Notches and axial fasteners

What this page computes

• §6.5 — beams notched at supports, expressions (6.60)–(6.63), plus §6.6 system strength;
• §8.7.2 — axially loaded screws, expressions (8.38)–(8.41) and Table 8.6;
• §8.3.2(7)–(8) — the penetration factor for nails;
• §8.3.3 / §8.7.3 — the axial–lateral interaction, expressions (8.27) and (8.28).

A notch costs far more than the material it removes

Intuition says: "I cut away 25% of the depth, I lose 25%." No.

For a 120×400 beam with h_ef = 300 (so α = 0.75), a square notch on the support side, solid timber:

The loss compounds: the stress is computed on the reduced depth and the strength is multiplied by k_v. Less than a third of the capacity survives.

The physical reason is a crack starting at the inner corner of the notch and running along the grain. That is why the slope of the transition zone, i, appears in the formula — it enters as i^1.5, so tapering helps, but with diminishing returns. And that is why the diagram marks the corner explicitly: k_v is not an abstract coefficient, it is a crack with somewhere to start.

The asymmetry that surprises

§6.5.2(2) gives k_v = 1.0 for a notch on the side away from the support. The same cut, moved to the other face, costs nothing at all.

This is not an oversight: there the crack would have to open against the compression from the bearing. The practical consequence is immediate — if you are free to choose the face, choose the top one.

§8.7.2 — three things you would not guess

\(F_{ax,\alpha,Rk} = n_{ef}\,(\pi\, d\, l_{ef})^{0.8}\, f_{ax,\alpha,k}\)

The exponent 0.8 applies to the product, not to each factor. Doubling l_ef buys 2^0.8 = 74%, not 100%. A screw twice as long does not carry twice as much.

f_ax,k is the strength across the grain. At α = 0° — a screw driven into end grain — the denominator of (8.39) becomes 1.5, so the capacity drops to two thirds. Withdrawal from end grain is the weak case, and it is exactly the configuration you reach when fixing a beam to a plate.

n_ef = n^0.9 — unlike expression (8.71) for split ring connectors, this one increases for every n and never turns back.

The code also requires the threaded part to penetrate at least 6d, and the head pull-through capacity to be determined by test to EN 1383 — that one is not computed here.

The minimum penetration is not a threshold above which things "work"

The most counter-intuitive result in §8.3.2(7). For smooth nails the code requires t_pen ≥ 8d. But below 12d the withdrawal capacity is multiplied by:

\(\left(\frac{t_{pen}}{4d} - 2\right)\)

At exactly t_pen = 8d the factor is zero. Not "small" — zero. The capacity ramps from 0 to 1 over 8d…12d.

For threaded nails, the same pattern: minimum 6d, factor (t_pen/2d − 3), which also vanishes at the minimum and reaches 1 at 8d.

In other words: the minimum penetration is where capacity starts to count, not a value acceptable in design. A nail at exactly 8d carries nothing axially, according to the code.

Linear versus quadratic — a difference that is not marginal

§8.3.3 gives two interaction expressions:

\(\frac{F_{ax,Ed}}{F_{ax,Rd}} + \frac{F_{v,Ed}}{F_{v,Rd}} \le 1 \qquad (8.27) \text{ — smooth nails}\)

\(\left(\frac{F_{ax,Ed}}{F_{ax,Rd}}\right)^2 + \left(\frac{F_{v,Ed}}{F_{v,Rd}}\right)^2 \le 1 \qquad (8.28) \text{ — everything else, screws included via §8.7.3}\)

At two ratios of 0.5, the first gives exactly 1.000 — the joint is at its limit. The second gives 0.500 — half the reserve untouched. Same forces, same timber; only the fastener type differs.

The page plots both curves and the current point against each, so you can see what you gain.

System strength — §6.6

k_sys = 1.1 for similar equally spaced members connected by a lateral system able to transfer load to the neighbours.

For laminated deck panels the values come from Figure 6.12, not from an expression. Both curves are straight lines between (1; 1.0) and (8; cap) — 1.1 for nailed or screwed laminations, 1.2 for prestressed or glued ones — and the endpoints fall on gridlines, so the reading is unambiguous. The values are shown as such, so they can be checked against the drawing.

What it does not cover

• The head pull-through capacity of the screw — §8.7.2(6)P refers it to EN 1383 testing.
• §8.5.2 — axially loaded bolts, where the washer and the bearing under it come in.
• §6.5.1 — stress concentrations at notches away from supports, distinct from the support notch.
• Reinforcement of the notch, which is the usual answer once α drops below 0.5.

The texts of §6.5, §6.6, §8.3.2, §8.3.3 and §8.7.2 are transcribed from EN 1995-1-1:2004, pages 51–52, 67–69 and 74.

Related calculations

• Dowel-type connections — lateral capacity, Johansen's theory.
• Splitting and connectors — §8.1.4, §8.9, §8.10.
• Timber member — the shear check on the full section.