In a frame joined by pins, every member either pulls (tension) or pushes (compression). Students test a roof truss, read which members pull and push, find that a taller roof means smaller forces, and choose a roof height that keeps every member within its limit and the budget.
A roof holds up a load of tiles. Which of its beams are being stretched, and which are being squashed?
A structure holds a load up without moving. A truss is a frame of straight members joined at pins, like a roof frame, a crane arm or a bridge. Because the joints are pins, each member can only pull or push along its length:
Tension: the member is being stretched; it pulls on its joints (blue on the board).
Compression: the member is being squashed; it pushes on its joints (red).
The roof truss here is 4 m wide. A sits on a fixed support (a pin), B on a roller that can slide sideways. A 1000 N load presses on the top joint, C. Forces are in newtons; a minus sign means a push.
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.
Which member pulls?
TryTry it on the board and compare the result with your prediction.
Try: test the roof
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Press Test it. Which members turn blue (pull) and which turn red (push)?
Use the board. This ticks when you get there.
How hard does A-B pull, in newtons?
InvestigateWork out why it happens, one step at a time.
Worked example: height changes the forces
Worked exampleBefore each step, say what you think comes next.
height 1 m: A-B=1000 NTest the roof with C at 1 m: the bottom pulls 1000 N.
height 2 m: A-B=500 NTwice as tall: half the pull.
height 4 m: A-B=250 NTwice again: half again.
A-B=4×height1000×4The pull is load × span ÷ (4 × height).
Now a 2000 N load on the same 4 m roof, 2 m tall.
Span 4 m, height 2 m, and a 2000 N load. How hard does the bottom member pull, in newtons?
ModifyChange the problem on purpose and see what happens.
Vary: raise the roof
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Raise or lower C until the bottom member pulls exactly 250 N, then test it.
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Forces in a 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?
Pull or push? Sort each member.
A rope holding up a swing
A table leg
The cable of a crane
A pillar holding up a roof
The bottom member of a roof truss
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
A roof to a brief
Need a hint?
Members here can only take 600 N, pulling or pushing.
Another hint
Taller makes the forces smaller, but the members longer and dearer.
Another hint
Test each height from 3 m up and watch both the forces and the cost.
Try it yourselfYour edits are saved in this browser.
Choose a height where every member is within 600 N and the roof costs $125 or less, then test it.
Use the board. This ticks when you get there.
For teachers
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. About 40 minutes.
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.
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
A student thinks the bottom member is squashed. Ask: If you cut it, what would the feet do? Fix: They would spread apart, so the member is holding them together: tension.
A student expects the slanted push to be 500 N. Ask: How much of a slanted push points straight up? Fix: Only part, so the push must be bigger.
A student keeps raising the roof to cut forces. Ask: What happens to the cost? Fix: Taller means longer members: a trade-off.
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.
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.
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.
Now you can
Say whether a member of a frame is in tension (pulls) or compression (pushes).
Explain why a flatter roof has bigger forces in its members.
Choose a design that meets a force limit and a budget.