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Connections with metal dowel-type fasteners

Lateral load-carrying capacity by Johansen's theory — nails, screws, bolts and dowels, EN 1995-1-1 §8.2.

Configuration
Expression (8.6), six failure modes: a, b without yielding of the fastener; c with rotation; d, e with one plastic hinge; f with two. Rope effect cap for this type: 25% of the Johansen term — §8.2.2(2).
Geometry
For single shear: t₁ = thickness of the outer member, t₂ = penetration depth. For double shear: t₁ = outer member, t₂ = central member. Figure 8.4.
Materials
The characteristic densities of the two members. The ratio of embedment strengths gives β, expression (8.8). For C24, ρ_k = 350 kg/m³. It enters through k_90, expressions (8.31) and (8.33). For nails under 8 mm it has NO effect: expression (8.15) does not contain the angle.
Rope effect
0 = the rope effect is taken as ZERO, as the text of §8.2.2(2) requires when the value is unknown. The contribution is F_ax,Rk/4, capped by a percentage depending on the fastener type.
Fastener layout
The number of fasteners in a row along the grain. They do NOT load equally, which is why the code replaces this with a smaller effective number.
The distances you have provided. 0 = not entered, so not checked. a₁ also feeds n_ef; if left blank the code minimum is used.
§8.3.1.1(8): if the nails in a row are staggered perpendicular to the grain by at least 1d, the n_ef reduction does NOT apply at all. A few millimetres of offset can recover half the capacity. Only for the pre-drilling requirement, expressions (8.18) and (8.19). 0 = not checked.

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Tool information

What this page computes

The lateral load-carrying capacity of a connection with metal dowel-type fasteners — nails, screws, bolts or plain dowels — to EN 1995-1-1:2004, §8.2, Johansen's theory. Seven configurations: timber-to-timber with one or two shear planes, plus five steel-to-timber variants.

It is not a formula, it is a competition between mechanisms

This is the thing to understand before any number. The fastener and the timber fail together, and the capacity is the minimum of several mutually exclusive modes:

  • crushing of the timber, with no yielding of the fastener — modes a, b, g, h;
  • crushing plus one plastic hinge in the fastener — d, e, j;
  • two plastic hinges, the fastener bending into an S — f, k.

Which one wins depends on the slenderness of the fastener. A thick fastener in thin timber crushes the timber; a thin fastener in thick timber bends.

That is why the page shows all the modes, not just the result. The governing mode tells you what to change:

  • crushing governs → increase the timber thickness or density; the diameter helps little;
  • bending governs → increase the diameter or the fastener strength; timber thickness no longer helps.

The comparison also shows how close the next mode was. If the second is within a few percent, the result is sensitive to material variation.

The rope effect and its caps

The second term in each expression, \(F_{ax,Rk}/4\), comes from a concrete phenomenon: the bent fastener stretches and pulls its ends towards each other, compressing the timber between them and increasing friction.

The code caps it as a percentage of the Johansen term, and the caps differ sharply by type — §8.2.2(2):

fastener cap
round nails 15 %
square nails 25 %
other nails 50 %
screws 100 %
bolts 25 %
plain dowels 0 %

Plain dowels get zero because they have neither thread nor head — they cannot grip the timber and pull. Screws get everything, because their thread genuinely holds.

Two details that matter in implementation: the cap applies to each mode separately, as a percentage of that mode's Johansen term, not to the final minimum. And pure crushing modes get no contribution at all — the fastener does not bend, so it does not stretch, so it does not pull.

If \(F_{ax,Rk}\) is unknown, the code states explicitly that the influence is taken as zero. The page does that, and says so.

Embedment strength — two different regimes

For nails under 8 mm, expression (8.15) without pre-drilling and (8.16) with. Neither contains the angle to the grain: for thin nails the grain direction does not matter.

For bolts, dowels and nails over 8 mm, expressions (8.31)–(8.33) do contain the angle, through \(k_{90}\).

Here is a value that surprises. For hardwood, \(k_{90} = 0.90 + 0.015d\) — so less than one below 6.7 mm diameter. That means embedment perpendicular to the grain comes out stronger than parallel. Counter-intuitive, but that is what (8.33) says.

And a requirement that gets missed: §8.3.1.1(2) requires pre-drilling if the characteristic density is at least 500 kg/m³, or if the nail diameter exceeds 8 mm. The page flags when the calculation used the non-pre-drilled expression although the code required otherwise.

How many fasteners actually work

\(F_{v,Rk}\) is for one shear plane and one fastener. The row capacity is not \(n \cdot F_{v,Rk}\) but \(n_{ef} \cdot F_{v,Rk}\) — because in a row parallel to the grain the fasteners do not load equally: the first takes more, and the timber between them splits progressively.

For nails, expression (8.17) gives \(n_{ef} = n^{k_{ef}}\), with \(k_{ef}\) from Table 8.1. The reduction is exponential, so the consequence is brutal: 10 nails at \(a_1 = 7d\) give \(10^{0.7} = 5.01\). Half the nails do not count. And the longer the row, the lower the efficiency — doubling the number of nails does not double the capacity.

There is a complete escape, though: §8.3.1.1(8) states that if the row is staggered perpendicular to the grain by at least \(1d\), the reduction does not apply at all. A few millimetres of offset recover half the capacity — probably the best effort-to-gain ratio in the whole of section 8.

For bolts, expression (8.34): \(n_{ef} = \min\left(n,\ n^{0.9}\sqrt[4]{a_1/13d}\right)\).

And one thing that gets missed: perpendicular to the grain there is no reduction at all, \(n_{ef} = n\) by (8.35). The same connection rotated by 90° carries more. Between 0 and 90° it interpolates linearly.

Minimum spacings — a different check, a different failure mode

Failing the spacings does not reduce the capacity computed above. It produces splitting — a brittle failure mode that appears nowhere in Johansen's expressions. That is why it is a separate check, and when a spacing fails, the capacity result becomes irrelevant until it is corrected.

Table 8.2, for nails, has three columns — no pre-drilling below 420 kg/m³, no pre-drilling between 420 and 500, pre-drilled — and some rows branch further by diameter below or above 5 mm. Table 8.4, for bolts, is simpler, but \(a_{3,c}\) has a plateau between 150° and 210° where it is constantly \(4d\).

Each spacing has an angle range in which it applies: the loaded and unloaded ends exclude one another, and so do the edges. The page computes all six and marks those that do not apply at the given angle.

Pre-drilling is mandatory by three independent routes: density from 500 kg/m³, diameter above 8 mm, or timber thickness below the threshold of (8.18) — or (8.19) for splitting-sensitive species (fir, Douglas fir, spruce), where the threshold is exactly double.

What it does not cover

  • Splitting under an inclined force — §8.1.4, with expression (8.4).
  • Punched metal plate fasteners (§8.8) and ring or toothed-plate connectors (§8.9–8.10).
  • Axially loaded connections — the page gives the lateral capacity; withdrawal enters only as \(F_{ax,Rk}\), as an input.
  • Checking the steel plate in steel-to-timber connections, required explicitly by §8.2.3(2).

Expressions (8.6)–(8.16) and (8.30)–(8.33) are transcribed from EN 1995-1-1:2004, pages 59–71, and each has a test that reproduces it by hand.

  • Timber member — the section checks that precede the connection.
  • Deflections — where slip in the connections contributes to the total deformation.
  • Floor vibration — the other serviceability check.
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