Stress-Strain and Load-Extension Graphs
In the linear region, slope of stress versus strain is Young's modulus, slope of load versus extension is axial stiffness, and the area under stress versus strain is strain-energy density.
Why this shows up in the exam
Finding modulus from graphs · Comparing material stiffness · Extracting elastic energy density
Learn the idea
A graph's axes decide whether slope represents modulus, compliance, stiffness, or its reciprocal. Swapping axes flips a slope into its reciprocal, while the area under a stress-strain curve represents energy density only with stress on the vertical axis.
🧠 Memory hook: Read the axes before reading the slope or area.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- slope(sigma versus epsilon) = Y — Young's modulus for conventional axes
- slope(F versus Delta L) = AY/L — axial stiffness from a load-extension graph
- u = integral sigma d epsilon — energy density represented by area under a stress-strain curve
How to approach it
- 1Write vertical quantity over horizontal quantity
- 2Translate slope into the corresponding formula
- 3Use area only after confirming stress-strain axes
Common slip-ups that cost marks
- •Calling every straight-line slope Young's modulus
- •Ignoring reversed axes
- •Taking graphical area without checking axis units
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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