# Strength of Finger Joints

State of stresses in a finger joint subjected to bending was presented by Tomusiak (1988), specifying the relationship of tangential stresses in the glue-line from the value of bending moment caused by concentrated force. From the point of view of the constructor, it is also necessary to take into account the effect of tangential

stresses, whose distribution, for the purposes of the calculations below, was brought to the form of a triangle (Fig. 6.80).

Vectors of stresses Sa and Qa constitute the sum of vectors of tangential stresses rsa, tq and vectors of normal stresses osa, oQ, whereas in points A and A’ stresses Sk=1 = Smax, and Qk=4 = Qmin = 0, and in point B stresses Sk=4 = Smin = 0, and

Qk=1 = Qmax. Stresses on the surface of the glue-line A = bh(1/sin a) can be reduced to the form of concentrated forces Pk and Rk. Their values are expressed by the equations:

where

n — 2k — 2

a ;

n = H/h, (6.211)

k < n/2, (6.212)

b, H dimensions of the cross section of the beam, h scale of finger joints,

a angle of inclination of the side of the finger joint.

Resultant vector of all forces Pk and Rk is the sum of component vectors:

In order to determine the values of the stress та caused by bending moment, the moment of external forces should be compared with the moment of the two forces Wp:

4 bH2 _ PL

3 a n sin a 4 ’

where

P external force,

L spacing between supports of the bent beam.

Because tangential stresses in general form can be expressed by the equation,

(6.216)

expression determining the value of tangential stresses at any point k of the glue-line, caused by bending moment, will therefore take the form:

And tangential stresses tq caused by cutting forces are described by the equation:

sin a cos a

bH

 Fig. 6.81 Load schemes, taking into account the load-carrying capacity of the nail for pulling: a axial load, b load at an angle to the axis of the nail, c load causing bending and pulling nails

where

d nail diameter,

l working length of the nail, and it has to be assumed that l < 12d for nails with smooth cores and l > 8d for other types of nails,

kmod, t/h,1,k

f1d = ; (6.224)

Ум

f2d = fcmod-fh-2-k ; (6.2245)

Ум

fh,1,k = (18 x 10-6)p2, (6.226)

fh,2,k = (300 x 10-6)p2, (6.227)

pk density of wood,

kmod partial modification coefficient (Table 6.5), yM partial safety coefficient (Table 6.6).

There are general rules for selecting the diameter of nails, which recommend using connectors with diameters from 1/6 to 1/11 of the thickness of the thinnest of the joined elements. To join elements made of hard fibreboard and plywood with a thickness of 8 mm, it is recommended to use nails with a diameter of 2-4 mm, and for chipboards with a thickness of up to 25 mm, it is recommended to use nails with a diameter of 2.5-5.0 mm.

When choosing the length of the nail, the necessary depth of setting of the connector should be taken into account, assuming additionally 1 mm for each connection of joined elements and 1.5 of the nail diameter that corresponds to the length of its sharp end (Fig. 6.82).

Table 6.5 Values of the coefficient kmod (PN-B-03150:2000)

 Material/class of load duration Class of use 1 2 3 Hard wood, glued from layers, plywood Permanent 0.60 0.60 0.50 Long term 0.70 0.70 0.60 Medium term 0.80 0.80 0.70 Short term 0.90 0.90 0.80 Momentary 1.10 1.10 0.90 Chipboards (PN-EN 312-6:2000), Oriented Stress Boards class 3, 4 (PN-EN 300:2000) Permanent 0.40 0.40 Long term 0.50 0.50 Medium term 0.70 0.70 Short term 0.90 0.90 Momentary 1.10 1.10 Chipboards (PN-EN 312-4:2000, PN-EN 312-5:2000), Oriented Stress Boards class 2 (PN-EN 300:2000), hard fibreboards (PN-EN 662-2:2000) Permanent 0.30 0.20 Long term 0.45 0.30 Medium term 0.65 0.45 Short term 0.85 0.60 Momentary 1.10 0.80 Hard and medium fibreboards (PN-EN 622-3:2000) Permanent 0.20 Long term 0.40 Medium term 0.60 Short term 0.80 Momentary 1.10

Table 6.6 Values of the coefficient yM (PN-B-03150:2000)

 Border states Value of the coefficient Border states of load-carrying capacity Basic combinations of loads 1.3 Wood and wood-based materials 1.1 Exceptional states 1.0 Border state of usability 1.0

When connecting two elements using nails, the satisfactory length of the insert (without taking into account the length of the sharp blade) should amount to 8 times nail diameters (Fig. 6.82). Joining three elements requires the nail to pierce one or two pieces and stick in the second middle or third external at a depth of eight times diameters (Fig. 6.83a, b).

 Fig. 6.84 Methods of connecting wood and board wood-based materials using nails: a single shear hammered unilaterally, b single shear hammered bilaterally, c double shear hammered bilaterally

 Fig. 6.85 Hammering patterns, distances and spacing of connectors (nails and bolts) according to PN-B-03150:2000: a rectangular layout, b alternate layout, c distance between the connector and loaded end, d distance between the connector and unloaded end, e distance between the connector and loaded edge, f distance between the connector and unloaded edge

Table 6.7 Minimal spacing and distances between nails according to PN-B-03150:2000

 Distance signature Minimal distances of connectors with drilled holes Minimal distances of connectors without drilled holes Pk ^ 420 kg/m3 420 < pk < 500 kg/m3 Й1 (4 + 3|cosa|)d d <5 mm: (5 + 5|cosa|)d d > 5 mm: (5 + 7|cosa|)d (7 + 6|cosa|)d a2 (3 + 1|sina|)d 5d 5d a3t (7 + 5cosa)d (10 + 5cosa)d (15 + 5cosa)d a3c Id 10d 15d a4t (3 + 4sina)d (5 + 5sina)d (5 + 5sina)d a4c 3d 5d 7d