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 Q2If 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 Q2Shafts Subjected to Bending Moment OnlyWhen the shaft is subjected to a bending moment only, then the maximum stress (tensile orcompressive) is given by the bending equation. We know thatм..(i)...(1)IywhereM = Bending moment,I = Moment of inertia of cross-sectional area of the shaft about theaxis of rotation,O, = Bending stress, andy = Distance from neutral axis to the outer-most fibre.We know that for a round solid shaft, moment of inertia,dI =64-× d* andy =2Substituting these values in equation (î), we haveMM=32dor64From 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,)%3D64andy = d/2Again substituting these values in equation (i), we haveмX Og (d,)³ (1 – k*)M=d.(d)* (1 – k*)or32642From this equation, the outside diameter of the shaft (d) may be obtained. Question.02Attachment 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 eachaxle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is1.4m.50 kN50 kN100 mm-1.4 m100 mmABRcRpFigure Q2If the stress is not to exceed 100MP,, find,a) the diameter of the axle between the wheels, andb) if a hollow circular shaft is to be used in place of the solid shaft, find the inside and outsidediameter when the ratio of inside to outside diameter is 0.5.

Given:- P=50kN Gauge length= 1.4m Max stress=100MPa k=dido=0.5 To find:- 1) Diameter of axel, d 2)…

Answered: Consider the case of shafts subjected…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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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.

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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