Question 3

[1 mark] Simple familiar

Topic guidePremiumTopic guide 12 · Reading a stress–strain diagram

Game plansPremium5.3 Read a stress–strain diagram Reading a stress–strain diagram

The question

A stress–strain diagram with stress on the vertical axis and strain on the horizontal axis. The curve rises in a straight line from the origin, labelled J. At the top of the line there is a small kink, labelled K. The curve then rises in a broad hump whose peak is labelled L, and falls away to the right, ending in an arrowhead labelled M.

The stiffness of a material can be identified using which area of the stress–strain diagram?

That is it. Step through the hints below to see why. In 2021, 71.6% of Queensland students chose (A).

Not quite. K is the kink at the top of the straight line, the yield point. It tells you the stress at which the material starts to deform permanently. That is a strength reading. Stiffness is the slope of the line below it. In 2021, 16.5% of Queensland students chose (B).

Not quite. L is the peak of the curve, the ultimate tensile strength. It is the most stress the material can carry, which measures strength. Stiffness is read from the straight line at J. In 2021, 9.8% of Queensland students chose (C).

Not quite. M is where the curve falls away after the peak towards fracture, the necking region. How far the curve runs tells you about ductility. Stiffness is read from the straight line at J. In 2021, 1.9% of Queensland students chose (D).

Trace along the curve

Jump to a lettered area

Stiffness is how hard a material resists stretching elastically. On a stress-strain diagram that is the slope of the straight line from the origin, Young’s modulus.

$$\begin{gathered}E=\frac{\sigma}{\varepsilon}\\=\text{slope of the straight line}\end{gathered}$$

The 2021 subject report describes Young’s modulus the same way: stiffness, the ability to withstand elastic deformation within the proportional limit.

J sits on the straight line. A steeper line means more stress for the same strain, so the material is stiffer. The slope of the region at J is the stiffness.

The question says “area”, but it means a part of the diagram. Area under the curve would be toughness, and none of the letters marks an area in that sense.

Name the other three letters so you can rule them out.

K is the yield point, where permanent deformation begins. L is the peak, the ultimate tensile strength. M is the fall after the peak as the bar necks, ending at fracture. All three are strength or ductility readings.

Stiffness is Young’s modulus, the slope of the straight line from the origin. J labels that straight line. K is the yield point, L the ultimate tensile strength and M the necking that ends in fracture.

(A)

How Queensland students answered in 2021

(A)

71.6%

(B)

16.5%

(C)

9.8%

(D)

1.9%

The most common wrong answer was (B), the yield point K. It sits at the top of the straight line, so it is easy to grab. Stiffness lives in the slope below it, along J. Stress-strain diagrams are reduced content in the 2025 syllabus, yet one appeared in every paper from 2020 to 2025, so learn to read the slope on sight.

Only mark this done when you could do it without help. Reading the solution does not count.

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Question wording and any figures are from the 2021 QCAA Engineering external assessment, © State of Queensland (QCAA) 2021, licensed under CC BY 4.0, and have been adapted, except where a third-party source is named. Tangent Tuition is not affiliated with the QCAA.

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