A rod is 2m long at temperature of 10oC. Find the expansion of the rod, when the temperature is raised to 80oC. If this expansion is prevented, find the stress induced in the material of the rod. Take E = 1.0 x 105 MPa and α = 0.000012 per degree centigrade?
Answers
Answer:
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Explanation:
Free expansion of the rod =αLΔθ
=15×10
−60
C×2m×(50−20)
0
C
=9×10
−
4m=0.9mm
If the expansion is fully prevented, then
Strain=
2
9×10
−4
=4.5×10
−4
Temperature Stress = Strain ×Y
=4.5×10
−4
×2×10
11
=9×10
7
N/m
2
If 0.4 mm expansion is allowed, then length restricted to expand
=0.9−0.4=0.5mm
Strain=
2
5×10
−4
=2.5×10
−4
Temperature stress = Strain ×Y=2.5×10
−4
×2×10
11
=5×10
7
N/m
2
A steel bolt of cross-sectional area A
b
=5×10
−5
m
2
is passed through a cylindrical tube made of aluminium. Cross-sectional area of the tube material is A
t
=10
−4
m
2
and its length is l=50 cm. The bolt is just taut so that there is no stress in the bolt and temperature of the assembly increases through △θ=10
∘
C. Given coefficient of linear thermal expansion of steel, α
b
=10
−5
/
∘
C.
Young's modulus of steel Y
b
=2×10
11
N/m
2
.
Young's modulus of Al,Y
t
=10
11
N/m
2
, coefficient of linear thermal expansion of Alα
t
=2×10
−5
/
∘
C.