Numerical - Compressive stress on rod, given Young's modulus, gap & temperature

Q.  In a circuit box, a copper rod at room temperature of 25o C has a gap of 0.3 mm between the end of the rod Q and the rigid wall. If temperature of the rod increases to 70o C ,then what is the compressive stress acting on the rod PQ? (Assume Young's modulus = 100 Gpa & α = 15 x 10–6 /oC)
- Published on 21 Sep 15
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a. 6 Mpa
b. 7.5 Mpa
c. 8.2 Mpa
d. None of the above

ANSWER: 7.5 Mpa

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    Discussion

  • Sravanthi   -Posted on 24 Nov 15
    - Given: Gap = 0.3 mm, Young's modulus = 100 Gpa & α = 15 x 10-6 /°C,

    Solution:

    Free expansion of copper rod = α t L = 15 x 10-6 x (70 - 25) x 500

    = 0.3375

    Actual expansion prevented = Free expansion of copper rod - gap

    = 0.3375 – 0.3

    = 0.0375

    Temperature strain (e) = (δL/L) = (0.0375/ 500) = 7.5 x 10-5

    Temperature stress = e E = (7.5 x 10-5 x 100 x 103) = 7.5 Mpa

    Compressive stress acting on the rod PQ = 7.5 Mpa

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