A shaft running at 400 r.p.m. transmits 10 kW. Assuming allowable shear stress in shaft as 40 MPa, (Ans. 35 mm] find the diameter of the shaft.
A shaft running at 400 r.p.m. transmits 10 kW. Assuming allowable shear stress in shaft as 40 MPa, (Ans. 35 mm] find the diameter of the shaft.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![EXERCISES
1. A shaft rumning at 400 r.p.m. transmits 10 kW. Assuming allowable shear stress in shaft as 40 MPa,
[Ans. 35 mm]
find the diameter of the shaft.
2. A hollow steel shaft transmits 600 kW at 500r.p.m. The maximum shear stress is 62.4 MPa. Find the
outside and inside diameter of the shaft, if the outer diameter is twice of inside diameter, assuming that
the maximum torque is 20% greater than the mean torque.
[Ans. 100 mm : 50 mm]
3.
A hollow shaft for a rotary compressor is to be designed to transmit a maximum torque of 4750 N-m.
The shear stress in the shaft is limited to 50 MPa. Determine the inside and outside diameters of the
shaft, if the ratio of the inside to the outside diameter is 0.4.
[Ans. 35 mm ; 90 mm]
4. A motor car shaft consists of a steel tube 30 mm internal diameter and 4 mm thick. The engine
develops 10 kW at 2000 r.p.m. Find the maximum shear stress in the tube when the power is transmit-
ted through a 4 : 1 gearing.
5. A cylindrical shaft made of steel of yield strength 700 MPa is subjected to static loads consisting of a
[Ans. 30 MPa]
bending moment of 10 kN-m and a torsional moment of 30 kN-m. Determine the diameter of the shaft
using two different theories of failure and assuming a factor of safety of 2.
[Ans. 100 mm)
6. A line shaft rotating at 200 r.p.m. is to transmit 20 kW. The allowable shear stress for the material of
the shaft is 42 MPa. If the shaft carries a central load of 900 N and is simply supported between
bearing 3 metre apart, determine the diameter of the shaft. The maximum tensile or compressive stress
is not to exceed 56 MPa.
[Ans. 50 mm]
7. Two 400 mm diameter pulleys are keyed to a simply supported shaft 500 mm apart. Enach pulley is 100
mm from its support and has horizontal belts, tension ratio being 2.5. If the shear stress is to be limited
to 80 MPa while transmitting 45 kW at 900 r.p.m., find the shaft diameter if it is to be used for the
input-output belts being on the same or opposite sides.
[Ans. 40 mm]
8. Acast gear wheel is driven by a pinion and transmits 100 kW at 375 rp.m. The gear has 200 machine cut
teeth having 20° pressure angle and is mounted at the centre of a 0,4 m long shaft. The gear weighs 200)
N and its pitch circle diameter is 1.2 m. Design the gear shaft. Assume that the axes of the gear and
pinion lie in the same horizontal plane.
(Ans. 80 mm)
9. Fig. 14.17 shows a shaft from a hand-operated machine. The frictional torque in the journal bearings
ut A and B is 15 N-m cach. Find the diameter ( d) of the shaft (on which the pulley is mounted) using
maximum distortion energy criterion. The shaft material is 40 C 8 steel for which the yield stress in
tension is 380 MPa and the factor of safety is 1.5,
[Ans. 20 mm]
Shafts - 553
Pulley
-Shaft
B
A
300
200 - 200
T, + T;
T= 1200 N
T,= 800 N
All dimensions in mm.
Fig. 14.17
10. A line shaft is to transmit 30 kW at 160 r.p.m. It is driven by a motor placed directly under it by means
of a belt running on a 1 m diameter pulley keyed to the end of the shaft. The tension in the tight side
of the belt is 2.5 times that in the slack side and the centre of the pulley over-hangs 150 mm beyond
the centre line of the end bearing. Determine the diameter of the shaft, if the allowable shear stress i
56 MPa and the pulley weighs 1600 N.
11. Determine the diameter of hollow shaft having inside diameter 0.5 times the outside ummeter. The
nermissible shear stress is limited to 2(0 MPa The shaft carries a 900 mm diameter cast iron nulley](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f8fde67-01ea-4ce1-ba0b-b8a35abcd779%2F6f6caa0f-ba17-4e89-a828-584f2024961c%2F64yebyp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISES
1. A shaft rumning at 400 r.p.m. transmits 10 kW. Assuming allowable shear stress in shaft as 40 MPa,
[Ans. 35 mm]
find the diameter of the shaft.
2. A hollow steel shaft transmits 600 kW at 500r.p.m. The maximum shear stress is 62.4 MPa. Find the
outside and inside diameter of the shaft, if the outer diameter is twice of inside diameter, assuming that
the maximum torque is 20% greater than the mean torque.
[Ans. 100 mm : 50 mm]
3.
A hollow shaft for a rotary compressor is to be designed to transmit a maximum torque of 4750 N-m.
The shear stress in the shaft is limited to 50 MPa. Determine the inside and outside diameters of the
shaft, if the ratio of the inside to the outside diameter is 0.4.
[Ans. 35 mm ; 90 mm]
4. A motor car shaft consists of a steel tube 30 mm internal diameter and 4 mm thick. The engine
develops 10 kW at 2000 r.p.m. Find the maximum shear stress in the tube when the power is transmit-
ted through a 4 : 1 gearing.
5. A cylindrical shaft made of steel of yield strength 700 MPa is subjected to static loads consisting of a
[Ans. 30 MPa]
bending moment of 10 kN-m and a torsional moment of 30 kN-m. Determine the diameter of the shaft
using two different theories of failure and assuming a factor of safety of 2.
[Ans. 100 mm)
6. A line shaft rotating at 200 r.p.m. is to transmit 20 kW. The allowable shear stress for the material of
the shaft is 42 MPa. If the shaft carries a central load of 900 N and is simply supported between
bearing 3 metre apart, determine the diameter of the shaft. The maximum tensile or compressive stress
is not to exceed 56 MPa.
[Ans. 50 mm]
7. Two 400 mm diameter pulleys are keyed to a simply supported shaft 500 mm apart. Enach pulley is 100
mm from its support and has horizontal belts, tension ratio being 2.5. If the shear stress is to be limited
to 80 MPa while transmitting 45 kW at 900 r.p.m., find the shaft diameter if it is to be used for the
input-output belts being on the same or opposite sides.
[Ans. 40 mm]
8. Acast gear wheel is driven by a pinion and transmits 100 kW at 375 rp.m. The gear has 200 machine cut
teeth having 20° pressure angle and is mounted at the centre of a 0,4 m long shaft. The gear weighs 200)
N and its pitch circle diameter is 1.2 m. Design the gear shaft. Assume that the axes of the gear and
pinion lie in the same horizontal plane.
(Ans. 80 mm)
9. Fig. 14.17 shows a shaft from a hand-operated machine. The frictional torque in the journal bearings
ut A and B is 15 N-m cach. Find the diameter ( d) of the shaft (on which the pulley is mounted) using
maximum distortion energy criterion. The shaft material is 40 C 8 steel for which the yield stress in
tension is 380 MPa and the factor of safety is 1.5,
[Ans. 20 mm]
Shafts - 553
Pulley
-Shaft
B
A
300
200 - 200
T, + T;
T= 1200 N
T,= 800 N
All dimensions in mm.
Fig. 14.17
10. A line shaft is to transmit 30 kW at 160 r.p.m. It is driven by a motor placed directly under it by means
of a belt running on a 1 m diameter pulley keyed to the end of the shaft. The tension in the tight side
of the belt is 2.5 times that in the slack side and the centre of the pulley over-hangs 150 mm beyond
the centre line of the end bearing. Determine the diameter of the shaft, if the allowable shear stress i
56 MPa and the pulley weighs 1600 N.
11. Determine the diameter of hollow shaft having inside diameter 0.5 times the outside ummeter. The
nermissible shear stress is limited to 2(0 MPa The shaft carries a 900 mm diameter cast iron nulley
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