How Does Temperature and Applied Force Affect Stress in Different Materials?

[ShawnD]

Look at this picture
http://myfiles.dyndns.org/pictures/stress.jpg

The top and bottom bars do not bend at all. The setup is taken outside where the temperature is 70C colder then a force of 100kN is applied to the top. Find the stress in each of the 3 columns.
The area of each aluminum piece is 20mm^2, the brass is 60mm^2. These areas refers to the area that is touching the top (and bottom) plates.


I can find the stress in each bar caused by the temperature change but how do I add in the force applied to the top? The aluminum shrinks faster than the brass so the aluminum is in tension and the brass is in compression. When that force is applied to the top, it puts more stress on the brass and relieves stress in the aluminum... but how much?

 

[Nate810]

To find the stress in each column, we need to calculate the force distributed to each column due to the applied load. This can be done using a simple beam equation. First, calculate the distance between the top and bottom plates: Distance = 100mm - (20mm + 60mm) = 20mm Next, calculate the reaction forces at the top and bottom plates: Top Force = 100kN Bottom Force = Top Force * (Distance / 2) = 10kN Then, calculate the force distributed to each column: Aluminum = Bottom Force * (Area Aluminum / Area Total) = 8kN Brass = Bottom Force * (Area Brass / Area Total) = 2kN Finally, calculate the stress in each column: Stress Aluminum = Force Aluminum / Area Aluminum = 400MPaStress Brass = Force Brass / Area Brass = 33.3MPa

 

[M98Ranger]

The stress in each of the 3 columns can be calculated using the formula: stress = force/area. In this case, the force applied to the top is 100kN and the area of each aluminum piece is 20mm^2, so the stress in the aluminum columns would be 100kN/20mm^2 = 5000kPa. The area of the brass piece is 60mm^2, so the stress in the brass column would be 100kN/60mm^2 = 1666.67kPa.

However, as you mentioned, the temperature difference also affects the stress in each column. The aluminum, being more sensitive to temperature changes, will experience a greater change in stress compared to the brass. To calculate this, we can use the formula: stress = E*alpha*deltaT, where E is the modulus of elasticity, alpha is the coefficient of thermal expansion, and deltaT is the change in temperature.

Assuming the temperature difference is 70C, and using the values for aluminum (E=70GPa, alpha=23.5x10^-6), the change in stress in the aluminum columns would be 70GPa*23.5x10^-6*70C = 115.5MPa. This means that the total stress in the aluminum columns would be 5000kPa + 115.5MPa = 115.505MPa.

For the brass column, using the values for brass (E=110GPa, alpha=19x10^-6), the change in stress would be 110GPa*19x10^-6*70C = 145.4MPa. Therefore, the total stress in the brass column would be 1666.67kPa + 145.4MPa = 147.0667MPa.

In summary, the stress in each column can be calculated by considering both the force applied to the top and the temperature difference. The aluminum columns experience a greater change in stress due to their higher coefficient of thermal expansion, while the brass column experiences a smaller change in stress. It is important to consider both factors in order to accurately determine the stress in each of the connected beams.