Principal stresses in 3D, step by step — a TI-89 Titanium program

By E-Code · updated 2026-09-26

PRINSTR is a TI-89 BASIC program for the TI-89 Titanium. A full 3D stress state (three normal and three shear stresses). Step by step: the stress tensor, the invariants I1, I2, I3, the characteristic cubic built and solved by the CAS, the three principal stresses in order, the check against I1, the maximum shear stress and the von Mises stress.

What it asks for and what it shows

It asks for 6 values at its prompts. In the example below it shows I1=σx+σy+σz, -τxy²-τyz²-τzx², I3=det(σ), σ1 MPa, σ2 MPa, σ3 MPa, τmax MPa, σvm MPa, 1 STRESS TENSOR (MPa), 3 CHARACTERISTIC EQ, 4 ROOTS (CAS zeros), 6 ANSWER.

Example run

One of its oracle test cases. The inputs are typed in order, and the results are the values the case expects on the screen.

Step	Value
You enter
Input 1	50
Input 2	-20
Input 3	10
Input 4	30
Input 5	-10
Input 6	20
The screen shows
`I1=σx+σy+σz=`	40
`-τxy²-τyz²-τzx²=`	-2100
`I3=det(σ)=`	-28000
`σ1 MPa=`	65.52685208
`σ2 MPa=`	11.5308281
`σ3 MPa=`	-37.05768018
`τmax MPa=`	51.29226613
`σvm MPa=`	88.88194417
Text	1 STRESS TENSOR (MPa)
Text	3 CHARACTERISTIC EQ
Text	4 ROOTS (CAS zeros)
Text	6 ANSWER

How it's checked

4 test cases, each checked against an independent method. Replayed key by key on a virtual TI-89 Titanium, they make 56 checks.

How E-Code checks every program

Run it or put it on your calculator

Open the library in the TI-89 Titanium calculator and pick “Principal stresses in 3D, step by step” (PRINSTR).
Put it on your own calculator with a computer and a USB cable, or type it in by hand.

Related programs

All TI-89 Titanium engineering programs · All TI-89 Titanium programs