Worth starting with what does exist, because there is plenty of it and it is good. Anyone teaching structures today has first-rate free tools available, and several of them do their job better than we do ours.
The free landscape, by name
| Tool | Free | What it does very well | Conceptual development |
|---|---|---|---|
| Ftool | Yes | Modelling plane frames and reading diagrams and influence lines, with a fluency few match | Shows the behaviour, not the development behind it |
| MASTAN2 | Yes (on MATLAB or its runtime) | Linear and non-linear matrix analysis, tied to McGuire, Gallagher and Ziemian | The theory is in the book; the program runs the analysis |
| SkyCiv | Free tier | Step-by-step hand calculations: free bodies, equilibrium equations before substitution, moment distribution for indeterminate beams | Substituted arithmetic, and over basic statics |
| sectionproperties | Yes, open source | Warping, shear centre and the Saint-Venant constant by finite elements | A Python library: it returns numbers, with no interface and no explanation |
Of that list SkyCiv comes closest to what we usually call "showing the working", and it deserves saying plainly: its hand calculations are good. It draws the free body, writes ΣM = 0 before any number goes in, and solves by moment distribution when the beam is indeterminate. Anyone claiming no free program shows its steps is refuted in about a minute.
The difference is not showing steps. It is saying when the formula does not apply
Substituting numbers into a correct formula and explaining why that formula is the right one are different things. The first saves you the arithmetic. The second saves you from the error the arithmetic cannot catch, because the error sits one layer above it.
The torsion calculators floating around illustrate the point in reverse: you pick the section type — solid, closed tube, rectangle — and the program applies the matching formula. It never tells you that you picked wrong, or what the other theory would have given, or which side of the error you are on.
A program that only computes will never warn you that you are computing the wrong thing.
Three tools with no equivalent we could find
- Kinematic analysis, explained. We looked for software and there is none: what turns up is lecture material in PDF. The "educational software for kinematic analysis" that does exist is for machine mechanisms — linkages and cranks — not for classifying structures.
- Rebar detailing. The only free thing we found is AutoRebar, and it is an AutoCAD add-on, so using the free part requires an expensive licence. It also draws: you place the bars, it builds the schedule. The rest are seven-day trials or commercial software. Open source, nothing.
- Section analysis, developed. Here there is a serious free option, sectionproperties, and on warping finite elements it probably beats us. But it is a library with no interface: it hands you the shear centre, it does not explain why it is where it is.
No free tool does two of the three. None approaches any of the three conceptually. That is the gap, and it is smaller and more precise than "we are the only ones who teach".
One screen where the whole difference shows
Below is a two-span beam on three supports. All three restrain vertical movement only. It is the textbook case, and also the one I have seen marked correct more often than any other.
The degree formula gives g = 3·m + r − 3·n = 3×2 + 3 − 3×3 = 0. Zero means isostatic, and any program that stops at the formula will report exactly that. But nothing holds the beam horizontally: it is a mechanism, and it cannot be solved.
| Step | What it looks at | Result |
|---|---|---|
| 2 · Static indeterminacy | g = 3·m + r − 3·n | 0 |
| 3 · Stiffness matrix | Mechanism modes detected | 1 |
| 3 · Stiffness matrix | Unconstrained degrees of freedom | 1 |
| 4 · Suggestions | Verdict on screen | Cannot be solved |
The app does not report the zero and wash its hands: it contradicts it, in the same step 2 that produced it — "The formula gives g = 0 (necessary condition for isostatic), but NOT sufficient". Step 3 assembles the global stiffness matrix, 6×6 here, and flags "Detected 1 mechanism mode" in spite of g = 0 ≥ 0. It names node 3 and its horizontal displacement, points out that the step 2 equation counts constraints without checking where they sit, and closes with "✗ Mechanism — cannot be solved".
Why a department might care
A student who learns the degree formula and never watches the sufficient condition fail walks away with an incomplete rule and does not know it. It is hard to show on a blackboard, because the example that breaks it looks like a typo. Here it is on one screen, with the number and the contradiction side by side.
And nothing has to be installed, licensed, or bought by the faculty. It opens in a browser and the model travels as a link.