Solve Volumetric Strain | Question 3 on http://img201.imageshack.us/my.php

[johnboy14]

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.

 

[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?

 

[johnboy14]

yes I do

E = 200x10^9
v = 0.3

 

[FredGarvin]

Those are constants, not the relations themselves. I meant the entire relations, i.e. equations.

Hint: There are three equations you're looking for and each equation will have one strain element and all three stress elements.