HP F2226A - 48GII Graphic Calculator - Example 2 - Stresses in a Thick Wall Cylinder

Page 7-2
At this point, we need only press K twice to store these variables.
To solve, first change CAS mode to
Exact, then, list the contents of A2 and A1,
in that order: @@@A2@@@ @@@A1@@@ .
Use command SOLVE at this point (from the S.SLV menu: „Î) After
about 40 seconds, maybe more, you get as result a list:
{ ‘t = (x-x0)/(COS(θ0)*v0)’
‘y0 = (2*COS(θ0)^2*v0^2*y+(g*x^2(2*x0*g+2*SIN(θ0))*COS(θ0)*v0^2)*x+
(x0^2*g+2*SIN(θ0)*COS(θ0)*v0^2*x0)))/(2*COS(θ0)^2*v0^2)’]}
Press µ to remove the vector from the list, then use command OBJ, to get
the equations listed separately in the stack.
Note: This method worked fine in this example because the unknowns t and
y0 were algebraic terms in the equations. This method would not work for
solving for θ0, since θ0 belongs to a transcendental term.
Example 2 – Stresses in a thick wall cylinder
Consider a thick-wall cylinder for inner and outer radius a and b, respectively,
subject to an inner pressure P
i
and outer pressure P
o
. At any radial distance r
from the cylinder’s axis the normal stresses in the radial and transverse
directions, σ
rr
and σ
θθ
, respectively, are given by
,
)(
)(
222
22
22
22
abr
PPba
ab
PbPa
oioi
−⋅
−⋅⋅
+
−
⋅−⋅
=
θθ
σ
.
)(
)(
222
22
22
22
abr
PPba
ab
PbPa
oioi
rr
−⋅
−⋅⋅
−
−
⋅−⋅
=σ