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

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 20^oC. 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.

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

• 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,
  
       δ_T= 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.