HP 48gII User Manual
Page 217
Page 6-16
• The user then highlights the field corresponding to the unknown for
which to solve the equation, and presses
@SOLVE@
• The user may force a solution by providing an initial guess for the
solution in the appropriate input field before solving the equation.
The calculator uses a search algorithm to pinpoint an interval for which the
function changes sign, which indicates the existence of a root or solution. It
then utilizes a numerical method to converge into the solution.
The solution the calculator seeks is determined by the initial value present in
the unknown input field. If no value is present, the calculator uses a default
value of zero. Thus, you can search for more than one solution to an
equation by changing the initial value in the unknown input field. Examples
of the equations solutions are shown following.
Example 1 – Hooke’s law for stress and strain
The equation to use is Hooke’s law for the normal strain in the x-direction for a
solid particle subjected to a state of stress given by
zz
zy
zx
yz
yy
yx
xz
xy
xx
σ
σ
σ
σ
σ
σ
σ
σ
σ
The equation is
,
)]
(
[
1
T
n
E
e
zz
yy
xx
xx
∆
⋅
+
+
⋅
−
=
α
σ
σ
σ
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
∆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,
∆T = 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