Thermal Expansion, Young's Modulus

In summary, the conversation discusses the use of a steel beam in a bridge and the compressional stress required to keep it from expanding due to temperature changes. The co-efficient of linear expansion for steel and Young's modulus for steel are also mentioned. The formula for calculating stress and the relationship between stress and Young's modulus are referenced. The question of finding Young's modulus for paper is also raised.
  • #1
pat666
709
0

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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  • #2
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.
 
  • #3
ok i have never seen this formula is stress defined as force of force/unit area??
 
  • #4
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
 
  • #5
ok i remember that from an early lecture thanks
 
  • #6
How/where can I find Young's Modulus for paper?
 

1. What is thermal expansion?

Thermal expansion is the tendency of a material to increase in size when exposed to higher temperatures and decrease in size when exposed to lower temperatures. This occurs due to the increase or decrease in the vibration of atoms and molecules within the material.

2. How is thermal expansion measured?

Thermal expansion is measured using the coefficient of thermal expansion (CTE), which is a measure of how much a material expands or contracts per degree of temperature change. It is typically expressed in units of length per unit of temperature (e.g. mm/m°C).

3. What is Young's Modulus?

Young's Modulus, also known as the modulus of elasticity, is a measure of a material's stiffness or resistance to deformation when a force is applied. It is defined as the ratio of stress (force per unit area) to strain (change in length per unit length) in a material.

4. How does temperature affect Young's Modulus?

Temperature can affect Young's Modulus by altering the molecular structure and arrangement within a material. In general, as temperature increases, the molecular vibrations and movement increase, causing the material to become less stiff and decrease in Young's Modulus.

5. Why is understanding thermal expansion and Young's Modulus important?

Understanding thermal expansion and Young's Modulus is important in fields such as engineering, materials science, and physics. It allows us to predict and account for changes in size and shape of materials due to temperature changes, and helps determine the strength and stability of structures and materials under different conditions.

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