To determine the increase in stress due to temperature rise in the tubing, we need to calculate the thermal stress induced in the material. The formula for thermal stress (\( \sigma \)) is given by:
\( \sigma = E \cdot \alpha \cdot \Delta T \)
Where:
- \( E \) is the Young's modulus of elasticity of the material,
- \( \alpha \) is the linear coefficient of thermal expansion,
- \( \Delta T \) is the change in temperature.
Given values:
- \( E = 3000 \, \text{N/m}^2 \),
- \( \alpha = 5 \times 10^{-6} \, \text{per °C} \),
- \( \Delta T = 20 \, \text{°C} \).
Substituting these values into the formula:
\( \sigma = 3000 \times 5 \times 10^{-6} \times 20 \)
This yields:
\( \sigma = 3000 \times 100 \times 10^{-6} \)
\( \sigma = 300 \times 10^{-4} \)
\( \sigma = 0.3 \, \text{N/m}^2 \)
The calculated stress is \( 0.3 \, \text{N/m}^2 \), which falls outside the expected range of 0.28,0.28. This discrepancy suggests a need to double-check inputs and calculations. However, the procedure followed is correct given the values. Thus, the increase in stress due to temperature rise is approximately 0.3 N/m².