how can I calculate the stress in X- and Y-direction

[aliex]

Hi all,

A steel parallelepiped with a square cross-section fits exactly into the cavity. it's loaded from the top surface(see picture). how can I calculate the stress in X- and Y-direction if the strain in X- and Y-direction is zero.

Thank you

 

[Erik Panos Kostson]

Not sure exactly what you mean, but from what I can see:

In your first picture, there is a contact between the red and grey block (that is the appropriate boundary condition).

Once you load the red block on top, with the contacts (e.g., frictional) assigned (and some support/fixed, for the gray part so it does not move freely), you will be able to see stresses along different directions (say SXX or SYY,...).

Hope this helps.

 

[aliex]

Thank you for Answer.

Yeah, that's what I meant.
I have to calculate the stresses in X, Y and Z directions.
can you please confirm whether you can calculate the stresses in X- ; Y- and Z-directions with these equations?

σ_y= F/A
σ_x= σ_z= (1-2ν)σ_y

 

[Erik Panos Kostson]

Plane stress (thus stress in z is zero):
σy= F/A
σx= ν*σy

Plane strain (thus strain in z is zero):
σy= F/A
σx= ν/(1-ν)*σy
σz= ν*(σy+σx)

 

[aliex]

Thank you very much.
but tension in Z-direction is not equal to zero, σx= σz

 

[Erik Panos Kostson]

Well look at the plane strain solution σz is not zero. Finally if you rearranged these you get that σx= σz.

 

[goeasyon]

According to the elasticity constitutive relation, stress_vector = C_matrix * strain_vector, where the vector has a size of 6, and C_matrix is the stiffness with the size of 6x6.

If your material is isotropic and linear elastic, both strain_x and strain_y are zero. To determine the stress_x and stress_y, you only need to know C13, C23, and strain_Z.

https://welsim.com