Radius of Curvature of Bimetallic Strip

[e(ho0n3]

Homework Statement

A temperature controller, designed to work in a steam environment, involves a bimetallic strip constructed of brass and steel, connected at their ends by rivets. Each of the metals is t thick. At 20 degrees C, the strip is L₀ long and straight. Find the radius of curvature of the assembly at 100 degrees C.

Homework Equations

The equation of linear thermal expansion and some circle geometry.

The Attempt at a Solution

Before I attempt anything, I would like to know if the radius of curvature includes the thickness of both metals. I would think so but I'm sure.

 

[Chi Meson]

In a problem such as this, the thickness of the metal strips would be small compared to the entire radius of curvature; this way, you don't need to worry about the effect of expansion in thickness on the radius. I'd say the radius was to the point where the two strips are joined.

 

[e(ho0n3]

Another question: What is the length of the part of the strip where the metals join? Is it the length of the metal that expanded the most or that which expanded the least or neither?

 

[Archduke]

What I did when I did this problem is say that the radius of curvature was where the two points were joined, and the mid-point of the two strips (ie. the mid-point of the brass and steel strips) had the average thermal expansion, given by the equation of thermal expansion. So, in other words, the length of the strip where the metals join is neither that of the length of the most or least expanded metal.

 

[e(ho0n3]

I see. I guess this is the tricky part about this problem. I think the proper way to deal with this problem would be to specify how I'm measuring the radius of curvature, whether it is to the midpoint of the strips or to one of the ends.

 

[Chi Meson]

What is the distance between the midpoints of each strip. This is an important consideration.

 

[e(ho0n3]

The distance between the midpoints of each strip is t. I don't understand why this is important though.