Murray State University · Part four · Example projects

Truss Bridge Builder

Murray State University
Demo 8 of 17 · Part four · Engineering · Stage 1

A shape that cannot hold still

Why does a flat roadway fold under a car before any member is overloaded?

Before you start. A truss is a frame of straight members meeting at joints. Every joint here is a pin — it carries no bending — so a member can only be pulled (tension) or pushed (compression) along its own length. A mechanism is a frame that can change shape without any member changing length. Demo 7 handed forward one habit: commit a prediction before you run anything, so the run is a measurement and not a show.

Predict

Level 1 opens with nothing but the gap. Lay the flat roadway alone and call it under the canvas: does it hold, snap, buckle — or fold?

Try

With Draw selected, drag members along the deck line from the left abutment to the right, commit your call, then press ▶ Load test.

Takeaway

A frame with a four-sided panel folds without straining any member; a triangle cannot change shape without changing a member's length — and the solver finds the fold as a rank deficiency, not as a rule someone typed in.

Live a direct-stiffness truss solve on your design, re-run on every change and at every vehicle position

Bridge Works Level –

Illustrative costing model: $4.80/kg steel + $180 a joint $0 Measuredpar: deterministic — no seed; test-physics.js reproduces it

You are the fabricator: get the vehicle across for less money than par, golf-style, and the cheapest surviving bridge tops the leaderboard. Drag between grid points to lay steel. Red members are being pulled, blue squashed, brighter is nearer its limit, grey is carrying nothing you paid for. The orange anchors are the abutments the level gives you; nothing longer than 4 m.

Tool Draw lays a member; Erase removes one; Check a joint draws every force meeting at a joint and prints their sum, which is always zero.
View X-ray parks the level's vehicle at mid-span and colours every member by force before you commit; Numbers prints kN on each member; Dead load adds the steel's own weight, 900 N/m.
Live member forces from the current solve tension — pulled apart compression — squashed carrying nothing brighter = closer to its limit · sag drawn ×45
Weakest link No load test yet on this level.
Before you test — what goes first? Commit a call to unlock Load test. Being wrong costs nothing; committing first is what turns the crossing into a measurement.
Run and compare Load test drives the level's vehicle across, re-solving at every position. Levels and Gallery change what you are working on; the Leaderboard is this machine's class list.

Check yourself

Level 2's rectangular frame folded with no member overloaded. Why could no member resist?

You watched the dashed ghost rock, and the debrief listed the joints that ran away.

Bryant Harrison · Murray State University
One HTML file · runs offline

Guidehow to use this demo

One game across four stages: carry the load for less than par — and before each test, call which member goes first. Cheapest surviving bridge wins; the leaderboard keeps score.

Where this sits: the second AI-built classroom tool in Part four, after the orbital game. Its solver is the real direct-stiffness method, so every collapse you watch is a computed result, and its assumptions are one tap away in Details.

  1. Mechanisms. With Draw, drag a roadway across Level 1. Commit a call under the canvas, press ▶ Load test, watch it fold, then add a triangle.
  2. Compression buckles. Level 3's truck. Turn on Numbers, call it, test it, and read Weakest link.
  3. Load paths. Level 4 forbids building below the deck; Level 5 adds a pier. Load a Gallery truss and use Check a joint.
  4. Sandbox. Any vehicle, no par. Outside the path.

Getting around

The four tabs switch stages; Levels inside the activity moves them too. Details opens the formulas, assumptions and sources for the current stage. Guide reopens this card; Settings holds Open Presenter Notes, Presentation mode and Reset. ↶ Undo is Ctrl+Z.

Time

Thirty minutes for stages 1–3, most of it on Level 2's frame and Level 3's truck. A load test takes a few seconds; the debrief is where the time goes.

Settings

Presenter notes

The printable session plan, on screen — the thirty-minute run of show, the statics behind each stage, the misconceptions to catch and the pars.

Presentation mode

Scales the page up one notch for projecting to a room, and puts a Notes button in the header.

Reset

Back to the start: Level 1 with an empty gap, saved designs and personal bests cleared, the Draw tool, X-ray on, every call and check answer forgotten, stage 1. The class leaderboard is left alone — it holds other people's results; use the two-step clears under Class data for that. Presentation mode stays as you set it.

Display

Options the game had before it joined the lesson shell.

Demonstrations

For showing a class what happens when a bridge that comfortably carried a car meets a 20 t crane. Runs with a non-standard vehicle are marked as demos and stay off the leaderboard.

Class data

Scores are stored in this browser only — each machine keeps its own class list. Each button asks twice.

Printable guide

The presenter notes above are the complete teacher guide — same words, one source. This opens the printable copy in a new tab.

Open the printable copy

DetailsMechanisms

What is live

What this page actually computes

Live the canvas, the colours, the joint tool, the fold

Every member force on screen comes from assembling this design's stiffness matrix and solving K·u = F in your browser, again on every edit. The dashed fold you watch on a rectangle is not an animation someone drew: it is the null-space direction the solver found when K came out singular, projected back onto exact member lengths so nothing stretches.

Measureddeterministic — no seed; 86 checks in test-physics.js the pars

Each par is a budget a triangulated design can beat, found offline against this same solver: Level 1's best surviving design in the search costs $929 against a par of $1,050, and no un-triangulated ladder survives any level at any depth or panel count (80 variants tried per level). Nothing in the solver is random, so re-running the suite reproduces every figure.

Illustrative the bill

Steel at $4.80/kg on a 9.42 kg/m section (about $45 a metre) and $180 per joint are invented so that panel count is a real trade-off. The shape of the bill — connections roughly 45% of a typical design — is the teaching point; the dollar figures are not a quotation.

How it works

k = (EA/L)·[c² cs; cs s²]  →  K·u = F

The direct stiffness method: each member is a two-force axial element whose stiffness EA/L is rotated into global coordinates by the cosines of its direction, every element is added into a global matrix K, the supports are applied as boundary conditions, and the displacements u are solved for. Member forces follow from the strains. Because it is a stiffness solve and not a joint-by-joint walk, designs with extra members, two pinned ends or a pier — statically indeterminate designs — solve correctly, with load split by stiffness.

The reduced matrix is factored by Gaussian elimination with full pivoting, which reports the rank honestly. Rank deficiency means a motion that strains nothing exists; the solver returns that null-space vector, and the game projects it onto exact member lengths (largest amplitude with under 0.5% length change) before drawing it.

Assumptions and simplifications

  • Two-dimensional, pin-jointed. No bending in any member, no out-of-plane behaviour.
  • Linear elastic, small displacement. Deflections are drawn 45× life size (capped at 1.3 m so a near-failure design stays on screen) but solved at true scale.
  • One steel section for everything, so the design problem is about geometry rather than shopping for sections.
  • Ideal supports. The left abutment is a pin (fixed both ways); the others are rollers (fixed vertically, free to slide).
  • A joint dropped mid-member splits it, and two members meeting in a straight line at an unloaded joint are condensed back into one (springs in series, EA/Ltotal, exact) — otherwise a pure pin idealisation would call every such joint a mechanism.
  • Members no longer than 4 m, on a 0.5 m grid.
  • Joints never fail. This is a steel truss with idealised pins: member buckling and yield are modelled, connection failure is not. See the Reasoned note below.
Reasoned why the joints are idealised, and what that leaves out

In real structures — especially glued or nailed ones like a craft-stick bridge — the connection is often what goes first, and this model cannot represent that failure at all. The steel pin-jointed idealisation is chosen precisely because it isolates the two things statics can teach cleanly: a shape that cannot hold still, and a member that buckles or yields. That choice is the honest one for this lesson, and the reason engineers model what they model is a lesson in itself.

Sources

Boundary: this is a truss idealisation. Real bridge joints are bolted or welded and carry some bending; real members have imperfections; real decks span between joints as beams. The solver shows why triangles work and where load goes. It is not a design tool and its numbers should not be carried into one.

Presenter Notesthe printable guide, on screen

Teacher and presenter guide · Statics you can watch fail, on a real direct-stiffness solver

Truss Bridge Builder

Demo 8 of 17 · Part four, Example projects · Engineering · 30 minutes for stages 1–3, plus the Sandbox

You need: index.html open in any modern browser — projector, Chromebook or phone, mouse or touch. No network, no install, no accounts; nothing is fetched at run time and nothing leaves the machine.

Learning goals

One per stage, in the words the learner reads on the Takeaway card. Each is what its stage demonstrates, and each stage's check-yourself item tests exactly that. The game underneath all four is the same: carry the load for less than par.

  • Mechanisms. A frame with a four-sided panel folds without straining any member; a triangle cannot change shape without changing a member's length — and the solver finds the fold as a rank deficiency, not as a rule someone typed in.
  • Compression buckles. Compression capacity falls as 1/L² — 180 kN at 2 m, 80 kN at 3 m, 45 kN at 4 m — while tension stays at 300 kN at any length, which is why cheap designs shorten their struts or hang the deck so the long members are pulled.
  • Load paths. Load splits by stiffness, not by counting: a stiffer path attracts more force, a mid-span pier turns one 16 m span into two 8 m ones and cuts the chord forces far more than in half, and a member drawn grey is steel you paid for that carries nothing.
  • Sandbox. Every result on this span comes from the same three facts: triangles hold shape, compression capacity falls with L², and load follows stiffness.

Where this sits on the path

The second of Part four's AI-built classroom tools and the second of its games, after Orbital Mechanics Golf. Demo 7 hands forward one habit — commit a prediction before you run anything — and this demo makes it structural: before every load test the learner calls which member goes first, and the engine's own record answers. The solver is the real direct stiffness method, so every collapse is a computed result.

One question for the session

Ask it before anyone touches a control; return to it at the debrief.

"When a bridge fails, which piece goes first — and could you have called it before the truck rolled on?"

Most of the room expects the thinnest-looking member to snap. The demo's answer is that the frame usually folds before anything snaps, and when something does go it is a long pushed member, not a pulled one. Both surprises are the statics.

Running it

Open ⚙ Settings → Presentation mode first: it scales the page for the back row and adds a Notes button that reopens this guide. The Guide card opens on load; dismiss it with Start with Mechanisms. Reset (in Settings) puts the demo back to Level 1 in place — no reload — and leaves the class leaderboard alone; the two-step clears under Class data are the only way to empty that.

  • 0–4Stage 1, Level 1. Build only the flat roadway. Take the room's call under the canvas — most say "it holds" — and press ▶ Load test. It folds. Name what they saw: joint, member, tension, compression, support, mechanism. Add a post and two struts; run it again, and read the cost against par.
  • 4–10Pairs play Level 1 with X-ray on. Have them use Check a joint: every force meeting there and their sum, always zero. That panel is the method of joints.
  • 10–18Level 2 — the lesson. It opens with a rectangular frame already built. The Notice line under the canvas says the stiffness matrix is singular; the dashed ghost rocking on the canvas is the fold the solver found. Call it, test it, watch it fold into a parallelogram. Let them add diagonals and watch the cue flip to Rigid. Par forces a second pass: which members do nothing?
  • 18–25Stage 2, Level 3 — Heavy Haul. Four times the load. Point them at Weakest link under the canvas and the debrief's buckles at column: compression rating depends on length and tension rating does not.
  • 25–30Stage 3. Project a student's debrief. Load Pratt, Howe and Warren from the Gallery at equal depth and compare where the forces go. Post the leaderboard. Levels 4–5 and the Sandbox make good homework — the gate opens for free play once a stage has been tested once.

Stage 1 · Mechanisms (Levels 1–2)

Question. Why does a flat roadway fold under a car before any member is overloaded?

Predict prompt. Lay the flat roadway alone and call it: does it hold, snap, buckle, or fold?

Activity. ~2 minDraw the deck; call; test. ~4 minLevel 2's frame: call; test; add diagonals until the cue reads Rigid; test again.

Expected observation. The flat deck and the rectangle both fold with every member at 0% of its limit. The debrief's How it moved table names the joints that ran away. One diagonal per four-sided panel removes exactly one fold; the cue counts them down.

Check-yourself key. The fold changed no member's length, and a member only resists a change in its own length. "Too weak" and "loose joints" are both refuted: strength never entered it, and the pins are ideal.

Teaching limit. Every joint is an ideal pin. Real connections carry some bending and can fail; glued or nailed models usually fail at the joint, which this solver cannot show.

Stage 2 · Compression buckles (Level 3)

Question. The same 4 m member holds 300 kN pulled. Why does it fail at 45 kN pushed?

Predict prompt. A 125 kN truck over 10 m: call the first failure of your first design.

Activity. ~3 minBuild or load a Gallery truss; turn on Numbers; call; test. ~4 minFlip a working design under the deck and test again.

Pcr = π²EI / L² ≈ 720 kN·m² / L², capped at 180 kN
Length1 m2 m3 m4 m
Pulled (σyA)300 kN300300300
Pushed (Euler, capped)180 kN1808045

Expected observation. The first member to go is a long blue one, and the weakest-link line reports it buckling at a fraction of the 300 kN the same member would hold pulled. The regression suite measures the propped design peaking at 37% of limit and the same steel hung at 32%.

Check-yourself key. No — a pushed member fails by buckling sideways, at a load that falls with the square of its length. Second item: the long members are now in tension, so the 300 kN limit applies.

Teaching limit. Euler with a 0.6 cap is a stand-in for real column curves; effective length is taken as the whole unbraced run with K = 1; the section values are the authors' choices (Details labels which are sourced).

Stage 3 · Load paths (Levels 4–5)

Question. How does a wheel's weight find its way to the ground when you cannot build below the deck, or when a pier appears mid-span?

Predict prompt. Level 4 forbids building below the deck: call the first failure of your first design there.

Activity. ~4 minGallery bowstring or Pratt at 2–3 m depth; Check a joint on a deck joint; call; test. ~3 minLevel 5: build two short bridges that share a deck.

Expected observation. In a Pratt the verticals are blue and the diagonals red; in a Howe the reverse; in a Warren the diagonals alternate. On Level 5 the pier drops par from $3,600-class spans to the forces of two 8 m ones. Grey members are the debrief's under-5% rows.

Check-yourself key. Not necessarily — a stiffer added path attracts more force and can overload its neighbour. Second item: the verticals carry each panel's shear to the top chord; erase one and its panel becomes a rectangle.

Teaching limit. The moving load is quasi-static — no dynamics, no impact — and the deck members carry wheels straight to their two joints with no bending.

Stage 4 · Sandbox (Level 6)

Question. With no par and any vehicle, which of your ideas about trusses survive a 20 t crane?

Predict prompt. Pick a Gallery truss and a vehicle; call it before the test.

Activity. Free build on 18 m; vary Depth and Panels; swap vehicles. Nothing is saved to the leaderboard.

Expected observation. Deeper trusses lower the chord forces; more panels shorten the struts; the crane finds the long compression members first.

Check-yourself key. Shortening the compression members, or hanging the deck so they pull instead of push. "Shallower" is refuted: chord force is roughly bending over depth.

Teaching limit. The vehicles are invented, sized to make par interesting.

Misconceptions

"More members always makes it stronger." Load shares by stiffness, so an added member can pull force onto a neighbour and overload it, and every member costs steel and a joint. The debrief flags members under 5% of limit. Try it: add one to a design that just made par and watch the peak move.
"The verticals do nothing — they're spacers." In a Pratt they carry each panel's shear in compression; in a Howe, in tension. A member genuinely carrying nothing is drawn grey, and that is a different thing. Try it: erase one vertical with X-ray on.
"Tension and compression are just plus and minus." The same 4 m member holds 300 kN pulled and 45 kN pushed. The sign selects a different failure mode. Try it: rebuild a design upside down under the deck.
"It failed because the steel was too weak." On Levels 1 and 2 the frame folds with every member at 0% of its limit. Strength cannot fix a mechanism; a diagonal can.

Why connections are priced

Costing follows a fabricator's bill: steel by weight (9.4 kg/m at $4.80/kg, about $45 a metre) plus $180 per joint for the gusset, bolts and labour. A flat price per metre makes extra panels free, which hides a real design driver; here connections run roughly 45% of a typical bill, so bracing a panel you already have costs steel only while adding a panel costs a joint too. The figures are illustrative; the shape of the bill is the point.

Static determinacy, plainly

Count members m, reactions r, joints j; each joint gives two equations. m + r < 2j: a mechanism — it folds and strength cannot help. m + r = 2j: determinate — every member is critical. m + r > 2j: indeterminate — load now splits by stiffness, which is why the game solves K·u = F instead of walking joint to joint. The count is necessary, not sufficient: members in the wrong places leave a local mechanism, and the solver checks the matrix, not the count.

Discussion questions

  1. The bare rectangle folded without any member changing length. Where did the load go, and why could no member resist it?
  2. Two designs, same cost and same joints: one props the deck from above, one hangs it from below. Predict which is safer, then check. What in Pcr = π²EI/L² explains it?
  3. A Warren's diagonals alternate tension–compression along its length. Take one bottom joint and use ΣFy = 0 to show why its two diagonals must have opposite signs.
  4. Why is the bottom chord's force greatest at mid-span and near zero at the supports?
  5. One member snapped and the whole bridge came down. What does that say about its spare load paths, and what would a spare path cost?
  6. Turn on Dead load and retest a design that just made par. What happens, and why does it matter more as spans grow?

Levels, par and logistics

#LevelSpan / vehicleParStage
1First Crossing6 m · car 30 kN$1,0501 Mechanisms
2The Long Gap12 m · car 30 kN$2,8001 Mechanisms
3Heavy Haul10 m · truck 125 kN$2,8002 Compression buckles
4High Water12 m · van 60 kN$3,1003 Load paths
5Island Pier16 m · truck 125 kN$3,6003 Load paths
6Sandbox18 m · your choice—4 Sandbox

Every par is beatable by a triangulated design and by no un-triangulated ladder at any depth or panel count — verified by test-physics.js, 86 checks, deterministic.

Presenter controls

  • ⚙ Settings: Open Presenter Notes (this guide), Presentation mode, Reset (Level 1, in place, leaderboard kept), then Show par budgets, Keyboard editing, pick-the-vehicle demos, and the two-step leaderboard clears.
  • Details in each stage intro: what is live, how it works, assumptions, sources, boundary.
  • Keys: 1 2 3 Draw / Erase / Check a joint · Ctrl+Z undo · Space test (once a call is committed) · X X-ray · F numbers.
  • Boards and saved designs live in each machine's browser storage.
Truss Bridge Builder (Bridge Works) · Bryant Harrison · Murray State University · one HTML file, runs offline. Physics: 2D pin-jointed truss by the direct stiffness method; mechanisms detected as rank deficiency and animated along the null-space mode; Euler buckling governs compression; overloaded members are removed and the structure re-solved. Sources for every cited figure are in the app's Details drawer with the date read.

Open the printable copy (teacher-guide.html) — the same document, laid out for print; the PDF beside it is a render of that file.

Debrief Live read from this crossing's test record

Levels — picking one moves the stage tabs with it

Famous trusses Sourced dates from the patents · Details, stage 3

Load one into the current level, run the test, and compare where the forces go. They all cross the same gap — they route the load differently.

Class leaderboard — this browser only
Bryant Harrison · Murray State University