Grade by Grade
D. Structures and Mechanisms · Form and Function

Design Challenge: An Efficient Paper Bridge

A1.3 A1.2 A1.4 A1.5 A3.2 D2.1 D2.3 D2.4 D2.5 D2.6About 60 minutes
Learning goals
  • I can use the engineering design process to design, build, test and improve a structure.
  • I can use what I know about structure types, forces, symmetry, materials and failure to make design decisions.
  • I can calculate a structure's efficiency (load held ÷ its own mass) and use data to improve my design.

Words to know

engineering design process
A series of steps engineers use to solve problems: define, research, plan, build, test, improve and communicate.
criteria
What a design must do to be successful.
constraints
Limits on a design, like the materials, size, cost or time allowed.
prototype
A first working model of a design, built to be tested and improved.
efficiency (of a structure)
How much load a structure holds compared with its own mass. Efficiency = mass of load held ÷ mass of structure.
iterate
To repeat the design process to improve a design step by step.

Hook: more strength, less stuff

Engineers don't just want strong structures. They want structures that are strong without wasting material. Using less material saves money, energy and resources.

Your challenge: build the most efficient paper bridge you can: the one that holds the most load for its own mass.

A folded accordion-style paper bridge spanning the gap between two stacks of books, with metal washers resting on its middle.
Folding the paper into pleats makes it much stiffer, so a single sheet can hold a load of washers across the gap. AI-generated image

Remember from Grade 6

In Grade 6 you used the engineering design process to build and improve a glider: you set criteria and constraints, built a prototype, tested it fairly, and iterated. Now you will use the same process for a structure, with a new measure of success: efficiency.

Criteria (must do)Constraints (limits)
span a 30 cm gap between two stacks of booksuse only paper (up to 10 sheets of printer paper) and up to 1 m of masking tape
have a flat deck at least 5 cm wide (wide enough for a toy car)may rest on the book stacks, but may not be taped or glued to them
hold a cup of load at the middle of the deckbuild time: about 1 hour
be as efficient as possibleno other materials (no glue, no straws, no cardboard)
Design brief
load cupbooksbooks30 cm gapsymmetrical paper truss
Test setup: the bridge rests on two equal stacks of books with a 30 cm gap. A cup hangs from the middle of the deck (or sits on it), and dried beans are added until the bridge fails. Not to scale.

Use what you learned in this unit

  • Structure types: a frame of rolled-paper tubes in triangles (a truss), a folded shell like a corrugated or tube-shaped deck, or a combination.
  • Forces: the load is at the middle of the deck (point of application), acting down (direction) on the top surface (plane). The top of your bridge will be in compression and the bottom in tension.
  • Forms: triangles stay rigid; folds and tubes make paper much stiffer; a beam on its edge resists bending.
  • Symmetry: a symmetrical bridge shares the load equally between both halves.
  • Materials: paper is quite strong in tension but buckles easily in compression, so roll or fold parts that will be squeezed.
  • Failure: watch where and how it fails (buckling, tearing, a joint coming apart). That tells you what to improve.
1. DEFINE: read the criteria and constraints.
2. RESEARCH and BRAINSTORM: look at real bridges; sketch 3 ideas.
3. PLAN: choose one idea; draw it with measurements; list materials.
4. BUILD a prototype.
5. TEST: weigh the bridge; add load until it fails; weigh the load.
6. EVALUATE: calculate efficiency; note where and how it failed.
7. IMPROVE: change ONE thing; build and test again (iterate).
8. COMMUNICATE: share your design, data and what you learned.

The engineering design process for this challenge

Worked example

Let's calculate efficiency

Bridge A has a mass of 45 g and held 1 800 g of beans. Bridge B has a mass of 80 g and held 2 400 g. Which bridge held more? Which is more efficient?

  1. Bridge B held more load: 2 400 g vs 1 800 g.
  2. Efficiency of A = 1 800 ÷ 45 = 40 (it held 40 times its own mass).
  3. Efficiency of B = 2 400 ÷ 80 = 30.
  4. A is more efficient: it held more load for each gram of bridge.

B is stronger, but A is more efficient (40 vs 30).

Load held (g)1 800Bridge A2 400Bridge BEfficiency (load ÷ mass)40Bridge A30Bridge BA: 45 g bridge · B: 80 g bridge1800 ÷ 45 = 40 · 2400 ÷ 80 = 30
Bridge B held more beans, but Bridge A held more for each gram of paper. In this challenge, the taller bar on the right is the one that wins.
Worked example

Let's use a failure to improve a design

A student's truss bridge failed when the top rolled-paper tube in the middle bent sideways suddenly. What kind of failure is it, and what is one good improvement to test next?

  1. The top of a bridge loaded at the middle is in compression.
  2. Bending sideways suddenly under compression is buckling.
  3. Improvements: roll the top tube tighter or with more layers, make it thicker, or add cross-braces so it is held in the middle and is effectively shorter.
  4. Change one thing at a time, so you know what caused any improvement.

The top chord buckled in compression. Next test: a tighter, thicker top tube (only that change).

Just for fun

Why was the paper bridge so calm during the test?

It knew how to handle the pressure... at least until the very last spoonful of beans.

Hands-on activity

Build, test and improve your bridge

You need: up to 10 sheets of printer paper, up to 1 m of masking tape, scissors (with a grown-up's help), a ruler, two equal stacks of books, a paper cup with a string or paper-clip hanger, dried beans or rice, a kitchen scale, and safety glasses (or sunglasses).

  1. Define and brainstorm: sketch three different ideas (for example, a truss of rolled tubes, a deck folded like an accordion, an arch under the deck).
  2. Plan: choose one. Draw it with measurements. Predict how much it will hold.
  3. Build your prototype. Weigh it on the kitchen scale and record its mass in grams.
  4. Test: set the books 30 cm apart. Place the bridge across. Hang or set the cup at the middle. Add beans a spoonful at a time, gently, until the bridge fails (collapses, tears, or sags so the cup touches the table). Weigh the cup and beans it held just before failing (the total from the last spoonful it held). Wear eye protection; keep your face away from the bridge as it nears failure.
  5. Evaluate: calculate efficiency = load held ÷ bridge mass. Note where and how it failed.
  6. Improve: change one thing and build and test again. Do at least 2 versions.
  7. Communicate: make a short report or video with your sketches, data table, efficiency for each version, and what you learned. Clean up spilled beans right away, as they are slippery on the floor.

What to look for: a design that meets the criteria and constraints, a data table (mass, load, efficiency, how it failed) for each version, one change at a time between versions, and explanations that use unit words: compression, tension, buckle, triangle, symmetry, point of application. Many well-built paper bridges hold well over 20 times their own mass, but any honest result is fine: the improvement between versions is what matters.

Your turn

1

What is the difference between criteria and constraints?

2

How do you calculate the efficiency of a bridge?

3

A bridge of mass 50 g holds 1 500 g. What is its efficiency?

4

Which part of a bridge loaded in the middle is in compression?

5

Why should you change only one thing between versions?

6

Name one safety rule for this challenge.

More practice: warm-up

1

What is a prototype?

2

What does iterate mean?

3

Why are triangles useful in a paper bridge?

4

Is "use only 10 sheets of paper" a criterion or a constraint?

5

Why is symmetry helpful in a bridge?

More practice: on your own

1

Three tests of the same bridge design held 1 200 g, 1 350 g and 1 260 g. What is the average load?

2

Bridge C has a mass of 60 g and an efficiency of 25. How much load did it hold?

3

A bridge's bottom layer of paper tore in the middle. Which force caused this, and how could you fix it?

4

Why is flat paper weak as a deck, but folded paper much stronger?

5

Why do engineers care about efficiency, not just strength?

Challenge

1

Version 1: mass 40 g, held 1 000 g. Version 2: mass 55 g, held 1 650 g. Version 3: mass 50 g, held 1 600 g. Which version is most efficient? Did adding mass always help?

2

A real bridge engineer must also think about factors that a paper bridge does not. Name three.

3

Math connection: explain how ratios and averages helped you make decisions in this challenge.

Check your understanding

Quiz

1.

Efficiency of a structure is...

2.

A 40 g bridge holds 2 000 g. Its efficiency is...

3.

Which is a constraint?

4.

A bridge's top tube bent sideways suddenly. This is...

5.

Between test versions, you should change...

6.

Which step comes right after testing a prototype?

For parents and teachers

Big idea (A1.3 with D2): Students use the engineering design process (A1.3) to design, build, test and improve a structure, applying solid/frame/shell ideas (D2.1), forces (D2.3), symmetry (D2.4), failure (D2.5) and materials (D2.6). They test fairly (A1.2), follow safety rules (A1.4), communicate results (A1.5), and use math (ratios and averages) to solve a real problem (A3.2).

How to help: Let your child lead. Ask questions instead of fixing things: "Where did it fail? Which force caused that? What one change will you try next?" Celebrate improvement between versions more than the final number.

Common difficulties:

  • Changing many things at once. Encourage one change per version.
  • Thinking the strongest bridge is the best. The goal is efficiency: strength for its mass.
  • Safety: supervise scissors, use eye protection during load tests, and sweep up beans or rice right away.