Students find a pinned deck collapses and a big triangle buckles, learn that a member's buckling load falls with its length squared, build a bridge of short triangles that holds 1000 N, then refine it to cost $300 or less and fail only at 1400 N or more.
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Students will be able to
I can explain why long members buckle under a push.
I can design a truss whose pushed members are short and whose long members pull.
I can test a design to failure and talk about its safety factor.
Timing
Predict and Try 10 min · Worked example 8 min · Vary 12 min · Practise and Make 20 min
Before class
Do Pull or push and Triangles hold their shape first.
The model: a pin-jointed truss; any member pulls up to 2000 N; a member L m long buckles under 8000 ÷ L² N (Euler's buckling falls with length squared; the constant is chosen for the lesson). The load hangs at C only. A Pratt or Howe truss of 13 members ($293) is the cheapest design that meets the Make brief on this grid; teachers may find others.
A spaghetti or straw bridge tested to failure is the natural class follow-up, using the same rules.
Curriculum hooks: Design and Technologies, engineering principles and systems (primary); Science, forces; Maths, powers and inverse proportion.
Running the lesson
Predict: hang a chain between two hands: why does it sag?
Try: ask what made A-G fail when its force was under 2000 N.
Worked example: push on a long straw and a short one.
Make: share costs and failure loads on the board; who was cheapest and still safe?
The hard part (on purpose)
Building takes trial and error, and a design can collapse for a missing member or fail for a long pushed one. Ask which of the two happened.
When students get stuck
What you will see
A question to ask
The fix
The bridge collapses.
Which joint has members in only one direction?
Every joint needs members in two directions.
A long member fails.
Is it red (pushed)? Can you make it shorter, or make it pull?
Short pushes, long pulls.
It is over budget.
Which members carry 0 N?
Zero-force members may be removable, but test: some hold a joint in place.
Answers to the checks
just a deck: The bridge is only its deck: A-B, B-C, C-D, D-E, joined by pins. With 1000 N at C, it… It collapses. Pins let each joint turn, so a straight row of members folds at C like a chain. Every joint needs members in two directions.
The deck: Press Test it.
It collapses: the deck folds at its pins.
A big triangle: Build one big triangle: add A-G, G-E and C-G, then B-G and D-G so B and D are held too. Test it.
It holds its shape, but A-G and G-E, 4.5 m long, buckle under the push.
Why A-G?: Why did A-G fail when no member pulls more than 2000 N? It is long and pushed: a long member buckles under a much smaller push A 4.5 m member buckles at about 400 N. Long members should pull, or be cut into short ones.
Buckling: On this board, at what push does a 2.83 m member buckle, to the nearest 10 N? 1000 8000 ÷ 2.83² = 8000 ÷ 8 = 1000 N.
Shorter: A pushed member is cut in half by bracing it at its middle. How much bigger a push can each half take? 4 times Buckling goes with 1 ÷ length², so half the length takes 2² = 4 times the push.
Vary: a bridge that holds: Build a bridge that holds 1000 N with every member within its limit. Test it.
A row of short triangles: every joint is held and the long members pull.
Buckling: On this board, at what push does a 4 m member buckle, in newtons? 500 8000 ÷ 16 = 500 N.
Safety: A bridge carries 1000 N and fails at 1400 N. What is its safety factor (failure load ÷ working load)? 1.4 1400 ÷ 1000 = 1.4.
Cost: A bridge uses 14 members of 2 m and 4 of 2.83 m, at $10 a metre. What does it cost, in dollars, to the nearest dollar? 393 28 + 11.32 = 39.32 m, × $10 = $393.
The cheapest safe bridge: Build a bridge that holds 1000 N, costs $300 or less, and gives way only at 1400 N or more. Test it, then load it until it fails.
A Pratt (or Howe) truss: 13 members, $293, failing at about 1414 N.
Solutions
One possible solution for each task. Other correct programs are fine.
Vary: a bridge that holds
Open task: any program that does what the step asks.
the cheapest safe bridge › The cheapest safe bridge
Open task: any program that does what the step asks.
the cheapest safe bridge › Evaluate
Open task: any program that does what the step asks.
Stretch and support
Stretch: Find a design that fails at 2000 N or more. What does it cost, and is the extra safety worth it?
Support: Give the Pratt truss as a member list to type in, then ask students to remove one member and test.
Exit ticket
A 3 m member on this board is pushed with 1000 N. Will it buckle? Show the sum.
8000 ÷ 3² = 8000 ÷ 9 ≈ 889 N, less than 1000 N, so it buckles.
What each step is for
just a deck: A row of members along the bottom looks like a bridge. Committing first makes the collapse instructive: pinned joints need members in two directions.
Try: deck, then a big triangle: The deck collapses; a single big triangle holds its shape but its long sides buckle. Two failures, two different reasons.
Worked example: short pushes, long pulls: Buckling falls with the length squared, so halving a pushed member's length makes it four times stronger. That is why trusses are panels of short triangles, with diagonals arranged to pull.
Vary: a bridge that holds: Students apply both rules (every joint held, short pushes) to build any bridge that holds.
bridges: Buckling numbers, safety margins and cost.
the cheapest safe bridge: Three criteria at once: hold the load, cost no more than $300, and keep a safety margin (fail at 1400 N or more). Students build, test, and test to failure.
Where it leads
Next: the Capstone projects, where a lift or drive base meets a real structure.
Real examples: Pratt and Howe trusses (railway bridges), Warren trusses, the Sydney Harbour Bridge arch, roof trusses.