Shear between web and flange — EN 1992-1-1 §6.2.4

What this page computes

The page checks the junction between the web and the flange of a T or L section, to EN 1992-1-1 §6.2.4. It gives the shear stress in the plane of the junction, the transverse reinforcement required in the flange, and checks the compression struts.

Why it is a separate check

In a T section the flange takes part in bending — it carries compression (or tension, if it lies on the tension side). But the force in the flange does not appear there by itself: it has to be transferred from the web, through the vertical plane of the junction.

This is shear in a completely different plane from ordinary shear to §6.2.2/6.2.3, which acts in the horizontal plane of the section. A member can pass the shear check comfortably and still fail at the junction — particularly with wide, thin flanges, exactly the case of slabs cast monolithically with the beams, where the slab acts as flange and is 120–180 mm thick.

It is the check most often forgotten, because it does not sit next to the others in the design flow.

The shear stress

\(v_{Ed} = \frac{\Delta F_d}{h_f \, \Delta x}\)

ΔF_d is the change in longitudinal flange force over the length Δx, obtained from the bending moment diagram: ΔF_d = ΔM/z.

Δx is not free to choose. The code limits it to half the distance between the point of zero moment and the point of maximum moment; and where concentrated loads act, to the distance between loads. Too large a Δx spreads the same force over a greater length and underestimates v_Ed.

The two checks

The code requires two distinct things, resolved in different ways:

\(\frac{A_{sf}}{s_f} \ge \frac{v_{Ed} \, h_f}{f_{yd} \cot\theta_f} \qquad\text{(6.21)}\)

\(v_{Ed} \le \nu f_{cd} \sin\theta_f \cos\theta_f \qquad\text{(6.22)}\)

The first gives the reinforcement. The second limits the stress in the compression struts within the flange.

The distinction matters in practice: if the second fails, reinforcement does not help. The concrete crushes before the steel yields, so the answer is a thicker flange, a higher concrete class, or a smaller cot θ_f.

The range of θ_f differs between compression and tension flanges

From the NOTE below (6.22):

This is not a subtlety. In a tension flange, cracking reduces the ability of the struts to incline — a shallow strut would have to cross many cracks, and transfer across them is unreliable. Hence the narrower range.

The ratio of the maximum cot values is 2.0/1.25 = 1.6. So using the compression-flange range on a tension flange underestimates the reinforcement by 37%, on the unsafe side. The page caps automatically within the range for the selected state and says when it had to.

Choosing θ_f is a trade-off in both directions

A large cot θ_f (shallow strut) reduces the reinforcement — the shear is distributed over a greater length. But it also lowers the strut limit, because sinθ·cosθ is greatest at 45°, that is at cot θ_f = 1.

The page defaults to the maximum permitted value, the one giving the least reinforcement. If the strut check fails, lowering cot is the first thing to try — at the cost of more bars.

Combination with transverse bending

Clause (5): if the flange is also bent transversely — the usual case of a floor slab serving both roles — the reinforcement is taken as the greater of:

• A_sf from (6.21), or
• half of A_sf plus the area required for transverse bending.

The page reports which of the two governed. Otherwise it is not visible what determined the result.

The threshold below which nothing extra is needed

Clause (6): if v_Ed ≤ k·f_ctd, with k = 0.4 recommended, no reinforcement beyond that for bending is required. The page shows the threshold alongside the stress, and says explicitly when it governs — the reinforcement values stay visible for comparison.

What it does not cover

• Deriving ΔF_d from the moment diagram — it is an input, not a result.
• Shear along construction joints (§6.2.5), which is a different mechanism, with roughness coefficients.
• Ordinary web shear (§6.2.2 and §6.2.3) — see the RC section page.
• Anchorage of the longitudinal flange reinforcement, required by clause (7): it must be anchored beyond the strut that carries the force back to the web. The check here gives the transverse reinforcement, not the anchorage of the longitudinal bars.

Expressions 6.20–6.22 and clauses (5)–(7) are transcribed from SR EN 1992-1-1:2004, page 84, and each expression has a test that reproduces it by hand.