Students test a roof truss and read which members pull (tension) and push (compression), explain why slanted members carry more than their share, find that a taller roof halves the forces each time its height doubles, and choose a height that keeps every member within 600 N and the timber within budget.
Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.
SlidesDownload Present from the browser, or export to PowerPoint or PDF.
WorksheetDownload Print the student copy; the Teacher edition has the answers.
Students will be able to
I can say whether a member of a frame is in tension (pulls) or compression (pushes).
I can explain why a flatter roof has bigger forces in its members.
I can choose a design that meets a force limit and a budget.
Timing
Predict and Try 8 min · Worked example 10 min · Vary 6 min · Practise and Make 16 min
Before class
The board is a pin-jointed truss: members are straight, joined by pins that can't hold a turn, so each member only pulls or pushes along its length; loads act at joints; members weigh nothing. It is solved by the stiffness method (all members equally stiff), so frames with spare members work too.
A quick demonstration: two rulers leaning together on a table, feet free, then with a string tying the feet. The string goes tight.
Curriculum hooks: Design and Technologies, engineering principles and systems (primary); Science, forces (Year 7); Maths, proportion.
Running the lesson
Predict: draw the roof and ask students to mark each member 'stretch' or 'squash' before testing.
Try: point at the colours; blue pulls, red pushes.
Worked example: fill in the three heights from the board as a table, then find the rule.
Make: let students tell you why 3 m fails (force) and 4 m fails (cost).
The hard part (on purpose)
Students think a load only squashes. Ask what would happen to the feet if the bottom member were cut.
When students get stuck
What you will see
A question to ask
The fix
A student thinks the bottom member is squashed.
If you cut it, what would the feet do?
They would spread apart, so the member is holding them together: tension.
A student expects the slanted push to be 500 N.
How much of a slanted push points straight up?
Only part, so the push must be bigger.
A student keeps raising the roof to cut forces.
What happens to the cost?
Taller means longer members: a trade-off.
Answers to the checks
which member pulls?: The load presses down on C. Which member is being stretched (pulled)? A-B. The sloping members push the feet A and B outwards; the bottom member holds them together, so it is stretched.
Test it: Press Test it. Which members turn blue (pull) and which turn red (push)?
A-B pulls (blue); A-C and B-C push (red).
The pull: How hard does A-B pull, in newtons? 500 500 N. Each support holds up half the load, and the bottom member holds the feet together.
Why 707?: A-C pushes with 707 N, more than the 1000 N load shared between two sides (500 N each). Why more? It pushes at a slant: only part of its push holds the load up, so it must push harder Only the upward part of a slanted push holds the load up. The flatter the slope, the smaller that part, so the bigger the push.
Three heights: Span 4 m, height 2 m, and a 2000 N load. How hard does the bottom member pull, in newtons? 1000 2000 × 4 ÷ (4 × 2) = 1000 N.
Flatter: A builder wants a flatter roof (lower C) to save timber. What happens to the forces? They get bigger: flatter members must pull and push harder A flatter roof needs bigger forces in every member. That is the trade: less material, more force.
Vary: raise the roof: Raise or lower C until the bottom member pulls exactly 250 N, then test it.
C at 4 m: 1000 × 4 ÷ (4 × 4) = 250 N.
A wider roof: A roof 6 m wide and 3 m tall holds 1200 N at the top. How hard does the bottom member pull, in newtons? 600 1200 × 6 ÷ (4 × 3) = 600 N.
Pull or push: Pull or push? Sort each member. A rope holding up a swing → Tension (pulls); A table leg → Compression (pushes); The cable of a crane → Tension (pulls); A pillar holding up a roof → Compression (pushes); The bottom member of a roof truss → Tension (pulls) Ropes and cables can only pull. Legs and pillars push back against the load.
A brief: Choose a height where every member is within 600 N and the roof costs $125 or less, then test it.
3.5 m: the biggest push is 576 N and the timber costs $120.62. At 3 m a side pushes 601 N; at 4 m it costs $129.
Solutions
One possible solution for each task. Other correct programs are fine.
Vary: raise the roof
Open task: any program that does what the step asks.
a roof to a brief › A brief
Open task: any program that does what the step asks.
a roof to a brief › Evaluate
Open task: any program that does what the step asks.
Stretch and support
Stretch: Add a vertical member from C down to the middle of A-B (add a joint there in your head). What force would it carry, and why?
Support: Give a table: height, pull in A-B, push in A-C, cost. Fill the first row together.
Exit ticket
A roof truss 6 m wide and 1.5 m tall carries 900 N at the top. How hard does the bottom member pull, and is it in tension or compression?
900 × 6 ÷ (4 × 1.5) = 900 N, in tension.
What each step is for
which member pulls?: Students expect every member under a load to be squashed. Committing first makes the tension in the bottom member a surprise worth explaining: it stops the feet spreading.
Try: test the roof: Testing settles the prediction with colours and numbers; the number task makes students read the board.
Worked example: height changes the forces: The worked example turns board readings into a rule: for this roof, the bottom pull is load × span ÷ (4 × height). Taller means smaller forces but longer members.
Vary: raise the roof: The slider lets students check the rule against the board.
forces in a roof: Tension or compression by reasoning, and the rule with new numbers.
a roof to a brief: Two criteria pull in opposite directions: a taller roof means smaller forces but costs more timber. Only one height meets both.
Where it leads
Next: Triangles hold their shape.
Real examples: roof trusses, A-frames, ladders, crane jibs, the Sydney Harbour Bridge's arch and deck.