ENGR0135 - Statics and Mechanics of Materials 1 (2211)Homework #10

1. For the steel shaft shown below,

(a) Determine the torques transmitted by cross sections in intervals AB, BC, CD,and DE.

(b) Draw a torque diagram for the shaft.

A B C D E

25 kip · ft 40 kip · ft

45 kip · ft

80 kip · ft

100 kip · ft

2. The solid circular steel (G = 12, 000 ksi) shaft shown below has a diameter of 8 in. Ifthe gears are spaced at 2 ft intervals, determine

(a) The maximum shearing stress in the shaft.

(b) The rotation of a section at D with respect to a section at B.

(c) The rotation of a section at E with respect to a section at A.

A B C D E

25 kip · ft 40 kip · ft

45 kip · ft

80 kip · ft

100 kip · ft

3. A solid circular aluminum alloy (G = 4000 ksi) shaft is subjected to a torque T , asshown below. The shearing stress is limited to 8000 psi and the angle of twist in the7 ft length cannot exceed 0.04 rad. Determine the maximum permissible value of T .

AB C

T

3 ft4 ft

2.5 in 1.75 in

4. The hollow circular steel (G = 80 GPa) shaft shown below has an outside diameter of120 mm and an inside diameter of 70 mm. Determine the maximum compressive stressin the shaft.

AB

T = 8kN ·m

2m

5. A 100 kg block is pushed at constant speed for a distance of 20 m along a level floorby a force F that makes an angle of 35◦ with the horizontal, as shown below. Thecoefficient of kinetic friction between the block and the floor is 0.30. Determine thework done on the block

(a) By the force F.

(b) By gravity.

(c) By the floor.

35◦

F

6. The hydraulic turbines in a water-power plant rotate at 60 rpm and are rated at20, 000 hp. The 30 in-diameter shaft between the turbine and the generator is made ofsteel (G = 12, 000 ksi) and is 20 ft long. Determine

(a) The maximum shearing stress in the shaft at the rated load.

(b) The magnitude of the angle of twist in the shaft at the rated load.

7. A steel (G = 80 GPa) tube with an inside diameter of 100 mm and an outside diameterof 125 mm is encased in a Monel (G = 65 GPa) tube with an inside diameter of 125 mmand an outside diameter of 180 mm. The tubes are connected at the ends to form acomposite shaft. The shaft is subjected to a torque of 12 kN · m. Determine

(a) The maximum shearing stress in each material.

(b) The angle of twist in a 2 m length.

8. A disk and two circular shafts are connected and supported between rigid walls, asshown below. Shaft AB is made of brass (G = 39 GPa) and has a diameter of 100 mmand a length of 800 mm. Shaft BC is made of Monel (G = 65 GPa) and has a diameterof 80 mm and a length of 600 mm. If a torque of 20 kN · m is applied to the disk,determine

(a) The maximum shearing stress in each of the shafts.

(b) The angle of rotation of the disk with respect to its no-load position.

A BC

T