Steel Poisson Coefficient

Poisson's ratio of steel

Pull on a bar and it gets longer, but it also gets thinner. Poisson's ratio ν measures how much: it's the negative of the transverse strain divided by the axial strain under a uniaxial load, ν = −ε_transv / ε_axial. Structural steel sits at ν ≈ 0.30, the value used in NBR 8800 and AISC. Concrete falls in the 0.15–0.20 band, aluminium runs about 0.33, rubber climbs to 0.49 (it's nearly incompressible), and cork is close to 0. The elastic constants tie together through E = 2G·(1 + ν), where G is the shear modulus, while K = E / (3·(1 − 2ν)) gives the bulk modulus. Plug in steel at E = 200 GPa and ν = 0.30 and you get G ≈ 77 GPa.

The Brazilian codes follow suit: NBR 8800 takes ν = 0.3 for steel and NBR 6118 takes ν = 0.2 for concrete in serviceability checks. The ratio carries no units and holds steady through the elastic range. Push a metal past yield and it drifts toward 0.5, because plastic flow keeps the volume constant.

Applications

It shows up wherever materials are modelled in detail: finite-element analysis (FEM) of plates and shells, the steel-to-concrete handoff in composite structures, plane-stress and plane-strain problems, backing out G from tensile-test data, contact mechanics (Hertz), and thermal-stress work where lateral restraint matters. Leave ν out and you can't assemble the full 3D constitutive matrix at all.

FAQ

Why is ν ≤ 0.5? Thermodynamics says K > 0. Look at K = E/(3(1−2ν)): for that to stay positive the denominator can't go negative, which forces ν < 0.5. The lower bound of −1 comes out the same way from G > 0.

Can ν be negative? It can. Auxetic materials such as certain foams and polymer meshes actually widen sideways when you stretch them. You won't see this in metals or concrete, though.

Does ν depend on temperature? A little. Steel runs from about 0.28 at room temperature to about 0.32 near 600 °C, but the design value still sits at 0.30.

Why does concrete use 0.2? Once it cracks, concrete acts like a granular composite, and the micro-cracks cut down on lateral contraction. That's why NBR 6118 §8.2.9 sets ν = 0.2 for service loads.