E-Code

Mohr's circle and plane-stress transformation, step by step — a TI-89 Titanium program

By E-Code · updated

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.

StepValue
You enter
Input 140
Input 2-20
Input 330
Input 425
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
Text1 TRANSFORMATION
Text2 WITH YOUR NUMBERS (CAS)
Text4 MOHR'S CIRCLE
Text7 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

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