The load factor in bolted timber joints under external tensile loads

These experiments sought to empirically determine how the initial tightening force influences the ratio of the axial bolt force to the tensile load (load factor) and the load required to separate the joint interface (interface separation load) in tensile bolted joints of glued laminated timber. Load factor decreases with increasing initial tightening force; however, this tendency is reduced the greater the washer–member-end distance. In addition, tensile stiffness increases with decreasing load factor, and the interface separation load increases with increasing initial tightening force. However, in actual testing, the joint interface separated at a lower load that predicted mathematically based on the load factor and initial tightening force.


Introduction
Bolted joints are the most common type of joining method utilized in wooden structures [1]. Bolted joints are tightened with a nut during their installation, however, the force generated (initial tightening force) cannot hold up in the long term due to stress relaxation of the wood [2]. However, the frictional resistance between members produced by this force not only improves the joint's stiffness and strength, but also its long-term damping capacity [3][4][5][6][7][8]. The authors have long been interested in developing load-bearing walls, which leverage the friction created when wooden members are fastened together (or to steel plate) with bolts or lag screws. Our team has already reported on the structural performance of these joints [9][10][11], how to control the initial tightening force [12][13][14][15], and their long-term stress relaxation behavior [16][17][18]. In the last case, we have shown that these joints can withstand relatively high stress when the initial tightening force exceeds the compressive yield point of the wood, even when exposed to repeated wetdry cycles [18]; and that they can withstand at least 70% of any vertical compressive stress applied to the wood, even in a high-temperature, constant-humidity environment [17].
While our understanding of the mechanical properties and stress relaxation behavior of bolted joints under an initial tightening force (simply "fastened" below) continues to improve, nearly all studies on the subject have concerned their shear resistance. The resistance of bolted joints can be analyzed in two respects-in response to a tensile force, or a shear force-but there have been no basic research to date into the behavior of fastened bolted joints subjected to a load parallel to the bolt axis.
When a tensile load acts on fastened bolted joint, not all of it is counteracted by the axial bolt force: some is borne by a clamp force at the joint interface (resulting from the initial tightening force). The ratio of the increase in the bolt axial force to the load is known as the load factor, an important value in design specifications; however, nearly research on it has been in the context of bolted joints in mechanical structures (e.g., pressure vessels, plants, automobiles) [19][20][21][22][23][24][25][26]. When a tensile load acts on an unfastened bolted timber joint, the concept of load factor can be applied to deduce that, since 100% is borne by the bolt, the clamping force at the interface is reduced to zero, and the two members completely separate. Conversely, fastening the bolt with the initial tightening force both decreases the axial load on the bolt itself and prevents the members from separating at the interface. This makes the load factor a crucial quantity for our understanding of the behavior of fastened bolted joints under tensile loads. However, there have been no studies that explore the effects of the initial tightening force on the load factor, or the force at which the members come apart (interface separation load), in bolted timber joints.
This study consisted of tensile testing of tensile bolt joints, a tension/moment-resistance type of joint [27][28][29][30][31][32], fastened by an initial tightening force. The specific goals were to gain basic knowledge about how this force affects the load factor and interface separation load in bolted timber joints. Figure 1 shows a bolted joint. Two wooden members are clamped together with a bolt and nut by initial tightening force F f . When external load W acts parallel to the bolt axis, the bolt axial force increases by F t , while the force at the interface decreases by F c . This can be expressed as:

Load factor
This equation can be applied until the joint interface is completely separated. Unfortunately, this equation has two unknowns, making it a statically indeterminate system.
The ratio of F t (the increased axial force on the bolt) to W is expressed by φ, a quantity known as the load factor [19]: If φ is known, F t and F c can be derived. These series of equations imply that lower values of φ result in greater F c and less residual stress at the joint interface. In addition, higher values of φ result in greater F t , a greater proportion of W acting on the bolt, and greater axial deformation. Figure 2 is a schematic diagram of how φ should be conceived based on the equations above. Axial bolt force (F f + F t ) is on the vertical axis, the external load (W) is on the horizontal axis, and φ is the slope of the initial line. Once W becomes large enough to completely separate the joint interface, the axial bolt force becomes equal to W. This interface separation load (W sep ) can be expressed as This equation signifies that W sep can be increased by maximizing F f . While it likewise means that large values of φ would have the same effect, this would simultaneously increase the load on the bolt, as noted above. The salient points to remember when designing a bolted timber joint with minimal bolt deformation and interfacial separation are to configure φ as low as possible, and F f as large as possible. Figure 3 shows a schematic of the experimental set-up. Wood specimens were heterogenous glued laminated timber ("glulam") of Japanese larch (Larix kaempferi, grade: E105-F300 (by Japanese agricultural standard), density [mean ± S.D.]: 541 ± 50.00 kg/m 3 , moisture content: 9.4 ± 1.05%). Bolts were M12 double-ended studs (pitch: 1.75 mm, material: Z mark fastener by standard of Japan Housing and Wood Technology Center). Washer A

Materials and methods
a Initial clamping state b When external tensile load is applied  Fig. 3). Three joints were tested in each condition (n = 36 total).

Results and discussion
Relationship between the axial bolt force and external load Figure 4 shows the representative curves of relationship between external load and displacement for all test conditions, as measured by the pair of transducers attached to the notched sides of the timber. Figure 5 shows the representative curves of relationship between axial bolt force and external load. First, in all series in Fig. 4, the profiles show a distinct pattern: a rapid and linear rise in external load early on, increasing proportional to the external load as the slope changes. Shear failure was observed under the L = 100 mm condition in the area from the lower washer (washer A: see Fig. 3) to where the legs meet the wood block (see Fig. 6a) in 6/9 specimens (n = 2 at F f = 13 kN, 3 at 21 kN, and 1 at 30 kN). Shear failure occurred in the screw thread in the remaining three specimens in this condition, and in all specimens in the L = 160 and 190 mm conditions (see Fig. 6c), and tensile  Fig. 6b). Next, in all series in Fig. 5, after an initial linear segment, the axial bolt force approaches equivalence with the load at higher loads. In addition, W sep -i.e., the external load at which the initial linear segment intersects with the 45° 'identity' line (axial bolt force = external load)-becomes greater with increasing F f , irrespective of L. This trend is identical to that reported in [19]. Table 1 shows values for load factor φ calculated from the initial linear segment using the least-squares method. The table also shows stiffness K, calculated by the least-squares method for the initial linear slope in Fig. 4, as well as maximum tensile strength P max and the displacement at maximum strength δ max . The initial linear slope of φ and K were decided as the interval from external load 1 kN to 6.5 kN (when F f is 13 kN), from 1 to 10.5 kN (F f = 21 kN), and from 1 to 15 kN (F f = 30 kN). φ ranges from 0.02 to 0.04, meaning that 2-4% of the external load is borne by the bolt axis. According to Eq. (1), the remaining more than 95% is  acting to separate the joint interface. In addition, average values of φ decreases with increasing F f in the L = 100, 130, and 160 mm conditions, but this relation grows weaker at higher L. K also increases with increasing F f under the L = 100, 130, and 160 mm conditions. Figure 7 shows the relationship between K and φ. This correlation is relatively distinct, showing decreasing K with increasing φ. This tendency is presumed to be due to the tensile elongation of the bolt. Under the L = 190 mm condition, however, F f has no apparent associations with either φ or K.
Yoshimoto et al. found φ to be near constant and independent of F f [19], contrasting with the trends observed here under most of the test conditions (L = 100, 130, 160 mm). Sawa [20] demonstrated, both theoretically and empirically, that in bolted-joint assemblies of metallic material, φ varies depending on the spring constant of the bolt and that of the material being fastened, and that it greatly varies depending on the position of the external load is applied. In this experiment, the position of external load application is same in all series. However, stress distribution may change to F f in region from the washer to the member end (L). Therefore, we can deduce that the spring constant and load factor varied in response to changes in stress distribution to F f in the L = 100, 130,  Fig. 7 Relationship between stiffness and load factor and 160 mm conditions; since stress distribution did not change with F f in the L = 190 mm condition, the load factor did not change appreciably. Figure 8 shows the representative curves of relationship between external load and the displacement between the glulam leg and steel foundation for all test conditions. These profiles are similar to in Fig. 4: the external load increases as the initial slope changes, in a manner proportional to F f . Initially, the joint is stiff, with almost no displacement. These figures can be used to determine W sep-exp. -the observed load required to completely separate the joint interface-and compare it with corresponding theoretical values derived from Eq. (4) above (W sep-cal. ). W sep-exp. was defined as the external load of just before the gradient changes in initial behavior. Figure 9 shows the results. Overall, W sep-cal. tended to be greater than W sep-exp. It is considered that most of W sepexp. was evaluated as start of separation load. This can be seen from, for example, L = 100 mm × F f = 21 kN condition in Fig. 5, the curve starts to become non-linear at the external load lower than W sep-cal. On the other hand, four specimens with W sep-exp. clearly larger than W sep-cal. For example, when focusing on L = 130 mm × F f = 30 kN condition in Fig. 5, the bolt axial force indicates a linear inclination of 45° with the external load larger than W sep-cal . It is considered that the joint interface was not completely separated until the external load larger than W sep-cal.

Interface separation load
From these results, the joint interface begins to separate at the lower external load than W sep-cal. On the other hand, there is also the behavior of completely separating under the external load greater than W sep-cal. Therefore, its care must be taken when evaluating the joint interface separation behavior.

Conclusions
In this study, we empirically investigated the effects of the initial tightening force of a bolted, glued laminated timber joint on its load factor and interface separation load when placed under a tensile load. The following major findings can be concluded from the data: 1. Load factor decreases with increasing initial tightening force; however, this tendency is reduced, the greater the washer-member-end distance. 2. Stiffness decreases with increasing load factor. 3. Interface separation load increases with increasing initial tightening force. 4. The joint interface begins to separate at the lower external load than theoretical values for interface separation load calculated based on load factor and initial tightening force.