# Thermal deflections

1. Jan 6, 2010

### Dell

given an aluminium sleeve with a steel beam inside as seeen in the diagram below

knowing that the length of the steel beam is 5mm longer than the sleeve and that a rigid plate is connected to the end of the steel beam,

find the change in temperature needed to be able to connect the sleeve to the plate?

i base my answer on the assumption that when T=Tf

LAl=LSt

LAl=Lo(ΔT*αAl+1)
LSt=(Lo + 0.005)(ΔT*αSt+1)

after comparing i find that my expression for ΔT is dependant on Lo, but Lo, the original length of the sleeve, was not given in the question

is there any way to solve this without knowing Lo?? is there a way i can find Lo?

Last edited: Jan 7, 2010
2. Jan 7, 2010

### ponjavic

What happens if you divide the first equation with the second?

3. Jan 7, 2010

### Dell

that is more or less what i did

but im still going to have Lo in my equation

4. Jan 7, 2010

### ponjavic

I would say it is not possible and I cannot see anything you've done wrong.

I'd say it's logical that it would depend on the initial length due to 5mm being a fixed value.

Imagine L0 being 1e-10m. An large deltaT would be required. With L0 being extremely large, the opposite would apply.

Agree?

5. Jan 7, 2010

### nvn

Lo is a given parameter. You would, of course, solve for deltaT in terms of Lo.

6. Jan 7, 2010

### Dell

no, Lo isnt a given parameter, i added it in the hope that it would cancel out

7. Jan 7, 2010

### nvn

And what makes you think a given parameter must be a specific numeric value, instead of a variable? Why not solve for deltaT?

8. Jan 8, 2010

### Dell

JUST because all the other values were numerical