Elements of Mechanical Design

F18 Elements of Mechanical Design (ME 370) Homework 3: Due Class 6 50 Points

1.) (20 points) A pressurized capped pipe with

an outside diameter of 80 mm and a wall thickness of 5 mm is subjected to loading:

𝐹 25 𝑘𝑁 𝐹 8.5 𝑘𝑁 𝐹 7.5 𝑘𝑁

𝑇 1,500 𝑁 ∙ 𝑚 𝑝 2 𝑀𝑃𝑎

Determine the principal stresses (all three) and the absolute maximum shear stress at a point on the inside of the pipe corresponding with point H which is located 𝐿 150 𝑚𝑚 from the loads. Use the thick-walled pressure vessel equations. Include transverse shear stress by approximating that the value for the inside surface is the same as the outside at H.

2.) (10 points) Recalculate the hoop stress in problem 1 based on the thin-walled

approximation and compare to the hoop stress found from the thick-walled equation. Do you think this is an appropriate approximation? Explain.

3.) (20 points) A steel shaft with the dimensions shown in the table below is supported by

flexible bearings at A and B. Two pulleys are keyed to the shaft, and the pulleys carry belt tensions as shown (tension identified with “?” can be found with the information provided). Determine the location and value of the absolute maximum shear stress in the shaft (via principal stress calculations). Ignore transverse shear stress.

Be sure to follow: RULES FOR ALL HOMEWORK SUBMITTALS

Shaft diameter d = 1 in

Bearing A to Pulley C a = 5 in

Pulley C to Bearing B b = 5 in

Bearing B to Pulley D c = 3 in

Pulley C diameter DC = 12 in

Pulley D diameter DD = 8 in

Belt 1 on Pulley C FC1 = 500 lb

Belt 2 on Pulley C FC2 = 100 lb

Belt 1 on Pulley D FD1 = 1000 lb

Belt 2 on Pulley D FD2 = ? lb