Mechanics of Materials: Statically Indeterminate Problems

[jdawg]

Homework Statement

Hi! So my question isn't really about a specific problem, but more of when to use which method.
I'm having trouble knowing when to use the method of super position, the force method, or just being able to go straight into just writing the equilibrium equation and the compatibility relation.

Homework Equations

δ = (F*L)/(A*E)

The Attempt at a Solution

For example, in the problem I attached I originally just summed the forces in the x direction and then wrote out my compatibility relation:

F_EF - 2F_AB = 80 kN (Because of symmetry let F_AB = F_CD

δ_AB = δ_EF

And then I just solved for my forces using these two equations. But this was incorrect, I don't understand why this doesn't work (The solution I looked at used the method of super position). The total deformation between the two rigid walls should be zero, right? Shouldn't the compression in rods AB and CD equal the expansion in rod EF?

Thanks for any help!

 

[PhanthomJay]

Homework Statement

Hi! So my question isn't really about a specific problem, but more of when to use which method.
I'm having trouble knowing when to use the method of super position, the force method, or just being able to go straight into just writing the equilibrium equation and the compatibility relation.

Homework Equations

δ = (F*L)/(A*E)

The Attempt at a Solution

For example, in the problem I attached I originally just summed the forces in the x direction and then wrote out my compatibility relation:

F_EF - 2F_AB = 80 kN (Because of symmetry let F_AB = F_CD

ok

δ_AB = δ_EF

ok

And then I just solved for my forces using these two equations. But this was incorrect, I don't understand why this doesn't work (The solution I looked at used the method of super position). The total deformation between the two rigid walls should be zero, right? Shouldn't the compression in rods AB and CD equal the expansion in rod EF?

yes

Thanks for any help!

you have a signage error on your first equation. The left sections are in compression and the right section is in tension. Draw free body diagrams and correct your signage.

 

[jdawg]

Thanks so much! I can't believe I made that mistake. So just to clarify, you can pretty much use whichever method as long as you are careful?

 

[PhanthomJay]

Thanks so much! I can't believe I made that mistake. So just to clarify, you can pretty much use whichever method as long as you are careful?

Yes, use the method that is easier for you , they all lead to the same result.