Structural Steel Design / Connection and joint design

The T-stub, and the three ways it fails

Almost every bolted joint contains a piece of plate that bends to deliver tension into a bolt. One model covers all of them, and its three failure modes are derivable.

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

Mode 1 was a false-positive arithmetic warning: original Q=Mpl/n per side satisfies equilibrium. Per-side/total forces now distinguished; mode 2 no longer proves plastic rotation capacity.

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.
Effective lengths and row groups for actual geometry, support flexibility, bolt elongation, prying applicability, welds and rotation capacity.

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

An end plate, a column flange, an angle cleat, a base plate — they look like different details and they behave identically. Each is a piece of plate that bends, and each delivers its load into bolts that are trying to hold it flat. Reducing all of them to one model is what makes joint design tractable, and it also explains prying, which otherwise looks like an arbitrary penalty. The three failure modes fall out of statics, and one of them matters far more than its resistance suggests: it is the only one that gives any warning.

By the end of this lesson you should be able to

Recognise the T-stub in several details that look unrelated
Derive its three failure modes
Explain prying from equilibrium
Say which mode to aim for, and what it costs

What you should already know

Bolts in tension and the punching check (Module 12)
Prying as a mechanism (Module 12)
Plastic hinges and the plastic moment of a rectangular section (Module 6)
Work equations for a collapse mechanism — the Structural Analysis Fundamentals course covers this

One model, several details

A T-stub is a length of flange, bolted to something stiff, pulled by a web. Nothing else.

Once you look for it, it is everywhere:

Detail	The flange is…	The web is…
Bolted end plate	the end plate	the beam flange
Column flange in bending	the column flange	the column web
Angle cleat in tension	the outstanding leg	the bolt line to the beam
Column base plate	the base plate	the column flange

Each is a plate bending between a stiff line where the load arrives and a bolt that is trying to hold it down. The lever arm from the bolt to the web face is m, and the distance from the bolt to the free edge is n. Those two dimensions, the plate thickness and the bolt strength decide everything.

The one piece that does not come from statics is the effective length — how much of a real plate acts as an equivalent T-stub, when the yield lines can spread sideways, run round a bolt, or be cut off by an edge. That is a yield-line result, it is code-calibrated, and this course takes it as an input rather than tabulating it.

From first principles

The three T-stub failure modes

We want to show: Derive the resistance of a T-stub in each of its three modes, and see why one of them is the only one that gives warning.

Pull the web of a T-stub upwards. Either the flange is weak and bends into a mechanism while the bolts hold, or the flange is strong and the bolts break, or something in between — the flange bends enough to form one hinge and lever its own edge against the support, which loads the bolts harder than the applied force does. Those three pictures are the three modes, and the arithmetic of each is short.

Try it

The three T-stub resistance modes

An equivalent T-stub with assumed fy = 355 N/mm² and effective length 200 mm. The solid bar identifies the governing resistance model; rotation capacity is a separate check.

Flange thickness15 mm

Bolt to web face, m45 mm

Bolt to plate edge, n50 mm

Bolt resistance ΣF_t,Rd282 kN

Plastic moment M_pl: 3.99 kNm
Mode 1, flange yields: 355 kN
Mode 2, flange and bolts: 233 kN
Mode 3, bolts alone: 282 kN
Governing mode: 2
Resistance F_T,Rd: 233 kN
Prying force: 24.8 kN
Force in each bolt: 141.0 kN
Rotation capacity: Requires separate verification

Mode 2 governs at 232.5 kN. Each symmetric side carries 141.0 kN in the bolts and 24.8 kN at the edge contact. Mode 1 involves flange yielding; modes 2 and 3 involve bolt failure. Rotation capacity is not established by this mechanism calculation.

Things worth trying

At the default15 mm thickness, mode2 gives232.5 kN. Each symmetric bolt side carries141 kN including24.75 kN prying.
At8 mm, mode1 gives100.98 kN; each side carries73.21 kN, including22.72 kN prying.
Increasing thickness can move the governing mechanism towards bolt failure. This does not establish a rotation capacity.
The effective length and input strengths must represent the actual detail. Nominal grade alone is not a strength value for every thickness.

Worked example

An end plate T-stub, thickness by thickness

Given

Equivalent T-stub of effective length 200 mm in S355
Two M20 grade 8.8 bolts, F_t,Rd = 141.1 kN each, so ΣF_t,Rd = 282 kN
m = 45 mm from the bolt to the web face, n = 50 mm to the plate edge
γ_M0 = 1.0

Find

How the resistance and the failure mode change with the plate thickness.

Assumptions

l_eff is a calibrated yield-line result and is given, not derived
n is capped at 1.25m = 56.25 mm, so the full 50 mm counts here
The column flange the plate bolts to is assumed rigid

Predict first

A T-stub governed by mode 3 at 282 kN needs more resistance. The plate is thickened from 20 mm to 30 mm. What happens?

Practice

An equivalent T-stub flange is 200 mm long and 15 mm thick in S355. What is its plastic moment, in kNm? Take γ_M0 = 1.0.

Practice

With M_pl = 4.0 kNm and m = 45 mm, what is the mode 1 resistance in kN?

Practice

With M_pl = 4.0 kNm, m = 45 mm, n = 50 mm and ΣF_t,Rd = 282 kN, what is the mode 2 resistance in kN?

Practice

In that mode 2 case the prying force is 24.8 kN and each bolt takes half the 233 kN. What total force does each bolt carry, in kN?

Check yourself

Why is mode 1 the mode to aim for, despite giving the lowest resistance?

Summary

A T-stub is a flange bending between a web and a bolt — end plates, column flanges, cleats, base plates
Mode 1 = 4M_pl/m, from a four-hinge work equation. The bolts do not appear
Mode 2 = (2M_pl + nΣF_t,Rd)/(m+n), from equilibrium with prying
Mode 3 = ΣF_t,Rd. The flange does not appear
Prying is a consequence of the flange bending, not a code penalty
In mode 2 the bolt force comes out at exactly F_t,Rd — a free consistency check
15mm gives232.5kN in mode2;20mm reaches the282kN bolt limit; verify rotation separately
l_eff is a calibrated yield-line result and is the one piece not derived here