1. The problem statement, all variables and given/known data This is for Statics and mechanics of materials 1... In this project, we were tasked with the re-design of a cheap thermal switch that is to be a component of a low cost product. The switch consists of three metal strips that are bounded on the top and bottom by a rigid plate (the plate is not bounded tho). The two outer strips are steel, and the one in the middle is aluminum. The only loads on the switch are the loads generated by the strips expanding due to heat. Since the middle strip is aluminum, its coefficient of thermal expansion is greater than the steel outer strips. Because of this, the aluminum strip will expand faster than the steel strips, which results in an internal force being generated. When the forces in the aluminum strip reach its critical axial compressive load, it will buckle, which will cause it to contact one of the steel strips. This will cause a circuit to be completed, which will signal the product that it has reached a certain temperature. We are given dimensions for a thermo switch that completes its circuit at 180 degrees, and we are to change the dimensions of the aluminum strip so that it completes its circuit at 100 degrees instead. Height of strips = 4 in width of alum. strip for 180 degree switch = 1/16 in "" "" steel strip """ """ """ """ = 1/16 length of alum. strip = 1/4 in """ """ steel """ = 1/8 in coef. thermal expansion for alum. (alpha) = 12.5E-6 """" """" """" "" steel (alpha) = 6.6E-6 Youngs modulus of alum (E) = 10,000 ksi = 10,000,000 psi """""""""" steel (E) = 30,000 ksi 2. Relevant equations Formula for critical axial load = (4*Pi^2*E*((length*width^3)/12))/Height^2 Width must be < length so the alum. strip buckles in the direction of the steel. 3. The attempt at a solution Well what I tried doing is first using the equation: (alpha alum. * deltaT * height) - (alpha steel * deltaT * height) = how much more the alum. expands than the steel Then I reduced it to: DeltaT * 2.4E-5 = how much more the alum. expands (Deformation) By plugging in both alphas and the height of 4 in. Then I used: Deformation = (P*L)/(E*A) with P=force and L=height and A=cross section area. I changed that to: (Deformation * E * A)/L = P Plugging in I get (DeltaT*A*2.4E-5*1E7)/4 Which is: DeltaT*A*60 = Force in lb I then set that equal to the formula for critical axial load, because you want the strip to reach the critical axial load at the temperature you specify. Now here is the problem, when I set them equal to each other, it cancels out the length of the strip, and I get: sqrt((DeltaT*11328)/(4*Pi^2*1E7)) = width of the strip I plugged in 180 degrees, and got .07 inches, which is 8 hundredths off the 1/16 it should be.. Please help me, ive been on this for like 4 hrs now, am I approaching this wrong? It cant be right that the length of the strip cancels out, because it affects the critical axial load! Right?