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MECHANICS - CASE STUDY

    Introduction


Initial Condition of Circular Shelf System
Before at Room Temperature, 20oC.


Circular Shelf System Graphic

 

A circular shelf system with two shelves is installed inside a large walk-in drying oven. There is a 1 mm gap between the ceiling and the central support pipe at room temperature of 20oC. The shelf system is designed to support sixteen, 70 kg items (8 items on each shelf).

What is known:

  • The pipe inside and outside diameter is 4.5 cm and 5.0 cm, respectively.
  • Eight items are placed on each of the two shelves, giving a total of 16 items. Each item has a mass of 70 kg.
  • The oven temperature during the installation of the pipe and shelves is 20 oC.
  • Oven temperature during operation is 50 oC.
  • The Young's modulus and the coefficient of thermal expansion of the aluminum pipe is 73 GPa and 23×10-6/oC, respectively.
   
  Question

 

What is the reaction force in the vertical pipe at the ceiling and floor when the drying oven is at 50oC?

     
    Approach

   
  • The shelf loads will compress the pipe.
  • The pipe will probably press against the ceiling due to the thermal loads.
  • The rack pipe will expand due to the temperature change.
  • To determine the change in the pipe length, use the thermal expansion equation,

         δT= L α (ΔT)
  • The ceiling will compress the pipe.
  • The deflections from the loads, thermal expansion and the ceiling reaction must equal the initial gap distance of 1 mm.
     
   
 
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