Numerical - Elongation of rod, given force, dimensions, Young's modulus

Q.  Force of 100 kN is applied on 900 mm long rod of 20 mm diameter and is simultaneously heated at 70o C. What is the total elongation of the rod? (Assume coefficient of thermal expansion = 10 x 10–6 oC, Young's modulus = 150 Gpa)
- Published on 21 Sep 15

a. 2.54 mm
b. 2.00 mm
c. 1.27 mm
d. 0.63 mm

ANSWER: 2.54 mm

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    Discussion

  • Sravanthi   -Posted on 24 Nov 15
    Given: Diameter of rod = 20 mm, length of rod (L) = 900 mm, heating temperature (t)= 70 °C, coefficient of thermal expansion (α) = 10 x 10-6 /°C, Young's modulus = 150 Gpa

    Formula: 1) Total elongation = elongation when heated + elongation due to pull

    2) Elongation due to pull (δL) = (PL/AE)

    3) Elongation due to heating = α t L

    Solution:

    1) Elongation due to pull (δL) = (PL/AE)

    = [100000 x 900] /[(π/4) x 202 x 150 x 103]

    = 1.9098

    2) Elongation due to heating = α t L

    = 10 x 10-6 x 70 x 900

    = 0.63

    3) Total elongation = elongation when heated + elongation due to pull

    Total elongation = 1.9098+0.63 = 2.54 mm

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