Mohr's circle and plane-stress transformation, step by step — a TI-89 Titanium program
MOHR2D is a TI-89 BASIC program for the TI-89 Titanium. σx, σy, τxy and a plane angle θ. Step by step: the transformation equations, σx'(θ) and τx'y'(θ) with your numbers from the algebra system, the principal angle (checked: zero shear and zero slope there), Mohr's circle center and radius, the principal stresses, the maximum in-plane shear and its plane, and the stresses on your plane.
What it asks for and what it shows
It asks for 4 values at its prompts. In the example below it shows θp deg, τx'y'(θp), dσx'/dθ at θp, σ1=σx'(θp) MPa, C=(σx+σy)/2, R MPa, σ1=C+R MPa, σ2=C-R MPa, θs=θp-45 deg, τx'y'(θs) MPa, σx' MPa, σy' MPa, τx'y' MPa, 1 TRANSFORMATION, 2 WITH YOUR NUMBERS (CAS), 4 MOHR'S CIRCLE, 7 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 | 40 |
| Input 2 | -20 |
| Input 3 | 30 |
| Input 4 | 25 |
| The screen shows | |
θp deg= | 22.5 |
τx'y'(θp)= | 0 |
dσx'/dθ at θp= | 0 |
σ1=σx'(θp) MPa= | 52.42640687 |
C=(σx+σy)/2= | 10 |
R MPa= | 42.42640687 |
σ1=C+R MPa= | 52.42640687 |
σ2=C-R MPa= | -32.42640687 |
θs=θp-45 deg= | -22.5 |
τx'y'(θs) MPa= | 42.42640687 |
σx' MPa= | 52.26496158 |
σy' MPa= | -32.26496158 |
τx'y' MPa= | -3.697705003 |
| Text | 1 TRANSFORMATION |
| Text | 2 WITH YOUR NUMBERS (CAS) |
| Text | 4 MOHR'S CIRCLE |
| Text | 7 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 76 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 “Mohr's circle and plane-stress transformation, step by step” (MOHR2D).
- Put it on your own calculator with a computer and a USB cable, or type it in by hand.
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All TI-89 Titanium engineering programs · All TI-89 Titanium programs