HP 50g Graphing Calculator - Manual (Page 222)

Page 6-16
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
T n
E
e
zz yy xx xx
Δ ⋅ + + ⋅ − = α σ σ σ