The load factor in bolted timber joints under external tensile loads

Abstract

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 wet–dry 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.

Load factor

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:

$$ W = F_{\text{t}} + F_{\text{c}} . $$

(1)

Fig. 1

A bolted joint under an external tensile load

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]:

$$ \phi = \frac{{F_{\text{t}} }}{W} $$

(2)

Substituting (2) into (1) yields

$$ F_{\text{c}} = \left( {1 - \phi } \right){\kern 1pt} {\kern 1pt} W. $$

(3)

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

$$ W_{\text{sep}} = {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \frac{{F_{\text{f}} }}{1 - \phi }. $$

(4)

Fig. 2

Schematic diagram of the relationship between axial bolt force and external load

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.

Materials and methods

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/m³, 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 was 88 × 88 × 24 mm (bolt hole: Φ14.5 mm). Three and four different conditions were chosen, respectively, for initial tightening force (F_f) and distance from the washer to the member end (L)—a potential contributor to shear fracture—to determine their effects on load factor: F_f = 13, 21, 30 kN, L = 100, 130, 160, 190 mm (respective bolt lengths = 210, 240, 270, 300 mm). These F_f values correspond to 30, 50, and 70% of the bolt’s 0.2% strength, determined by bolt tensile tests conducted in advance. The initial tightening force was applied by tightening the nut with a torque wrench, until the predetermined axial force appeared on a washer-type load cell installed in the steel base of the test apparatus (LCW-S-60KNSD22, Rated capacity: 60 kN, Kyowa electronic instruments corp.). Expecting some initial stress relaxation to F_f, the bolt was tightened to 0.3–0.5 kN higher than this value; testing started once the pre-set F_f was reached. Tests were done using a universal tester (AG-100kNX Plus, Shimadzu Corp.). A tensile load was applied parallel to the bolt axis, which was measured by a load cell attached to the crosshead, and increased monotonically until timber member or bolt destruction was observed. Crosshead speed was 5 mm/min. Displacement was measured by two pairs of transducers (DTH-A-30-K, Rated capacity: 30 mm, Kyowa electronic instruments corp.): one on either notched sides of the timber, and a front/rear pair between the ‘legs’ of the member end and the steel foundation (see configuration in Fig. 3). Three joints were tested in each condition (n = 36 total).

Fig. 3

Tensile test method for glued laminated timber joints with a tensile bolt

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 failure of the bolt occurred in fully threaded portion in all specimens in the L = 130 mm condition (see 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.

Fig. 4

Representative curves of relationship between external load and displacement of notch

Fig. 5

Representative curves of relationship between axial bolt force and external load

Fig. 6

Failure states of glued laminated timber members and tensile bolts after tensile test

Table 1 Results of load factor and mechanical properties of joints

Fig. 7

Relationship between stiffness and load factor

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, 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.

Interface separation load

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_sep-exp. 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.

Fig. 8

Representative curves of relationship between external load and displacement of joint interface

Fig. 9

Comparison between calculated and experimental values of W_sep

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.