Thermal deflection of aluminum sleeve and steel beam with 5mm gap

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

q1.jpg


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 dependent 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?
 
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What happens if you divide the first equation with the second?
 
that is more or less what i did

but I am still going to have Lo in my equation
 
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?
 
Lo is a given parameter. You would, of course, solve for deltaT in terms of Lo.
 
no, Lo isn't a given parameter, i added it in the hope that it would cancel out
 
And what makes you think a given parameter must be a specific numeric value, instead of a variable? Why not solve for deltaT?