Radius of Curvature of Bimetallic Strip at T+dT

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SUMMARY

The radius of curvature, R, of a bimetallic strip when heated from temperature T to T+dT can be derived using the coefficients of linear expansion, a1 and a2, for each metal. The equations L1 = L0(1 + a1 dT) and L2 = L0(1 + a2 dT) describe the lengths of the metals at the new temperature. The hint provided indicates that L2 = (R + x/4)θ and L1 = (R - x/4)θ, where the ±x/4 accounts for the thickness of each metal layer in relation to the center radius R. This relationship is crucial for understanding the curvature changes in the bimetallic strip.

PREREQUISITES
  • Understanding of thermal expansion coefficients (a1, a2)
  • Familiarity with geometric relationships in bimetallic strips
  • Knowledge of basic calculus for deriving curvature
  • Ability to manipulate equations involving angular displacement (θ)
NEXT STEPS
  • Study the principles of thermal expansion in materials
  • Learn about the mechanical properties of bimetallic strips
  • Explore the derivation of curvature in composite materials
  • Investigate applications of bimetallic strips in temperature sensing
USEFUL FOR

Mechanical engineers, materials scientists, and students studying thermodynamics or material properties will benefit from this discussion, particularly those interested in the behavior of bimetallic strips under temperature changes.

Winzer
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Homework Statement


the bimetallic strip has a thickness x and is straight at temp T.
What is the radius of curvature of the strip, R, when it is heated to temp T+dT
Coeff. of linear expansion: a1, a2.
Assume each each metal has a thickness of x/2 and X<<R


Homework Equations


L1=L0(1+a1 dT)
L2=L0(1+a2 dT)

The Attempt at a Solution


I was givin the hint that:
L2=(R+x/4)theta
L1=(R-x/4)theta
Where on Earth do this +-x/4 come from?!
 
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Winzer said:
Where on Earth do this +-x/4 come from?!
If R is the radius corresponding to the center of the strip, then R ± x/4 describes the radius at the center of each metal.
 

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