The aluminum rod (E1 = 68 GPa) is reinforced with the firmly bonded steel tube (E2 = 201 GPa). The diameter of the aluminum rod is d = 25 mm and the outside diameter of the steel tube is D= 45 mm. The length of the composite column is L = 761 mm. A force P = 88 kN is applied at the top surface, distributed across both the rod and tube. Required:
Determine the normal stress σ in the steel tube.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.