Module 5 · Lesson 5.2

The four classes, and what a section is allowed to do

Classification is not a property of a section. It is a property of a section carrying a particular thing, and the same beam can be Class 1 in bending and Class 4 in compression.

Why this matters

The class decides which section modulus you may use, and therefore how much of the section you have paid for is actually available. It also decides whether plastic analysis is permitted at all. Getting it wrong is not a small error — the difference between Class 2 and Class 4 on the same section can be a third of its bending capacity.

By the end of this lesson you should be able to

State what each of the four classes permits
Classify a section plate by plate under a stated action
Show that the same section classifies differently in bending and compression
Compute the effective width of a Class 4 plate and say what has been lost

What the four classes mean

The classes are defined by behaviour, not by geometry. The c/t limits are how that behaviour is identified in practice.

Class 1. The section reaches its plastic moment AND can rotate at it while local buckling stays away. This is the only class for which plastic global analysis is permitted, because a plastic hinge has to rotate.

Class 2. The section reaches its plastic moment but cannot hold it through much rotation. So W_pl may be used for the section's resistance, while the global analysis must remain elastic.

Class 3. The extreme fibre reaches yield, and local buckling arrives before yielding can spread through the depth. Only W_el may be used — the reserve between first yield and the plastic moment is not available.

Class 4. Local buckling arrives before even first yield. Part of the compressed plate must be discounted, and effective section properties used.

The section takes the worst class of any of its plates. One slender element is enough, because that is the one that will buckle.

And this is the part people get wrong

A section does not have a class. Classification depends on the stress distribution on each plate, and that depends on what the section is carrying.

A web in bending has only its top half in compression, and the tension half stabilises it — so it tolerates a c/t of up to 124ε. The same web in pure compression is compressed over its whole depth, with nothing stabilising it, and the limit falls to 42ε.

That is a factor of three, on the same piece of steel. Asking "what class is this section?" is not a well-formed question until you say what it is carrying.

Worked example

One section, two actions, two different classes

Given

Welded I section: 600 mm deep, 200 mm wide, 8 mm web, 15 mm flanges
S355 steel, so ε = √(235/355) = 0.814
Considered first in major-axis bending, then in pure compression

Find

The class in each case, and which plate governs.

Assumptions

Welded, so no root radii — the clear widths are the plate dimensions
The class limits are code-calibrated and are not verified in this course

Try it

Classify this section

Each plate is classified separately, and the section takes the worst. Change what the section is CARRYING without touching a single dimension, and watch the class move.

What is it carrying?

Steel grade

Depth h600 mm

Flange width b200 mm

Web thickness t_w8 mm

Flange thickness t_f15 mm

Steel grade and f_y: S355, 355 N/mm²
ε = √(235/f_y): 0.814
Flange outstand c/t: 6.4
Web c/t: 71.3
Governing plate: Web (internal element)
SECTION CLASS: Class 3
Modulus that may be used: elastic
Plastic analysis permitted?: no

Class 3, governed by the web (internal element). The section takes the WORST class of any of its plates — one slender element is enough, because that is the one that will buckle. Note that the class limits are code-calibrated design boundaries, not the slenderness at which a plate physically buckles. Use W_el. The extreme fibre can reach yield, but local buckling arrives before the section can spread yielding through its depth — so the reserve between first yield and the plastic moment is not available.

Things worth trying

Start with the defaults in bending, then switch to pure compression WITHOUT touching a dimension. The web limits collapse from 72/83/124 ε to 33/38/42 ε and the class falls, because in bending only half the web is compressed and the tension half stabilises it.
Now change the grade from S355 to S235 in bending. The section improves — often by two whole classes — because every limit is a multiple of ε and weaker steel gets more generous limits. Stronger steel makes local buckling MORE likely.
Thicken the web by 2 mm. The web c/t falls in direct proportion and the class can jump immediately. Web thickness is the cheapest lever on classification there is.
Make the section deeper without thickening the web. The class deteriorates — depth is bought at the cost of web slenderness, which is exactly why deep plate girders are routinely Class 4.
Widen the flange without thickening it. Watch the flange outstand approach its limit while the web is untouched. The section takes the WORST plate, so one slender element is enough.
Get the section into Class 4 in compression and read the effective width. A fifth or more of the web can be discounted, and that material is present in every other respect — weight, cost, paint area — while carrying nothing.

Predict first

The 600 × 200 × 8 × 15 section above is Class 3 in bending when made of S355. What class is the same section in S235?

Class 4: discounting what has buckled

A Class 4 plate has buckled before reaching yield. It has not collapsed.

What happens is that the middle of the plate — furthest from the supported edges — drops out of the load path, while the strips near the edges carry on. The plate behaves as though it were narrower than it is. That is post-buckling reserve, and it is real: a buckled plate goes on carrying load, just not across its whole width.

So a Class 4 section is designed using an effective width: part of the compressed plate is removed from the calculation, and the resulting effective section is used for area and section modulus.

The idea is mechanics. The reduction factor

ρ = [λ̄_p − 0.055(3 + ψ)] / λ̄_p²

is calibrated — the form has a rational ancestry but the coefficients are fitted.

Two consequences worth carrying:

The effective centroid moves. Removing material from one part of the section shifts the neutral axis, which introduces a moment under what was supposed to be pure axial load. This catches people out.
Class 4 is a signal, not just a calculation. A section that classifies as Class 4 is being asked to do work that a thicker plate should be doing. Sometimes that is the right answer — plate girders are routinely Class 4 in the web — but it is always worth asking whether it was intended.

Worked example

How much of that web is actually working?

Given

The same welded section: 570 mm web, 8 mm thick, in pure compression
S355, ε = 0.814
Class 4, as established above

Find

The effective width of the web, and what has been lost.

Assumptions

Uniform compression across the web, so ψ = 1
k_σ = 4.0 for an internal element in uniform compression
The reduction factor is code-calibrated

Practice

A welded I section has a 500 mm deep web, 10 mm thick, with 20 mm flanges. What is the web's c/t ratio?

Practice

That web is in S355 (ε = 0.814) and the section is in pure BENDING. The Class 2 limit for an internal element in bending is 83ε. What is the limit, and does the web pass it?

Practice

The same web in pure COMPRESSION. The Class 3 limit for an internal element in compression is 42ε, with ε = 0.814. What is the limit?

Check yourself

What does a Class 3 section lose compared with a Class 2 one?

Summary

Class 1: plastic moment plus rotation — the only class allowing plastic analysis
Class 2: plastic moment, limited rotation — W_pl for resistance, elastic analysis
Class 3: first yield only — W_el, losing about 13% on an I section in major-axis bending
Class 4: buckles before first yield — effective properties, part of the section discounted
The section takes the WORST class of any of its plates
A section has no class until you say what it carries — bending and compression differ by a factor of three on the same web
A lower grade gives MORE generous limits, and can move a section from Class 3 to Class 1
Never write a class on a schedule without the action it applies to

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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