Thermal stress of two peices of metal attacthed to two plates.

In summary, the brass tube and steel rod are attached to end plates with respective diameters of 5.4 cm and 3.0 cm. The brass has an alpha value of 19x10^-6/degree Celsius and an E value of 210 GPa, while the steel has an alpha value of 12x10^-6/degree Celsius and an E value of 105 GPa. After a temperature increase of 58 degrees Celsius, the distance between the end plates changes and the resulting stresses in the brass tube and steel rod (counting tension as positive and compression as negative) need to be determined. The equation used is ΔL/L=(σ/E)+alpha(ΔT), where L is the
  • #1
larz19943
2
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Homework Statement


2)Both, a brass tube and the steel rod located inside the brass tube are solidly attached to common end plates A and B at either end.
The respective diameters are :

Do = 5.4 [cm]
Di = 3.0 [cm]
d= 2.8[cm]
Brass:
alpha=19x10^-6/degree celcius
E=210GPa
Steel:
alpha=12x10^-6/degree celcius
E=105GPa
Initially the assembly is stress free.
Now the temperature increases simultaneously for the brass tube and steel rod by 58oC. As a result the distance L between the two end plates will change.
Determine the resulting stresses in the brass tube and the steel rod, counting tension as positive and compression as negative.

Following Questions to be answered:
Stress in Brass in MPa
Stress in Steel in MPa


Homework Equations


ΔL/L=(σ/E)+alpha(ΔT)



The Attempt at a Solution


I solved for L in the equation above since the length is the same. then I pluged the know values in them but now I have a sigma on both sides and that is what I need to find out and I can't figure out how to solve it.
 
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  • #2
It's not clear, but is the distance between the plates supposed to remain constant after the temperature change?
 
  • #3
Yes but that distance is not given, the plates move a distance delta L apart after the tempature change.
 

FAQ: Thermal stress of two peices of metal attacthed to two plates.

1. What is thermal stress?

Thermal stress refers to the strain or deformation of a material due to changes in temperature. When a material is exposed to high temperatures, it expands and when it is exposed to low temperatures, it contracts. This expansion and contraction can cause stress on the material, especially when it is attached to other structures.

2. How does thermal stress affect two pieces of metal attached to two plates?

When two pieces of metal are attached to two plates, they are constrained by the plates and cannot freely expand or contract when exposed to temperature changes. This can lead to thermal stress between the metal and the plates, causing deformation or even failure of the material if the stress becomes too high.

3. What factors contribute to thermal stress in this scenario?

The amount of thermal stress in this scenario is influenced by several factors, including the difference in temperature between the metal and the plates, the thermal expansion coefficients of the materials, and the degree of constraint between the metal and the plates.

4. How can thermal stress be minimized in this situation?

To minimize thermal stress, it is important to choose materials with similar thermal expansion coefficients and to properly design the attachment between the metal and the plates to allow for some degree of movement. Additionally, using materials with high thermal conductivity can help to distribute the stress and prevent localized hot spots.

5. What are the potential consequences of ignoring thermal stress in this scenario?

If thermal stress is not taken into consideration, it can lead to material failure, warping, or cracking. This can compromise the structural integrity of the attached pieces and potentially cause safety hazards. It can also result in costly repairs or replacements. Therefore, it is important to carefully consider thermal stress in the design and use of materials in this scenario.

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