WORLD FOR CIVIL

Statics & Strength of Materials

Topic 6.4d - Problem Assignment 4 - Torsion

Modulus of Rigidity for several materials:
Steel = 12 x 10⁶ lb/in².; Brass = 6 x 10⁶ lb/in².; Aluminum = 4 x 10⁶ lb/in².

1. A hollow steel shaft with an outer diameter of 2 inches and an inner diameter of 1.75 inches is attached to circular disk with a radius of 5 inches, as shown in Diagram 1. A force of 2,000 lb. is applied to the outer edge of the disk.
A. What is the maximum shear stress which develops in the hollow shaft?
B. What is the angle of twist which develops in the shaft?
C. If the maximum allowable shear stress in the shaft is 20,000 lb/in², how large a force could be applied to the outer edge of the disk?

(Answers: A.15,400 lb/in², B. .031 radians, C. 2,600 lb.)

2. A 2 foot long hollow steel shaft with an outer diameter of 1 inches is to transmit 100 horsepower while being driven a 1800 rev/min.
A.) If the allowable shear stress in the shaft is 20,000 lb/in², what is the maximum possible value of the inner diameter of the shaft.
B.) If we were not given the outer diameter of the shaft, but were told that the inner diameter was to be nine-tenths of the outer diameter, what would be the minimum outer diameter of the shaft which could safely transmit the horse power ? (The allowable shear stress in the shaft is 20,000 lb/in²)

(Answers: A. di = .573" , B. do = 1.37")

3. A 2 foot long hollow brass shaft with an outer diameter of 1.5 inches and an inner diameter of 1 inches is to transmit power while being driven a 3600 rev/min.
A.) If the allowable shear stress in the shaft is 18,000 lb/in²., what is the maximum horsepower which can be transmitted down the shaft ?
B.) If we were to transmit the maximum power, what would be the resulting angle of twist of the shaft due to the applied torque.
C.) If we were not given the outer diameter of the shaft, but were told that the inner diameter was to be six-tenths of the outer diameter, what would be the minimum outer diameter of the shaft which could safely transmit the horsepower found in part A? (The allowable shear stress in the shaft is 18,000 lb/in². )

(Answers: A 548 hp., B. .096 radians, C. 1.46")

4. A compound shaft is attached to the wall at point C, as shown in Diagram 4. Shaft section BC is aluminum and has a diameter of 3 inches. Shaft section AB is steel and has a diameter of 2 inches. The allowable shear stress in the aluminum is 14,000 lb/in², and the allowable stress in the steel is 18,000 lb/in². Torque of T1 and T2 are applied to the shaft in the directions shown in Diagram 4. Determine the maximum values of the applied torque, T1 and T2, such that the allowable shear stress is not exceeded in either shaft section.

(Answers: T1=2360 ft-lb., T2 = 8545 ft-lb.)

5. A compound shaft with applied torque is shown in Diagram 5. Section AB is made of steel. Section BC is made of brass. Section CD is made of aluminum. A driving torque of 1,800 ft-lb. is applied at point B. Load torque of 500 ft-lb., 1000 ft-lb., and 300 ft-lb. act at points A, C and D. The shaft is rotating at 2,400 rev/minute. The allowable shear stress in the steel is 20,000 lb/in², the allowable shear stress in the brass is 16,000 lb/in², and the allowable shear stress in the aluminum is 14,000 lb/in². For this shaft:
A. Determine the horsepower being transferred through each shaft.
B. Determine the minimum diameter for each shaft, such that it can carry the transmitted power within the allowable stress limit.
C. Using the diameters determined in part B, calculate the angle of twist of end D with respect to end A.

(Answers: A. AB=228 hp, BC=594 hp, CD=137 hp; B. AB=1.15", BC=1.71", CD=1.09"; C AB=.035 rad-cw, .BC=056 rad-ccw, CD=078 rad-ccw, Total = .099 rad-ccw)