--- title: "Design a bridge" subtitle: "Structures · Frames and trusses · Lesson 3" --- # Design a bridge **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** 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? :::teacher-note **In one sentence:** 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. **Students should be able to say:** 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. **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 bridge is only its deck: A-B, B-C, C-D, D-E, joined by pins. With 1000 N at C, it…** ☐ Holds: 1000 N is less than 2000 N ☐ Holds, because the supports are strong ☐ Bends but holds ☐ Collapses: the pins let it fold at C My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 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. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Worked example: short pushes, long pulls :::keep-together ### Buckling 1. $\text{buckles at } \frac{8000}{L^2}$ — Long pushed members are the weak spot. 2. $L = 4.47 \text{ m: } \frac{8000}{20} = 400 \text{ N}$ — The big triangle's sides push about 1118 N: they buckle. 3. $L = 2 \text{ m: } \frac{8000}{4} = 2000 \text{ N}$ — Short members take five times the push. 4. $\text{pulls don't buckle}$ — So 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?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1000 8000 ÷ 2.83² = 8000 ÷ 8 = 1000 N. ::: :::keep-together ### 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 ☐ 2 times ☐ The same ☐ Half as much ::: :::teacher-note **Answer:** 4 times Buckling goes with 1 ÷ length², so half the length takes 2² = 4 times the push. ::: :::typical ## Vary: a bridge that holds Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Bridges :::keep-together ### Buckling **On this board, at what push does a 4 m member buckle, in newtons?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 500 8000 ÷ 16 = 500 N. ::: :::keep-together ### Safety **A bridge carries 1000 N and fails at 1400 N. What is its safety factor (failure load ÷ working load)?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1.4 1400 ÷ 1000 = 1.4. ::: :::keep-together ### 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?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 393 28 + 11.32 = 39.32 m, × $10 = $393. ::: ## Make: the cheapest safe bridge **The cheapest safe bridge.** **Evaluate.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A 3 m member on this board is pushed with 1000 N. Will it buckle? Show the sum.** {{lines-3}} ::: :::teacher-note **Answer:** 8000 ÷ 3² = 8000 ÷ 9 ≈ 889 N, less than 1000 N, so it buckles. :::