A program to calculate principal stresses – HP 48gII User Manual
Page 754

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
φn, press $. Then type the list corresponding to
the values {
σx σy τxy}, 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
φn.
A program to calculate principal stresses
The procedure followed above to calculate
φn, can be programmed as
follows:
Program PRNST:
«
Start program PRNST (PRiNcipal STresses)
INDAT
Enter data as in program MOHRCIRC
CC&r
Calculate
σc, r, and fn, as in MOHRCIRC
“
φn” TAG
Tag angle for principal stresses
3 ROLLD
Move tagged angle to level 3
R C
DUP
Convert
σc and r to (σc, r), duplicate
C R + “
σPx” TAG
Calculate principal stress
σPx, tag it
SWAP C R - “
σPy” TAG Swap,calculate
stress
σPy, tag it.
»
End
program
PRNST
To run the program use:
J@PRNST
Start
program
PRNST
25˜
Enter
σx = 25
75˜
Enter
σy = 75
50`
Enter
τxy = 50, and finish data entry.