Module 1 · Lesson 1.2

Residual stress, thickness and toughness

Three properties that are invisible in a tensile test, absent from most calculations, and responsible for a surprising share of what goes wrong.

Why this matters

A steel member arrives on site already stressed, before any load is applied. Its strength depends on how thick it is, which the grade name does not tell you. And it can fail in a way the tensile test never shows — suddenly, at low stress, with no yielding at all. None of these appears in a routine calculation, and all three change design decisions.

By the end of this lesson you should be able to

Explain where residual stresses come from and why they matter for buckling
Say why thicker product has a lower nominal yield strength
Distinguish toughness from strength and from ductility
Recognise lamellar tearing as a through-thickness problem, not a weld problem

Steel is already stressed before you load it

A hot-rolled section leaves the mill at around 1000 °C and cools in air. It does not cool evenly. The flange tips and the outside surfaces are exposed on more sides, so they cool first; the web–flange junction is buried in the middle of a mass of hot steel and cools last.

The parts that cool first contract first, and set. The parts that cool later then try to contract, and cannot — the already-solid material is in the way. So the late-cooling regions end up in tension, and to balance them the early-cooling regions end up in compression.

For a rolled I section that means:

flange tips in residual compression, typically 30% of f_y or so;
web–flange junction in residual tension;
the whole pattern self-balancing, because no external load is applied.

Welding does the same thing far more sharply. A weld is a small volume of molten metal cooling against a large cold mass, so it contracts hard and ends up in high residual tension — often right up to yield — with compression balancing it nearby.

Residual stresses do not reduce the squash load. Add up the pattern and it sums to zero. What they do is make part of the section yield early.

Take care

Why early yielding matters so much for buckling

Take a column with flange tips in residual compression at 0.3 f_y. Apply an axial load. Those tips reach f_y when the applied stress is only 0.7 f_y — they yield before the rest of the section.

A yielded fibre has no stiffness left to contribute. So the section's effective stiffness for resisting buckling starts falling while the member is still, on average, well below yield.

And it is the worst possible fibres to lose. The flange tips are the material furthest from the minor axis — precisely the material contributing most to I_z. Losing them early is why minor-axis buckling is penalised relative to major-axis buckling, and why a welded section takes a worse buckling curve than a rolled one.

This is the physical content of the buckling curve selection table. It looks like arbitrary lettering; it is a residual-stress story.

Worked example

Where the flange tips start yielding

Given

A rolled I section in S355
Residual compression at the flange tips of about 0.3 f_y
Residual tension at the web–flange junction, balancing it

Find

The applied stress at which the flange tips first yield, and what it means.

Assumptions

An idealised residual pattern — real distributions are measured and vary
The 0.3 f_y figure is typical of rolled sections and is not a code value

Thicker steel is weaker

The grade name gives one number. The material does not.

S355 means 355 N/mm² of yield strength — for product up to a stated thickness. Above it, the guaranteed value falls, to about 335 N/mm² and then further for very thick material.

The reason is the same cooling story. Thick product cools more slowly, which produces a coarser grain structure, and it receives less rolling reduction, which does less to refine that structure. Fine grains resist dislocation movement; coarse grains resist it less. So thicker material is genuinely weaker, not conservatively rated.

Two consequences catch people out:

A thick flange and a thin web may have different strengths in the same section. The classification of the flange and of the web then use different ε values, which is fiddly and is easy to miss.

Thickness hurts twice. A thick-flanged section has lower f_y and takes a worse buckling curve, because it also cooled more unevenly. The two effects compound.

Try it

What the grade name does not tell you

Choose a grade and a thickness, and watch two things move in opposite directions: the strength you can use goes up, and the slenderness you are allowed goes down. Specifying a stronger steel is not a free improvement.

Steel grade

Element thickness15 mm

Web slenderness c/t60

Nominal strength for the grade: 355 N/mm²
Strength at this thickness: 355 N/mm²
Thickness reduction applied: no
ε = √(235/f_y): 0.814
Class 1 limit: 58.6
Class 2 limit: 67.5
Class 3 limit: 100.9
Element class: Class 2

Class 2: the plastic modulus W_pl may be used — though not plastic analysis, because the rotation capacity is limited.

Things worth trying

Fix c/t at 75 and raise the grade from S235 to S460. The element goes from Class 2 to Class 3 or worse with NO change of geometry. Stronger steel makes local buckling more likely — this is the single most counter-intuitive result in cross-section design.
Raise the thickness past 40 mm and watch two things happen at once: the usable strength falls, and ε rises so the limits get slightly more generous. The weaker steel is easier to classify, which is a small consolation.
Set the grade to S235 and note that ε = 1.000 exactly. S235 is the reference grade the limits were written for, which is why 235 appears in the formula at all.
Push c/t past the Class 3 limit. Nothing physically dramatic happens at that line — it is a calibrated design boundary, not the slenderness at which the plate actually buckles. What changes is which resistance you are allowed to claim.

Toughness: a different failure mode entirely

Everything so far has been about yielding. Toughness is about not yielding — about a crack running through material that never gets the chance to deform.

Brittle fracture needs three things at once:

1.A flaw — a notch, a crack, a sharp re-entrant corner, a weld defect.
2.Tensile stress across it.
3.Low toughness, which means low temperature, high thickness, or high strain rate.

Given all three, a crack can run across a member at close to the speed of sound, at a stress well below yield, with no warning and no visible deformation. It is not a ductile failure that happened quickly; it is a different mechanism.

Toughness is measured by a Charpy test — the energy absorbed breaking a notched specimen — and the striking feature is the transition. Above a certain temperature the specimen absorbs a lot of energy and tears; below it the specimen absorbs very little and snaps. The change happens over a few tens of degrees.

So steel is specified not only by strength but by a sub-grade: the J and K designations record the temperature at which a stated Charpy energy is achieved. Choosing a sub-grade is choosing where that transition sits relative to the coldest temperature the structure will see.

Where this stops working

Lamellar tearing is not a welding defect

Rolled steel is not isotropic. Rolling elongates the inclusions in the material into flat plates lying parallel to the surface, so the steel is measurably weaker and much less ductile in the through-thickness direction than along it.

Normally this never matters, because structural members are loaded along their length. It matters when a detail pulls through the plate thickness — most often a full-penetration weld onto the face of a flange, whose contraction as it cools applies exactly that pull.

The result is a step-like tear inside the parent metal, below the weld, following the rolled inclusions.

The important point is where the fault lies. The weld may be perfect. The problem is a DETAIL that loads the plate through its thickness, and the fixes are a designer's:

rearrange the detail so the force runs along the plate, not through it;
specify steel with proven through-thickness properties;
reduce the weld volume, and so the contraction, where the detail cannot change.

This is the module's first example of a theme that runs through the whole course: a design decision that is fine on paper can be unbuildable, or can create a failure mode that no calculation in the set will reveal.

Practice

A rolled section in S355 has residual compression at the flange tips of 0.25 f_y. At what applied stress do the tips first yield, in N/mm²?

Practice

A 70 mm thick S355 plate is used as a flange. Taking the reduced nominal strength as 335 N/mm², what is ε for classifying that flange?

Practice

Comparing S235 and S460, by what factor do the classification limits (which are multiples of ε) tighten?

Check yourself

Residual stresses in a rolled section sum to zero over the cross-section. Why do they still matter?

Summary

Residual stress comes from uneven cooling: early-cooling regions end in compression, late in tension
The pattern sums to zero, so the SQUASH load is unaffected
But the flange tips yield early, and they are the fibres that matter most about the minor axis
That is the physical content of the buckling curve selection table
Welding produces a far sharper pattern than rolling, hence a worse curve
Thicker product has a lower nominal yield strength — the grade name is not enough
Toughness is a separate failure mode: flaw plus tension plus low temperature
Lamellar tearing is a DETAILING fault, not a weld fault — the load runs through the plate thickness

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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