ME 603 - KEYS AND SPLINES
Problems:
1. A flat key is to be designed for 75 mm diameter shaft which will transmit 150 kW at 400 rpm. If allowable shearing stress is
200 MPa and key width is 15 mm, determine the length of the key.
a. 30.65 mm b. 31.83 mm* c. 33.75 mm d. 32.85 mm
2. A rectangular key is used in a pulley connection to transmit 100 kW at 100 rpm on a 50 mm shaft diameter. Determine the
force required to remove the shaft from the hub? If f = 0.4.
a. 33.24 kN b. 36.85 kN c. 38.19 kN d. 30.55 kN*
3. A 7/16” height x 3” length flat key is keyed to a 2 inches diameter shaft. Determine the torque developed in key if bearing
stress allowable is 25 ksi.
a. 16,406.25 in-lb* b. 15,248.56 in-lb c. 17,420 in-lb d. 16,246.75 in-lb
4. A rectangular key was used in a pulley connected to a line shaft at 15 kW and 600 rpm. If shearing of key is 230 MPa,
determine the force acting on key length if key width is one fourth of shaft diameter and key length of one inch.
a. 43 kN b. 48 kN c. 45 kN* d. 46 kN
5. A 100 kN force is acting on a key that has a length of 4 times its height. If bearing stress of key is 400 MPa, determine the
height of the key.
a. 10.54 mm b. 11.18 mm* c. 12.65 mm d. 15.25 mm
6. A one-meter pulley is fastened to a 100 mm shaft by mans of 25 mm square key with 150 mm length. What force tangent to the
pulley rim will shear the key if shearing stress is 200 MPa.
a. 65 kN b. 70 kN c. 75 kN* d. 80 kN
7. A 4-spline shaft (d = 0.75D, w = 0.24D, h = 0.125D) and to slide when not under load has a diameter of 2.5 in. Find the
shearing stress if shearing force is 2500 lbs., hub length is 2 in.
a. 420.83 psi b. 520.83 psi* c. 620.83 psi d. 720.83 psi
8. A 1.5 in diameter 10-spline shaft (d = 0.91D, w = 0.156D, h = 0.045D) and permanent fit has a compressive force of 2200 lbs.
Find the torque applied if hub length is 1 ¾ in.
a. 1,575.75 psi* b. 1,675.75 psi c. 1,775.75 psi d. 1,875.75 psi
9. A 1.2-meter pulley is fastened to a 120 mm shaft by means of a square key 140 mm long. What force tangent to the pulley will
crush the key if bearing strength is 410 MPa. Assume shaft and key are of the same material.
a. 160.25 kN b. 172.20 kN c. 180.42 kN d. 86.10 kN*
10. Determine the length of the square key for gear driven shaft transmits 40 kW at 300 rpm. The shaft diameter is 60 mm with
design stress of 70 MPa in shear, the thickness and width of the key is 3/8 in.
a. 43 mm b. 64 mm* c. 56 mm d. 72 mm
11. A key is to be designed for 16 cm shaft which will transmit power of 180 kW at 380 rpm. The width of the key is 4 cm and a
height of 3 cm. If the allowable shear stress for the key is 950 kg/cm2 and the allowable compressive stress is 1300 kg/cm2,
determine the length of the key to be used.
a. 2 cm b. 3 cm* c. 4 cm d. 10 cm
12. A solid steel shaft with a safe shearing stress of 7000 psi transmits a torque of 10,500 in-lb. A square key is used whose width
is equal to one-fourth the shaft diameter and whose length is equal to 1 ½ time =s the shaft diameter. Find the key dimensions.
a. ½ in and 3 in* b. ¾ in and 2.5 in c. ½ in and 2/5 in d. ¾ in and 3 in
13. In problem no. 13, determine the crushing stress of the key.
a. 7,000 psi b. 14,000 psi* c. 9,000 psi d. 17,000 psi
14. From problem no. 13, Determine the factor of safety of the key in crushing if ultimate shearing stress is 50,000 psi and
ultimate stress for compression is 60,000 psi.
a. 2.5 b. 7.4 c. 3.4 d. 4.3*
15. A square key is to be used in a 40 mm diameter shaft that will develop a 2 kN-m torque. If bearing stress of the key is 448
MPa, determine the cross-sectional dimension of flat key to be used using key length of 21.12 mm.
a. 21.14* b. 25.61 c. 28.21 d. 18.61
16. A 100 kN force is acting on a key that has a length of 4 times its height. If bearing stress of key is 400 MPa, determine the
height of the key.
a. 10.54 b. 11.18* c. 12.65 d. 15.25
