Consider the case of shafts subjected to bending moment only. Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is 1.4m.
Consider the case of shafts subjected to bending moment only. Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is 1.4m.
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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Question
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Consider the case of shafts subjected to bending moment only.
Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is 1.4m.
Figure Q2
If the stress is not to exceed 100MPa, find,
- the diameter of the axle between the wheels, and
- if a hollow circular shaft is to be used in place of the solid shaft, find the inside and outside diameter when the ratio of inside to outside diameter is 0.5.
![Attachment Q2
Shafts Subjected to Bending Moment Only
When the shaft is subjected to a bending moment only, then the maximum stress (tensile or
compressive) is given by the bending equation. We know that
м
..(i)
...(1)
I
y
where
M = Bending moment,
I = Moment of inertia of cross-sectional area of the shaft about the
axis of rotation,
O, = Bending stress, and
y = Distance from neutral axis to the outer-most fibre.
We know that for a round solid shaft, moment of inertia,
d
I =
64
-× d* and
y =
2
Substituting these values in equation (î), we have
M
M=
32
d
or
64
From this equation, diameter of the solid shaft (d) may be obtained.
We also know that for a hollow shaft, moment of inertia,
[d.)* - (4,)*] = (d." (1 – k*)
..(where k= d;/ d,)
%3D
64
and
y = d/2
Again substituting these values in equation (i), we have
м
X Og (d,)³ (1 – k*)
M=
d.
(d)* (1 – k*)
or
32
64
2
From this equation, the outside diameter of the shaft (d) may be obtained.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F685d5111-7372-4863-a6da-fda0d5313222%2F8c43e5ff-5f21-44eb-a117-0cbd1d265033%2Fkjmmtd_processed.png&w=3840&q=75)
Transcribed Image Text:Attachment Q2
Shafts Subjected to Bending Moment Only
When the shaft is subjected to a bending moment only, then the maximum stress (tensile or
compressive) is given by the bending equation. We know that
м
..(i)
...(1)
I
y
where
M = Bending moment,
I = Moment of inertia of cross-sectional area of the shaft about the
axis of rotation,
O, = Bending stress, and
y = Distance from neutral axis to the outer-most fibre.
We know that for a round solid shaft, moment of inertia,
d
I =
64
-× d* and
y =
2
Substituting these values in equation (î), we have
M
M=
32
d
or
64
From this equation, diameter of the solid shaft (d) may be obtained.
We also know that for a hollow shaft, moment of inertia,
[d.)* - (4,)*] = (d." (1 – k*)
..(where k= d;/ d,)
%3D
64
and
y = d/2
Again substituting these values in equation (i), we have
м
X Og (d,)³ (1 – k*)
M=
d.
(d)* (1 – k*)
or
32
64
2
From this equation, the outside diameter of the shaft (d) may be obtained.
![Question.02
Attachment Q2 refers.
Consider the case of shafts subjected to bending moment only.
Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each
axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is
1.4m.
50 kN
50 kN
100 mm-
1.4 m
100 mm
A
B
Rc
Rp
Figure Q2
If the stress is not to exceed 100MP,, find,
a) the diameter of the axle between the wheels, and
b) if a hollow circular shaft is to be used in place of the solid shaft, find the inside and outside
diameter when the ratio of inside to outside diameter is 0.5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F685d5111-7372-4863-a6da-fda0d5313222%2F8c43e5ff-5f21-44eb-a117-0cbd1d265033%2Fmghjcm_processed.png&w=3840&q=75)
Transcribed Image Text:Question.02
Attachment Q2 refers.
Consider the case of shafts subjected to bending moment only.
Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each
axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is
1.4m.
50 kN
50 kN
100 mm-
1.4 m
100 mm
A
B
Rc
Rp
Figure Q2
If the stress is not to exceed 100MP,, find,
a) the diameter of the axle between the wheels, and
b) if a hollow circular shaft is to be used in place of the solid shaft, find the inside and outside
diameter when the ratio of inside to outside diameter is 0.5.
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