Radius of curvature of a bimetallic strip

In summary: It's just that I'm struggling to understand the formula given in the question.In summary, the task is to calculate the radius of curvature of a bimaterial strip consisting of glass and iron, with the glass section at 160°C and the iron section at 180°C. By using the coefficients of expansion for each material and the formula r = LT/dL, the radius of curvature can be determined.
  • #1
drakierd
1
0

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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  • #2
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:
 
  • #3
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?
 
  • #4
welcome to pf!

hi shouhardo! welcome to pf! :smile:

can't you use coefficients of expansion in exactly the same way?
 
  • #5
yeah I can. You are right, that's how I have to do it.
 

Related to Radius of curvature of a bimetallic strip

What is the radius of curvature of a bimetallic strip?

The radius of curvature of a bimetallic strip refers to the distance between the center of the strip and the point where it begins to curve.

What causes the bimetallic strip to have a specific radius of curvature?

The radius of curvature of a bimetallic strip is determined by the difference in thermal expansion coefficients of the two metals that make up the strip.

How does the radius of curvature affect the functionality of a bimetallic strip?

The radius of curvature is directly related to the sensitivity and responsiveness of the bimetallic strip. A smaller radius of curvature means a more sensitive strip, while a larger radius of curvature results in a less sensitive strip.

Can the radius of curvature be adjusted?

The radius of curvature of a bimetallic strip can be adjusted by changing the composition of the two metals or by altering the dimensions of the strip.

What is the significance of the radius of curvature in bimetallic strips in practical applications?

The ability to adjust the radius of curvature in bimetallic strips makes them useful in various practical applications, such as in thermostats, thermometers, and switches. The specific radius of curvature can be tailored to suit the desired function of the device.

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