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)

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)

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.