DESIGN EQUATIONS FOR EMBEDMENT...

DESIGN EQUATIONS FOR EMBEDMENT STRENGTH OF WOOD FOR THREADED FASTENERS IN THE CANADIAN TIMBER DESIGN CODE Shawn Kennedy1, Alexander Salenikovich2, Williams Munoz3, Mohammad Mohammad4, Derek Sattler5

ABSTRACT: The Canadian standard for engineering design in wood (CSA O86) adopted the European yield model for calculations of the lateral resistance of connections with dowel-type fasteners. This model takes into account the yielding resistance of the fastener, the assembly’s geometry and the embedment strength of wood. The latter is considered a function of the relative density of wood and diameter of the fastener. The purpose of this study is to verify the significance of these variables as applied to the embedment strength for threaded dowel-type fasteners of diameters 6.4 mm and greater in Canadian glulam products. The importance of this research is justified by the growing interest in the use of large-diameter threaded fasteners in heavy timber and hybrid structures of high load-bearing capacity. Based on the results of 960 tests, a new design model for the embedment strength is proposed for potential implementation in CSA O86 standard and the impact of such a change is presented.

KEYWORDS: Dowel-type fasteners, dowel bearing strength, sawn timber, glued-laminated timber.

1 INTRODUCTION 123 In the 1990s, the Canadian standard for engineering design in wood (CSA O86) [1] has adopted the European yield model for lateral resistance of connections with dowel-type fasteners. It takes into account the yielding resistance of the fastener, the assembly’s geometry and the embedment strength of wood. The latter is expressed as a function of the relative density of wood and diameter of the fastener. According to the design equations, the embedment strength increases in direct proportion with the relative density and decreases for the fasteners of greater diameters.

Since the embedment strength of wood is expressed as a material property, i.e., bearing resistance, the influence of the size (diameter) of the fastener is questionable. Therefore, the key purpose of this study is to verify the significance of these variables as applied to the embedment strength for threaded dowel-type fasteners of diameters 6.4 mm and greater. The importance of this study is justified by the growing interest in the use of large-diameter threaded fasteners in heavy timber and hybrid structures of high load-bearing capacity.

Furthermore, since the shanks of threaded fasteners are usually composed of a threaded and an unthreaded (smooth shank) portions, another goal of this study is to compare the influence of the shank section geometry on the embedment properties of wood. 1 Shawn Kennedy, Université Laval, 2425 rue de la Terrasse, Quebec, Canada. Email: [email protected] 2 Alexander Salenikovich, Université Laval, Quebec, Canada 3 Williams Munoz, Nordic Structures Bois, Montreal, Canada 4 Mohammad Mohammad, FPInnovations, Ottawa, Canada 5 Derek Sattler, University of Alberta, Edmonton, Canada

2 BACKGROUND The earliest studies on the embedment strength conducted in 1932 by Trayer [2] established the relationship between bearing strength and length to diameter ratios (l/d) for bolts. In 1949, Johansen [3] presented a yield model theory, which, according to Soltis [4], was best to describe the Trayer’s experimental observations. This model was then modified by Larsen et al. (1986) and became the well known European yield model (EYM). In the 1980s, several studies were carried out in Europe and in North America for potential adoption of the EYM for design of dowel-type connections. As a result in Canada, the embedment strength equations based on the work of Smith et al. [5] were developed. The Eurocode 5 [6] equations for fasteners installed into wood with pre-drilled holes are equivalent to those in CSA O86 for parallel-to-grain direction and different for fasteners of diameters greater than 6 mm loaded perpendicular-to-grain. In the US timber design code (NDS) [7], the embedment strength is called “dowel bearing strength” and its values are based on the work of Wilkinson [8] who proposed equations that are independent of the fastener diameter in the parallel-to-grain direction. In 2002, Sawata and Yasumura [9] showed that it was also true for the embedment strength perpendicular to grain when it is measured as 5%-diameter offset. Later, Chui et al. [10] reported test results for threaded fasteners of small diameters, which were different from those currently adopted in the design codes due to the inclusion of the axial tensioning effect.

3 MATERIALS The experimental program conducted jointly at FPInnovations and Laval University [11] included

approximately 960 embedment tests performed with lag screws of six diameters (from 6.35 mm to 19.1 mm), which were commodity off-shelf products.

All tests were carried out on glued-laminated timber (glulam) produced in Canada. One group of samples was made of Black spruce (Picea mariana) grown in Quebec province and two other groups were made of Spruce-pine-fir and Douglas-fir species groups grown in the province of British Columbia. All specimens were conditioned at standard ambient environment (65 ± 5% of relative humidity and 20 ± 2°C temperature) prior to testing.

Two embedment lengths were evaluated depending on the fastener diameter. For the three smaller diameters, tests were performed using 76.2 mm long fasteners while for the three larger ones the fasteners were twice as long (see Table 1). The specimen width and depth were 5 and 6 times the fastener diameter, respectively, but not less than 50 mm (see Figure 1). Ten replications were tested for each test configuration.

Table 1: Lag screw dimensions

Figure 1: Embedment specimen dimensions

4 TEST PROCEDURES Embedment tests were performed in accordance with ASTM D5764 [12] half-hole test method with the fasteners inserted perpendicular to the lamination face of the glulam blocks and loaded at 90°, 45° or 0° angles to grain direction (except that black spruce glulam was not tested at 45°). Tests were conducted separately on the smooth shank (unthreaded) portion and on the threaded portion of the lag screw. Test specimens were prepared by drilling a hole in the centre of a glulam block and then cutting it into halves to obtain two specimens. For tests on the smooth shank portion, the hole diameter was equal to the nominal fastener diameter. For the threaded shank, the hole was 70% of the nominal diameter, and the lag screw was carefully inserted in and out of the hole using a wrench before cutting the block in half.

The load was applied to the specimen using a fastener welded to a steel plate attached to the loading head of a hydraulic actuator (Figure 2). The specimen was loaded at a constant speed of 1.0 mm/min, and test was stopped when the load decreased to 80% of the peak load unless the displacement first reached the lesser of 7.0 mm or half the diameter of the fastener. The displacement was calculated as the average of measurements recorded using two laser sensors on the opposite ends of the specimen as shown in Figure 2. After the test, a sample was extracted from each specimen to determine the relative density and moisture content in the vicinity of the loaded zone.

Figure 2: Embedment test set-up

5 ANALYSIS OF RESULTS First, the experimental data (yield load, maximum load, and stiffness) were compared for threaded and non-threaded shank portions of the lag screws (Section 5.1). Then experimental embedment strength values were compared with three design models:

Fastener diameter mm (in.)

Threaded (T) or non-threaded (NT) portion

Lead hole diameter

mm

Embedment length

mm 6.35 (1/4)

NT 6.35 76.2 T 4.39 76.2

7.94 (5/16)

NT 7.94 76.2 T 5.56 76.2

9.53 (3/8)

NT 9.53 76.2 T 6.75 76.2

12.7 1(/2)

NT 12.7 152 T 9.13 152

15.9 (5/8)

NT 15.88 152 T 11.91 152

19.1 (3/4)

NT 19.05 152 T 14.29 152

1. CSA O86 [1], 2. NDS [7], and 3. Eurocode 5 (EN) [6].

Individual experimental data were compared with the values predicted for the average embedment strength at 5-min. load duration. Then the experimental lower 5th percentile values based on 75% confidence obtained per series of ten replications were adjusted for the standard load duration (multiplied by 0.8 according to the CSA O86 Commentary [13]) and compared with design values predicted by the design equations (5th percentile values at standard load duration). Statistical comparisons of the predictions are discussed in Section 5.2.

Next, a statistical analysis was performed to investigate the relationship between the diameter and the measured embedment strength. The analysis was extended to determine the significance of the diameter as a variable for each of the standard design models (Section 5.3).

Finally, a new embedment strength design model for CSA O86 standard was developed based on statistical analyses and the impact of the change is described in Section 5.4.

5.1 COMPARISON BETWEEN THREADED (T) AND NON-THREADED (NT) PORTIONS OF LAG SCREWS

This section focuses on the differences in embedment strength properties for the threaded and non-threaded shank portions of the lag screws. For each series of tests, statistical analysis was performed to compare the 5% diameter offset load, maximum load and initial stiffness.

5.1.1 5% diameter (5%d) offset load Statistical comparisons between threaded and non-threaded of the lag screws show that the loads measured at 5% diameter offset were generally somewhat higher for non-threaded portion, although the opposite was observed in some cases (see Figure 3). Nonetheless, in most cases the differences were not statistically significant (see Table 2).

Table 2: Comparison of the 5% offset loads for threaded (T) and non-threaded (NT) portions of the lag screws

* Indicates a significant difference when the p-value is less than 0.05.

According to Table 2, differences were found to be statistically significant for lag screws with diameter of 3/8 in. (9.53 mm) and higher in several instances. This outcome may be explained by the fact that for this lag

screw, a larger portion of the tip was embedded into wood during the tests compared to the other diameters.

a = 1/4 in., b = 5/16 in., c = 3/8 in., d = 1/2 in., e = 5/8 in., and f = ¾ in. Figure 3: Typical comparison of 5% diameter offset load for threaded (T) and non-threaded (NT) portions

5.1.2 Maximum load Comparisons of maximum loads between the two lag screw sections present almost the same results as for the 5% diameter offset load. Generally, maximum loads were higher for the non-threaded portions with generally no significant differences. As given in Table 3, the statistically significant differences were found for the fasteners of larger diameters in some instances. Table 3: Comparison of maximum loads for threaded (T) and non-threaded (NT) portions of the lag screws


5.1.3 Stiffness (K) In the case of stiffness, statistical comparisons showed somewhat different results from the 5% diameter offset and the maximum loads. Tests on SP glulam at a 90° angle showed significant differences between the threaded and non-threaded portions, and the 19.1-mm (3/4-in.) diameter fasteners showed a higher percentage of statistical differences. Other than that, the comparison presents generally no significant differences in the stiffness for smooth shank compared to threaded portion.

1/4x3 5/16x3 3/8x3 1/2x6 5/8x6 3/4x6Glulam BS 90° 1.0000 1.0000 1.0000 0.1274 1.0000 0.1197Glulam BS 0° 1.0000 1.0000 * 0.01633 *1.1e-09 * 9.8e-12 * <2e-16Glulam SPF 90° 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000Glulam SPF 45° 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000Glulam SPF 0° 1.0000 1.0000 0.4236 *0.0011 1.0000 * <2e-16Glulam D.Fir 90° 1.0000 1.0000 1.0000 * <2e-16 1.0000 * 0.0016Glulam D.Fir 45° 1.0000 1.0000 1.0000 1.0000 * 3.2e-16 0.1480Glulam D.Fir 0° 1.0000 1.0000 1.0000 1.0000 1.0000 * 8.1e-10

COMPARISON T vs. NT

1/4x3 5/16x3 3/8x3 1/2x6 5/8x6 3/4x6Glulam BS 90° 1.0000 1.0000 1.0000 * 5.9e-06 0.0515 0.1197Glulam BS 0° 1.0000 1.0000 * 0.00074 *4.6e-08 * 1.2e-15 * 2.0e-16Glulam SPF 90° 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000Glulam SPF 45° 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000Glulam SPF 0° 1.0000 1.0000 0.2415 *0.0165 0.7585 * 2.0e-16Glulam D.Fir 90° 1.0000 1.0000 1.0000 * 1.3e-12 1.0000 * 0.0059Glulam D.Fir 45° 1.0000 1.0000 1.0000 1.0000 * 2.0e-10 0.6484Glulam D.Fir 0° 1.0000 1.0000 1.0000 1.0000 1.0000 * 1.7e-06

COMPARISON T vs. NT

Table 4: Comparison of stiffness (K) for threaded (T) and non-threaded (NT) portions of the lag screws


Overall, the statistical comparisons showed that differences in the performance parameters between threaded and non-threaded portions were minimal and mostly statistically insignificant and may be explained by variability in wood properties rather than by the differences due to lag screw section properties.

5.2 EVALUATION OF DESIGN EQUATIONS Although design models for embedment strength parallel- and perpendicular-to-grain differ between codes, there has been general agreement about the Hankinson formula for the strength at any angle expressed as follows:

θθθθθ22

90

0

02

902

0

900

cossincossin +=

+⋅

=

ff

ffffff (1)

where, f0 = embedment strength parallel to grain; f90 = embedment strength perpendicular to grain; θ = angle of load to the grain.

All further discussion of the design models is built on the equations expressed in this format. The following notation is used in the equations presented in this section:

fθ,avg = average embedment strength (N/mm²); d = fastener nominal diameter (mm); ρ12 = measured density based on volume and mass at

12% moisture content (g/cm3); G0 = measured relative density based on oven-dry mass

and volume; G = mean relative density for the species or species

group based on oven-dry mass and volume (according to CSA O86); and

θ =loading angle relative to the specimen grain orientation (°).

In the comparisons of the design models, the experimental embedment stress (fi) is expressed as the 5% diameter offset load (Py) divided by the embedded length (l) and the nominal diameter (d) of the fastener as follows:

dlP

f yi ⋅=

(2)

Non-linear regression analysis was performed for each model and statistics were evaluated, as presented in [14].

5.2.1 CSA O86 model

5.2.1.1 Average values Using the adjustments explained in 5.2.3.2 the average embedment strength at any angle to the grain can be calculated as follows:

fθ ,avg =82ρ12 (1− 0.01d )2.27sin2θ + cos2θ

(3)

Non-linear regression analysis of the average predicted vs. experimental values for all three tested angles combined (see Figure 4) shows the following results:

- R² = 70% - Mean Error = -0.90, - Root Means Square Error (RMSE) = 5.85, and - Absolute Percent Error = 20.5%.

These errors show that, generally, Equation (3) over-estimates the average strength by 5.85 MPa. Also, it can be noted that the equation does not perform equally well for different loading directions (see Figure 4) and deviate significantly from the test results. Statistical comparison of Equation (3) with other models is presented in 5.2.4.

Figure 4: Comparison of Equation (3) vs. test data (MPa)

5.2.1.2 Design values CSA O86 embedment strength equations may be combined in the Hankinson formula as follows:

fθ ,k =50G 1−0.01d( )2.27sin2θ + cos2θ

(4)

As shown in Figure 5, the design equation tends to over-estimate the embedment strength. Nearly 15% of the predicted values are non-conservative. Moreover, there is no clear tendency associated with any particular variable.

1/4x3 5/16x3 3/8x3 1/2x6 5/8x6 3/4x6Glulam BS 90° 1.0000 * 1.8e-06 * 0.0014 * <2e-16 *4.4e-14 * 0.0274Glulam BS 0° 1.0000 1.0000 1.0000 1.0000 1.0000 * 3.5e-09Glulam SPF 90° 1.0000 1.0000 1.0000 0.5400 0.1870 *0.0270Glulam SPF 45° 1.0000 1.0000 1.0000 0.9683 1.0000 * 0.0003Glulam SPF 0° 1.0000 1.0000 1.0000 0.4149 1.0000 1.0000Glulam D.Fir 90° 1.0000 1.0000 1.0000 0.1533 * 0.0002 * 0.0010Glulam D.Fir 45° 1.0000 1.0000 1.0000 0.7506 * 1.2e-06 * 0.0009Glulam D.Fir 0° 1.0000 1.0000 1.0000 1.0000 0.4605 * 6.6e-06

COMPARISON T vs. NT

0

10

20

30

40

50

60

0 10 20 30 40 50 60

f θ,av

g (M

Pa)

fi (MPa)

Equation 3

0°

45°

90°

Figure 5: Comparison of Equation (4) vs. test data adjusted to standard load duration (MPa)

5.2.2 National Design Specification (NDS) model

5.2.2.1 Average values The average embedment strength equation in the NDS in inch-pound units is given as follows:

fθ ,avg =12000G0

0.55G0−0.45d 0.5( )sin2θ + cos2θ

(5)

where, fθ,avg = average embedment strength (psi); d = fastener nominal diameter (in.);

In SI units, the same equation is presented as follows:

fθ ,avg =77G0

0.36G0−0.45d 0.5( )sin2θ + cos2θ

(6)

where fθ,avg = average embedment strength (N/mm²); d = fastener nominal diameter (mm).

Regression analysis shows that the NDS embedment equation has lower accuracy than Equation (3) when compared with the measured strength. Overall, the NDS equation tends to over-predict results at lower end and under-predict at higher end (see Figure 6). Comparisons at various loading directions show even higher biases between predicted and measured stresses. The non-linear regression analysis gives the following results: - R² = 51%, - Mean Error = -4.37, - Root Means Square Error (RMSE) = 7.50 and - Absolute Percent Error = 22.9%.


5.2.2.2 Design values If the NDS average embedment strength were to be converted to the CSA O86 design format, a factor of 0.574 would be applied to account for adjustment from the average values at 12% MC to the specified values at 15% MC at standard load duration and the following expression would be obtained:

fθ ,k =44G0

0.42G0−0.45d 0.5( )sin2θ + cos2θ

(7)


In the CSA O86 format, the NDS model for embedment strength presents a weak level of safety: 22% of the values in Figure 7 show higher predictions than measured stresses.

0

10

20

30

40

0 10 20 30 40

f θ,k (M

Pa)

.

fi,std (MPa)

Equation 4

0°

45°

90° 0

10

20

30

40

50

60

0 10 20 30 40 50 60

f θ,av

g (M

Pa)

fi (MPa)

Equation 6

0°

45°

90°

0

10

20

30

40

0 10 20 30 40

f θ,k (M

Pa)

.

fi,std (MPa)

Equation 7

0°

45°

90°

5.2.3 Eurocode 5 (EN) model

5.2.3.1 Average values Average embedment strength according to Eurocode 5 may be expressed as follows:

fθ ,avg =82ρ12 1− 0.01d( )

1.35+ 0.015d( )sin2θ + cos2θ (8)

The non-linear regression analysis between measurements and predictions shows a poor fit. Figure 8 shows large differences between predictions and measured strength for all loading directions. The low level of goodness of fit is also expressed in statistics with the following parameters:

- R² = 38%, - Mean Error = -5.53, - Root Means Square Error (RMSE) = 8.41 and - Absolute Percent Error = 26.01%.

Just like the NDS model, the European model tends to over-estimate the embedment strength at low level and under-estimates at high level of stress.


5.2.3.2 Design values To convert the European model to the CSA O86 design values, the following adjustments are made:

1. Conversion from characteristic density at 12% moisture content to characteristic density at 15% moisture content (0.89);

2. Conversion from characteristic density at 15% moisture content to oven-dry characteristic density (relative density) (1.075);

3. Conversion from oven-dry characteristic density to mean relative density (0.8);

4. Conversion from short term to standard term (0.8).

The European embedment equation converted to the CSA O86 format is then:

fθ ,k =50G 1− 0.01d( )

1.35+ 0.015d( )sin2θ + cos2θ (9)

Figure 9 shows that approximately 40% of predictions made with Equation 9 are non-conservative.


5.2.4 Statistical comparison of design models Table 5 summarises the statistical errors and regression factors obtained from comparisons between average predicted embedment strength and the experimental values for each design model and direction of loading. As mentioned in Section 5.2.1, the CSA O86 equation performs better than other evaluated models. It tends to under-estimate predictions for 90° loading and to over-estimate for 45° and 0° angles. As the Pseudo R² factors indicate, the CSA O86 equation gives predictions that have reasonable fit for 90° and 0° angles but a weak fit for 45°. In case of the NDS and the EN equations, both tend to over-estimate the embedment strength against experimental values and both show questionable fit with measurements at 90° and 45° angles. However, for 0° loading both show R² values similar to that of CSA O86. However, even though the Canadian embedment strength model behaves better than the American and European models, the statistics presented in Table 5 suggest that prediction equations may be improved.

0

10

20

30

40

50

60

0 10 20 30 40 50 60

f θ,av

g (M

Pa)

fi (MPa)

Equation 8

0°

45°

90°

0

10

20

30

40

0 10 20 30 40 f θ,

k (M

Pa)

.

fi,std (MPa)

Equation 9

0°

45°

90°

Table 5: Statistical comparison of three design models

Design Method

Mean Error RMSE Abs. %

Error Pseudo

R²

f90

CSA 1.48 4.64 24.7% 31.2%

NDS -4.76 7.38 25.8% -74.2%

EN -6.48 7.89 28.6% -99.5%

f45

CSA -3.33 4.76 19.4% -7.79%

NDS -7.40 8.56 29.2% -249%

EN -9.60 10.3 35.4% -403%

f0

CSA -1.73 7.43 16.9% 39.1%

NDS -1.86 6.77 15.5% 49.5%

EN -1.73 7.43 16.9% 39.1%

5.3 INFLUENCE OF DIAMETER A simple relationship between the measured stress and the diameter was examined using experimental data for each loading direction separately.

Figure 10: Relationship between measured stress and the diameter for 0°, 45° and 90° loading directions

Figure 10 represents the experimental stresses vs. fastener diameter for samples with 0°, 45° and 90° loading angles. Straight lines represent the least squares fit from a linear regression in the form of y = a + bX. Results of the simple linear regression indicate that for all angles the diameter was not significantly related to the measured stress (p-value equals 0.771 for 90°, 0.743 for 45° and 0.169 for 0° angles). Figure 10 confirms this conclusion with a near zero slope of the least squares fit for all angles.

Second method to investigate the influence of the diameter (d) on the embedment strength (fθ) used non-linear regression analysis to fit each model for each angle (θ).

For example, the CSA O86 equations were expressed as follows (MPa):

f90 = β1a × G × (1 - β2a × d) f0 = β1b × G × (1 - β2b × d) (10) f45 = β1c × G × (1 - β2c × d)

As a result, the optimum coefficients (β1, β2, β3, etc.) were estimated for each angle in each model. In addition, the statistical analysis allowed evaluating the significance of each variable. A p-value < 0.05 indicates that the coefficient and thus the associated variable (i.e., G or d) is significant. The analysis indicated that for all design models, the coefficient associated with the diameter was close to zero and the p-value was always greater than 0.05. Therefore, the influence of the diameter was not significant for any loading angle in any design model. This finding corresponds to those previously observed by Whale et al. [15], Wilkinson [8] and Sawata and Yasumura [9].

5.4 A NEW EMBEDMENT STRENGTH MODEL Since the discussed design models showed to be inefficient in predicting the embedment strength for the large diameter fasteners and since the influence of diameter in the tested range was found to be weak, a new design equation was investigated for potential implementation in the CSA O86. First, a new model for the average strength was developed using a non-linear regression analysis where the embedment strength is dependent only on the relative density of wood. Then, a model for the design value was derived representing the 5th percentile value at standard load duration.

5.4.1 Average values The best fitting model expressed in the format of the Hankinson equation was investigated:

( ) θθρββ

ρβ

ββ

β

θ22

123

1

121,

cossin42

2

+⎟⎟⎠

⎞⎜⎜⎝

⎛=

−avgf

(11)

The optimum coefficients for this model are given in Table 6, which can be expressed as follows:

fθ ,avg =108ρ12

1.7

1.54ρ12−0.5( )sin2θ + cos2θ

(12)

Table 6: Parameter estimation resulting from the non-linear regression analysis

Coefficient Estimate Stdn Error

t-value

p-value

β1 108 4.92 22.0 <2e-16 *** β2 1.67 0.07 24.5 <2e-16 *** β3 70.1 5.70 12.3 <2e-16 *** β4 2.17 0.12 17.7 <2e-16 ***


This new model, which does not take into account the fastener diameter, provides fair predictions for the average embedment strength. As shown in Figure 11, predictions present a better fit with the experimental values for all loading angles combined. Indeed, Equation 12 shows the best R² values from the non-linear analysis in comparison with other design models considered. Even though this equation tends to slightly over-predict the strength at the lower end and to under-predict at the higher end, it generally performs well with the following statistical results:

- R² = 79%, - Mean Error = 0.0352, - Root Means Square Error (RMSE) = 4.88 and - Absolute Percent Error = 16.1%.

5.4.2 Design embedment strength values The design equation for the new embedment strength model was determined by taking the average embedment strength in Equation (12) and applying the same reduction ratio to the perpendicular and parallel equation until the percentage of non-conservative values would decrease under the 5% limit (see Figure 12). This specified embedment strength equation can be written as follows:

fθ ,k =42G1.7 27G2.2!" #$

1.54G−0.5( )sin2θ + cos2θ (13)


5.4.3 Impact study of the proposed model Tables 7 to 9 and Figures 13 to 15 show comparisons of the design embedment strength values calculated with the current Canadian design model (Eq. 4) and with the proposed one (Eq. 13), for 0°, 45° and 90° loading angles.

The proposed model is different from the one currently used in CSA O86, because it is independent of the fastener diameter. It is noticeable that for all wood densities, the new equation is more conservative, especially for fasteners of smaller diameters. The discrepancy between the proposed equation and the actual CSA dowel embedment equation is considerable with differences varying from 30% to 60% depending on the loading direction.

6 CONCLUSION Embedment tests were conducted on various species of Canadian glulam products with lag screws. Three design models (Canadian, American and European) predicting embedment strength were evaluated statistically. None of these design models appeared to provide accurate predictions of the embedment strength in comparison with test results. Moreover, it was shown that, in the tested range, the diameter included in these design equations had no influence on the embedment strength expressed as 5% diameter offset. Based on these findings, the authors felt compelled to introduce a new embedment strength equation for the CSA O86 design standard, which does not account for the fastener diameter. Equation 12 gives a better fit to measured stresses when analysed with nonlinear regression analysis for all tested loading angles.

0

10

20

30

40

50

60

0 10 20 30 40 50 60

f θ,av

g (M

Pa)

fi (MPa)

Equation 12

0°

45°

90° 0

10

20

30

40

0 10 20 30 40

f θ,k (M

Pa)

.

fi,std (MPa)

Equation 13

0°

45°

90°

Table 7: Comparison between Equation (4) (CSA) and Equation (13) (UL) for 0° loading



Figure 13: Comparison between Equation (4) (CSA) and Equation (13) (UL) for 0° loading



CSA UL Diff. CSA UL Diff. CSA UL Diff.mm (in.) (MPa) (MPa) (% ) (MPa) (MPa) (% ) (MPa) (MPa) (% )6.4 (1/4) 16.4 7.05 -57.0% 20.6 10.4 -49.5% 22.9 12.5 -45.5%9.5 (3/8) 15.8 7.05 -55.5% 19.9 10.4 -47.8% 22.2 12.5 -43.7%12.7 (1/2) 15.3 7.05 -53.9% 19.2 10.4 -45.8% 21.4 12.5 -41.6%15.9 (5/8) 14.7 7.05 -52.1% 18.5 10.4 -43.8% 20.6 12.5 -39.4%19.1 (3/4) 14.2 7.05 -50.2% 17.8 10.4 -41.6% 19.8 12.5 -37.0%22.2 (7/8) 13.6 7.05 -48.2% 17.1 10.4 -39.2% 19.1 12.5 -34.5%25.4 (1) 13.1 7.05 -46.0% 16.4 10.4 -36.6% 18.3 12.5 -31.7%

Specific Gravity0.35 0.44 0.49

Diameter



Diameter


Diameter


0

5

10

15

20

25

5 10 15 20 25

Embe

dmen

t Stre

ngth

(MPa

)

Diameter (mm)

CSA (SG=0.35) UL (SG=0.35) CSA (SG=0.44) UL (SG=0.44) CSA (SG=0.49) UL (SG=0.49)

0

5

10

15

20

25

5 10 15 20 25

Spec

. Em

bedm

ent S

treng

th (M

Pa)

Diameter (mm)


0

5

10

15

20

25

5 10 15 20 25

Spec

. Em

bedm

ent S

treng

th (M

Pa)

Diameter (mm)


ACKNOWLEDGEMENT Authors would like to acknowledge FPInnovations and suppliers of wood products: Nordic Engineered Wood and Structurlam. The authors also express their gratitude to all interns and technicians who participated to the project including l’Échole Supérieur du Bois, Université Paris-Est Marne-la-Vallée, Université Laval and FPInnovations.

REFERENCES [1] CSA Standards. 2009. CSA O86-09 Engineering

design in wood, Canadian Standards Association. Mississauga, ON, Canada.

[2] Trayer, G. W. 1932. The bearing strength of wood under bolts. Technical bulletin No. 332. USDA Forest Serv., Forest Prod. Lab., Madison, WI.

[3] Johanson, K. W. 1949. Theory of timber connections. International Association for Bridge and Structural Engineering, Vol. 9, pp. 249-26

[4] Soltis, L. A., F. K. Hubbard and T. L. Wilkinson. 1986. Bearing strength of bolted timber joints. Journal of Structural Engineering, Vol. 112, No. 9, September, 1986.

[5] Smith, I., L.R.J. Whale, C. Anderson, B.O. Hilson, and P.D. Rodd.1988. Design properties of laterally loaded nailed or bolted joints. Can. J. Civ. Eng. 15(4): 633-643.

[6] European Committee for Standardization (CEN). 2004. Eurocode 5. Design of timber structures. Part 1-1. General. Common rules and rules for buildings. EN1995-1-1: 2004. CEN Brussels.

[7] ANSI/AWC. 2012. National design specification for wood construction. NDS-2012. American Wood Council. Washington, D.C., USA.

[8] Wilkinson, T.L. 1991. Dowel bearing strength. Res. Pap. FPL-RP-505.USDA Forest Serv., Forest Prod. Lab., Madison, WI.

[9] Sawata, K. and M. Yasumura. 2002. Determination of embedding strength of wood for dowel-type fasteners. J. Wood Sci. 48:138-146.

[10] Chui, Y. H., I. Smith, Z. Chen. 2006. Influence of fastener size on lateral strength of steel-to-wood screw joints. Forest Prod. J. 56(7/8): 49-54.

[11] Kennedy, S. 2014. Withdrawal and embedding resistance of fasteners in timber and CLT panels. Master’s Thesis. Université Laval, Quebec, CA.

[12] American Society for Testing and Materials (ASTM). 2007. D5764-97a (2007). Standard test method for evaluating dowel-bearing strength of wood and wood-based products. ASTM, West Conshohocken, PA.

[13] Canadian Wood Council (CWC) and Canadian Standard Association (CSA O86-09). 2010. Wood design manual, 2010: the complete reference for wood design in Canada. CWC. Ottawa, ON, Canada.

[14] Kennedy, S., A. Salenikovich, W. Munoz, and M. Mohammad. 2014. Design equation for withdrawal resistance of threaded fasteners in the Canadian timber design code. WCTE 2014 Proceedings, Québec, QC, Canada.

[15] Whale, R.J., I. Smith, H.J. Larsen. 1987. Design of nailed and bolted joints. Proposal for the revision of existing formulae in draft Eurocode 5 and the CIB code. Proceedings of CIB-W18A meeting, Dublin, Ireland.

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