**Cyclic behavior of self-tapping screwed laminated bamboo lumber connections subjected to cycle loadings**,"

*BioRes*. 14(4), 7958-7976.

#### Abstract

Self-tapping screws are commonly used to connect critical structural components, such as legs to rails in chair construction, using laminated bamboo lumber (LBL) materials. The loosening of a connection is commonly seen in self-tapping screwed LBL connections before actual breakage of connections happens. The loosening of connections, especially those associated with chair legs, can significantly affect chair stability. Current furniture performance test standards have not address this issue, i.e., the minor loosening of a connection is not treated as a failure in the current standard because of the lack of better understanding the load-rotation-time behavior of various connections subjected to the cyclical loads. The effects of cyclic loading magnitude and orientation on the load-rotation-time behavior of L-shaped, end-to-side, single self-tapping screwed LBL connections were investigated. Results indicated that the Burger and Kelvin models could be used to describe the cyclic and recovery behavior of studied connections. Increasing the cyclic loading magnitude resulted in a decreasing trend for all viscoelastic constants. The most significant decrease in all viscoelastic constants occurred when the cyclic loading magnitude applied to connections increased from 50 to 60% of its corresponding ultimate static resistance loads.

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#### Full Article

**Cyclic Behavior of Self-tapping Screwed Laminated Bamboo Lumber Connections Subjected to Cycle Loadings**

Chen Chen,^{a,b }Zhangning Ye,^{c} Xiaohong Yu,^{c,}* Onder Tor,^{d} and Jilei Zhang ^{a,b,*}

Self-tapping screws are commonly used to connect critical structural components, such as legs to rails in chair construction, using laminated bamboo lumber (LBL) materials. The loosening of a connection is commonly seen in self-tapping screwed LBL connections before actual breakage of connections happens. The loosening of connections, especially those associated with chair legs, can significantly affect chair stability. Current furniture performance test standards have not address this issue, *i.e*., the minor loosening of a connection is not treated as a failure in the current standard because of the lack of better understanding the load-rotation-time behavior of various connections subjected to the cyclical loads. The effects of cyclic loading magnitude and orientation on the load-rotation-time behavior of L-shaped, end-to-side, single self-tapping screwed LBL connections were investigated. Results indicated that the Burger and Kelvin models could be used to describe the cyclic and recovery behavior of studied connections. Increasing the cyclic loading magnitude resulted in a decreasing trend for all viscoelastic constants. The most significant decrease in all viscoelastic constants occurred when the cyclic loading magnitude applied to connections increased from 50 to 60% of its corresponding ultimate static resistance loads.

*Keywords: Laminated bamboo lumber; Cyclic loading; Cyclic behavior; Recovery; Burger model; Kelvin model; Connection; Furniture; Self-tapping screw*

*Contact information: a: College of Furnishings and Industrial Design Nanjing Forestry University Nanjing, Jiangsu 210000 China; b:* *Department of Sustainable Bioproducts, Mississippi State University, 201 Locksley Way, Mississippi State, MS 39762-9820, USA; c: School of Engineering, Zhejiang Agriculture and Forestry University, Zhejiang, China; d: Department of Forest Industry Engineering, Faculty of Forestry, Kastamonu University, Turkey; * Corresponding author:* *jz27@msstate.edu and yuxiaohong@zafu.edu.cn*

**INTRODUCTION**

Laminated bamboo lumber (LBL) is made through hot pressing of anti-deterioration, insect-treated, and planed bamboo strands together with thermoset adhesives, such as phenol-formaldehyde, to form rectangular cross sections. LBL materials have tremendous growth potentials in furniture applications such as chairs as frame stocks.

Self-tapping screws are commonly used to connect critical structural components, such as legs to rails in chair construction, using LBL materials. These connections in daily chair usage are commonly subjected to repeated forces associated with opening and closing, which can yield significant moments applied to these critical connections, such as the leg-to-front rail. An opening force acting on a chair leg tends to push the leg in, *i.e.*,* *it tends to open the angle between the leg member and a rail member, while a closing force tends to push the leg outward, *i.e.*, tends to close the angle between the leg and its connected rail member. The loosening of a connection is commonly seen in self-tapping screwed LBL connections, before actual breakage of connections happens. The loosening of connections, especially those associated with chair legs, can significantly affect chair stability. The durability performance of chair leg connections could be evaluated using cyclic loads, or subjecting chair legs to front to back or side-thrust one-sided (zero-to-maximum) cyclic loads (GSA 1998). However, minor loosening of a connection is not treated as a failure in the current standard. The leg performance tests of current BIFMA (2012) and CNS (2013) chair testing standards are based on the static loading concept, and they have not addressed the failure of connections associated with chair legs subjected to cyclic loading.

Understanding the behavior of connections under moment rotation are essential for many applications (Bodig and Jayne 1982). The relationships between the applied moment, in terms of static, creep, and cyclic moment, and the angle of rotation is commonly measured, therefore assisting in the design of a structure. Zhang *et al.* (2001, 2003) investigated moment-rotation behaviors of T-shaped, two-pin, wooden dowel connections in solid wood, and wood-based composites. The relationship between the moment (*M*) and internal connection rotation (*ϕ*) was obtained through fitting the linear regression function (*ϕ* = *ZM* + *b*) to the observed moment-rotation data, which ranged from the zero-rotation point to the point where the connection reached its ultimate moment resistance. Experimental results indicated that the connection stiffness *Z*-values were of the approximate magnitude of 10^{-6} rad./lb.-in. Furthermore, Zhang *et al.* (2003a, b) studied the fatigue life of T-shaped, end-to-side, two-pin dowel connections subjected to different levels of one-sided constant amplitude and stepped cyclic bending loads. The moment *versus* the log number of cycles to failure was obtained, but no moment-rotation relationship was investigated.

There is limited literature studying the cyclical behavior of self-tapping screwed LBL connections in terms of its moment-rotation-time relationship when subjected to cyclic loading. Similar to its creep behavior, the cyclic behavior of a material can be defined as the time-dependent deformation phenomena exhibited by a material under sustained loading for extended periods (Bodig and Jayne 1982). Cyclic loading commonly occurs in furniture daily usage, and its performance testing is similar to a chair leg test (GSA 1998), where the leg and its associated connections are subjected to cyclic loading. The cyclic behavior of a time-dependent material can be represented mathematically with the Burger model to account for its elastic, delayed elastic, and viscous behaviors, while the Kelvin model is commonly used for predicting the deformation recovery behavior of deformed materials.

The cyclic behavior of a self-tapping screwed LBL connection needs to be investigated, not only for developing mathematical models of the connection for theoretically understanding the problem, but also for practically understanding how the loosening of the connection is developed during a cyclic loading process. Furthermore, it needs to be understood how this loosening process is related to the angle of rotation of the studied connection. Therefore, a future quality assurance testing program can be proposed to address this issue of loosening connections through setting. For instance, the minimum angle of rotation for a tested connection needs to be evaluated, with the fundamentals being understood.

This study investigated the cyclic behavior of self-tapping screwed LBL connections subjected to one-sided constant amplitude cyclic moment loads. The intention was to propose a mathematical model to represent the moment-rotation-time behavior of self-tapping screwed LBL connections in furniture applications such as frame stocks. The specific objectives were to 1) use the Burger model to describe the cyclic behavior of self-tapping screwed LBL connections subjected to cyclic loads; 2) use the Kelvin model to describe the recovery behavior of self-tapping screwed LBL connections after cyclic loads were released; 3) derive mathematical equations for estimating the angle of rotation of self-tapping screwed LBL connections after being subjected to cyclic loads and releasing cyclic loads; and 4) evaluate the effects of the cyclic loading level and loading orientation on viscoelastic constants of derived empirical equations.

**EXPERIMENTAL**

**Materials**

Two sizes of pre-fabricated LBL materials, 400 mm long × 50 mm wide × 20 mm thick and 140 mm long × 50 mm wide × 20 mm thick, were supplied by Zhejiang Yongyu Bamboo Co., Ltd, Huzhou, Zhejiang, China as structural members for the connections evaluated in this study. Stainless steel self-tapping sheet metal screws (Table 1 and Fig. 1) were purchased from a hardware store (Linan, Zhejiang, China).

**Table 1.** Self-tapping Sheet Metal Screw Critical Dimensions

Note: Values in parentheses are coefficients of variation in percentage.

**Fig. 1. **The general configuration of a self-tapping screw with its critical dimensions

**Experimental Design**

*Static loading tests*

The general configuration of an L-shaped, end-to-side, single self-tapping screwed LBL connection is shown in Fig. 2. In general, a self-tapping screwed LBL connection consisted of a LBL post member attached to a LBL rail member through a single self-tapping screw. The post member measured 400 mm long × 50 mm wide × 20 mm thick with a 7 mm diameter through hole, and an 11 mm diameter and 3 mm deep sink hole drilled with their centers located at the center-line of the post member width and 50 mm from one end (Fig. 2c). The rail member measured 140 mm long × 50 mm wide × 20 mm thick with a 5 mm diameter and 45 mm deep pilot-hole drilled at an end of the rail member.

**Fig. 2.** The configuration of an L-shaped, end-to-side, single self-tapping screwed laminated bamboo lumber connection evaluated in this study: its top view (a), side view (b), and the location and size of pilot-holes drilled to connection members (c)

A complete one-factor factorial experiment was conducted in ten replications for each configuration to evaluate the ultimate vertical moment load carrying capacity of the self-tapping screwed LBL connections. The factor was the orientation of an applied vertical load on a post member (opening and closing loadings). Opening loading (Fig. 3a) refers to a vertical load applied to the end of a post member, which tends to enlarge the connection angle between the post and rail members, while closing loading (Fig. 3b) refers to the load applied to the end of a post which tends to reduce the connection angle between two connection members. Therefore, a total of 20 connections were evaluated in connection static testing.

**Fig. 3.** Loading orientations and setups for evaluating the ultimate vertical moment load carrying capacity of self-tapping screwed laminated bamboo lumber connections subjected to (a) static opening and (b) closing loadings, respectively

*Cyclic loading tests*

A complete two-factor factorial experiment, with five replications per combination, was conducted to evaluate the factors on the cyclic and recovery behaviors of self-tapping screwed LBL connections.

The two factors studied were the orientation of an applied vertical cyclic load on a post member (opening and closing loadings) and cyclic load level (80, 70, 60, and 50 percent of the corresponding mean ultimate vertical load value measured in each of two static loading tests for self-tapping screwed LBL connections). Therefore, a total of 40 connections were subjected to one-sided (zero-to-maximum), constant amplitude cyclic loading tests in this study.

**Specimen Preparation**

Before the connection assembly operation, all pre-cut and pre-drilled connection member supplies, one source of post members, and one source of rail members were conditioned in a humidity chamber controlled at 20 ± 2 ℃ and 50% ± 5% RH for two weeks. All post and rail members for constructing connections for static and cyclic loading testes were randomly selected from the two connection member supplies, respectively.

All static and cyclic tests were performed right after the connection assembly operation. The environmental condition for the cyclic testing room was measured at an average temperature of 26 ℃ and a relative humidity of 50%. The specific gravity and moisture content of LBL materials were tested according to CNS (2009a, 2009b), respectively.

**Testing**

*Static loading tests*

All connections were tested on a DNS50 universal testing machine (CRIMS, Jilin, China) at a loading rate of 10 mm/min. Figure 3 shows the set-ups for measuring the ultimate vertical load exerted on the self-tapping screwed LBL connections. All opening or closing loads were applied to the post 275 mm in front of the rail. Ultimate vertical load values and connection failure modes were recorded.

*Cyclic loading tests*

Connection cyclic loading tests were conducted with a specially designed air cylinder and pipe rack system; *i.e. *the connection rail was clamped down to a fixture attached to the flat surface of a metal base. All one-sided, constant amplitude cyclic opening or closing loadings were applied to the post 275 mm in front of the rail (Fig. 4). Each of four cyclic load levels was applied to the connection at a rate of 8 cycles per minute for 5000 cycles. The instantaneous angle of rotation for a tested connection was measured at the beginning of each test, followed by measuring the angle of rotation at 500-cycles intervals. After the cyclic loading was removed, the recovery angle of rotation was measured for 12 h. The angle of rotation for an unloaded connection was measured in 5 min intervals at the beginning. After 30 min, the angle of rotation was measured in 30 min intervals.

The angle of rotation of a post member in a tested connection was measured through the end displacement of the post member, *Δ *(mm), with its point located at the end of the post 325 mm in front of the rail. Specifically, the internal connection rotation angles, *ϕ* and *θ* (degree), were calculated using Eq. 1 (Fig. 4a) and Eq. 2 (Fig. 4b), respectively, for opening and closing loading.

(a) |
(b) |

**Fig. 4.** Diagrams illustrating where connections were loaded and angles of rotation were measured for evaluating cyclic and recovery behaviors of self-tapping screwed laminated bamboo lumber connections subjected to one-sided, constant amplitude cyclic (a) opening and (b) closing loadings

**RESULTS AND DISCUSSION**

**Basic Physical Properties**

The LBL specific gravity averaged 1.09 with a coefficient of variation (COV) of 6.4%, while the moisture content averaged 8.5% with a COV of 7.0%.

**Static Loading Tests**

The ultimate vertical static load of self-tapping screwed LBL connections subjected to static closing loading averaged 330 N, while its corresponding COV value averaged 8.4%. Alternatively, the self-tapping screwed LBL connections subjected to static opening loading had its ultimate vertical loads average 272 N with an averaged COV value of 8.3%. In general, connections failed with typical modes of rail member end splitting, the self-tapping screw bending, and screw withdrawal from the rails (Fig. 5).

(a) |
(b) |

**Fig. 5.** Typical failure mode of post member end splitting for connections subjected to (a) static opening and (b) closing loadings

Based on the static loading test results, the levels of one-sided, constant amplitude cyclic loadings applied to self-tapping screwed LBL connections were 264, 231, 198, and 165 N for opening loading, and 218, 190, 163, and 136 N for closing loading, respectively.

**Cyclic Loading Tests**

Figure 6 shows the typical cyclic and recovery curves recorded in this study in terms of the angle of rotation between post and rail members of self-tapping screwed LBL connections as a function of cyclic time.

Primary and secondary stages of rotation as a function of time (Bodig and Jayne 1982) were identified for all cyclic curves recorded for evaluated self-tapping screwed LBL connections. The primary stage is the region in which the rate of rotation is decreasing, while the region in which the angle of rotation as a function of time is approximately linear is designated as the secondary stage.

Table 2 summarizes the mean values of elastic, total, and viscous rotations measured during the cyclic loading period and recovery process after cyclic loads were removed from all tested connections. Elastic rotation is the instantaneous rotation measured at the beginning of testing load application. This rotation will recover instantaneously after the applied cyclic load is removed. Total rotation is the sum of elastic, delayed elastic, and viscous rotations. Delayed elastic rotation is time dependent and recoverable. Viscous rotation is permanent and non-recoverable. Each value in Table 2 is a mean of five replicates.

**(a)**