Key Idea: Model a product as members and joints, add the real loads, follow them to the ground, name what each member does, and say where it fails first.\n\nE = σ ÷ ε, where σ = F ÷ A and ε = ΔL ÷ L — and the area goes into square metres before anything is divided.\n\nStructures fail from overloading, material, size or shape; cracks start at sharp corners, and FEA red means the highest stress in THAT model, not failure.\n\nA force diagram reads loads → reactions → moments → members, and equilibrium needs forces AND moments to balance.\n\nSF = ultimate ÷ allowable, and the maximum intended load always includes the dynamic peak.
Paper 1 — multiple choice
- Calculate a stress, a strain or a modulus
- Read yield, ultimate or fracture off a graph
- Find a reaction on a symmetrical beam
- Apply a safety factor to a failure load
Paper 2 — analysing a product
- Model the forces in a real product and strengthen it
- Calculate a modulus from test data and name a material
- Explain a failure using FEA data and a time clue
- Size a member for a stated load and safety factor
Carried into the design project
- Criterion D — a structural claim must be modelled and tested
- Photograph your model failing, with the load written beside it
- Every safety factor you quote needs a justification
Almost every mark in this topic comes from four pieces of arithmetic, and the same two errors lose them: the wrong unit, and the ratio the wrong way up.
| Quantity | Formula | The error to avoid |
|---|---|---|
| Stress | σ = F ÷ A, using the ORIGINAL area | Leaving the area in mm², which makes the answer a million times too small |
| Strain | ε = ΔL ÷ L, both in the same unit | Giving it a unit — strain has none |
| Young's modulus | E = σ ÷ ε, on the STRAIGHT part of the graph | Taking the gradient past yield, where it means nothing |
| Reactions | Forces balance AND moments balance | Assuming the reactions are equal when the load is off-centre |
| Safety factor | SF = ultimate ÷ allowable | Multiplying where you should divide |
The test piece beside the graph, so each quantity is measured on the thing it comes from.
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Important: Square millimetres left in a stress calculation.\n\nEqual reactions assumed for an off-centre load.\n\nA stronger material recommended for a part that is sagging — strength and stiffness are different properties.\n\nThe static load used as the design load, when the product is jumped on, swung on or dropped onto.
| What the analysis shows | The strengthening | Why it works |
|---|---|---|
| A rectangle folding into a parallelogram | Triangulate it | A triangle cannot change shape — the cheapest strengthening there is |
| A member sagging in bending | Increase the DEPTH, or add a lip or rib | Bending stiffness rises with the CUBE of depth |
| A long span deflecting | Add a support in the middle | Deflection falls with the FOURTH power of span |
| A slender column bowing | Add a stretcher part-way down | It halves the effective length, making it about four times harder to buckle |
| A joint tearing out | Spread the load — a washer, a plate, more fixings | The material was never the problem; the stress concentration was |
Loads, reactions, moments, members — the order a force diagram is read in.
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Steel 200 GPa, aluminium 70, timber 10-15, polymers 1-3 — the fastest way to catch a unit error.\n\nDepth cubed for bending stiffness; span to the fourth for deflection.\n\nCracks start at corners, holes and tool marks.\n\nMoments about a support make that reaction drop out.\n\nThe support nearer the load always carries more.
A 4 m footbridge plank on two end supports carries a 900 N person 1 m from the left. The plank is 200 mm × 40 mm in section. Apply equilibrium and the stress formula to find both reactions and the stress at the left support.
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A school stool has splayed tubular legs that bow outwards when a heavy student stands on the seat. Analyse the failure and recommend two changes.
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A designer specifies a safety factor of 6 for a climbing-wall hold and 1.8 for its mounting bracket in a display case. Justify the difference.
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State the three stiffness formulae.
How do you find an unequal pair of reactions?
Why do cracks start at sharp internal corners?
What does red on an FEA plot mean?
What is the maximum intended load?
Why is a stronger material rarely the fix for sagging?
Exam tips
- Convert the area to square metres before dividing anything.
- Take moments about a support to make its reaction drop out, then sense-check which side carries more.
- Name the failure as strength, stiffness or stability — two of the three break nothing.
- Change the geometry before the material, and say what it does to depth, span or effective length.
- Include the dynamic peak in any maximum intended load.
- In an FEA question, quote the peak stress against the yield and look for a time clue.