Poisson's Ratio and Lateral Strain
Poisson's ratio is minus transverse strain divided by longitudinal strain for small uniaxial deformation, so measured lateral strain can determine axial strain and elastic energy.
Why this shows up in the exam
Diameter-change measurements · Three-dimensional deformation estimates · Inferring axial strain from transverse data
Learn the idea
Axial stretching is accompanied by transverse contraction characterized by Poisson's ratio. Pulling a wire makes it longer and usually thinner; Poisson's ratio compares the magnitude of those perpendicular fractional changes.
🧠 Memory hook: Stretch long, shrink sideways; Poisson compares the fractions.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- nu = -epsilon_transverse/epsilon_longitudinal — signed definition under uniaxial loading
- epsilon_longitudinal = -epsilon_transverse/nu — axial strain inferred from lateral strain
- u = (1/2)Y epsilon_longitudinal² — energy density for linear uniaxial loading
How to approach it
- 1Identify axial and transverse directions
- 2Use Poisson's ratio to obtain axial strain
- 3Apply Young's law or energy only to the corresponding strain
Common slip-ups that cost marks
- •Dropping the sign convention without stating magnitudes
- •Using absolute diameter change instead of fractional strain
- •Substituting transverse strain directly into Young's-law energy
🌟 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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