HP 49g+, Руководство пользователя, Страница: 750 / 862

Page 22-38
To find the principal normal values press
š
until the cursor returns to the
intersection of the circle with the positive section of the
σ
-axis. The values
found at that point are φ = 59
o
, and (
σ
’
xx
,
τ
’
xy
) = (1.06E2,-1.40E0) = (106, -
1.40). Now, we expected the value of
τ
’
xy
= 0 at the location of the principal
axes. What happens is that, because we have limited the resolution on the
independent variable to be
∆φ
= 1
o
, we miss the actual point where the shear
stresses become zero. If you press
š
once more, you find values of are φ
= 58
o
, and (
σ
’
xx
,
τ
’
xy
) = (1.06E2,5.51E-1) = (106, 0.551). What this
information tell us is that somewhere between
φ
= 58
o
and
φ
= 59
o
, the shear
stress,
τ
’
xy
, becomes zero.
To find the actual value of
φ
n, press
$
. Then type the list corresponding to
the values {
σ
x
σ
y
τ
xy}, for this case, it will be
{ 25 75 50 } [ENTER]
Then, press
@CC&r
. The last result in the output, 58.2825255885
o
, is the
actual value of
φ
n.
A program to calculate principal stresses
The procedure followed above to calculate
φ
n, can be programmed as
follows:
Program PRNST:
«
Start program PRNST (PRiNcipal STresses)
INDAT Enter data as in program MOHRCIRC
CC&r Calculate
σ
c, r, and fn, as in MOHRCIRC
“
φ
n” TAG Tag angle for principal stresses
3 ROLLD Move tagged angle to level 3
R C DUP Convert
σ
c and r to (
σ
c, r), duplicate
C R + “
σ
Px” TAG Calculate principal stress
σ
Px, tag it
SWAP C R - “
σ
Py” TAG Swap,calculate stress
σ
Py, tag it.
»
End program PRNST
To run the program use:
J @PRNST
Start program PRNST
25˜
Enter
σ
x = 25
75˜
Enter
σ
y = 75
50`
Enter
τ
xy = 50, and finish data entry.