--- title: "Pull or push" subtitle: "Structures · Frames and trusses · Lesson 1" --- # Pull or push **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A roof holds up a load of tiles. Which of its beams are being stretched, and which are being squashed? :::teacher-note **In one sentence:** 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. **Students should be able to say:** 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. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **The load presses down on C. Which member is being stretched (pulled)?** ☐ All three: the load stretches everything ☐ A-B, along the bottom ☐ None: a load only squashes ☐ A-C, a sloping side My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** A-B. The sloping members push the feet A and B outwards; the bottom member holds them together, so it is stretched. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: height changes the forces :::keep-together ### Three heights 1. $\text{height } 1 \text{ m: } A\text{-}B = 1000 \text{ N}$ — Test the roof with C at 1 m: the bottom pulls 1000 N. 2. $\text{height } 2 \text{ m: } A\text{-}B = 500 \text{ N}$ — Twice as tall: half the pull. 3. $\text{height } 4 \text{ m: } A\text{-}B = 250 \text{ N}$ — Twice again: half again. 4. $A\text{-}B = \frac{1000 \times 4}{4 \times \text{height}}$ — The 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?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1000 2000 × 4 ÷ (4 × 2) = 1000 N. ::: :::keep-together ### Flatter **A builder wants a flatter roof (lower C) to save timber. What happens to the forces?** ☐ They stay the same: the load hasn't changed ☐ They get bigger: flatter members must pull and push harder ☐ They get smaller: less timber, less force ☐ Only the bottom member changes ::: :::teacher-note **Answer:** 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. ::: :::typical ## Vary: raise the roof Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Forces in a roof :::keep-together ### 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?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 600 1200 × 6 ÷ (4 × 3) = 600 N. ::: :::keep-together ### Pull or push **Pull or push? Sort each member.** Groups: Tension (pulls), Compression (pushes) - A rope holding up a swing: {{field-15}} - A table leg: {{field-15}} - The cable of a crane: {{field-15}} - A pillar holding up a roof: {{field-15}} - The bottom member of a roof truss: {{field-15}} ::: :::teacher-note **Answer:** 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. ::: ## Make: a roof to a brief **A brief.** **Evaluate.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **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?** {{lines-3}} ::: :::teacher-note **Answer:** 900 × 6 ÷ (4 × 1.5) = 900 N, in tension. :::