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Design of a nailed timber lap joint

A tension member 50 mm × 150 mm carries a working tensile load of 9 kN. It is connected by a single lap joint to a similar member using 4 mm diameter round wire nails driven in single shear. The safe lateral load per nail is 0.42 kN and the permissible tensile stress parallel to grain is 7.5 N/mm². Find the number of nails, show a suitable layout (use spacing 10d10d along grain, 5d5d across grain, end distance 15d15d, edge distance 5d5d) and check the net tension in the member.

Given data

Load P=9P = 9 kN, d=4d = 4 mm, safe load per nail =0.42= 0.42 kN, member 50×15050 \times 150 mm, σt=7.5\sigma_{t} = 7.5 N/mm².

Number of nails

n=90.42=21.4  ⇒  provide 24 nails (6 rows×4 columns)n = \frac{9}{0.42} = 21.4 \;\Rightarrow\; \text{provide } 24 \text{ nails (6 rows} \times 4 \text{ columns)}

24 nails give a symmetrical arrangement.

Layout

Minimum distances: along grain 10d=4010d = 40 mm; across grain 5d=205d = 20 mm; end 15d=6015d = 60 mm; edge 5d=205d = 20 mm.

  • Across the 150 mm width: 6 rows with edge distance 20 mm each side, so spacing =(150−40)/5=22= (150 - 40)/5 = 22 mm >20> 20 mm. OK.
  • Along the grain: 4 columns at 40 mm pitch, so lap length ≥60+3×40+60=240\geq 60 + 3 \times 40 + 60 = 240 mm. Provide a lap of 250 mm.
  <-60->|<-40->|<-40->|<-40->|<-60->
  +--------------------------------+  ^
  |   o      o      o      o       | 20
  |   o      o      o      o       | 22
  |   o      o      o      o       | 22     50x150
  |   o      o      o      o       | 22     member
  |   o      o      o      o       | 22
  |   o      o      o      o       | 22
  +--------------------------------+ 20
      Lap length = 250 mm

Check of net tension

Net section is reduced by one row of nail holes (6 holes). Conservatively the holes are deducted fully:

Anet=50×150−6×(4×50)=7500−1200=6300 mm2σt=90006300=1.43 N/mm2<7.5 N/mm2\begin{aligned} A_{net} &= 50 \times 150 - 6 \times (4 \times 50) = 7500 - 1200 = 6300\ \text{mm}^2 \\ \sigma_t &= \frac{9000}{6300} = 1.43\ \text{N/mm}^2 < 7.5\ \text{N/mm}^2 \end{aligned}

The member is safe in tension. The joint is also checked so that the nail length gives penetration of at least 10d=4010d = 40 mm into the second member.

Answer: 24 nails of 4 mm diameter (6 rows × 4 columns), lap length 250 mm; net tension 1.43 N/mm² < 7.5 N/mm², safe.

✓ Answer checked by Claude Sonnet 5.5

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