.

What is known:

  • The Young modulus of the aluminum and steel pipes are 10,000 ksi and 29,000 ksi, respectively.
  • The aluminum and steel pipes are 5 ft and 3 ft long, respectively.
  • The coefficient of thermal expansion of the aluminum and steel pipes are 13 ×10-6/oF and 6.5×10-6/oF, respectively.
  • The diameter of both pipes are 1/2" with a wall thickness of 1/16".
  • Two equipment packages, 200 lb and 300 lb, are placed 5 ft and 2 ft, respectively, from the right side.
     
    Question

   

What is the rotation angle of the rack platform in the summer (temperature 125o F) with both packages on the rack?

     
    Approach

   
  • Each end of the rack will expand differently due to the temperature change from winter to summer. This will cause the rack to rotate.
  • The thermal expansion equation can be used to determine the change in length of both pipes,

         δT= L α (ΔT)
  • The equipment will cause the each side of the rack to deflect downward (opposite to the thermal expansion) that will also effect the rack rotation.
     
   
 
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