Calc. Thermal Deflection for Alum. Sleeve & Steel Beam

  • Thread starter Dell
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In summary: Lo would also be numericalIn summary, the conversation is discussing how to find the change in temperature needed to connect an aluminium sleeve to a steel beam with a rigid plate attached. The length of the steel beam is 5mm longer than the sleeve, and the equations for finding deltaT depend on the initial length of the sleeve, which was not given. The speakers discuss the possibility of solving for deltaT in terms of the initial length, but one speaker argues that it is not possible as the initial length is not a given parameter.
  • #1
Dell
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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 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?
 
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  • #2
What happens if you divide the first equation with the second?
 
  • #3
that is more or less what i did

but I am still going to have Lo in my equation
 
  • #4
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
Lo is a given parameter. You would, of course, solve for deltaT in terms of Lo.
 
  • #6
no, Lo isn't a given parameter, i added it in the hope that it would cancel out
 
  • #7
And what makes you think a given parameter must be a specific numeric value, instead of a variable? Why not solve for deltaT?
 
  • #8
JUST because all the other values were numerical
 

What is the purpose of calculating thermal deflection for alum. sleeve and steel beam?

The purpose of calculating thermal deflection for alum. sleeve and steel beam is to determine the amount of deflection that may occur due to changes in temperature, and to ensure that the structural integrity of the beam is not compromised.

What factors affect thermal deflection in alum. sleeve and steel beam?

The factors that affect thermal deflection in alum. sleeve and steel beam include the material properties of the beam, the temperature difference between the top and bottom of the beam, and the length and thickness of the beam.

How is thermal deflection calculated for alum. sleeve and steel beam?

Thermal deflection for alum. sleeve and steel beam is calculated using the coefficient of thermal expansion for each material, the temperature difference, and the length and thickness of the beam. The equation used is: ΔL = αLΔT, where ΔL is the deflection, α is the coefficient of thermal expansion, L is the length of the beam, and ΔT is the temperature difference.

Why is it important to consider thermal deflection in structural design?

Thermal deflection must be considered in structural design to ensure that the beam can withstand changes in temperature without experiencing excessive deflection. Neglecting to account for thermal deflection can lead to structural failure and potential safety hazards.

How can thermal deflection in alum. sleeve and steel beam be minimized?

Thermal deflection in alum. sleeve and steel beam can be minimized by using materials with lower coefficients of thermal expansion, minimizing temperature differences, and using beams with thicker cross-sections.

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