Module 1 · Lesson 1.1

What steel does when you load it

The stress–strain curve, region by region, and what each one lets a designer get away with.

Why this matters

Almost everything peculiar about steel design follows from the shape of one curve. Why plastic design is allowed at all, why a beam can be designed to yield and still be safe, why a structure gives warning before it fails, and why 'just use a stronger grade' is usually the wrong answer — all of it is visible in the stress–strain diagram before any code is opened.

By the end of this lesson you should be able to

Identify the elastic range, yield point, plateau and strain-hardening region
Say what design decision each region supports
Explain why the yield plateau is the feature that matters most
Quantify steel's ductility rather than asserting it

What you should already know

Stress, strain and Hooke's law (Structural Analysis Fundamentals, Module 8)
Bending of a section and the idea of a section modulus

One curve, four regions

Pull a steel coupon and record stress against strain. Four things happen in order, and each one licenses something different in design.

The elastic range. Stress and strain are proportional, and the constant is E ≈ 210 000 N/mm². Unload here and the specimen returns exactly to where it started. Everything in elastic analysis lives in this region.

The yield point. Structural steel has a sharp one. Many materials do not — for aluminium you have to define a proof stress at some arbitrary offset, because there is no moment where behaviour visibly changes. Steel simply stops being elastic, and it does so at a repeatable stress.

The yield plateau. This is the important one, and it is the region most other structural materials do not have at all. The specimen goes on straining at essentially constant stress — it gets longer while the stress does not rise.

Strain hardening. Eventually the stress starts to climb again, up to the ultimate strength, before the specimen necks and breaks.

If you remember one thing from this lesson, make it the plateau. Nearly everything steel is allowed to do that concrete is not comes from it.

Note

Why the plateau is what makes plastic design possible

Consider a beam whose most-stressed fibre has just reached yield.

If steel had no plateau — if stress fell away once yielding began — that fibre would shed load the instant it yielded, the next fibre would be overloaded, and failure would run through the section immediately. First yield would be failure.

Because there IS a plateau, the yielded fibre keeps carrying its f_y while it strains. So the next fibre in can be brought up to yield too, and the next, and yielding spreads through the depth of the section until the whole of it is at f_y. That state is the plastic moment, and it is substantially more than the moment at first yield.

The same argument at the next scale up is what allows plastic hinges: a section can hold its plastic moment while it rotates, which lets moment redistribute to less-stressed parts of the structure.

So the plateau is not a curiosity of the tensile test. It is the physical permission for W_pl, for plastic analysis, and for the redistribution that makes steel frames robust.

Try it

The curve, and what you can do in each region

Move along the curve and watch which region you are in. Then change the grade: every curve shares the same initial slope, because E does not depend on the grade. That one observation explains most of what is surprising in steel design.

Steel grade

Strain0.50 %

Thickness15 mm

Grade and thickness: S355, 15 mm
Yield strength f_y: 355 N/mm²
Ultimate strength f_u: 510 N/mm²
Strain at yield: 0.169 %
Current strain: 0.50 %
Current stress: 355 N/mm²
Region: yield plateau
Strain as a multiple of yield: 3.0 × ε_y
Modulus E: 210 000 N/mm² — the same for every grade
ε for classification: 0.814

On the plateau, at 3.0 times the yield strain. The material is straining at constant stress, which is what lets yielding spread through a section instead of failing the first fibre. This region is the physical permission for W_pl and for plastic hinges.

Things worth trying

Switch between grades and watch the initial slope. It does not move. E is about 210 000 N/mm² for all of them, which is why deflection, buckling and vibration do not improve when you specify stronger steel.
Set the strain to 0.1% and then to 10%. You have gone from invisible to enormous, and the material is still carrying load — that hundred-fold reserve is what ductility actually means.
Watch ε at the bottom of the readout as you raise the grade. It FALLS, which tightens every classification limit. Stronger steel makes local buckling more likely, not less.
Raise the thickness past 40 mm. The strength drops, because thick product cools slowly and is rolled less. The grade name alone does not tell you the strength you have.
Compare the strain at yield across grades. S235 yields at 0.112% and S460 at 0.219% — so the higher grade reaches yield later but breaks at about the same strain, which is why it is less ductile.

Worked example

How much reserve does steel actually have?

Given

S355 steel, E = 210 000 N/mm²
Yield strength 355 N/mm², ultimate strength about 510 N/mm²
Ultimate strain about 15%

Find

The strain at yield, and how far past it the material can go.

Assumptions

Nominal values; real coupons scatter above them
The idealised curve, with a flat plateau and a smooth hardening branch

Predict first

A beam is deflecting too much. Someone proposes changing the steel from S275 to S460 — a 67% increase in strength. What happens to the deflection?

The one fact that explains most of steel design

Every structural steel grade has essentially the same stiffness. Only the strength changes.

E ≈ 210 000 N/mm² for S235 and for S460 alike. This is not an approximation adopted for convenience; it is a property of the material. Alloying and heat treatment change how easily the atoms slip past one another — which is strength — and barely touch how stiffly the bonds stretch, which is stiffness.

The consequences run right through the subject:

Deflection does not improve with grade. If a beam is governed by deflection, a stronger steel is money spent on nothing.
Buckling barely improves. The Euler load is π²EI/L², and there is no f_y in it. A slender column gains almost nothing from a higher grade.
Local buckling gets WORSE. A plate buckles at a stress that depends on E and geometry. Raise f_y and you have raised the stress the plate must reach without raising the stress at which it buckles — so it is now relatively more slender. This is exactly what ε = √(235/f_y) encodes, and we will meet it properly in Module 5.
Vibration does not improve. Natural frequency goes with √(EI/m).

Higher-strength steel is worth buying for one situation: a member governed by cross-section resistance, where the material is actually being asked to reach f_y. A short tension member, a stocky column, a beam with plenty of restraint. Everywhere else, it is the wrong lever.

Practice

What is the strain at first yield for S355 steel, expressed as a percentage? Take E = 210 000 N/mm².

Practice

S275 steel fails at about 15% strain. By what factor does it stretch beyond its elastic limit? Take E = 210 000 N/mm².

Practice

A 355 N/mm² steel member is in pure shear. At what shear stress does it yield, on the von Mises criterion?

Check yourself

Which feature of the stress–strain curve is what permits plastic design?

Summary

Four regions: elastic, yield point, plateau, strain hardening
The PLATEAU is what permits plastic design — a yielded fibre keeps carrying f_y
Strain hardening is why a hinge can rotate without shedding moment
Steel yields at about 0.17% strain and fails near 15% — a reserve of roughly ninety
Higher grades are LESS ductile by that measure: strength and ductility trade
E is the same for every grade, so deflection, buckling and vibration do not improve with strength
τ_y = f_y/√3 is derived from von Mises, not chosen by a code

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This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint