Elastic interaction in laminated beam glued-laminated bolted timber joints with circular bolt arrangements

In multiple-bolted joints of timber structures, the tightening of bolts induces elastic interaction, wherein the initial axial bolt force changes under the influence of deformation around adjacent bolts. In this study, tightening experiments and finite-element analysis (FEA) are conducted on a laminated beam-type glued-laminated bolted timber joint featuring eight bolts in a circular arrangement to investigate the influence of the tightening sequence on the axial force of each bolt. The results show that the bolt positions where the axial bolt force is significantly reduced due to elastic interaction differ between the counterclockwise and diagonal tightening sequences. For counterclockwise tightening, the most affected bolts are located at 135° and their diagonal counterparts relative to the center of the bolt arrangement. In this case, FEA indicates that the reduction in axial bolt force is caused by a decrease in the embedment stiffness of the washers into the wood, which in turn is due to the diagonal contact surface between the washers and the wood beneath adjacent bolts. For diagonal tightening, the most prominent reductions occur at 180° and their diagonal counterparts, which are attributed to a cumulative reduction in axial bolt force resulting from the sequential tightening of both adjacent bolts.

Bolted joints are among the most common methods for joining timber structures [1]. The frictional resistance force between members that is generated by the initial bolt-tightening force (hereinafter referred to as the axial bolt force) enhances the stiffness, bearing capacity, and damping performance of the joint [2,3,4,5,6,7]. Awaludin et al. reported that even when the axial bolt force is reduced by stress relaxation in the wood, frictional damping effects can still contribute to the overall damping behavior, depending on the residual axial bolt force [8]. The authors have previously proposed wood friction joints employing vertical compression of the wood and have demonstrated the overall damping effects, etc., through shake table tests and stress relaxation experiments conducted on load-bearing walls incorporating dampers [9,10,11,12]. Given that the frictional resistance force is proportional to the vertical force, i.e., the axial bolt force, managing the axial bolt force is critical. However, no axial bolt force management method has been established for timber structures, and it is only stated in the literature [13] that the washers should be slightly embedded into timber. In our previous study, methods such as torque control [14, 15] or the rotation angle approach [16] are viable options for axial bolt force management. However, for joints with multiple bolts, the phenomenon of elastic interaction, wherein axial force changes as a result of deformation around adjacent bolts, poses a significant challenge. For wood friction joints, achieving uniform axial bolt force is essential to ensure consistent performance. Therefore, identifying the bolt positions that are most affected by elastic interaction is critical for effective axial bolt force management.

In a previous report, the authors analyzed a wood friction joint with four bolts arranged in a single row, with parameters including tightening order, bolt spacing, and wood thickness. The findings revealed that as the bolt spacing increased, the variation of axial force was reduced, regardless of the tightening order [17]. On the other hand, when bolts are placed in a circular arrangement, the extent to which embedment deformation of the washer into the wood affects adjacent bolts varies with position. Therefore, the degree of variation in axial bolt force is expected to be different from the case where bolts are placed in a linear arrangement. However, to the authors’ knowledge, there has been no research on the elastic interaction associated with circular bolt arrangements in bolted timber joints. Therefore, this study investigated the elastic interaction in laminated beam-type glued-laminated bolted timber joints with circularly arranged bolts, focusing on changes in the axial bolt force due to elastic interaction. A tightening experiment was conducted, with the bolt-tightening sequence as a parameter, to determine the degree of variation in axial bolt force and the most affected bolt positions. The experimental results are presented alongside findings from finite-element analysis (FEA).

Bolt tightening test of moment-resisting bolted timber joints

Figure 1 shows the experimental setup. The specimen size and bolt arrangement were determined according to reference [18]. The wood material used was glued-laminated timber (E105-F300, Japanese Agricultural Standards; density: 521 ± 30.9 kg/m³) composed of layers of Pinus sylvestris of different grades. It measured 1000 mm (longitudinal direction) ×ばつ 300 mm (radial direction) ×ばつ 55 mm (tangential direction). Eight M12 bolts (Z-mark fastener conforming to the standards of the Japan Housing and Wood Technology Center; length: 150 mm; thread pitch: 1.75 mm) were used to fasten the steel plate to two pieces of laminated timber in a circular arrangement, as shown in Fig. 1. After inserting the bolt, the nut was lightly hand-tightened. The lamina designated as L100 was positioned directly under the washers of bolts 3 and 7, while lamina L80 was situated under the washers of the remaining bolts. The L100 lamina exhibited a Young’s modulus of 10,000 MPa in the grain direction. The outermost layer of the laminated timber consisted of an L125 lamina. Axial bolt forces were measured using strain gauges embedded in the bolts, as shown in Fig. 2, and were calibrated using a universal testing machine before the experiment. The washers employed were φ32 mm ×ばつ 3.2 mm thick with a 13.5 mm bolt hole in the center and φ45 mm ×ばつ 4.5 mm thick with a 13-mm bolt hole. Bolts were tightened by applying torque to the nut on the φ32 mm ×ばつ 3.2 mm washer side using a torque wrench. Two tightening sequences were tested: Pattern A, wherein bolts were tightened sequentially in a counterclockwise direction, and Pattern B, wherein bolts were tightened diagonally (Fig. 1). In addition, the bolt was tightened once in order to understand the effect of axial force changes due to basic elastic interactions in this study. Tightening was halted when the axial bolt force reached 2 kN, which is considered to be within the elastic range. A period of 1 min was allowed to pass before tightening the next bolt in the sequence. Axial bolt force was measured using a data logger with a sampling frequency of 10 Hz. A total of six specimens were tested.

Finite-element analysis

FEA of the specimen was performed using Abaqus 2019. Figure 3 illustrates the finite-element models, comprising wood, bolts, washers, and steel plates near the joint. The models were developed using the incompatible-mode eight-node brick element (C3D8I). The dimensions of the components were based on the experimental setup, as shown in Fig. 3. Distinctions were made between the material properties of L125, L100, and L80 lamina, as shown in Fig. 3. Nuts were omitted to minimize computational load and bolts were directly connected to washers in the model. The finite-element model consisted of 83,780 nodes and 63,693 elements.

The yz-plane at the base of the steel plate was assumed to be completely fixed. The augmented Lagrangian method was used to solve the contact problems between wood and washers (φ30) and wood and steel plates. However, the wood–washer (φ45) contact was coupled to prevent separation and divergence due to elastic interaction during bolt tightening. The coefficient of friction between wood and washer and between wood and steel plate was set to 0.3 [19,20,21]. A bolt tension of 2 kN was applied using the bolt load function in Abaqus. In order to account for the contact damage zones of wood, the contact stiffness of wood was evaluated using the formula [22]:

where A is the contact area and S_c is a constant that varies depending on the wood type. Given that the S_c value for lamina is unknown, a value of 2600 N/mm² from the literature [22] was used. Table 1 presents the material properties of the laminated timber. Poisson’s ratios were sourced from the literature [23], while nominal Young’s moduli were used in the longitudinal direction. Young’s moduli in the radial and tangential directions, as well as shear moduli in the LT, LR, and RT planes, were determined based on ratios derived from softwood lumber data [24]. The Young’s modulus E and Poisson’s ratio ν for bolts, washers, and steel plates were set to 205 GPa and 0.3, respectively.

Residual axial bolt force

Figure 4 shows a typical graph of axial bolt force ratio versus time obtained from the experiment, while Fig. 5 shows the axial bolt force ratios and their variations after completion of the bolt-tightening sequence. Here, the axial bolt force ratio, α, was calculated using:

where F_f is the axial bolt force measured 1 min after tightening, and F_T is the axial bolt force at T s after tightening.

First, for Pattern A, the axial bolt force ratio of bolt 2, as shown in Fig. 4(a), decreased immediately after tightening bolt 3. Similarly, the axial bolt force ratios of bolts 3, 6, and 7 also decreased, but the decreases in bolts 4 and 5 were less pronounced. This behavior can be attributed to the relative positioning of bolts 4 and 5, which are almost parallel to each other in the width direction (perpendicular to the grain direction). Consequently, the deformation of the washer caused by tightening bolt 5 had minimal impact on bolt 4. By contrast, the axial bolt force ratio of bolt 1increased slightly immediately after tightening bolt 2, and then decreased slightly immediately after tightening bolts 5, 6, and 7. Given that bolts 1 and 5 are arranged diagonally in the longitudinal direction (aligned with the grain direction), washer deformation in bolt 5 may have affected bolt 1. However, the effect was limited because the bolts were separated by a distance of 200 mm. The spread of embedment deformation in the longitudinal direction is proportional to the thickness of the material, with the displacement effectively dissipating at a distance approximately 1.5 times the material thickness [25]. For this specimen, the calculated distance was 165 mm (= 1.5 ×ばつ (55 mm ×ばつ 2)). As the washer ends of bolts 1 and 5 were 168 mm apart, it is assumed that, even if the deformation of the washer of bolt 5 reached bolt 1, the amount of deformation would be minimal, and thus the reduction in the axial bolt force ratio would also be minimal. On the other hand, the axial force ratio of bolt 1 slightly increased immediately after tightening bolt 2, presumably because the washer of bolt 1 tilted slightly due to the tightening and the tightening of bolt 2 created a levering action. In general, the axial bolt force ratios of bolts 2 and 6 were lower than those of the other bolts, although their variations were slightly larger.

On the other hand, for Pattern B, depicted in Figs. 4b and 5b, the axial bolt force ratios of bolts 3 and 7 were lower than those of the other bolts. This reduction can be attributed to the axial bolt force ratios decreasing twice because of the tightening of bolts on both sides. In Pattern A, the axial bolt force ratio exhibited a significant reduction due to stress relaxation immediately after tightening. Conversely, in Pattern B, stress relaxation was notably suppressed. During the experiment, after completing Pattern A, the nuts were loosened to eliminate the axial bolt force before proceeding with Pattern B. It is believed that stress relaxation was suppressed because creep recovery was insufficient between the two patterns. The results indicate that the bolt positions with more prominent reductions in the axial bolt force ratio due to elastic interactions depend on the tightening sequence. Within the scope of this experiment, these positions were the 135° direction and its diagonal bolts when tightened in for counterclockwise sequence (Pattern A) and the 180° direction and its diagonal bolts when tightened in the diagonal sequence (Pattern B), relative to the center of the bolt placement circle.

Comparison of finite-element analysis and experimental results

Figure 6 presents a comparison between the axial bolt force ratios obtained from FEA and the experimental average values after the completion of bolt-tightening sequences. In Pattern A, the analytical values slightly exceeded the experimental values but qualitatively captured the observed trends. In Pattern B, on the other hand, the analytical values closely matched the experimental results and accurately reproduced the observed trends.

Figure 7 shows a contour plot of displacement in the Z direction (thickness direction) based on the FEA results. The contour plot represents the rear side of the tightened surface. For Pattern A, immediately after tightening bolt 1, the displacement spread radially in a circular distribution centered on the bolt hole. Next, when bolt 2 was tightened, a similar circular displacement distribution emerged, although it did not appear to affect bolt 1. However, upon tightening bolt 3, the displacement around bolt 2 increased and took on an elliptical shape. A similar interaction was observed when bolt 4 was tightened, further increasing the elliptical displacement around bolts 2 and 3. Notably, by tightening bolt 4, the displacement near bolt 1 also increased, forming a circular distribution that expanded further when bolt 5 was tightened. The deformation distribution observed for Pattern B exhibited similar characteristics to that for Pattern A. Thus, elastic interactions notably influence bolts 2, 3, and 4, as well as their diagonals (bolts 6, 7, and 8), which are aligned along the grain direction. Qualitatively, the FEA results aligned closely with the experimental results.

The mechanical behavior was further analyzed by evaluating the embedment stiffness of the washer into the wood at each bolt position for Pattern A. Figure 8 shows the relationship between axial bolt force and axial displacement calculated by FEA, where displacement is defined as the change in distance between the two ends of the bolt, while embedment stiffness is represented by the slope. The results indicate that the embedment stiffness for bolts 1, 2, 5, and 6 remained largely unchanged. By contrast, bolts 3, 4, 7, and 8 exhibited slip-like nonlinear behavior in the initial phase, resulting in lower initial embedment stiffness compared to the other bolts. The slope of the linear region for bolts 3 and 7 was steeper than that for the other bolts, which is likely due to the presence of the L100 lamina directly under these positions. The reduced initial embedment stiffness of bolts 3, 4, 7, and 8 may be attributed to the elastic interactions with adjacent bolts and the oblique contact between the washer and wood surface. Figure 9 shows a magnified view of the deformation around bolt 3. These observations indicate that the low axial bolt force ratios observed for bolts 2 and 6 were due to the tightening of 2 and 6 reducing the embedment stiffness at bolts 3 and 7, which in turn increased the embedment deformation at bolts 2 and 6.

The changes in axial bolt force resulting from elastic interactions were investigated both experimentally and analytically for a laminated beam-type glued-laminated bolted timber joint with eight bolts arranged in a circular arrangement, with the tightening sequence considered as a parameter. The key findings of this study are summarized as follows:

1. 1.

   When the bolts were tightened in a counterclockwise sequence, there was a significant reduction in the axial bolt force ratio at positions aligned with the grain direction. The most pronounced reductions occurred at the bolts positioned at 135° and their diagonal counterparts relative to the center of the circular bolt arrangement. Finite-element analysis showed that this reduction could be attributed to a decrease in the embedment stiffness of the washers into the wood directly beneath adjacent bolts. This reduction in stiffness was caused by the diagonal contact surface formed between the washers and the wood.

2. 2.

   In the case of diagonal tightening, as in the case of counterclockwise tightening, the axial bolt force ratio at positions oriented along the grain direction exhibited significant reductions. The most notable reductions occurred at the bolts located at 180° and their diagonal counterparts relative to the center of the circular bolt arrangement. This reduction was attributed to a cumulative decrease in axial force due to the sequential tightening of bolts on both sides.

Not applicable.

FEA:

Finite-element analysis

We would like to thank Uni-edit (https://uni-edit.net/) for editing and proofreading this manuscript.

This work was supported in part by the research grant of the Maeda Engineering Foundation.

Authors and Affiliations

1. Tokyo University of Agriculture and Technology, 3-5-8, Saiwai-cho, Fuchu-shi, Tokyo, 183-8509, Japan

   Doppo Matsubara

2. The University of Kitakyushu, 1-1, Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka, 808-0135, Japan

   Masaki Teranishi

3. Forestry and Fisheries Research Center, Toyama Prefectural Agricultural, 4940, Imizu, Toyama, 939-0311, Japan

   Yoshiaki Wakashima

Contributions

DM designed and performed the experiments and analyzed the data. MT performed finite-element analysis and analyzed the data. YW analyzed the data. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Doppo Matsubara.

Ethics approval and consent to participate

Not applicable.

Consent for publication

We agree to allow our manuscript being published.

Competing interests

The authors declare that they have no competing interests.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions