# Volumetric strain

## Homework Statement

How do I solve the following block to find the volumetric strain. Its question 3 on the link

http://img201.imageshack.us/my.php?image=file0001pf0.jpg

I know that volumetric strain is equal to change in volume EV/ origninal volume(V)

Is Ev = Ex + Ey + Ev equal to volumetric strain.

I was told that the volumetric strain should be about 6.8 x 10^-4

Any help would be appreciated people.

Related Engineering and Comp Sci Homework Help News on Phys.org
FredGarvin
I am used to seeing volume dilation as the sum of the principal strains.

$$D = [\epsilon_1 + \epsilon_2 + \epsilon_3] = J_1$$ where $$J_1$$ is the first strain invariant.

I would tackle the problem that way. Calculate the principal strains and add them together.

EDIT: After looking at the problem, it is in a state of zero shear. Therefore $$\sigma_x$$, $$\sigma_y$$ and $$\sigma_z$$ are going to be the principal stresses. So, if you calculate the strains from the principal stresses you will be calculating the principal strains. Things should be pretty straight forward. I ended up calculating $$6.5 x 10^{-4}$$

Do you know the 3 dimensional stress-strain relations that involve E and $$\nu$$?

Last edited:
yes I do

E = 200x10^9
v = 0.3

FredGarvin