Withdrawal Behavior of the Self-Tapping Screws in Bamboo/Wood-Oriented Strand Board

Abstract

This study examines how screw diameter, penetration length, and aperture ratio affect self-tapping screw (STS) withdrawal resistance in bamboo/wood-oriented strand board (WOSB/BOSB) to increase bamboo use in construction and furniture. It proposes a widely applicable empirical formula for calculating withdrawal resistance. With its high specific strength, uniformity, and STS withdrawal resistance, BOSB is a promising material for engineering and furniture applications, according to experiments. Screw diameter, penetration length, and aperture ratio significantly influence the STS’s withdrawal behavior. Among these, screw diameter and penetration length are the primary factors affecting screw withdrawal behavior. As the two factors increase, withdrawal resistance increases linearly. However, the relationship between withdrawal resistance and aperture ratio is non-linear, initially increasing and then decreasing as the aperture ratio increases. With an optimal mounting aperture ratio, the STS withdrawal forces in the BOSB face and edge are approximately 3 and 3.5 times greater than in WOSB, respectively. Traditional formulas for withdrawal resistance were refined based on the fitting equation of aperture ratio and withdrawal force, significantly reducing the relative errors of the modified formulas. Notably, the withdrawal resistance results for STSs calculated using the refined equation based on the CCMC 13677-R standard achieve an accuracy of up to 93%.

1. Introduction

Oriented strand board (OSB) is a material made from large, flat pieces of particleboard that are glued together in a specific direction to create a layered structure. This process preserves the high strength and toughness of OSB while maximizing the utilization rate of the raw material, achieving rates of up to 95% or more. As a result, OSB has become a popular choice in construction and manufacturing, providing an eco-friendly alternative to solid wood products. Its versatility allows for a variety of applications, ranging from flooring to wall sheathing, making it an essential component of modern building practices. OSB is primarily used as a structural material for applications such as single-layer flooring, wall and roof sheathing, and furniture components [1,2,3]. Sun et al. evaluated the potential of bamboo-oriented strand board (BOSB) to be used as an alternative structural sheathing for shear walls and diaphragms and concluded that BOSB joints showed a pattern of superior lateral load capacity [3]. In comparison to traditional wood-oriented strand board (WOSB), BOSB has rapidly developed over the past two years and offers superior strength, dimensional stability, and environmental protection characteristics [3,4,5]. Sun et al. reported that BOSB’s density and modulus of rupture were higher than those of Douglas fir and southern pine, and the average ultimate stress exceeded that of hollow columns constructed from southern pine sawn timber [4]. Furthermore, all of these studies suggest that the mechanical properties of columns constructed from bamboo-based composites compare favorably with those of common wood. Additionally, bamboo serves as a renewable biomass resource with a short growth cycle and a strong carbon sequestration capacity—three times that of wood—making it an optimal alternative to traditional building materials in alignment with the “dual carbon” goal [2,3,5,6].

The stability and endurance of a structural element of a board mostly rely on the efficacy of its connectors [7]. Self-tapping screws (STS) are extensively utilized across diverse applications owing to their straightforward installation and exceptional connection efficacy. Guo et al. found that the screw withdrawal resistance of BOSB is much higher than conventional particleboard in all directions [8]. Zhang et al. determined experimentally the strength of BOSB joint fixed with STSs and two-in-one and metal nuts utilizing threads embedded in the board have better strength and stiffness compared with common eccentric connections [2]. STSs can reduce the likelihood of splitting when employed with minimal spacing and edge distances, thereby improving operating efficiency [9]. Moreover, connections formed using STSs are not only visually appealing but also demonstrate strong mechanical properties [10]. The thread spacing and depth of STSs are engineered to divide the load appropriately between the screw and the material, thereby assuring a robust gripping force and effective connection performance [11,12]. The withdrawal resistance of STSs in oriented strand board (OSB) is a crucial factor in this scenario. Multiple studies have demonstrated that the withdrawal performance of STSs in OSB markedly exceeds that of conventional particle board (PB), with variables including the dimensions, configuration, arrangement of wood particles, and board density all affecting the withdrawal resistance of STSs [13,14,15,16]. Moreover, the diameter of the screws, the dimensions of the guide holes, and the depth of installation can influence the pull-out resistance of the screws [8,16,17]. Although previous studies have predominantly concentrated on the withdrawal force of screws, there has been insufficient examination of their comprehensive connection performance. Furthermore, investigations into the withdrawal resistance of STSs in wood-oriented strand board (WOSB) are limited and do not comprehensively examine withdrawal strength. These investigations also lack a thorough analysis of STS withdrawal resistance and a theoretical model to forecast withdrawal resistance.

Compared with WOSB, BOSB is a new type of engineering material characterized by high strength and adequate dimensional stability [4,18,19,20]. Previous studies on BOSB have primarily focused on optimizing mechanical properties, with limited exploration of screw-holding performance. Zhang et al. examined the compressive and tensile properties of L-shaped components fastened with screws, taking into account variables such as screw installation spacing and connection type [2,6]. Xu et al. developed two varieties of plug-in connectors specifically adapted to the properties of BOSB materials and evaluated them against six conventional connector kinds. Their findings demonstrate that connector performance substantially affects connection strength, implying that various boards are appropriate for distinct connectors [21]. Moreover, Guo et al. determined that screw diameter, pilot hole diameter, and installation position significantly influence the withdrawal resistance of BOSB, observing that withdrawal resistance in all directions is markedly superior to that of traditional wood particle board [8]. However, there is a gap in understanding the influence of the installation aperture ratio on the withdrawal resistance of the STSs in BOSB, and the calculation of withdrawal resistance has not been thoroughly examined. The formulation of a theoretical model is essential for the practical application of these materials in engineering contexts. Multiple researches have assessed the withdrawal performance of STS and presented theoretical models to forecast withdrawal resistance [22,23,24]. Pang et al. conducted tests on STS withdrawal resistance in hybrid cross-laminated timber composed of solid wood and plywood [25], proposing a theoretical model based on the shear mechanism. The discrepancy between predicted and experimental results ranged from 86% to 88%. Kim analyzed the withdrawal resistance of layers made from Japanese larch and yellow poplar, considering variables such as nail layer type, adhesive type, and screw direction, and introducing a formula to predict withdrawal resistance [26]. Li et al. investigated the withdrawal resistance of bamboo scrimber and established a formula for estimating the withdrawal resistance of STS in bamboo scrimber [9].

This paper presents an experimental investigation into the withdrawal resistance of STSs inserted in WOSB/BOSB for structural applications. The influences of STSs penetration length, screw diameter, and aperture ratio on the failure mode and withdrawal resistance are systematically investigated. Additionally, several relevant calculation formulas are applied to estimate the withdrawal resistance of STSs in OSB. And modified formulas for calculating the withdrawal resistance of STSs in WOSB and BOSB are proposed.

2. Materials and Methods

2.1. Materials

The BOSB and WOSB with aligned faces and random core used in the experiments were supplied by Anhui Longhua Bamboo Flooring Co., Ltd., located in Lu’an, China, and Shanghai Huqiang Wood Industry (Group) Co., Ltd., based in Shanghai, China, respectively. The thicknesses of the BOSB and WOSB are 15 mm and 18 mm, respectively (as shown in Figure 1). The BOSB was hot-pressed under a pressure of 4 MPa at 160 °C for 15 min. The hot-pressing conditions for WOSB were as follows: hot-pressing temperature of 170–210 °C, hot-pressing pressure of 4 MPa, and hot-pressing time of 10 minutes. They all have a three-layer structure and used PMDI (polymeric methylene di isocyanate) as adhesive. The STSs were made of stainless steel 304, manufactured and supplied by Fastening Star Hardware Co., Ltd., based in Zhejiang, Shanghai, China, with a length of 40 mm.

Table 1. Specification of STSs.

Outside Diameter (D) mm	Root Diameter (d) mm	Total Length (L) mm	Tail Thread Length (l) mm	Head Diameter (dk) mm	Head Length (k) mm
3	2.6	40	1.8	5.3	2
4	2.9		2.5	7.2	2.6
5	3.4		3	8.7	3
6	4.4		5.6	11.8	4.7
8	6.2		6	14.1	5.2

provides detailed dimensions of the various STSs.

The OSB cross-section (Figure 1b) demonstrates that the face and edge of both BOSB and WOSB are identical and display a pronounced layered structure. The employed particle paving method was orthogonal, indicating that the directional characteristics in the length and width of the OSBs are uniform. This experiment primarily examines the pullout performance of STSs on the face (aligned with the thickness direction of production) and the side (aligned with either the length or width direction of production) of the board.

2.2. Tests for Materials Properties

The board’s density and moisture content were assessed using ASTM D4442-92 [27] and ASTM D2395-93 [28], respectively. The static bending strength and elastic modulus of the board were evaluated using the three-point bending test method, in accordance with the standards of GB/T 17657-2022 [29]. Test specimens for materials properties testing were randomly cut from the sheet material. These samples were cut from three OSB boards sourced from different production batches, in both the parallel direction (|| along the major axis) and the perpendicular direction (⊥ along the minor axis) relative to the long edge of the board. Five specimens each were cut in the parallel and perpendicular directions. Figure 2 illustrates the testing and calculating process. The static bending strength σ (MPa) and elastic modulus E (MPa) were determined as specified by:

$$\mathsf{\sigma }={\displaystyle \frac{3\times {\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\times \mathrm{l}}{2\times \mathrm{b}\times {\mathrm{t}}^2}}$$

(1)

$$\mathrm{E}={\displaystyle \frac{{\mathrm{l}}^3}{4\times \mathrm{b}\times {\mathrm{t}}^3}}-{\displaystyle \frac{{\mathrm{F}}_2-{\mathrm{F}}_1}{{\mathrm{a}}_2-{\mathrm{a}}_1}}$$

(2)

where F_max is the maximum failure load of the sample (N), l is the span between two supports (mm), b and t are the width and thickness of the samples (mm), respectively, F₂−F₁ is the load increase determined from the straight-line section of the load–deflection curve, and a₂−a₁ is the deformation increase measured at the middle of the sample (mm).

In the Young’s Modulus, tensile strength (σ_T) and tangent modulus were measured by uniaxial tension test [30,31,32]. They were calculated as follows:

$$\mathrm{M}\mathrm{O}\mathrm{E}={\displaystyle \frac{{\mathsf{\sigma }}_2-{\mathsf{\sigma }}_1}{{\mathsf{\epsilon }}_2-{\mathsf{\epsilon }}_1}}$$

(3)

$${\mathsf{\sigma }}_{\mathrm{T}}={\displaystyle \frac{{\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{{\mathrm{S}}_0}}$$

(4)

$${\mathrm{E}}_{\mathrm{t}\mathrm{a}\mathrm{n}}={\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{T}}-{\mathrm{R}}_{0.2}}{{\mathsf{\epsilon }}_{\mathrm{T}}-{\mathsf{\epsilon }}_{0.2}}}$$

(5)

$${\mathrm{R}}_{0.2}={\displaystyle \frac{{\mathrm{F}}_{0.2}}{{\mathrm{S}}_0}}$$

(6)

where σ₂−σ₁ is the stress increase determined from the straight-line section of the stress–strain curve (MPa), and ε₂−ε₁ is the strain increase measured at the middle of the sample. F_max is the maximum failure load of the sample (N). S₀ is the area of the samples (mm²). The yield strength R_0.2 (MPa) represents the stress value that produces 0.2% residual deformation (shown in Figure 3). σ_T is the maximum stress of the sample (N), and ε_T and ε_0.2 were the strains corresponding to σ_T and R_0.2, respectively.

Test samples for determining internal bond strength (dimensions: 50 mm × 50 mm) were prepared according to GB T 17657-2022 [29]. Testing was conducted using a mechanical testing machine (model: WDW-100E, Jinan Chenda Testing Machine Manufacture Co., Ltd., Jinan, China). The crosshead speed was set to ensure that each specimen fails within 60 ± 30 seconds. The maximum load value, F_max, was recorded with an accuracy of 1%. The calculation formula is as follows:

$$\mathsf{\sigma }={\displaystyle \frac{{\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\mathrm{l}\times \mathrm{b}}}$$

(7)

where l and b were length and thickness of the samples (mm), respectively. F_max is the maximum failure load of the sample (N).

2.3. Tests for Screw Withdrawal

As per EN 1382–2016 [33], the sample size for the withdrawal test were 50 × 50 × 18 mm (length, width, height) for WOSB and 50 × 50 × 15 mm (length, width, height) for BOSB [34,35]. This study investigates the impact of screw diameter, penetration length, and penetration orientation (the planar side (face) and narrow side (edge)) on the pullout performance of OSB.

Table 2. Dimensional parameters of specimens.

Board	Direction	d (mm)	p	lef (mm) BOSB/WOSB	n
BOSB/ WOSB	Face/Edge	3	0.85	10/7	15
		4
		5
		6
		8
BOSB/ WOSB	Face/Edge	4	0.62	10/7
			0.70
			0.76
			0.80
			0.84
			0.90
			0.94
BOSB	Face/Edge	4	0.85	6.5/10.5
				8.5/12.5
				10.5/13.5
				12.5/14.5
				13.5/15.5
WOSB	Face/Edge	4	0.85	3.5/7.5
				5.5/9.5
				7.5/11.5
				9.5/13.5
				11.5/15.5

delineates the specific characteristics of the specimens, which were classified into three primary groupings. Group 1 was established to examine the impact of screw diameter, ranging from 3 mm to 8 mm, while maintaining constant values for STSs penetration length and aperture ratio. Thus, Group 1 comprised five specimens, as outlined in Table 2. Group 2 examined the influence of the aperture ratio on withdrawal resistance. Within this group, the penetration length and STSs diameter were maintained at a constant level. Consequently, six new series of specimens were evaluated in this group. Group 3 investigated the influence of penetration length on withdrawal resistance. The STSs diameter and aperture ratio were maintained at 4 mm and 0.85, respectively, with five series of specimens for each material. Each group was evaluated in two distinct installation orientations: frontal and lateral. Each specimen group, as indicated in Table 2, comprised fifteen replicates.

Before inserting the screws into the specimens, the materials were acclimatized at a relative humidity of 65% ± 3% and a temperature of 20 ± 2 °C for two weeks. Experiments were performed utilizing a mechanical testing machine (model: WDW-100E, Jinan Chenda Testing Machine Manufacture Co., Ltd., Jinan, China). A dowel-connected specialized device was employed to secure the specimen and STS. Figure 4 depicts the experimental loading device. All experiments were conducted under displacement control at a rate of 5 mm/min. All specimens were subjected to continuous loading until failure or until the applied load diminished to 80% of the maximum value attained. The experimental studies established a direct correlation between force P and displacement DP.

3. Results and Discussion

3.1. Properties of Materials

Figure 5 illustrates the failure modes of tensile and bending specimens. Figure 5a illustrates that the tensile fracture surface of the BOSB is markedly serrated and exhibits a stepped cross-section. Some bamboo shavings were extracted, while others were delineated at the cross-section. The observed appearance can be ascribed to performance discrepancies among the bamboo shavings in BOSB, where regions exhibiting diminished strength or inadequate adhesive bonding were adversely affected [19]. Conversely, the cross-section of the WOSB is comparatively flat and predominantly oriented in the vertical loading direction. This orientation minimizes crack propagation in the loading direction, ultimately resulting in a brittle fracture [36].

The bending failure morphology of BOSB and WOSB depicted in Figure 5b indicates that the elevated tensile stress on the exterior of the tensile section leads to more significant crack development. The cracks in BOSB alternate between longitudinal and transverse propagation, resulting in a serrated cross-section, mostly due to stress concentration at the bonding points of the bamboo chips. Larger bamboo shavings impeded longitudinal crack propagation, causing the cracks to spread along the edges of the bamboo shavings toward regions of lower strength and continue to propagate longitudinally [5,37]. In WOSB, the most noticeable trend of longitudinal crack propagation occurred along the growth ring boundary at the outermost tensile section, while crack propagation near the compression side was relatively limited. This limitation may be attributed to the lower strength of the wood shavings on the surface of WOSB, combined with the fact that the surface shavings were larger than those in the core layer, rendering them more susceptible to brittle fracture [5,38].

Figure 5 shows the tensile and bending loading curves of BOSB and WOSB materials. It can be seen that the tensile stress–strain curve of WOSB is approximately a straight line, and the load rapidly decreases after reaching the maximum value, indicating that the material has undergone brittle fracture [39]. The initial stage of BOSB’s load–displacement curve was linear, and the later stage was closer to the curve. This indicates that the BOSB material exhibits good toughness [2].

Table 3. Physical and mechanical properties of boards.

Material	BOSB	WOSB
Density (kg m−3)	806.61 ± 1.49	569.18 ± 7.11
Moisture content (%)	7.84 ± 0.09	6.05 ± 0.65
Modulus of rupture (MPa)	39.43 ± 3.16	16.07 ± 6.21
Modulus of elasticity (MPa)	3525.50 ± 143.3	2444.77 ± 1290.5
Tensile strength (MPa)	42.33 ± 2.65	5.97 ± 0.53
Young’s Modulus (MPa)	6743.34 ± 407	2333 ± 273.65
Yield strength (MPa)	36.54 ± 4.77	5.04 ± 0.42
Tangent modulus (MPa)	1871.85	1029.67
Internal bond (MPa)	1.34 ± 0.07	0.22 ± 0.1

presents the mechanical properties of OSB. In comparison, the density of BOSB was determined to be 806.61 kg/m³, approximately 1.4 times greater than that of WOSB. Nonetheless, the static bending strength, tensile strength, and internal bonding strength of BOSB were 2.5, 7.1, and 6.1 times more than those of WOSB, respectively, demonstrating that BOSB possesses superior specific strength [40,41]. Furthermore, the tensile strength of BOSB exceeded the static bending strength by 7%, whereas WOSB’s tensile strength surpassed it by 169%, suggesting superior homogeneity in BOSB [3]. In comparison to traditional wooden materials, it possessed superior strength and a comparable flexural modulus of elasticity [42,43]. Furthermore, the internal bonding strength associated with the withdrawal resistance of the board, BOSB, was 1.34 MPa, approximately six times greater than that of WOSB [44,45].

3.2. Withdrawal Resistance

3.2.1. Effects of Penetration Length on Withdrawal Resistance

Figure 6 depicts the correlation between the penetration length of screws and their withdrawal resistance. The results indicate that as the STSs penetration length increases, the maximum withdrawal resistance of both types of OSB also increases [8,46,47,48]. Linear regression analysis revealed a substantial linear correlation between penetration length and withdrawal resistance, with a coefficient of determination (R²) exceeding 0.91. The slope of the fitted line for the face of WOSB was 56.98, but for the edge, it was 36.44. This indicates that penetration length has a more substantial impact on the STSs withdrawal resistance of WOSB when measured on the face compared to the edge. The withdrawal resistance growth rate for BOSB was much superior to that of WOSB, suggesting that increasing penetration length can markedly enhance STSs withdrawal resistance in BOSB, which aligns with findings from Chen’s research [8]. Moreover, as illustrated in Figure 6, the withdrawal resistance value in the face direction for WOSB exceeded that in the edge direction. This observation was consistent with previous experimental results indicating that withdrawal resistance for perpendicular-to-grain directions (face and edge) was higher than for parallel-to-grain directions [7,9,48]. The higher withdrawal resistance in the surface direction could be attributed to greater fiber compaction and maximum peak density in the face layers, which were accompanied by stronger bonds [49]. For BOSB, when the penetration length was under 13 mm, the withdrawal resistance at the edge exceeded that at the face significantly. However, once the penetration length surpassed 13 mm, the withdrawal resistance on the edge became less than that on the face. This shift may be due to the high density of BOSB, which resulted in stronger adhesion between the shavings. The screws were inserted into the edge of the BOSB, aligning with the glue lines and shavings. Thus, when removing the screws, the adhesive layer and bamboo shavings’ shear strength had to be overcome [46]. Moreover, the internal bonding strength of BOSB was approximately six times that of WOSB. For smaller penetration lengths, the strength of the glue lines influenced the withdrawal resistance of STSs due to the less substantial engagement of fasteners with timber fibers [35].

3.2.2. Effect of Aperture Ratio on Withdrawal Resistance

The STS diameters and pilot hole substantially affected screw withdrawal resistance [7,46,50]. A significant correlation existed between the diameter of the pilot hole and the root diameter of the STS. The aperture ratio was defined as the ratio of the pilot hole diameter to the screw diameter. Figure 7 illustrates the effect of the STS’s aperture ratio on withdrawal resistance. It indicates that the resistance value in the withdrawal face direction (97 N to 500 N) for WOSB is greater than that in the withdrawal edge direction (226 N to 542 N). For BOSB, the screw penetration length in this section was 7 mm, suggesting that the withdrawal resistance on the edge is likely to exceed that on the face. Additionally, an increase in the aperture ratio was associated with higher STS withdrawal resistance. The findings corresponded with the research conducted by Farajollah and Leng [7,51], which indicated that increasing the pilot hole diameter or decreasing the screw diameter led to a reduced contact area between the STS and the test sample. Such changes diminished the shearing and squeezing action of the STS on the fibers due to insufficient threading, resulting in decreased withdrawal resistance [7,8,52]. However, when the aperture ratio was excessively small, the STS withdrawal resistance of the material weakens. This reduction was due to the fact that driving a screw into the material could cause shear failure at the contact surface between the layer and glue, damaging the fibers around the pilot hole and further diminishing the shearing and squeezing action of the screw on the fibers. Consequently, withdrawal resistance decreases [35].

At the optimal aperture ratio, the STS withdrawal force on the face and edge of BOSB was approximately 3 and 3.5 times greater than that of WOSB, respectively. Specifically, the aperture ratio of BOSB that yielded the highest screw withdrawal force on the face (1466 N) was around 0.71, while the aperture ratio on the edge was approximately 0.74 (1780 N). However, if the aperture ratio was too small, driving the screw into the material could resulted in protrusions or cracks around the installation holes, thereby impacting the board’s aesthetics (as illustrated in Figure 8a). Additionally, the screws may be more prone to being pulled apart [9,46]. At an aperture ratio of 0.75, the STS withdrawal force for BOSB was considerable, measuring 1265 N on the face and 1780 N on the edge, with no protrusions observed at the installation port. This finding suggests that this aperture ratio is optimal for securing BOSB.

Conversely, with WOSB, the optimal aperture ratio on the face was approximately 0.81, yielding an STS withdrawal force of 542 N. On the edge of WOSB, the withdrawal force decreased as the aperture ratio increased within the range of 0.63 to 0.95. This trend aligned with observations made in various types of wood-based panels [7,50,53]. The WOSB material has a lower density and softer texture compared to BOSB. Driving a screw into this material was more effective when utilizing a narrower pilot hole. Furthermore, the presence of more wooden materials with higher densities facilitated better trapping [7,53]. Similarly, the STS withdrawal resistance of the WOSB edge decreased with a narrower pilot hole due to damage incurred when driving the screw into the material [9,46].

The damage diagram of the board, illustrated in Figure 8. As loading increased, more and more sound was produced due to the failures of wood and bamboo fibers under the shear stress and tensile stress. Finally, when the loading reached the ultimate load, the STS was pulled out and more shear failures of the wood or bamboo occurred surrounding the STS. As shown in Figure 8b,c, the failure mode of BOSB resembles that of WOSB, where the shavings surrounding the screw were sheared and pulled out due to tensile stress. This was attributable to the fact that when an STS was inserted into the material at the edge, the shearing and squeezing action caused the fibers to shear under the ultimate load. In specimens where the screw pulled out at the edge, the failure mode combined splitting due to tension perpendicular to the grain with rolling shear failure, where the base material layer was lifted along with the screw connector [35]. Moreover, in oriented strand boards, the strands are arranged in an interlaced pattern, and the angle of the screw relative to the grain direction is not fixed, ranging from 0 to 90 degrees. Under shear forces, some wood or bamboo fibers undergo transverse tearing, and others are sheared along the grain direction and pulled out with the STSs. The final failure modes also involved cross-grain shear or splitting of the superficial first fiber layer of the block. Carradine et al.’s studied identified this failure mode as the most prevalent [54].

Figure 8d,e illustrate the failure modes of screw withdrawal from the faces of BOSB and WOSB. The withdrawal failure occurred in an infinitely thin shear layer at the surface of the OSB, which was penetrated by the screw thread, along with cross-grain shear or splitting of the superficial first fiber layer of the block [55]. As shown in the diagram, as the screw was pulled out, large bamboo shavings around the pilot hole on the BOSB face were pulled up, even causing the shavings to peel off. WOSB surfaces also exhibited bulging around pilot holes, but without significant particle delamination. This was primarily because the screw withdrawal direction was perpendicular to the particle surface, causing complete tearing of the bamboo fibers. In the later stage of loading, the load reduction rate was stable, and a certain residual withdrawal capacity remained.

3.2.3. Effects of STS Diameter on Withdrawal Resistance

The relationship graph in Figure 9 demonstrates that STS withdrawal resistance increases with an increase in screw diameter. Furthermore, a distinct linear relationship was observed between STS diameter and withdrawal force, with a fitting coefficient (R²) exceeding 0.7. The fitting coefficient for WOSB was higher than that for BOSB, indicating that linear equations offer a more precise estimation of withdrawal resistance for WOSB. Additionally, the slope of the fitted line for BOSB was steeper than that for WOSB, suggesting that the influence of STS diameter on the withdrawal resistance of BOSB was significantly stronger than that of WOSB. Moreover, the effect of STS diameter on the material edge was more pronounced than on the face.

Table 4. Results of multiple linear regression.

	Beta (Penetration length)	Beta (STS diameter)	Beta (Aperture ratio)	DW	F	p	VIF
BOSB-Face	0.715	0.396	−0.238	1.565	200.7	0.000	<10
BOSB-Edge	0.543	0.537	−0.333	1.738	183.9	0.000	<10
WOSB-Face	0.565	0.349	−0.308	1.336	81.1	0.000	<10
WOSB-Edge	0.547	0.37	−0.485	1.919	222.7	0.000	<10

presents the multivariate regression analysis investigating penetration length, aperture ratio, and STSs diameter. The Durbin–Watson (DW) value for the BOSB face is 1.565, which exceeds 1.556, indicating no correlation among the three variables. The results indicate an F-value of 200.7 and a p-value of less than 0.001, demonstrating that the regression model is statistically significant. Furthermore, the variance inflation factor (VIF) is below 10, confirming that the data adhered to the assumptions of multivariate linear analysis. A larger absolute value of the standardized regression coefficient indicates a greater impact of the independent variable on the dependent variable [56]. Table 4 illustrates that the Beta coefficient for penetration length (0.715) exceeds that for screw diameter (0.396), which is bigger than the Beta coefficient for aperture ratio (−0.238). This suggested that STSs penetration length significantly influenced the screw withdrawal resistance of the BOSB face. The primary factors influencing screw withdrawal behavior were identified as screw diameter and penetration length [51]. Penetration length at the BOSB edge significantly affected withdrawal resistance, followed by STSs diameter and aperture ratio. All three factors equally affected the screw withdrawal resistance of the WOSB face relative to the BOSB face; however, the impact of the aperture ratio at the edge was smaller than that of penetration length but greater than that of screw diameter. Thus, augmenting the screw penetration length was recognized as the most efficacious method for improving the screw withdrawal resistance of WOSB and BOSB.

3.3. Theoretical Calculation of Withdrawal Resistance

3.3.1. Existing Calculation Formulas

Currently, Eurocode 5 [57] and industry standards such as CCMC 13677-R [58] provided formulas for calculating the 5th percentile value of STSs withdrawal resistance for design purposes. Prior research on the screw withdrawal resistance of full culm bamboo, bamboo scrimbers, and laminated bamboo resulted in empirical equations that align closely with the formulas outlined in Eurocode 5 and CCMC 13677-R [24,59]. The calculation formulas specified in Eurocode 5 are as follows:

$${\mathrm{F}}_1={\displaystyle \frac{{\mathrm{n}}_{\mathrm{e}\mathrm{f}}\left(0.52{\mathrm{d}}^{-0.5}{{\mathsf{\rho }}_{\mathrm{k}}}^{0.8}\right)\mathrm{d}{\mathrm{l}}_{\mathrm{e}\mathrm{f}}{\mathrm{k}}_{\mathrm{d}}}{1.2{\cos \mathsf{\alpha }}^2+{\sin \mathsf{\alpha }}^2}}$$

(8)

where F₁ is the characteristic withdrawal force of the connection to the grain, in N; n_ef is the effective number of screws; d is the diameter of the screw; l_ef is the penetration length of the threaded part, in mm; ρ_k is the characteristic density, in kg/m³; α is the angle between the screw axis and the grain direction; and k_d is the diameter parameter, taking the smaller value of 1 and d/8, in mm.

The calculation formula specified in CCMC 13677-R is expressed as:

$${\mathrm{F}}_2={\displaystyle \frac{0.8\mathsf{\phi }\mathsf{\delta }{\left(0.84\mathrm{b}\mathsf{\rho }\right)}^2\mathrm{d}{\mathrm{l}}_{\mathrm{e}\mathrm{f}}.{10}^{-6}}{\frac{4}{3}{\cos \mathsf{\alpha }}^2+{\sin \mathsf{\alpha }}^2}}·{\mathrm{K}}_{\mathrm{D}}·{\mathrm{K}}_{\mathrm{S}\mathrm{F}}$$

(9)

where F₂ is factored withdrawal resistance; φ is the resistance factor for design purpose, =1; δ is material adjustment factor: δ = 82 for ρ ≥ 440 kg/m³, δ = 85 for ρ < 440 kg/m³; b is the material factor, b = 1; ρ = mean oven-dry relative density, in kg/m³; d is the outside screw diameter (mm); l_ef is the penetration length: l_ef = thread length − tip length (mm); K_D and K_SF are the load duration factor and service condition factor, 1.25 and 0.75, respectively [9]; and α is the angle between the screw axis and the grain direction.

Table 5. Comparison of withdrawal strength of BOSB between calculated values and test results.

Specimens	Test Result		Eurocode 8				Eurocode 9
	5th Percentile/N	Mean/N	5th Percentile/N	Relative Error/%	Estimated Average/N	Relative Error/%	5th Percentile/N	Relative Error/%	Estimated Average/N	Relative Error/%
F-P-D3	672.6	922.5	1097.7	63.2	1638.4	77.6	790.5	17.5	1179.9	27.9
F-P-D4	829.9	1041.9	1267.5	52.7	1891.8	81.6	1054.0	27.0	1573.2	51.0
F-P-D5	910.0	1196.8	1417.1	55.7	2115.1	76.7	1317.6	44.8	1966.5	64.3
F-P-D6	1585.2	2088.7	1552.4	2.1	2317.0	10.9	1581.1	0.3	2359.8	13.0
F-P-D8	1466.3	1831.2	1792.5	22.3	2675.4	46.1	2108.1	43.8	3146.4	71.8
F-P-D-H6	263.1	421.9	679.2	158.2	1013.8	140.3	527.0	100.3	786.6	86.4
F-P-D-H8	864.9	1001.0	1020.2	18.0	1522.7	52.1	828.2	4.2	1236.1	23.5
F-P-D-H10	1267.3	1514.7	1348.7	6.4	2013.0	32.9	1129.3	10.9	1685.6	11.3
F-P-D-H12	1538.8	1977.0	1668.5	8.4	2490.2	26.0	1430.5	7.0	2135.1	8.0
F-P-D-H14	1992.2	2696.2	1981.5	0.5	2957.5	9.7	1731.6	13.1	2584.5	4.1
S-P-D3	676.4	865.2	914.7	35.2	1365.3	36.63	592.9	12.3	884.9	2.3
S-P-D4	902.8	1391.3	1056.3	17.0	1576.5	11.75	790.5	12.4	1179.9	15.2
S-P-D5	1070.1	1306.9	1180.9	10.4	1762.6	25.85	988.2	7.7	1474.9	12.9
S-P-D6	1869.3	2152.1	1293.7	30.8	1930.8	11.46	1185.8	36.6	1769.8	17.8
S-P-D8	2163.2	2529.0	1493.8	30.9	2229.5	13.43	1581.1	26.9	2359.8	6.7
S-P-D-H8	758.3	1047.7	850.2	12.1	1268.9	17.43	621.1	18.1	927.1	11.5
S-P-D-H10	1305.1	1825.6	1123.9	13.9	1677.5	8.83	847.0	35.1	1264.2	30.8
S-P-D-H12	1700.0	2126.7	1390.4	18.2	2075.2	2.48	1072.9	36.9	1601.3	24.7
S-P-D-H14	1700.0	2399.1	1651.2	2.9	2464.5	2.66	1298.7	23.6	1938.4	19.2
S-P-D-H16	2138.3	2727.3	1907.6	10.8	2847.1	4.21	1524.6	28.7	2275.5	16.6

presents the predicted withdrawal resistance calculated using equations from Eurocode 5 and CCMC 13677-R. The withdrawal resistance for BOSB-face and BOSB-edge, as calculated by Eurocode 5 (Equation (8)), exhibits average errors of 39% and 18%, respectively, when compared to the 5th percentile value of the test results. Conversely, the results from CCMC 13677-R (Equation (9)) yields average relative errors of 27% and 24%, respectively. The average relative error between the calculated values for BOSB-face and BOSB-edge, as determined by Eurocode 5 (Equation (8)), in comparison to the test results is 32% and 13%, respectively. The results calculated using CCMC 13677-R give average error of 24% and 19%, respectively, is employed. This data suggested that the accuracy of Equation (9) for predicting the withdrawal resistance of STS in BOSB was superior to that of the Eurocode 5 formula, with BOSB-edge performing better than BOSB-face [9]. However, the reliability of Eurocode 5 for WOSB and BOSB were lower than that of empirical formulas for raw bamboo and bamboo scrimber [24,59]. The observed differences may arise from variances in the aperture ratio for screw installation. Unlike natural and engineered wood, BOSB was classified as a distinct type of biomass composite material. Consequently, while the fundamental structure of the CCMC 13677-R formula can be applied, it was reasonable to expect that appropriate modifications were necessary to improve the prediction of the withdrawal resistance of STS in BOSB [46,59,60,61].

The withdrawal resistance of WOSB on the face and edge was calculated using Equations (8) and (9), with the results presented in

Table 6. Comparison of withdrawal strength of WOSB between calculated values and test results.

Specimens	Test Result		Eurocode 8				Eurocode 9
	5th Percentile/N	Mean/N	5th Percentile/N	Relative Error/%	Estimated Average/N	Relative Error/%	5th Percentile/N	Relative Error/%	Estimated Average/N	Relative Error/%
F-P-D3	330.0	477.3	572.3	73.4	854.2	78.9	316.1	4.2	471.8	1.2
F-P-D4	391.9	493.9	660.8	68.6	986.3	99.7	421.5	7.5	629.1	27.4
F-P-D5	465.0	613.2	738.8	58.9	1102.7	79.8	526.9	13.3	786.3	28.2
F-P-D6	412.5	663.6	809.4	96.2	1208.0	82.0	632.2	53.3	943.6	42.2
F-P-D8	600.0	744.4	934.6	55.8	1394.9	87.4	843.0	40.5	1258.2	69.0
F-P-D-H9	268.0	352.2	385.9	44.0	575.9	63.5	231.8	13.5	346.0	1.8
F-P-D-H11	302.7	516.3	510.1	68.5	761.3	47.4	316.1	4.4	471.8	8.6
F-P-D-H13	426.3	647.6	631.0	48.0	941.8	45.4	400.4	6.1	597.6	7.7
F-P-D-H15	545.2	722.0	749.4	37.5	1118.5	54.9	484.7	11.1	723.4	0.2
F-P-D-H17	551.6	851.4	865.8	56.9	1292.2	51.8	569.0	3.2	849.3	0.3
F-P-D-H18	634.0	910.1	924.6	45.8	1379.9	51.6	611.1	3.6	912.2	0.2
S-P-D3	120.0	206.9	476.9	297.4	711.8	244.0	237.1	97.6	353.9	71.0
S-P-D4	203.7	284.2	550.7	170.4	821.9	189.2	316.1	55.2	471.8	66.0
S-P-D5	163.9	293.5	615.7	275.7	919.0	213.1	395.1	141.1	589.8	100.9
S-P-D6	283.4	392.1	674.5	138.0	1006.7	156.7	474.2	67.3	707.7	80.5
S-P-D8	351.7	589.9	778.8	121.4	1162.4	97.0	632.2	79.8	943.6	60.0
S-P-D-H11	245.6	348.6	425.1	73.1	634.4	82.0	237.1	3.5	353.9	1.5
S-P-D-H13	251.8	404.1	525.9	108.9	784.9	94.2	300.3	19.3	448.2	10.9
S-P-D-H15	323.9	500.2	624.5	92.8	932.1	86.3	363.5	12.2	542.6	8.5
S-P-D-H17	418.7	594.7	721.5	72.3	1076.8	81.1	426.8	1.9	636.9	7.1
S-P-D-H19	457.8	628.3	817.0	78.5	1219.4	94.1	490.0	7.0	731.3	16.4
S-P-D-H21	526.1	840.0	911.3	73.2	1360.1	61.9	553.2	5.2	825.7	1.7

. The table reveals that the average errors for the withdrawal resistance of WOSB face and edge, as calculated by Equation (8), are 68% and 127%, respectively. Both of these figures exceed the errors associated with the CCMC 13677-R formula, which are 17% and 39%. This suggests the CCMC 13677-R formula was a more appropriate basis for assessing the withdrawal resistance of STS in WOSB compared to Eurocode 5 [9].

3.3.2. Calculation of the Withdrawal Resistance of STS in OSB

The examination of the experimental performance and withdrawal resistance of STSs in OSB, as stated in Section 3.2, reveals that the aperture ratio has significant effects on STS withdrawal resistance in OSB. However, the current formulas in Eurocode 5 and CCMC 13677-R do not include the aperture ratio as a variable. After completing a statistical study, we integrated the nonlinear fitting equation for the aperture ratio and changed the formula to the following expression:

$${{\mathrm{F}}_1}^{\mathrm{\prime }}={\displaystyle \frac{{\mathrm{n}}_{\mathrm{e}\mathrm{f}}\left(0.52{\mathrm{d}}^{-0.5}{{\mathsf{\rho }}_{\mathrm{k}}}^{0.8}\right)\mathrm{d}{\mathrm{l}}_{\mathrm{e}\mathrm{f}}{\mathrm{k}}_{\mathrm{d}}\left[{\mathrm{a}}_1-{\mathrm{b}}_1{(\mathrm{p}-{\mathrm{c}}_1)}^2\right]}{1.2{\cos \mathsf{\alpha }}^2+{\sin \mathsf{\alpha }}^2}}$$

(10)

where F₁′ is the characteristic withdrawal force capacity of the connection to the grain, in N; n_ef is the effective number of screws; d is the diameter of the screw; l_ef is the penetration length of the threaded part, in mm; ρ_k is the characteristic density, in kg/m³, ρ_k = 1; and p is the aperture ratio. a₁, b₁, and c₁ are coefficients. For the face of BOSB, a₁, b₁, and c₁ are 0.858, 4.63, and 0.66, respectively. For the edge of BOSB, a₁, b₁, and c₁ are 1.2, 8.33, and 0.646, respectively. The faces a₁, b₁, and c₁ of WOSB are 0.623, 16.2, and 0.77, respectively, while the edges a₁, b₁, and c₁ of WOSB are 0.457, 5.8, and 0.705, respectively.

$${{\mathrm{F}}_2}^{\mathrm{\prime }}={\displaystyle \frac{0.8\mathsf{\phi }\mathsf{\delta }{\left(0.84\mathrm{b}\mathsf{\rho }\right)}^2\mathrm{d}{\mathrm{l}}_{\mathrm{e}\mathrm{f}}.{10}^{-6}.\left[{\mathrm{a}}_2-{\mathrm{e}}_2{(\mathrm{p}-{\mathrm{c}}_2)}^2\right]}{\frac{4}{3}{\cos \mathsf{\alpha }}^2+{\sin \mathsf{\alpha }}^2}}·{\mathrm{K}}_{\mathrm{D}}·{\mathrm{K}}_{\mathrm{S}\mathrm{F}}$$

(11)

In the formula, φ is the design resistance coefficient, 1; δ is the material adjustment factor, when ρ ≥ 440 kg/m³, δ = 82, and when ρ < 440 kg/m³, δ = 85; b is the material factor, b = 1; ρ is the density in kg/m³; d is the outer diameter of the screw (mm); L_ef is the penetration length; and K_D and K_SF are the load duration factor and service condition factor, respectively, with values of 1.25 and 0.75, respectively. For the face of BOSB, a₂, e₂, and c₂ are 1.03, 5.57, and 0.66, respectively, while for the edge, a₂, e₂, and c₂ are 1.6, 11.13, and 0.646, respectively. For the faces of WOSB, a₂, e₂, and c₂ are 0.979, 25.43, and 0.77, respectively, while for the edges, a₂, e₂, and c₂ are 0.797, 10.11, and 0.705, respectively.

Figure 10 depicts the calculated results of the updated formula. The graph shows that, after optimization, the relative errors decreased significantly. In particular, the relative errors in the calculation results using Equation (10) compared to the test results for the BOSB face decrease from 39% to 22%, reflecting a 43% reduction for the 5th percentile value and 25% for the average value. The BOSB edge has relative errors of 14% and 16%, respectively. Furthermore, the average error of withdrawal resistance in the WOSB face and edge, calculated using Equation (11) relative to the test results for the average value, is lowered to 25% and 16%, respectively. This study demonstrates that the calculation accuracy of the optimized formula had improved significantly, achieving an average error of less than 25% for both formulas, which confirmed the optimized formula’s strong applicability [46]. Furthermore, similar to the findings in bamboo scrimber, the accuracy of Equation (10) for the withdrawal resistance of STS in BOSB surpassed that of the Eurocode 5 formula, with the accuracy for the BOSB edge being the highest.

The relative errors in the calculation results using Equation (10) compared to the test results for WOSB face and edge is 7% and 15%, respectively, for the average value. These errors represent a reduction of 89% and 88%, respectively, when compared to Eurocode 5, as illustrated in Figure 11. In contrast, when Equation (11) is compared to the test results for WOSB face and edge, the relative errors decreased by 24% and 67%, respectively, in comparison to CCMC 13677-R. This decrease indicated a significant improvement in accuracy when utilizing the formulas derived from Eurocode 5 and CCMC 13677-R.

4. Conclusions

The withdrawal performance of screw-type fasteners (STSs) in bamboo-oriented strand board (BOSB) and wood-oriented strand board (WOSB) was investigated using experimental and date analytical methods. The primary goal of this study was to determine how penetration length, screw diameter, and aperture ratio affect STS withdrawal resistance. The calculation formulas for withdrawal resistance in both BOSB and WOSB were evaluated by comparing them to experimental results. The study data resulted in the proposal of a modified calculation formula for STSs in oriented strand boards. The results of this investigation led to the following conclusions:

(1) Material property tests indicate that the tensile and static bending strengths of BOSB were quite similar, suggesting that BOSB could generally be regarded as a horizontally homogeneous material. Additionally, its density, static bending strength, tensile strength, and internal bonding strength were 40%, 150%, 610%, and 510% greater than those of WOSB, respectively. Moreover, the internal bonding strength relevant to the STSs withdrawal resistance was approximately six times that of WOSB, signifying that BOSB was characterized by high strength, uniformity, and toughness.

(2) The STSs diameter and penetration length were critical factors that influence screw withdrawal behavior. An increase in STSs diameter and penetration length enhanced STSs withdrawal resistance. The penetration length significantly affected the STS’s face STS withdrawal resistance more than the side, and it was more obvious in BOSB than in WOSB. When the penetration length was small, the STSs withdrawal resistance at the edge of BOSB was slightly higher than that on the face; however, once the penetration length exceeds 13 mm, the STS’s edge withdrawal resistance becomes slightly lower than that on the face. Furthermore, the aperture ratio significantly impacted the STSs withdrawal resistance. The STSs withdrawal resistance first increased and then decreased as the aperture ratio of OSB varied. At an optimal aperture ratio, the withdrawal resistance on the face and edge of BOSB was approximately 3 and 3.5 times that of WOSB, respectively.

(3) Comparative examinations of various withdrawal resistance formulas indicated that the withdrawal resistance results for STSs on BOSB and WOSB, calculated using the CCMC formula (Equation (8)), were more precise than those obtained from the EN 1995 formula (Equation (7)). Additionally, the accuracy for BOSB exceeded that for WOSB. Based on the fitting equation relating aperture ratio and withdrawal resistance, along with experimental data, the traditional empirical formula had been refined. The relative errors in the calculation results using the modified formulas (Equations (9) and (10)) compared to the test results have significantly decreased, with an average error of less than 25%. Furthermore, the modified formula’s accuracy in predicting results for WOSB was greater than that for BOSB. Based on the CCMC formula (Equation (8)), a modified formula (Equation (11)) was proposed as the most suitable basis for calculating the withdrawal resistance of STSs in both WOSB and BOSB, achieving an accuracy rate of up to 93%.

A model for screw withdrawal resistance based on the product of screw diameter, penetration length and aperture ratio was shown to capture behavior well. The model could create a suitable joint and provide reference basis to fabricate a joint with the best endurance during loading in different environmental conditions. The results of this study lay the foundation for a fundamental database pertaining bamboo-based materials. This database is anticipated to play a pivotal role in the field offering valuable insights for future research and practical applications. In addition, future research should aim at the withdrawal resistance of screws or other fasteners in real dimensions and modes which are used during interior or exterior designs.