Thermal Expansion, Young's Modulus

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SUMMARY

The discussion centers on calculating the compressional stress required to prevent thermal expansion of a steel beam mounted between concrete supports as the temperature rises from 23°C to 42°C. The coefficient of linear expansion for steel is given as 11 x 10-6K-1, and Young's modulus for steel is 210 GN/m2. The relevant equations include the relationship between strain and temperature change, as well as the definition of stress in terms of force and area. Participants clarify that the original length of the beam is not necessary for calculating stress when using the provided values.

PREREQUISITES
  • Understanding of thermal expansion principles
  • Familiarity with Young's modulus and its applications
  • Knowledge of stress and strain definitions
  • Basic algebra for manipulating equations
NEXT STEPS
  • Research the application of Young's modulus in different materials
  • Explore the effects of temperature changes on various structural materials
  • Learn about the calculation of compressive stress in engineering contexts
  • Investigate the coefficient of linear expansion for other materials
USEFUL FOR

Students in engineering or physics, structural engineers, and anyone involved in materials science or thermal expansion calculations will benefit from this discussion.

pat666
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Homework Statement


6. A steel beam is used in the road bed of a bridge. The beam is mounted between two concrete supports when the temperature is 23⁰C, with no room for thermal expansion. What compressional stress must the concrete supports apply to each end of the beam, if they are to keep the beam from expanding when the temperature rises to 42⁰C?
Co-efficient of linear expansion for steel = 11 x 10-6K-1
Young’s modulus for steel = 210GN.m-2

Homework Equations



deltaL/L=alpha deltaT
F/A*=delta L/L*Y

The Attempt at a Solution



Ive found delta L/L to be 2.09*10^-4 I've also done about a thousand other things but everything i try needs an original length, i feel like I've overlooked a simple step or something... can someone please give me a hand.
 
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You don't need the original length if you have ΔL/L
Young's modulus= stress / (ΔL/L)
You are given the modulus and need to calculate stress.
 
ok i have never seen this formula is stress defined as force of force/unit area??
 
pat666 said:
ok i have never seen this formula is stress defined as force of force/unit area??

Yes, stress is force per unit cross section area = F/A
strain is extension per unit length = ΔL/L
Young's modulus is stress/strain
 
ok i remember that from an early lecture thanks
 
How/where can I find Young's Modulus for paper?
 

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