Question

TASK 1
A brass tie bar of length 500 mm and diameter 20 mm undergoes a change in temperature from 25°C to 135°C. The linear expansivity of copper is 19 × 10−6°C−1 and its modulus of elasticity is 84 Gpa.
i) Determine the change of length that takes place.
This part of the task provides part of the evidence for the grading criterion P8.
ii) Determine the compressive force induced in the bar if it is rigidly held and expansion is prevented.

Answer 1

Answer on Question #60554-Engineering-Material Science Engineering

A brass tie bar of length $500\mathrm{mm}$ and diameter $20\mathrm{mm}$ undergoes a change in temperature from $25^{\circ}\mathrm{C}$ to $135^{\circ}\mathrm{C}$. The linear expansivity of copper is $19\times 10^{-6} \mathrm{C}^{-1}$ and its modulus of elasticity is 84 Gpa.

i) Determine the change of length that takes place.

This part of the task provides part of the evidence for the grading criterion P8.

ii) Determine the compressive force induced in the bar if it is rigidly held and expansion is prevented.

Solution

i)

$$d l = \alpha l \Delta T = 1 9 \cdot 1 0 ^ {- 6} \cdot 5 0 0 \cdot (1 3 5 - 2 5) = 1. 0 4 5 m m.$$

ii)

$$F = \sigma A = \alpha T E A = 1 9 \cdot 1 0 ^ {- 6} \cdot 8 4 \cdot 1 0 ^ {9} \cdot (1 3 5 - 2 5) \cdot \pi (0. 0 1) ^ {2} = 5 5. 1 5 k N$$

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