Splitting and connectors

What this page computes

Three things in Section 8 that the dowel formulae do not answer:

• §8.1.4 — splitting under an inclined force, expressions (8.2)–(8.5);
• §8.1.5 — connections subjected to alternating forces;
• §8.9 and §8.10 — split ring and shear plate connectors, and toothed-plate connectors.

Splitting is a different question from Johansen

§8.2 answers "how much does one dowel carry". §8.1.4 answers something else entirely: "does the beam split before the dowels fail?"

It is a block failure of the timber between the connection and the loaded edge. Look at the formula:

\(F_{90,Rk} = 14\, b\, w \sqrt{\frac{h_e}{1 - h_e/h}}\)

Neither the number of fasteners nor their diameter appears anywhere. You can double the number of dowels and the splitting capacity stays exactly the same. Only the width, the depth, and how high the connection sits in the section matter.

The term under the root blows up as h_e → h: if the connection reaches close to the opposite edge, there is no block left to break away. Conversely, a connection placed low has a small h_e and everything below it can come apart.

Hence the cheapest fix when the check fails: move the fasteners up. At b = 120, h = 500 and h_e = 300 it gives F_90,Rk = 46,009 N; moving them to h_e = 400 jumps past 75,000 N, without adding a gram of steel.

The code gives (8.4) for softwood only. For hardwoods EN 1995 offers no splitting capacity at all.

Alternating forces are not checked against the raw maximum

§8.1.5(2) is short and easy to misread. For long or medium term actions alternating between F_t,Ed and F_c,Ed, the connection is designed for both combinations:

\((F_{t,Ed} + 0.5\,F_{c,Ed}) \qquad \text{and} \qquad (F_{c,Ed} + 0.5\,F_{t,Ed})\)

With F_t = 20 kN and F_c = 30 kN these give 35 kN and 40 kN — both above the raw maximum of 30 kN. The change of sign leaves slack and degradation behind, and the code charges half the opposite force for it.

§8.9 — two mechanisms, and which wins is not obvious

\(F_{v,0,Rk} = \min \begin{cases} k_1 k_2 k_3 k_4 \cdot 35\, d_c^{1.5} & \text{(a) crushing} \\ k_1 k_3\, h_e \cdot 31.5\, d_c & \text{(b) shear of the embedment} \end{cases}\)

The first grows with d_c^1.5 and does not depend on the embedment depth; the second is linear in d_c but proportional to h_e. For a 100 mm ring with h_e = 15 mm and ρ_k = 380, they give 38,000 N and 51,300 N — crushing governs. With a smaller h_e, it flips.

Three things worth remembering:

• The minimum thicknesses of §8.9(2) — 2.25·h_e for the outer member, 3.75·h_e for the inner — are the condition that fails most often, and no factor compensates for it.
• At an unloaded end with one connector per shear plane, §8.9(7) removes condition (a) entirely. Not a reduction — a deletion.
• k_4 = 1.1 for timber–steel joints: 10% free, simply because the steel plate does not crush.

n_ef for connectors is not what it is for dowels

For dowels, n_ef = n^{k_ef} — exponential. Here it is linear, and the first two connectors are not reduced at all:

\(n_{ef} = 2 + \left(1 - \frac{n}{20}\right)(n-2)\)

Careful: it is a downward parabola. It peaks at n = 11 with n_ef = 6.05, then decreases — at n = 20 it returns to 2, exactly what two connectors give.

Physically it is impossible for adding connectors to reduce the effective number; the formula is calibrated for rows of ordinary length. The page applies it literally, as the code gives it, but posts a note once you pass the peak. It is not silently capped: that would mean a value not in the code, and one on the unsafe side.

The practical conclusion: past about ten connectors in a row, split the row rather than lengthening it.

§8.10 — the capacities add up

§8.10(1) says something often missed: the capacity of a toothed-plate connection is the sum of the connector capacity and that of the bolt to §8.5. Not the larger, not an interpolation. Forget the bolt and you lose a real part of the joint — in the page's example, 9,000 N out of 28,543 N, close to a third.

The k₃ trap

Both clauses have a k₃ of the form ρ_k/350, but the cap differs: 1.75 in §8.9, 1.5 in §8.10. Same form, different cap — with dense timber the difference is real.

Likewise, both have an identically shaped k₁, but h_e means something different: the ring embedment depth in §8.9, the tooth penetration depth in §8.10.

What it does not cover

• §8.8 — punched metal plate fasteners. Expressions (8.56)–(8.60) require the constants γ₀, k_v and the strengths f_a,0,0,k determined by test, per product, to EN 14545. They cannot be computed generically; you would need the plate's technical data sheet.
• Tables 8.7 and 8.8 — minimum spacings and end/edge distances, which depend on the angle to the grain.
• §8.7 — axially loaded connections.
• The bolt's F_v,Rk — that comes from the dowel connections page.

The texts of §8.1.4, §8.1.5, §8.9 and §8.10 are transcribed from EN 1995-1-1:2004, pages 58–59 and 79–82.

Related calculations

• Dowel-type connections — Johansen's theory, minimum spacings and n_ef for dowels.
• Tapered and curved beams — §6.4, where perpendicular-to-grain tension decides instead.
• Timber member — the basic section checks.