Radius of curvature of a bimetallic strip

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To calculate the radius of curvature of a bimetallic strip subjected to different temperatures, the relationship r = LT/dL can be used, where L is the strip length and dL is the difference in arc lengths due to temperature variations. The inner and outer arc lengths differ based on the thickness T of the metal layers, and this can be expressed through the angle theta, which is related to the radius r. For a bimaterial strip consisting of glass and iron, the same principles apply, utilizing the coefficients of thermal expansion for both materials to determine dL. The discussion emphasizes the importance of understanding material properties and their thermal responses in calculating curvature. Accurate calculations depend on correctly applying these concepts to the specific materials involved.
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Homework Statement



I need to calculate the radius of curvature of a bimetallic strip when the two strips are subjected to different temperatures. in the problem, the two metals themselves are in different temperatures. One at 180°C, other at 160°C. Anyone with good solid mechanics knowledge will do. Any suggestion will be highly appreciated.



Homework Equations



Define L = strip length, dL = L1-L2 at that temp. difference, and T = thickness of one metal layer. When bent to the required radius r, the inner-outer layer arc length difference due to a radius difference of T equals dL.

Thus theta*((r+T/2)-(r-T/2)) = dL, where theta = L/r.
Then LT/r = dL ==> r = LT/dL.

The Attempt at a Solution



Need help here
 
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welcome to pf!

hi drakierd! welcome to pf! :wink:
drakierd said:
r = LT/dL.

that's it! :smile:

you know T, and you can find dL/L from the given coefficients of expansion of the two metals (i assume they are given?) :wink:
 
Hi,

In my case, it is not a Bimetal strip, it is a bimaterial strip. And one material is glass and the other one is few microns Iron deposited on it. And finally the glass is 160C and the metal is 180C. And the question is that I need to know the radius of curvature of this thing. Any suggestions for that?
 
welcome to pf!

hi shouhardo! welcome to pf! :smile:

can't you use coefficients of expansion in exactly the same way?
 
yeah I can. You are right, that's how I have to do it.
 
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