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Question

A steel bolt of cross-sectional area Ab=5×105m2 is passed through a cylindrical tube made of aluminium. Cross-sectional area of the tube material is At=104m2 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 Δθ=10C. Given, coefficient of linear thermal expansion of steel, αb=105/C.
Young's modulus of steel Yb=2×1011N/m2.
Young's modulus of Al, Yt=1011N/m2, coefficient of
linear thermal expansion of Al αt=2×105/C.
The tensile stress in bolt is:

A
104N/m2
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B
107N/m2
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C
2×108N/m2
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D
1010N/m2
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Solution

The correct option is B 107N/m2
Tensile stress in bolt

σb=Yb(ΔllαbΔθ)l=107N/m2

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