National 5 · Mechanisms and Structures › Materials

🧱 Materials — Course Notes

Material properties, selection and justification, stress and strain calculations

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Section 1: Material Categories

Engineers must choose the most appropriate material for every part of a design. The choice depends on what the part needs to do, what forces it will experience, and the environment it will operate in. Materials are grouped into four main categories:

⛏️ Metals
  • Steel — structural beams, car bodies, tools
  • Aluminium — aircraft, packaging, bike frames
  • Copper — electrical wiring, plumbing
  • Titanium — aerospace, medical implants
🌳 Polymers (plastics)
  • Polyethylene (PE) — plastic bags, bottles
  • Polypropylene (PP) — food containers, rope
  • Nylon — gears, bearings, textiles
  • Acrylic — signs, windows, displays
🧱 Ceramics
  • Glass — windows, lenses, optical fibre
  • Concrete — foundations, roads, bridges
  • Porcelain — electrical insulators, tiles
  • Silicon carbide — cutting tools, brake discs
✨ Composites
  • Carbon fibre reinforced polymer (CFRP) — aircraft, F1 cars, bikes
  • Glass fibre (GRP/fibreglass) — boat hulls, helmets
  • Reinforced concrete — buildings, bridges

Section 2: Material Properties

To choose the right material, engineers consider a range of mechanical, physical and other properties. Understanding these properties allows you to justify a material choice in the exam.

PropertyDefinitionExample where important
StrengthAbility to withstand a force without breakingStructural beams, lifting cables
HardnessResistance to scratching or indentationCutting tools, drill bits, gear teeth
ToughnessAbility to absorb impact energy without fracturingHelmets, crash barriers, tool handles
DuctilityAbility to be drawn into wires or bent without breakingElectrical wiring, bent brackets
MalleabilityAbility to be hammered or pressed into shapeAluminium car body panels, coins
Stiffness (rigidity)Resistance to bending or deformation under loadMachine frames, structural columns
ElasticityAbility to return to original shape after a force is removedSprings, rubber seals
DensityMass per unit volume — how heavy the material isAircraft components — low density preferred
Thermal conductivityHow well the material conducts heatHeat sinks, cooking pans, insulators
Electrical conductivityHow well the material conducts electricityWiring (conductors), casings (insulators)
Corrosion resistanceResistance to chemical attack or rustingOutdoor structures, marine applications
CostMaterial and processing cost per unitAlways a factor in real engineering decisions
✏️ Task 1 — Material categories and properties
1. State which category (metal, polymer, ceramic or composite) each of the following belongs to: (a) copper, (b) nylon, (c) concrete, (d) carbon fibre reinforced polymer, (e) glass.
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2. Explain the difference between strength and toughness. Give an example of a material that is strong but brittle (not tough).
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3. State two properties that are important when selecting a material for electrical wiring. For each property, explain why it matters.
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Section 3: Selecting a Material

In the SQA exam you will be given a scenario and asked to select a suitable material and justify your choice. A good justification always links the properties of the material directly to the demands of the application.

A complete material selection answer always has two parts: (1) name the material and (2) state the specific property or properties that make it suitable, linked clearly to the application.

How to approach a material selection question

  1. Read the scenario carefully — identify what forces or conditions the part must withstand
  2. List the key requirements (e.g. must be lightweight, must conduct electricity, must resist corrosion)
  3. Match a material to those requirements
  4. Justify each property you mention — say why it matters for this specific application
Worked Example 1 — Bicycle frame

Question: A bicycle frame must be lightweight and strong. Select a suitable material and justify your choice.

✅ Good answer

Aluminium alloy would be a suitable material. It has a high strength-to-weight ratio, meaning the frame can withstand the forces from the rider without being unnecessarily heavy. Aluminium also has good corrosion resistance, which is important as bicycle frames are used outdoors in wet conditions. Its ductility allows it to be formed into the required tube shapes during manufacture.

Worked Example 2 — Electrical cable insulation

Question: Select a suitable material for the plastic insulation surrounding electrical cables and justify your choice.

✅ Good answer

PVC (polyvinyl chloride) is commonly used. It is an electrical insulator, which prevents the user from receiving an electric shock by stopping current flowing through the outer casing. It is also flexible, so the cable can be bent without cracking, and it is low cost making it economical to produce in large quantities.

Worked Example 3 — Bridge support cable

Question: A suspension bridge cable must carry very large tensile forces and operate outdoors for many years. Select a suitable material and justify your choice.

✅ Good answer

High-tensile steel wire is used. Steel has very high tensile strength, meaning it can carry the enormous pulling forces in the cables without breaking. It is also stiff, which limits the amount of sag in the bridge. Galvanised or stainless steel variants are used to provide corrosion resistance for long outdoor service life.

✏️ Task 2 — Material selection and justification
1. A cutting tool is used to machine hard metals in a factory. Select a suitable material for the cutting tool and justify your choice by referring to at least two properties.
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2. A designer is choosing a material for the body panels of a sports car. The panels must be lightweight, strong and able to be formed into curved shapes. Suggest a suitable material and justify your answer.
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3. A food packaging company needs a material for a disposable drinks bottle. The material must be lightweight, transparent, cheap to produce and safe for food contact. Select a suitable material and justify your choice.
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4. An engineer is designing a cooking pan. The base must conduct heat efficiently and be strong enough to survive being dropped. The handle must not conduct heat. Identify suitable materials for (a) the pan base and (b) the handle. Justify both choices.
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5. A wind turbine blade must be very stiff, lightweight and able to withstand continuous cyclic loading over many years. Suggest a suitable material and justify your choice.
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Section 4: Stress

When a force is applied to a structural member, the material inside it is being squeezed or stretched. The intensity of this internal force — the force per unit area — is called stress. Stress is what determines whether a material will fail: if the stress in a member exceeds the material's strength, it will break.

Stress (σ) = Force (N) ÷ Area (mm²)
Stress is measured in N/mm² (also written as MPa). The symbol is the Greek letter sigma (σ).
Rearrangements:   Force = Stress × Area   |   Area = Force ÷ Stress

The cross-sectional area is the area of the cut face of the member — perpendicular to the direction of the force. A smaller cross-section experiences greater stress for the same force. This is why load-bearing columns and cables are sized carefully.

Stress tells us how hard the material is being pushed or pulled internally. A high stress value means the material is close to its limit — choose a stronger material, or increase the cross-sectional area.

Calculating cross-sectional areas

The cross-section shape determines how you calculate the area:

  • Rectangle: A = width × height  (mm × mm = mm²)
  • Circle: A = πr² = π(d/2)²  —  where d is the diameter in mm
  • Square: A = side × side
Diagrams showing rectangular, circular and square cross-sections with area formulae labelled
Worked Example 1 — Stress in a square bar

A square bar of 20 mm × 20 mm cross-section is subjected to a tensile load of 500 N. Calculate the stress in the bar.

1
Write the formula: σ = F ÷ A
2
Calculate area: A = 20 × 20 = 400 mm²
3
Calculate stress: σ = 500 ÷ 400 = 1.25 N/mm²
Worked Example 2 — Maximum load on a column

A column of cross-section 0.25 m² has a maximum allowable stress of 50 N/mm². Calculate the maximum compressive load.

1
Convert area to mm²: 0.25 m² = 0.25 × 106 mm² = 250 000 mm²
2
Rearrange: F = σ × A = 50 × 250 000 = 12 500 000 N = 12.5 MN
Worked Example 3 — Minimum wire diameter

A steel wire supports a load of 8 kN. The stress must not exceed 200 N/mm². Find the minimum wire diameter required.

1
Convert load: 8 kN = 8 000 N
2
Find minimum area: A = F ÷ σ = 8 000 ÷ 200 = 40 mm²
3
Find diameter from circular area formula: A = πd²/4
d² = 4A ÷ π = (4 × 40) ÷ π = 50.93
d = √50.93 = 7.14 mm
✏️ Task 3 — Stress calculations

Show all working. Check units carefully — forces in N, areas in mm², stress in N/mm².

1. A rectangular steel bar has a cross-sectional area of 250 mm² and is subjected to a force of 50 kN. Determine the stress in the bar.
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2. A wire 4 mm in diameter is subjected to a force of 300 N. Find the stress in the wire.
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3. What diameter of round steel bar is required to carry a tensile force of 10 kN if the stress must not exceed 14.14 N/mm²?
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4. A piece of wire 0.75 mm in diameter is subjected to a force of 120 N. Calculate the stress.
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5. A mild steel tie-bar of circular cross-section has a diameter of 30 mm and is subjected to a tensile pull of 75 kN. Find the tensile stress in the bar.
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6. A concrete column has a square cross-section of 200 mm × 200 mm and supports a compressive load of 500 kN. Calculate the compressive stress. Would a material with an allowable stress of 12 N/mm² be suitable? Justify your answer.
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Section 5: Strain

Every material deforms slightly when a force is applied to it — it stretches under tension or shortens under compression. This change in length, expressed as a proportion of the original length, is called strain. Strain tells us how much a material has deformed relative to its size.

Strain (ε) = Change in length (ΔL) ÷ Original length (L)
Strain has no units — it is a dimensionless ratio. The symbol is the Greek letter epsilon (ε).
Both ΔL and L must be in the same units before dividing.
Rearrangements:   ΔL = ε × L   |   L = ΔL ÷ ε
Strain is always a very small number — often expressed in scientific notation (e.g. 5 × 10−4). It has no units because it is a ratio of two lengths.

Tensile and compressive strain

If a member is under tension (being stretched), ΔL is an increase in length — the strain is positive. If a member is under compression (being shortened), ΔL is a decrease in length — the strain is sometimes described as compressive.

Diagram showing a bar under tension with original length L and extension delta L labelled, alongside the strain formula
Worked Example 1 — Strain in a wire

A steel wire of length 5 m stretches 2.5 mm when a load is applied. Calculate the strain.

1
Write the formula: ε = ΔL ÷ L
2
Convert to consistent units: L = 5 m = 5 000 mm, ΔL = 2.5 mm
3
Calculate strain: ε = 2.5 ÷ 5 000 = 0.0005 (= 5 × 10−4)
4
State units: Strain has no units.
Worked Example 2 — Finding change in length

The allowable strain on a concrete column must not exceed 5 × 10−4. The column is 3 m tall. Find the maximum reduction in height.

1
Rearrange: ΔL = ε × L
2
Convert L: 3 m = 3 000 mm
3
ΔL = 5 × 10−4 × 3 000 = 1.5 mm
Worked Example 3 — Combined stress and strain

A mass of 2 500 kg is hung from a vertical steel bar. The bar has a rectangular cross-section of 75 mm × 50 mm and an original length of 0.5 m. The bar stretches by 2.5 mm. Calculate both the stress and the strain. (Use g = 9.81 m/s².)

1
Find the force: F = mg = 2 500 × 9.81 = 24 525 N
2
Find the area: A = 75 × 50 = 3 750 mm²
3
Calculate stress: σ = F ÷ A = 24 525 ÷ 3 750 = 6.54 N/mm²
4
Calculate strain: L = 0.5 m = 500 mm, ΔL = 2.5 mm
ε = 2.5 ÷ 500 = 0.005
✏️ Task 4 — Strain calculations

Show all working. Remember to convert both lengths to the same unit before dividing. State clearly that strain has no units.

1. A wire 10 m long stretches 5 mm when a force is applied. Find the strain.
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2. A tow bar 1.5 m long is compressed by 4.5 mm during braking. Find the strain.
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3. The allowable strain on a bar is 0.0075 and its length is 2.5 m. Find the maximum change in length.
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4. During testing, a shaft was compressed by 0.06 mm and the resulting strain was 0.00012. What was the original length of the shaft?
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5. A mild steel tie-bar, 5 m long with a 30 mm diameter, lengthens by 1.5 mm under a tensile pull of 75 kN. Calculate both the stress and the strain in the bar.
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6. An aluminium alloy rod (cross-section 40 mm × 20 mm, length 800 mm) is subjected to a compressive force of 64 kN and compresses by 0.4 mm. Calculate the stress and strain. Would a material with an allowable stress of 80 N/mm² be suitable? Justify your answer.
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