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Question 1A plastic-lined steel pipe has the cross-sectional shape shown in Figure Q1 The steel pipe100 mm and inner diameter d2 94 mm The plastic liner hashas an outside diameter dan inner diameter d, 82 mm The modulus of elasticity of the steel is 75 times the modulusof the plasticDetermine the allowable bending moment Mallow f the allowable stress in the steel is 35MPa and that in the plastic is 600 kPaIf the pipe and Iiner diameters remain unchanged, what new value of allowable stressfor the steel pipe will result in the steel pipe and plastic liner reaching their allowablestress values under the same maximum moment (e, a balanced design)?What is the new maximum moment?d3d27Figure Q1 Composite steel-plastic pipe.

Question
Question 1
A plastic-lined steel pipe has the cross-sectional shape shown in Figure Q1 The steel pipe
100 mm and inner diameter d2 94 mm The plastic liner has
has an outside diameter d
an inner diameter d, 82 mm The modulus of elasticity of the steel is 75 times the modulus
of the plastic
Determine the allowable bending moment Mallow f the allowable stress in the steel is 35
MPa and that in the plastic is 600 kPa
If the pipe and Iiner diameters remain unchanged, what new value of allowable stress
for the steel pipe will result in the steel pipe and plastic liner reaching their allowable
stress values under the same maximum moment (e, a balanced design)?
What is the new maximum moment?
d3
d2
7
Figure Q1 Composite steel-plastic pipe.
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Question 1 A plastic-lined steel pipe has the cross-sectional shape shown in Figure Q1 The steel pipe 100 mm and inner diameter d2 94 mm The plastic liner has has an outside diameter d an inner diameter d, 82 mm The modulus of elasticity of the steel is 75 times the modulus of the plastic Determine the allowable bending moment Mallow f the allowable stress in the steel is 35 MPa and that in the plastic is 600 kPa If the pipe and Iiner diameters remain unchanged, what new value of allowable stress for the steel pipe will result in the steel pipe and plastic liner reaching their allowable stress values under the same maximum moment (e, a balanced design)? What is the new maximum moment? d3 d2 7 Figure Q1 Composite steel-plastic pipe.

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check_circleAnswer
Step 1

a)

Elasticity of steel is equal to seven times of elasticity of plastic.

From the above statement:
E,
75
E
Calculate the moment of inertia ofthe outer side tube
(;p-p)
nm)' - (94 mm
64
64
1.076x 10-6 m4
Calculate the moment of inertia ofthe inner tube
64
n)']
m)-(82 mm
(94 mm
64
=1.613 x 10
m4
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From the above statement: E, 75 E Calculate the moment of inertia ofthe outer side tube (;p-p) nm)' - (94 mm 64 64 1.076x 10-6 m4 Calculate the moment of inertia ofthe inner tube 64 n)'] m)-(82 mm (94 mm 64 =1.613 x 10 m4

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Step 2

Calculate the allowable bending moment in the pipe.

E IEI
M
allowable
X
allowable
d
E.
2
+(1)
X
allowable
allowable
d
E
E
2
ix(1.076x10)+(1)(1.613x 10)
= (35 x 10 pa)
gllowable
50/1000
(75)
2
35x 82.313
allowable
3.75
- 768.25 N m
allowable
Thus, the moment allowable in the steel pipe is 768.25 N -m
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E IEI M allowable X allowable d E. 2 +(1) X allowable allowable d E E 2 ix(1.076x10)+(1)(1.613x 10) = (35 x 10 pa) gllowable 50/1000 (75) 2 35x 82.313 allowable 3.75 - 768.25 N m allowable Thus, the moment allowable in the steel pipe is 768.25 N -m

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Step 3

b)

Calculate the allowable bending mom...

E,I,+E
p 2
1
(M
X
allowable
=
allowable platic
E
2
E
|I,
E
+(1)
St
allowable platic
allowable
d
E
S
2
E
76 x 10)+(1)(1.613 x 10)
75 x(1.0
=(600x 10 pa) x
(M
allowable plestic
94/1000
(75)
2
600 x 82.313
(M
allowable platic
0.047
(MM
allowable plstic
1050.80 N m
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E,I,+E p 2 1 (M X allowable = allowable platic E 2 E |I, E +(1) St allowable platic allowable d E S 2 E 76 x 10)+(1)(1.613 x 10) 75 x(1.0 =(600x 10 pa) x (M allowable plestic 94/1000 (75) 2 600 x 82.313 (M allowable platic 0.047 (MM allowable plstic 1050.80 N m

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