1 Introduction
1.1 State of knowledge of axially loaded self-tapping screws positioned in the narrow face of CLT
1.2 State of knowledge of modelling of the load–displacement behaviour of single fasteners and groups of fasteners
-
The point (F max; w f), with w f as the deformation associated with the maximum load F max, is not part of the previous mentioned models; thus, the relationship between F max and w f may not be accurately represented;
-
The extensions for both models assume ideal plastic yielding after exceeding F max; this approximation appears suitable for dowel-type fasteners such as nails or dowels stressed in shear; however, non-linear softening after exceeding F max, which is typical for self-tapping screws failing in withdrawal, is not provided.
2 Motivation and objective
3 Materials and Methods
3.1 Series of withdrawal tests
3.1.1 Test series I
Parameter | Series I | Series II |
---|---|---|
Screw diameter, d
| 8 mm | 8 and 12 mm |
Penetrated layers | TL, CL, ML | TL, CL, ML, IL |
Thread-fibre angle, α | 0°, 30°, 45°, 60°, 90° | 0°, 0°|90°, 0°|90°|0° |
Pre-drilling | Yes | Yes |
Gaps | No | Yes |
Gap width, w
gap
| – | 0, 2 and 6 mm |
Gap type | – | Solid timber (ST), butt joint (BuJ), bed joint (BeJ), T-joint (TJ) |
Sample size | 20 specimens per parameter set → in total 300 tests | 20 specimens per parameter set, except joints with w
gap = 6 mm (5 per series) → in total 400 tests |
3.1.2 Test series II
3.2 Modelling the load–displacement behaviour of single self-tapping screws failing in withdrawal
-
At first, the approach is simplified by using F asym = 0. This is argued by the fact that a residual resistance F asym > 0 | w → ∞ cannot be observed in timber primarily stressed in longitudinal and / or lateral shear as this is the case in testing screws in timber against withdrawal.
-
Secondly, test data indicates delayed stiffening at the beginning of loading, which is a well-known characteristic of natural, hierarchically structured materials (e.g. see Gordon 1988). To account for this phenomenon, and as the principal shape of this first branch of the load–displacement curve is in general not decisive for engineering applications, a horizontal shift of the curve is introduced by Δw ini (see Fig. 2). This shift is not of relevance for single screws but may be of importance for investigations into the interaction of screws in groups. However, as a pre-load was applied (see Sect. 2.1) the available test data provides only underestimations for Δw ini. For modelling of single screws, Δw ini is set to zero.
-
As Glos’ model does not provide a linear-elastic part at the beginning of the load–displacement curve (see Fig. 2, right), which can be approximately observed from withdrawal tests with hysteresis loops, its stiffness parameter k ser | w = 0 does not correspond to k ser from tests usually determined according to EN 26891 (1991). This standard defines k ser as gradient of the load–displacement curve until 0.4 F max. For applicability of the standardized k ser as model parameter, a linear part Δw lin is introduced between w ini and w lin after which the model of Glos (1978) starts with k ser | w = w lin, see Fig. 2, left.
3.3 Statistical analysis and inference
4 Results and discussion
4.1 Series I: statistical analysis and definition of parameter settings
4.1.1 General data analysis
ρ12 [kg/m3] |
F
max [kN] |
k
ser [kN/mm] | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0° | 30° | 45° | 60° | 90° | 0° | 30° | 45° | 60° | 90° | 0° | 30° | 45° | 60° | 90° | |
TL | |||||||||||||||
Quantity | 17 | 17 | 18 | 15 | 18 | 17 | 17 | 18 | 15 | 18 | 17 | 17 | 18 | 15 | 18 |
X
mean
| 439 | 456 | 447 | 441 | 410 | 7.30 | 9.79 | 9.70 | 9.83 | 9.50 | 16.6 | 14.1 | 11.7 | 11.4 | 10.7 |
CV [%] | 7.6 | 9.5 | 4.9 | 6.9 | 4.8 | 13.4 | 15.7 | 10.0 | 8.8 | 11.7 | 14.4 | 19.0 | 12.2 | 14.7 | 16.7 |
CL | |||||||||||||||
Quantity | 16 | 19 | 18 | 12 | 18 | 16 | 19 | 18 | 12 | 18 | 16 | 19 | 18 | 12 | 18 |
X
mean
| 452 | 445 | 479 | 503 | 471 | 7.60 | 9.38 | 10.5 | 11.6 | 11.8 | 15.0 | 12.7 | 13.6 | 13.9 | 15.9 |
CV [%] | 9.1 | 16.7 | 15.9 | 14.7 | 14.3 | 16.9 | 25.0 | 22.9 | 18.3 | 20.8 | 18.6 | 31.5 | 23.8 | 20.4 | 19.4 |
ML | |||||||||||||||
Quantity | 17 | 18 | 14 | 16 | 16 | 17 | 18 | 14 | 16 | 16 | 17 | 18 | 14 | 16 | 15 |
X
mean
| 441 | 427 | 429 | 443 | 416 | 7.64 | 9.02 | 9.43 | 10.2 | 10.4 | 17.3 | 12.6 | 12.0 | 12.4 | 11.0 |
CV [%] | 8.9 | 6.7 | 6.2 | 9.0 | 8.2 | 18.6 | 10.7 | 8.6 | 15.3 | 16.5 | 16.4 | 14.1 | 14.7 | 19.1 | 16.0 |
Combined data set TL and ML | ||||||||
---|---|---|---|---|---|---|---|---|
α | Quantity | min[X] |
X
mean
|
q
50
| max[X] | CV [%] |
q
05,empD
|
q
05,2pLND
|
ρ12 [kg/m3] | ||||||||
0° | 34 | 388 | 440 | 434 | 522 | 8.1 | 394 | 384 |
30° | 35 | 382 | 441 | 428 | 520 | 8.8 | 390 | 380 |
45° | 32 | 395 | 439 | 436 | 495 | 5.8 | 402 | 399 |
60° | 31 | 390 | 442 | 437 | 508 | 7.9 | 394 | 387 |
90° | 34 | 375 | 413 | 408 | 497 | 6.6 | 380 | 369 |
F
max [kN] | ||||||||
0° | 34 | 5.97 | 7.47 | 7.10 | 11.0 | 16.2 | 6.08 | 5.66 |
30° | 35 | 7.28 | 9.40 | 9.20 | 12.8 | 14.0 | 7.41 | 7.40 |
45° | 32 | 7.79 | 9.58 | 9.46 | 12.1 | 9.4 | 8.46 | 8.18 |
60° | 31 | 7.89 | 10.0 | 10.0 | 13.0 | 12.6 | 8.07 | 8.09 |
90° | 34 | 7.91 | 9.92 | 9.52 | 15.4 | 14.9 | 8.28 | 7.69 |
k
ser [kN/mm] | ||||||||
0° | 34 | 12.4 | 17.0 | 17.0 | 22.1 | 15.4 | 13.3 | 13.0 |
30° | 35 | 9.95 | 13.3 | 13.2 | 19.2 | 17.6 | 10.3 | 9.85 |
45° | 32 | 8.88 | 11.8 | 11.8 | 16.1 | 13.2 | 9.24 | 9.44 |
60° | 31 | 8.87 | 11.9 | 11.8 | 18.0 | 17.5 | 9.39 | 8.81 |
90° | 34 | 7.98 | 10.8 | 10.6 | 14.7 | 16.2 | 8.14 | 8.22 |
c [–] | ||||||||
0° | 34 | 1.43 | 2.32 | 2.11 | 4.18 | 27.7 | 1.60 | 1.43 |
30° | 35 | 1.57 | 3.80 | 4.15 | 5.74 | 16.0 | 2.24 | 2.41 |
45° | 32 | 1.21 | 4.19 | 4.01 | 7.61 | 36.5 | 2.57 | 2.20 |
60° | 31 | 2.52 | 3.93 | 3.83 | 5.60 | 20.5 | 2.63 | 2.76 |
90° | 34 | 3.51 | 5.49 | 5.62 | 7.91 | 21.9 | 3.58 | 3.76 |
Δw
lin [mm] | ||||||||
0° | 34 | 0.107 | 0.234 | 0.233 | 0.423 | 27.8 | 0.135 | 0.144 |
30° | 35 | 0.186 | 0.301 | 0.283 | 0.453 | 25.1 | 0.189 | 0.195 |
45° | 32 | 0.000 | 0.378 | 0.381 | 0.525 | 27.5 | 0.230 | 0.234 |
60° | 31 | 0.232 | 0.358 | 0.360 | 0.583 | 23.0 | 0.239 | 0.240 |
90° | 34 | 0.216 | 0.334 | 0.304 | 0.531 | 25.1 | 0.244 | 0.216 |
Δ
w
f [mm] | ||||||||
0° | 34 | 0.47 | 0.70 | 0.69 | 1.00 | 18.3 | 0.53 | 0.51 |
30° | 35 | 1.41 | 1.89 | 1.96 | 2.28 | 11.3 | 1.46 | 1.56 |
45° | 32 | 1.79 | 2.24 | 2.26 | 2.85 | 12.0 | 1.82 | 1.82 |
60° | 31 | 1.83 | 2.32 | 2.34 | 2.68 | 8.9 | 1.96 | 2.00 |
90° | 34 | 2.24 | 2.63 | 2.60 | 3.04 | 8.9 | 2.29 | 2.26 |
4.1.2 Density correction and representative distribution models
4.1.3 Relationships between withdrawal properties and α
Model |
a
|
b
|
c
|
r
|
s
e
| |
---|---|---|---|---|---|---|
F
max ~ α | I | 2.00***a
| 1.45a
| – | 0.74 | 1050 |
II | 74.5a
| – | – | 0.75 | 952 | |
III
|
0.00941
*
|
1.52
**
|
97.7
***
|
0.81
|
826
| |
k
ser ~ α | I | 1.56***
| 0.71a
| – | 0.77 | 1640 |
II
|
–110
a
|
–
|
–
|
0.77
|
1870
| |
III | –0.00344 | –1.64 | –175***
| 0.77 | 1650 | |
c ~ α | I | 2.00***b
| 2.27a
| – | 0.59 | 1.22 |
II | 0.065a
| – | – | 0.60 | 1.16 | |
III
|
1.51 · 10
−5**
|
0.002
**
|
0.103
***
|
0.68
|
1.04
| |
Δw
lin ~ α | I | 2.00***b
| 1.41a
| – | 0.33 | 0.100 |
II
|
0.002
a
|
–
|
–
|
0.50
|
0.084
| |
III | –4.88 · 10−7
| –3.06 · 10−5
| 0.002 | 0.50 | 0.084 | |
Δw
f ~ α | I | 2.00***b
| 3.65a
| – | 0.69 | 0.796 |
II | 0.041a
| – | – | 0.94 | 0.245 | |
III
|
3.38 · 10
−6**
|
7.35 · 10
−4***
|
0.059
***
|
0.95
|
0.210
|
4.1.4 Correlations between model parameters
ln(ρ12) | ln(F
max) | ln(k
ser) | ln(c) | ln(Δw
lin) | ln(Δw
f) | |
---|---|---|---|---|---|---|
ln(ρ12) |
1.00
|
0.88
|
0.61
|
–0.19
|
–0.07
|
–0.26
|
ln(F
max) |
0.74
|
1.00
|
0.69
|
–0.14
|
–0.06
|
–0.18
|
ln(k
ser) |
0.61
|
0.69
|
1.00
|
–0.08
|
–0.47
|
–0.36
|
ln(c) |
–0.18
|
–0.05
|
–0.10
|
1.00
|
0.38
|
0.75
|
ln(Δw
lin) |
–0.04
|
–0.03
|
–0.43
|
0.35
|
1.00
|
–0.07
a
|
ln(Δw
f) |
–0.27
|
–0.11
|
–0.31
|
0.71
|
0.25
|
1.00
|
4.2 Multivariate model approach
4.3 Series II: statistical analysis and model verification
4.3.1 General data analysis
ρ12 [kg/m3] |
k
ser [kN/mm] |
F
max [kN] | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
ST | BuJ0
| BuJ2
| BuJ6
| ST | BuJ0
| BuJ2
| BuJ6
| ST | BuJ0
| BuJ2
| BuJ6
| |
TCML | d = 8 mm | ||||||||||||
Quantity [–] |
55
|
57
|
56
|
15
|
55
|
57
|
56
|
15
|
55
|
57
|
56
|
15
|
X
mean
|
445
|
464
|
454
|
481
|
18.8
|
19.6
|
13.9
|
7.91
|
8.87
|
8.63
|
6.82
|
3.89
|
18.5
|
18.2
|
13.3
|
6.92
|
8.79
|
8.05
|
6.55
|
3.41
| |||||
CV [%] |
8.5
|
6.8
|
6.2
|
5.5
|
15.6
|
21.4
|
18.7
|
20.6
|
15.6
|
13.1
|
16.1
|
20.0
|
11.4
|
18.8
|
16.9
|
16.5
|
16.4
|
12.7
|
16.4
|
15.6
| |||||
q
05,empD
|
390
|
422
|
410
|
449
|
14.5
|
14.4
|
10.3
|
5.69
|
7.07
|
6.94
|
5.33
|
2.90
|
15.1
|
14.0
|
10.4
|
5.53
|
6.76
|
6.50
|
5.06
|
2.54
| |||||
TCML | d = 12 mm | ||||||||||||
Quantity [–] |
59
|
60
|
60
|
15
|
–
|
–
|
–
|
–
|
60
|
60
|
60
|
15
|
X
mean
|
423
|
458
|
441
|
461
|
–
|
–
|
–
|
–
|
18.7
|
17.8
|
15.0
|
12.3
|
–
|
–
|
–
|
–
|
20.0
|
16.9
|
15.1
|
11.7
| |||||
CV [%] |
8.4
|
6.6
|
7.0
|
8.6
|
–
|
–
|
–
|
–
|
15.5
|
13.1
|
12.8
|
13.2
|
–
|
–
|
–
|
–
|
17.7
|
14.8
|
15.5
|
20.3
| |||||
q
05,empD
|
378
|
413
|
399
|
399
|
–
|
–
|
–
|
–
|
14.6
|
14.3
|
12.3
|
10.1
|
– | – | – | – | 14.6 | 13.3 | 11.1 | 8.92 |
BeJ | TJ0
| TJ2
| TJ6
| BeJ | TJ0
| TJ2
| TJ6
| BeJ | TJ0
| TJ2
| TJ6
| |
---|---|---|---|---|---|---|---|---|---|---|---|---|
IL | d = 8 mm | ||||||||||||
Quantity [–] |
19
|
19
|
19
|
5
|
19
|
19
|
19
|
5
|
19
|
19
|
19
|
5
|
X
mean
|
432
|
453
|
450
|
441
|
18.1
|
19.3
|
15.3
|
7.07
|
9.96
|
10.5
|
8.35
|
3.65
|
18.6
|
18.8
|
14.7
|
7.14
|
10.2
|
10.2
|
8.02
|
3.67
| |||||
CV [%] |
6.1
|
4.7
|
5.8
|
6.7
|
14.5
|
17.6
|
10.8
|
10.7
|
12.0
|
13.5
|
10.1
|
9.40
|
11.6
|
19.0
|
11.6
|
18.8
|
8.9
|
13.8
|
9.7
|
15.8
| |||||
q
05,empD
|
395
|
427
|
420
|
405
|
15.1
|
14.3
|
12.3
|
6.09
|
8.07
|
8.95
|
7.14
|
3.32
|
16.2
|
14.1
|
12.4
|
5.52
|
8.59
|
8.46
|
6.57
|
3.01
| |||||
IL | d = 12 mm | ||||||||||||
Quantity [–] |
20
|
20
|
19
|
5
|
–
|
–
|
–
|
–
|
20
|
20
|
19
|
5
|
X
mean
|
431
|
458
|
462
|
485
|
–
|
–
|
–
|
–
|
20.3
|
20.0
|
17.7
|
13.8
|
–
|
–
|
–
|
–
|
20.9
|
18.9
|
16.6
|
12.2
| |||||
CV [%] |
6.5
|
5.0
|
7.1
|
5.6
|
–
|
–
|
–
|
–
|
11.4
|
9.44
|
12.8
|
10.2
|
–
|
–
|
–
|
–
|
9.0
|
8.7
|
12.6
|
16.6
| |||||
q
05,empD
|
397
|
432
|
415
|
452
|
–
|
–
|
–
|
–
|
17.6
|
17.6
|
14.3
|
12.5
|
–
|
–
|
–
|
–
|
18.8
|
17.2
|
14.9
|
11.0
|
4.3.2 Model validation
-
BuJ0 vs. ST | α = 0°: for k ser, equivalence of mean values k ser,mean | BuJ0 ≈ k ser,0,mean together with a significant reduction in dispersion, with CV[k ser | BuJ0] ≈ CV[k ser,0] / √2, is expected. Due to the non-linear load–displacement behaviour before and after F max, there is a high potential for load-redistribution after partial failures, i.e. after exceeding the capacity of the screw in one layer or lamella. In comparison to F max,0, thus only a slightly lower F max,mean | BuJ0 is expected together with significantly reduced CV[F max | BuJ0] ≥ CV[F max,0] / √2.
-
BeJ0 vs. ST | α = 0°: due to the anchorage of the screw to 50% perpendicular to grain, F max,mean | BeJ0 higher than F max,0,mean is expected. However, because of the reverse relationships of F max and k ser vs. α, F max,mean | BeJ0 will be closer to F max,0,mean than to F max,90,mean. Also, a reduced CV[F max | BeJ0] is expected.
-
TJ0 vs. ST | α = 0°: because of the interaction 0°|90°|0° it is assumed that F max,mean | TJ0 ≤ F max,mean | BeJ0, and CV[F max | TJ0] slightly reduced.
-
BuJ0 vs. BuJ2 and BuJ6: it is expected an approximately continuous decreasing F max,mean, proportional to the loss of lateral area of the screw, without influence on CV[F max].
-
TJ0 vs. TJ2 and TJ6: increasing gap width comes along with decreasing shares of α = 0°. This, together with the loss of volume for anchoring, leads to a decrease in k ser,mean higher than in F max,mean. This is again motivated by the reverse relationship of both properties in respect to α. However, for each property the decrease will be proportional to the loss of lateral area within α = 0°. Thus, a minor raise of CV[F max] is also expected.
STa
| STa
| BuJ0
| BuJ2
| BuJ6
| BeJ | TJ0
| TJ2
| TJ6
| |
---|---|---|---|---|---|---|---|---|---|
0° | 90° | 0°|0° | 0°|90° | 0°|90°|0° | |||||
F
max [kN] | |||||||||
X
mean
| 7.49 | 10.8 | 7.46 | 6.26 | 3.43 | 8.11 | 8.12 | 7.66 | 6.63 |
CV [%] | 13.0 | 13.0 | 9.0 | 9.0 | 9.0 | 9.7 | 10.5 | 10.7 | 11.2 |
q
05,empD
| 6.00 | 8.69 | 6.40 | 5.37 | 2.95 | 6.95 | 6.96 | 6.53 | 5.54 |
k
ser [kN/mm] | |||||||||
X
mean
| 17.0 | 12.0 | 17.0 | 14.3 | 7.80 | 14.5 | 14.5 | 13.1 | 9.89 |
CV [%] | 16.0 | 16.0 | 11.0 | 11.0 | 11.0 | 11.3 | 9.5 | 9.7 | 10.8 |
q
05,empD
| 12.9 | 9.12 | 14.0 | 11.7 | 6.43 | 12.0 | 12.3 | 11.2 | 8.25 |
5 Conclusion
-
Application of screws with d ≥ 8 mm; the screw diameter should be significantly larger than the maximum gap width currently allowed in technical approvals for CLT, i.e. w gap ≤ 6 mm;
-
T-joints should be conservatively treated as butt-joints; secure positioning of screws in open T-joints even in pre-drilled holes is not possible, in particular for smaller screw diameters;
-
Screws should be positioned inclined parallel to the CLT side face at α = 30° to 60° and, if possible, also perpendicular to the side face at α ≥ 10°; inclined positioning minimizes the influence of gaps on withdrawal parameters as long as the load-bearing penetration length of screws in timber is sufficient (see e.g. Blaß and Uibel 2009).