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The equation is here e
xx
is the unit
strain in the x-direction,
σ
xx
,
σ
yy
, and
σ
zz
, are the normal stresses on the particle
in the directions of the x-, y-, and z-axes, E is Young’s modulus or modulus of
elasticity of the material, n is the Poisson ratio of the material,
α
is the thermal
expansion coefficient of the material, and
Δ
T is a temperature increase.
Suppose that you are given the following data:
σ
xx
= 2500 psi,
σ
yy
=1200 psi,
and
σ
zz
= 500 psi, E = 1200000 psi, n = 0.15, α = 0.00001/
o
F, ΔT = 60
o
F.
To calculate the strain e
xx
use the following:
‚Ï@@OK@@ Access numerical solver to solve equations
‚O Access the equation writer to enter equation
At this point follow the instructions from Chapter 2 on how to use the Equation
Writer to build an equation. The equation to enter in the Eq field should look
like this (notice that we use only one sub-index to refer to the variables, i.e., e
xx
is translated as ex, etc. -- this is done to save typing time):
Use the following shortcuts for special characters:
σ: ~‚s α: ~‚a Δ: ~‚c
and recall that lower-case letters are entered by using ~„ before the letter
key, thus, x is typed as ~„x.
Press `to return to the solver screen. Enter the values proposed above into
the corresponding fields, so that the solver screen looks like this:
,)]([
1
Tn
E
e
zzyyxxxx
Δ⋅++⋅−=
ασσσ