Stresses and strains in steel sheet

[*Alice*]

Dear all, I am trying to calculate the stresses and strains induced by a 40K change in temperature of a steel sheet of thickness 5mm, that is clad on both sides with 2mm thick layers of copper. For both materials E, alpha (í.e. the thermal expansion coefficient), as well as v (Poissons ratio are given).

My attempt was equating the forces (see attached word document).

This does unfortunately not work and the fact that the Poisson ratios are given makes me think that I have missed something out. Can anyone help?

Thanks a million for any help, hints and suggestions.

Alice

 

[ponjavic]

I do not see why the temperature change would induce a stress in the specimen as it is free to expand? Could you provide the full question?

 

[Pyrrhus]

where is the geometry?

 

[*Alice*]

The questions says:

A steel sheet of thickness 5cm is clad on both sides with 2mm thick layers
of copper. Determine the stresses and strains induces by a 40K change in
Temperature

given Data:

for steel: E=210kN/mm^2, v=0.3 (Poissons ratio), alpha=11*10^(-6) 1/K
for copper: E =180 kN/mm^2, v=0.35, aplpha = 30*10^(-6) 1/K

Solution: 70 N/mm^2, 87.5N/mm^2, 0.673 millistrain, 0.24millistrain, 1.77
millistrain


I thought there was geometry, since the steel is clad on top and bottom with 2mm thick layers of copper.