Structural Steel Design / Plate girders, built-up members and local effects

The girder, and the web it can afford

Depth is what carries moment, and depth is cheap in a welded girder. The price is a web too thin to behave like a plate in shear.

Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Corrections checked in this pass

Gross-section 6615 kNm no longer claimed as Class 4 resistance. Iterated effective compressed-web widths produce 5958.3 kNm for the stated conservative uniform fy=345 example. Lab computes this and uses thickness-dependent strength bands.

Checks needed for project use

A steel-design reviewer must check the first-generation calculation profiles, second-order analysis assumptions, connection rules and execution references against the applicable standards and amendments.
Selected standard edition and National Annex; flange effectiveness, shear lag, shear/moment interaction, patch loading, transverse/longitudinal stiffeners, welds and lateral stability. Helper is pure bending for a symmetric welded I-section with fully effective flanges.

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Why this matters

Rolled sections stop. The largest available is around a metre deep, and beyond that span or load a designer either uses several of them or welds plates into the shape that is actually wanted. The welded girder is startlingly efficient — the numbers below are better than most people expect. But the efficiency comes from making the web as thin as possible, and a thin web does something a rolled web never does: it buckles in shear, at a stress far below yield, and then carries on carrying load by a completely different mechanism.

By the end of this lesson you should be able to

Quantify what a plate girder buys over a rolled section
Say why the web can be so thin, and what that costs
Explain shear buckling and tension-field action physically
Read the effect of stiffener spacing and end-post detailing

What you should already know

Plate buckling and the (t/b)² dependence (Module 5)
Shear resistance and the shear-buckling threshold (Module 6)
Cross-section classification, and what a Class 3 or 4 web means (Module 5)
The relative-slenderness pattern λ̄ = √(resistance/critical) (Modules 7 and 8)

Why depth is worth so much

Second moment of area goes with the square of the distance from the neutral axis. Move a flange twice as far out and it contributes four times as much. A welded girder lets you choose that distance directly instead of accepting whatever the rolling mill produces.

The comparison in the worked example is the argument in one line: a 1550 mm deep girder weighing 275 kg/m has 44% more second moment of area than the largest rolled UB, which weighs 481 kg/m. More stiffness, on 57% of the steel.

And where does the material go? For that girder, the flanges supply 80% of the second moment of area while using 57% of the material. The web is not carrying much moment at all. Its job is to hold the two flanges apart and to carry shear — and since it is barely contributing to bending, there is no reason to make it thick.

So the designer makes it thin. On that girder the web is 1500 mm deep and 10 mm thick.

h_w/t_w = 150. That is not a plate you can push on.

The web buckles — and then does not fail

This is the part worth getting right, because it is genuinely surprising.

A web panel in shear is, at 45°, in tension along one diagonal and compression along the other. When the panel buckles, it is the compression diagonal that goes: it wrinkles out of plane and sheds its load.

The tension diagonal does not. Tension does not buckle.

So what forms is a band of tension running diagonally across the panel, anchored at its ends. The girder reorganises itself into a truss:

the tension field is a diagonal tie
the transverse stiffeners are the vertical posts
the flanges are the chords

The girder keeps carrying load, often a great deal more than the load at which the web first buckled. This is post-buckling reserve, and there is nothing like it in a column — a column that buckles is finished.

But the tension has to pull against something. At an internal stiffener the tension fields on either side balance each other. At the end of the girder there is nothing on the far side, so the end detail has to anchor the whole diagonal pull. A rigid end post — in effect a small vertical beam made of two stiffeners with the web between them — can do it. A non-rigid end-post arrangement has a different post-buckling resistance model; verify that model and its detailing rather than assuming the same benefit as a rigid post.

This is why the shear resistance of a girder depends on a detail at its very end that has nothing to do with the panel being checked.

Try it

Web thickness, stiffener spacing, end post

A 1500 mm deep web with 400 × 25 flanges, all S355. Three levers, and the mass alongside each so the comparison is fair. The reference case is a 10 mm web with stiffeners at 3 m and a rigid end post.

Web thickness10 mm

Stiffener spacing3.00 m

End post

Web thickness t_w: 10 mm
Web slenderness h_w/t_w: 150
Panel aspect a/h_w: 2.00
Shear buckling factor k_τ: 6.34
Critical shear stress τ_cr: 53 N/mm²
Web slenderness λ̄_w: 1.958
Reduction χ_w: 0.515
Shear resistance V_b,Rd: 1585 kN
Plastic resistance V_pl,Rd: 3074 kN
Available fraction: 52 %
Girder mass: 275 kg/m
Effective neutral-axis depth from top: 807.9 mm
Effective-web reduction: 0.668
Pure-bending effective section resistance: 5958 kNm
Gain over the reference: 1.00 ×
Extra mass over the reference: 1.00 ×
Worth of a rigid end post here: 22 %

λ̄_w = 1.96 gives χ_w = 0.515, so only 52% of the plastic shear resistance is available. The web buckled at τ_cr = 53 N/mm² against a shear yield of 205 — but it did not fail there, because a tension field formed. With a rigid end post that field can be anchored, and the resistance reflects it. Symmetric welded I-section, pure major-axis bending, fully effective flanges and uniform conservative strength input. Effective compressed-web widths are iterated with the neutral axis. Shear lag, axial force, shear interaction, lateral buckling, patch loading and stiffener checks are separate.

Things worth trying

Start at the reference: 10 mm web, 3 m stiffeners, rigid end post. 1585 kN against a plastic resistance of 3074 — only 52% is available.
Take the stiffener spacing to 1.5 m. The resistance rises to 1821 kN — 15% for twice as many stiffeners, and the girder's mass has not changed at all.
Put the spacing back to 3 m and take the web to 20 mm instead. 5214 kN, a factor of 3.3, for 1.4 times the mass. Web thickness is usually the better lever on a girder, and this is why.
Watch the available fraction as you thicken the web: 52% at 10 mm, 85% at 20 mm. The gain compounds, because the area and χ_w both improve.
Switch to a non-rigid end post at 10 mm. The resistance drops to 1303 kN — the tension field has nothing to pull against in the end panel.
Now switch the end post at 25 mm. Almost nothing happens, because at that thickness the web is stocky enough that there is no tension field to anchor. A rigid end post is worth a great deal on a slender web and nothing on a stocky one.
Take the stiffener spacing past 4.5 m and watch k_τ flatten out towards 5.34. Beyond about a/h_w = 3 there is nothing left for stiffener spacing to give.

Worked example

A 1550 mm welded girder in shear

Given

Web 1500 × 10 mm with fyw = 355 N/mm²; flanges 400 × 25 mm with fyf = 345 N/mm². Use conservative uniform fy = 345 N/mm² for the effective-section bending calculation.
Transverse stiffeners at 3.0 m centres
Rigid end posts
For stiffness comparison only, assume an unnamed reference member with I = 1 005 000 cm⁴ and mass = 481 kg/m. No rolled-section designation or availability claim is made.

Find

What the girder buys, and how much of its shear resistance survives.

Assumptions

Section properties computed from plate geometry — for a welded girder the weld fillets really are negligible, unlike the root radii of a rolled section
χ_w, k_τ and η are calibrated and unverified here
Pure major-axis bending with fully restrained compression flange, fully effective flange outstands, no axial force and negligible shear lag. Iterate the Class 4 web effective widths. The shear example is a separate resistance calculation; combined effects require their own check.

Predict first

The girder's web is thickened from 10 mm to 20 mm. The web area doubles. What happens to the shear buckling resistance?

Practice

A web is 1500 mm deep and 10 mm thick. What is h_w/t_w?

Practice

The web of that girder has τ_cr = 53.5 N/mm² and f_yw = 355 N/mm². What is λ̄_w? Take τ_y = f_yw/√3.

Practice

With χ_w = 0.515, what is V_b,Rd for a 1500 × 10 mm web in S355? Take γ_M1 = 1.0 and give the answer in kN.

Practice

The same girder has a non-rigid end post, giving V_b,Rd = 1303 kN instead of 1585 kN. By what percentage does the rigid end post increase the resistance?

Check yourself

What actually happens when a girder's web buckles in shear?

Summary

A welded girder puts the flanges where you want them — 44% more I than the largest UB at 57% of its weight
Its flanges carry 80% of the second moment on 57% of the material
So the web is made thin: h_w/t_w = 150 on the worked example
τ_cr goes with (t/h)², so this web buckles at 53.5 N/mm² against a shear yield of 205
λ̄_w = 1.96, χ_w = 0.515 — only 52% of the plastic shear resistance is available
But the web does not FAIL: a tension field forms and the girder acts as a truss
The tension field must be anchored — a rigid end post was worth 22%
Thickening the web from 10 to 20 mm more than TRIPLED the resistance, because χ_w improved too