IB Design Technology Topic B3.2.2 Young’s Modulus and Stiffness Revision Notes (HL)

IB Design Technology Topic B3.2.2 Young’s Modulus and Stiffness Revision Notes (HL) | RevisionDojo

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Young's Modulus: Putting a Number on Stiffness

Note

This lesson assumes A3.2.5 and A3.2.6, which introduced stress, strain and Young's Modulus. Go back to those first if the terms are unfamiliar.
Here you calculate with them, rather than define them.

Definition

Young's Modulus

A measure of a material’s stiffness, defined as stress divided by strain.

Note

$$E = \frac{\sigma}{\varepsilon} = \frac{\text{Tensile Stress}}{\text{Tensile Strain}}$$
Stress is the Greek letter sigma (σ), and it is force divided by cross-sectional area, measured in pascals (Pa).
Strain is the Greek letter epsilon (ε), and it is the change in length divided by the original length. It is a ratio, so it has no units.
Because strain has no units, E carries the units of stress, so it is quoted in Pa, and usually in GPa.
E is also the gradient of the straight elastic region of a stress-strain graph, which is why a steeper line means a stiffer material.

Interpreting Stress–Strain Graphs

Stress–strain graphs show how a material behaves when pulled:

Point on Graph	Meaning
Gradient (Linear region)	Young’s Modulus (stiffness)
Yield Strength	Point where the material begins to deform permanently
Ultimate Strength	Maximum stress the material can handle before weakening
Fracture Point	Where the material breaks

Example

Steel has a high Young’s Modulus: it resists stretching, making it ideal for bridges and high-rise buildings.
Rubber has a low Young’s Modulus: it stretches easily, which is useful for tyres and elastic bands.

Calculating Young's Modulus, Step by Step

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Note

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Young's Modulus: Putting a Number on Stiffness

Note

This lesson assumes A3.2.5 and A3.2.6, which introduced stress, strain and Young's Modulus. Go back to those first if the terms are unfamiliar.
Here you calculate with them, rather than define them.

Definition

Young's Modulus

A measure of a material’s stiffness, defined as stress divided by strain.

Note

$$E = \frac{\sigma}{\varepsilon} = \frac{\text{Tensile Stress}}{\text{Tensile Strain}}$$
Stress is the Greek letter sigma (σ), and it is force divided by cross-sectional area, measured in pascals (Pa).
Strain is the Greek letter epsilon (ε), and it is the change in length divided by the original length. It is a ratio, so it has no units.
Because strain has no units, E carries the units of stress, so it is quoted in Pa, and usually in GPa.
E is also the gradient of the straight elastic region of a stress-strain graph, which is why a steeper line means a stiffer material.

Interpreting Stress–Strain Graphs

Stress–strain graphs show how a material behaves when pulled:

Point on Graph	Meaning
Gradient (Linear region)	Young’s Modulus (stiffness)
Yield Strength	Point where the material begins to deform permanently
Ultimate Strength	Maximum stress the material can handle before weakening
Fracture Point	Where the material breaks

Example

Steel has a high Young’s Modulus: it resists stretching, making it ideal for bridges and high-rise buildings.
Rubber has a low Young’s Modulus: it stretches easily, which is useful for tyres and elastic bands.

Calculating Young's Modulus, Step by Step

Definition

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Duis aute irure dolor in reprehenderit

Note

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Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
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A. Design in theory8 subtopics

B. Design in practice8 subtopics

C. Design in context8 subtopics

IB Design Technology Topic B3.2.2: Young’s Modulus and Stiffness Notes

A. Design in theory8 subtopics

B. Design in practice8 subtopics

C. Design in context8 subtopics

Young's Modulus: Putting a Number on Stiffness

Interpreting Stress–Strain Graphs

Calculating Young's Modulus, Step by Step

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Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Young's Modulus: Putting a Number on Stiffness

Interpreting Stress–Strain Graphs

Calculating Young's Modulus, Step by Step

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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