4.A steel rod is heated to 200 degrees Celcius and is then rigidly clamped at both ends and allowed to cool. Determine the temperature at which the rod will break if the tensile strength, coefficient of linear thermal expansion and youngs modulus of
elasticity of the steel are 150MN/m^2, 12x10-6/ degrees celcius and 200GN/m^2
To determine the temperature at which the steel rod will break, we need to use the concept of thermal stress.
Thermal stress occurs when a material undergoes thermal expansion or contraction due to temperature change. This stress can lead to failure if it exceeds the strength of the material.
Here's how you can calculate the temperature at which the rod will break:
1. Determine the change in length of the rod due to temperature change:
- The coefficient of linear thermal expansion (α) is given as 12x10-6/°C.
- The initial length of the rod is not provided, so we'll assume it to be L.
- The change in length (∆L) can be calculated using the formula:
∆L = α * L * ∆T
where ∆T is the change in temperature.
2. Calculate the tensile stress (∆σ) due to the change in length:
- The tensile strength of the steel is given as 150 MN/m^2 (mega newtons per square meter).
- Assume the cross-sectional area of the rod to be A.
- The tensile stress (∆σ) can be calculated using the formula:
∆σ = ∆L * E / L
where E is the Young's modulus of elasticity of the steel.
3. Set the tensile stress (∆σ) equal to the tensile strength of the steel and solve for ∆T:
- ∆σ = ∆L * E / L = Tensile strength
- Substitute the given values and solve for ∆T.
4. Finally, add the calculated ∆T to the initial temperature of the rod (200°C) to obtain the temperature at which the rod will break.
Note: This calculation assumes a linear relationship between stress and strain, and it is based on the linear coefficient of thermal expansion. It's important to note that other factors such as impurities, defects, and non-linear behavior of the material may also contribute to failure.
Please provide the cross-sectional area of the rod (A) to proceed with the calculation.