What it shows
Floors, shelves and bridges bend under load. A strip of wood supported at both ends and loaded at the middle bends by an amount that depends on its depth, length and Young’s modulus. The project measures the deflection and calculates the modulus for different woods.
The science
For a beam of length L supported at its ends with a point load W at the middle, the central deflection is δ = W L³ / (48 E I), where I = b d³/12 is the second moment of area. So E = W L³ / (4 b d³ δ). Doubling the depth d reduces the deflection eight times, which is why joists are placed on their narrow edge.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Strips of wood or bamboo of about 60 cm length with rectangular section (for example 3 cm wide and 0.5 cm thick, such as a wooden ruler or bamboo splint)
- Two knife-edge supports made from nails or metal rods
- A hanger and 50 g weights
- A metre rule and a pointer or a dial gauge
- A vernier caliper
- A spreadsheet
Safety
For this project: Do not overload the strip because it can snap. Keep your feet away from the falling weights. An adult must supervise.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
Step by step
10 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Measure the width b and depth d of each strip at three points with the vernier caliper and take the average.
Set up the two supports at a span L of 50 cm and place the strip on them.
Fix the pointer or dial gauge at the centre so it can read the vertical movement.
Hang the empty hanger at the centre and note the reading as zero.
Add 50 g steps up to 500 g, recording the deflection each time, and then remove them to check that the strip returns to zero.
Plot load against deflection and find the slope W/δ.
Calculate E from the formula using the slope and show its units in GPa.
Repeat with the strip placed flat and then on its edge, and compare the deflection (the edge-up movement is very small, so use the dial gauge or a long pointer).
Repeat with the span at 40 cm and 60 cm to check the L cubed relationship.
Write the report and compare your values of E with typical tables (about 8 to 12 GPa for many woods).
What you should see
The graph is a straight line up to the limit of elastic behaviour. The edge-up strip bends much less than the flat strip, and the calculated E of the wood is of the order of 5 to 12 GPa.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01What is Young’s modulus?
The ratio of stress to strain in the elastic range, a measure of stiffness.
02Why does depth matter so much?
Stiffness depends on d cubed, so a small increase in depth gives a large increase in stiffness.
03What does elastic limit mean?
The largest load after which the material returns to its original shape.
04Why is the load graph linear?
Within the elastic range deflection is proportional to load, by Hooke’s law.
Take it further
Test a steel ruler and a bamboo strip and rank the materials by stiffness and strength to weight ratio.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
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Mini and Major Project Guide
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