Stress in open-end cylinder due to temperature change

In summary, an open-end cylinder with inner and outer diameters of 30mm and 60mm, respectively, is subjected to a uniform temperature change from 25 oC to 45 oC. The cylinder is resting on a table and free to move. Using the linear thermal expansion equation, the change in length and diameters can be determined. However, finding the stress requires knowing the material properties, such as elastic modulus and Poisson's ratio. If the cylinder is unconstrained, there will be no thermal stresses developed.
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Homework Statement


An open-end cylinder with inner and outer diameters of 2a=30 and 2b= 60 mm, respectively, is subjected to a uniform temperatures change from 25 oC to 45 oC. Assuming the cylinder is rest on a table and free to move, determine the stress and the final dimensions (i.e. length, outside diameter and inside diameter) of the cylinder. Length 20 cm; α=0.0000117 per oC.

Homework Equations


Linear thermal expansion: ΔL = (ΔT*α)*L

The Attempt at a Solution


Is it safe to assume that the change in length as well as the diameters will be found using the linear thermal expansion equations? If so that part is simple.

I am stuck trying to find the stress though. I cannot remember any stress equations where the change in temperature is incorporated, without having to know the material property - Elastic Modulus & Poisson's ratio.

Any help is appreciatd, thanks!
 
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  • #2
If the cylinder is unconstrained, then the traction stresses on the surfaces of the cylinder will be unchanged when it is heated. Each small element of the cylinder material will expand the same amount in all directions. There will be no thermal stresses developed.
 

1. What is stress in an open-end cylinder due to temperature change?

The stress in an open-end cylinder due to temperature change is the force per unit area that is created within the cylinder when there is a difference in temperature between the inside and outside. This stress is caused by the thermal expansion of the material of the cylinder, leading to the generation of internal stresses.

2. How does temperature change affect stress in an open-end cylinder?

An increase or decrease in temperature can cause the material of the cylinder to expand or contract, respectively. This leads to changes in the dimensions of the cylinder, resulting in the generation of internal stresses. The magnitude of the stress is dependent on the coefficient of thermal expansion of the material, temperature difference, and the dimensions of the cylinder.

3. What factors can affect the stress in an open-end cylinder due to temperature change?

The stress in an open-end cylinder due to temperature change is influenced by several factors, including the coefficient of thermal expansion of the material, temperature difference, and the dimensions of the cylinder. Additionally, the type of material, geometry of the cylinder, and the boundary conditions can also impact the stress.

4. How can stress in an open-end cylinder due to temperature change be calculated?

The stress in an open-end cylinder due to temperature change can be calculated using the formula σ = αET, where σ is the stress, α is the coefficient of thermal expansion, E is the modulus of elasticity, and T is the temperature difference. This formula assumes a linear relationship between stress and temperature difference.

5. What can be done to reduce stress in an open-end cylinder due to temperature change?

There are several ways to reduce stress in an open-end cylinder due to temperature change. One approach is to use materials with a lower coefficient of thermal expansion, which will result in lower stress levels. Another method is to design the cylinder with a larger diameter or higher wall thickness to accommodate thermal expansion. Additionally, proper insulation and temperature control can also help to minimize stress in the cylinder.

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