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

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SUMMARY

The discussion focuses on calculating the thermal stress in a brass tube and a steel rod, both attached to end plates A and B, when subjected to a temperature increase of 58°C. The properties of the materials are specified: brass has a coefficient of thermal expansion (alpha) of 19x10^-6/°C and Young's modulus (E) of 210 GPa, while steel has an alpha of 12x10^-6/°C and E of 105 GPa. The formula used for stress calculation is ΔL/L = (σ/E) + alpha(ΔT), where the change in length (ΔL) is determined by the temperature change and the resulting stresses in both materials need to be calculated.

PREREQUISITES
  • Understanding of thermal expansion coefficients for materials
  • Knowledge of Young's modulus and its application in stress calculations
  • Familiarity with the concept of stress in materials under temperature changes
  • Proficiency in algebraic manipulation to solve for unknowns in equations
NEXT STEPS
  • Study the derivation and application of the thermal stress formula ΔL/L = (σ/E) + alpha(ΔT)
  • Learn about the mechanical properties of brass and steel, focusing on their thermal expansion and elasticity
  • Explore examples of thermal stress calculations in composite materials
  • Investigate the effects of temperature changes on different materials in engineering applications
USEFUL FOR

Mechanical engineers, materials scientists, and students studying thermal stress in composite materials will benefit from this discussion.

larz19943
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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 celsius
E=210GPa
Steel:
alpha=12x10^-6/degree celsius
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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It's not clear, but is the distance between the plates supposed to remain constant after the temperature change?
 
Yes but that distance is not given, the plates move a distance delta L apart after the tempature change.
 

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