Long members buckle under a push long before they snap under a pull, so good bridges keep pushed members short. Students find a deck on pins collapses, a big triangle buckles, then design a bridge that holds 1000 N within a budget and test it to failure.
An 8 m gap, a 1000 N load in the middle, and $10 a metre for members. What is the cheapest bridge that won't fail?
A bridge must hold its load, stay within its budget, and fail at a load well above what it will carry (a safety margin).
The span is 8 m. Deck joints A to E sit along the bottom; F, G and H are above. A is on a pin, E on a roller, and 1000 N hangs from C. Members cost $10 a metre. Any member can pull 2000 N. A push is different: a long thin member buckles (bows sideways) under a much smaller push. Here a member L metres long buckles under 8000 ÷ L² newtons: 2000 N for a 2 m member, but only about 400 N for a 4.5 m one.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Just a deck
TryTry it on the board and compare the result with your prediction.
Try: deck, then a big triangle
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Press Test it.
Use the board. This ticks when you get there.
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.
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Worked example: short pushes, long pulls
Worked exampleBefore each step, say what you think comes next.
buckles at L28000Long pushed members are the weak spot.
L=4.47 m: 208000=400 NThe big triangle's sides push about 1118 N: they buckle.
L=2 m: 48000=2000 NShort members take five times the push.
pulls don’t buckleSo long diagonals should pull; pushed members should be short: a Pratt truss does both.
On this board, at what push does a 2.83 m member buckle, to the nearest 10 N?
ModifyChange the problem on purpose and see what happens.
Vary: a bridge that holds
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Need a hint?
Make every panel a triangle: top members F-G and G-H, end posts A-F and H-E.
Another hint
Hold B, C and D with members going up (verticals) or across (diagonals).
Another hint
Put the inner diagonals so they slope down towards C (F-C and H-C): they pull.
Build a bridge that holds 1000 N with every member within its limit. Test it.
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Bridges
On this board, at what push does a 4 m member buckle, in newtons?
A bridge carries 1000 N and fails at 1400 N. What is its safety factor (failure load ÷ working load)?
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?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
The cheapest safe bridge
Need a hint?
Start from the bridge you built in Vary.
Another hint
Take out any member that isn't needed: every joint still needs members in two directions.
Another hint
Press Load until it fails: it must hold 1400 N or more.
Try it yourselfYour edits are saved in this browser.
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.
Use the board. This ticks when you get there.
For teachers
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. About 50 minutes.
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.
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
The bridge collapses. Ask: Which joint has members in only one direction? Fix: Every joint needs members in two directions.
A long member fails. Ask: Is it red (pushed)? Can you make it shorter, or make it pull? Fix: Short pushes, long pulls.
It is over budget. Ask: Which members carry 0 N? Fix: Zero-force members may be removable, but test: some hold a joint in place.
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.
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.
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.
Now you can
Explain why long members buckle under a push.
Design a truss whose pushed members are short and whose long members pull.
Test a design to failure and talk about its safety factor.