- #1

konto77

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## Homework Statement

There are two rigid plates on the ends.

In between them are two steel plates and one aluminum plate. The aluminum one is in the center. When the temperature increases enough the aluminum will buckle and touch one of the steel plates to close the circuit.

alpha(alum) = 12.5 (10^-6) /degF

alpha(steel) = 6.6 (10^-6) /degF

E(al) = 10,000 ksi

E(s) = 30,000 ksi

t(a) = 1/16 in w(a) = 1/4 in These are thickness and width

t(a)<w(a) or else the aluminum will not buckle towards the steel

t(s) = 1/16 in w(s) = 1/8 in

Length = 4 in

With these conditions the aluminum buckles at 180 deg F

Find dimensions that will allow the circuit to close at 100 deg F

## Homework Equations

critical axial compressive load: P(cr) = 4 pi^2 E I/L^2

I = w(a)t(a)^3/12

alpha*deltaT*L + PL/E/A = 0 when there are rigid plates right?

and the problem also says "As the temperature increases, teh lengths of both aluminum and stell straps remain equal because of teh rigid end pieces." Does this mean that length of stell and aluminum will change and remain equal? Or that their change in length equals 0.

## The Attempt at a Solution

I used this equation

alpha*deltaT*L + PL/E/A = 0

with

this equation to get the square root of a negative number for thickness of a

P(cr) = 4 pi^2 E I/L^2