Linear elasticity theory. Part 2. Equilibrium equations.

Condition on the components of the stress tensor from considering the equilibrium equations; i.e. sum the forces and moments - except at each point!
Lectures created for Mechanics of Solids and Structures course at Olin College.

[@fabi0bmx]

Nice tutorial! Very helpful. The only thing I didn't understand is why you consider dx and dy as areas and not lengths.. You say in 5:54 that dy is the area. But at the beginning you said they correspond to width and height. The same for momemtum. This won't change the final equilibrium equations anyway if you get the correct units.

[@AwestrikeFearofGods]

14:05 The bottom-right tensor entry appears to be mislabeled (is: Tyx, s/b: Tyy). Good lectures.

[@mr.e4706]

THANK YOU!! really saving my life by remembering me all these concepts and explaining them really easily btw just to be sure... in the last paper you showed, there should be a T_yy in the matrix on the bottom right corner, correct?

[@asam1584]

yes

[@thejakartajasmine5613]

I think so, it should be a T_yy in 14:05

[@jaxcgerard]

Thank u for this. Appreciate them very much but just wondering why is it dx/2 ?

[@hugobadillo2799]

because it is the center of the cube

[@thejakartajasmine5613]

I think it uses the Taylor series approximation, f(x)=f(c)+f'(c)(x-c)+.... where x=dx (the right-hand side of the square) and c=dx/2 (the center of the square) so, x-c = dx-dx/2 = dx/2 CMIIW

[@yirong5407]

I believe it does not matter. If you use dx instead of dx/2, the same conclusion will be drawn as 2dxdy will be eliminated at the end.