Stress, Strain, and Hooke's Law
Normal stress is force per perpendicular area and longitudinal strain is fractional length change; in the proportional elastic region they satisfy sigma = Y epsilon.
Why this shows up in the exam
Sizing loaded rods and columns · Reading elastic stress-strain data · Estimating strain under a known axial load
Learn the idea
Within the linear elastic range, stress is proportional to the corresponding strain. A load tells how hard the material is pushed or pulled, while strain tells the fractional deformation; their ratio characterizes the material only while the response remains elastic and linear.
🧠 Memory hook: Stress is load per area; strain is change per original size.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sigma = F_perpendicular/A — normal tensile or compressive stress for a uniformly loaded section
- epsilon = Delta L/L — dimensionless longitudinal strain measured from the natural length
- sigma = Y epsilon — Hooke's law for small longitudinal deformation below the proportional limit
How to approach it
- 1Isolate the loaded section and find its internal force
- 2Use the area normal to that force
- 3Form stress or strain first, then apply the elastic relation
Common slip-ups that cost marks
- •Using total force instead of the tension in the selected section
- •Giving strain physical units
- •Applying the linear law beyond the elastic range
🌟 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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