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We know that when we heat bimetallic strip it bends. But I can't understand what force causes it to bend.

Like, suppose they are attached by a nail passing through them. Now, when the strip is heated, the metal with higher coefficient of linear expansion(α) tries to expand itself linearly. Meanwhile, the metal with lower α, does not expand that much so there is a force exerted on the nail and inturn (by Newton's Third Law) nail exerts opposite forces on the strip, along the strip. So intuitively,at equilibrium, there should be some tensile force in each strip and they must remain linear,without any bend, with neither of them achieving their desired expansion state. But it isn't so. They bend. My question is, For bending, there should be a force perpendicular to the length of the strip(force providing torque to bend). But i think, there isn't, so why does it bend?

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    $\begingroup$ There are shear stresses between the layers which cause thee higher expansion material to expand less and the lower expansion material to expand more. $\endgroup$ Jan 20 at 12:23
  • $\begingroup$ @ChetMiller okay? I mean that's what it should be like. With some tensile force , the strip should remain horizontal , without bend $\endgroup$
    – PinkAura
    Jan 20 at 16:09

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The longitudinal force that the strip with smaller expansion coefficient (say A) does on the other (say B) doesn't pass through the COM of B. The torque comes from that distance (about the thickness of the strip). It is similar to a simple bow made only of a thin stick and a string. By imposing a tensile stress on the string, we force the stick to bend.

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  • $\begingroup$ "The longitudinal force that the strip with smaller expansion coefficient (say A) does on the other (say B) doesn't pass through the COM of B" . Can you pls attach a diagram of this . I can't really get this $\endgroup$
    – PinkAura
    Jan 21 at 13:20
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bimetallicstrip

So lets imagine the two metals in the bimetallic strip to be brass and iron and assume coefficient of linear thermal expansion ($\alpha$) of brass be greater than iron's. The two metals are joined together maybe by an adhesive or welding or soldering or something else, assume the adhesive doesn't fail.
So no matter what, whatever area of brass is in contact with the iron, must remain in contact as the adhesive keeps it that way. So if we change the temperature of the bimetallic strip, the brass will want to expand more than the iron as brass has greater $\alpha$, but the brass has to remain in contact with the iron, so it can't stretch linearly as shown in the figure. Instead if the bimetallic strip curves such that brass is the outer part of the curve, then the brass can expand more than the iron while the area remains in contact. So if the brass expands linearly more than the iron a little bit then, the adhesive will pull it down with a force causing it to bend. enter image description here

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