A novel procedure for evaluating the rotational stiffness of traditional timber joints in Taiwan
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1 Structural Studies, Repairs and Maintenance of Heritage Architecture IX 169 A novel procedure for evaluating the rotational stiffness of traditional timber joints in Taiwan W.-S. Chang, M.-F. Hsu & W.-C. Chen Department of Architecture, National Cheng Kung University, Taiwan Abstract The timber joint is one of the most important factors that affect the global behavior of timber structures in all over the world. This paper aims at proposing a new procedure for evaluating the rotational stiffness of timber joints found in Taiwan. Firstly, dismantled surveys were conducted on five historic timber structures; the results showed that three various types of timber joints can be found in beam-to-column timber joints; a nondestructive testing method was proposed and applied on a total of 72 full-scale specimens to propose a method to classify the timber joints. The results showed that stress wave velocity and amplitude transmission ratios are feasible for distinguishing the joint types. Thirdly, bending tests were applied on these 72 specimens to obtain the bending slip characteristics and rotational stiffness of these timber joints. Statistical approach was employed to analyze the data and propose models to estimate the bending slip characteristics and initial rotational stiffness for each joint type. The results showed that the bending slip characteristics could be estimated by using slip due to rigid body motion, whereas dimensions and material properties of timber joints can help to predict initial rotational stiffness. Lastly, from the discussion previously, a reliable procedure for evaluation of rotational stiffness of beam-to-column timber joints was proposed. Keywords: Chuan-Dou timber structures, historic timber structures, timber joints, semi-rigid behavior. 1 Introduction The traditional timber structures in Taiwan were originated from Mainland China hundreds years ago, which can be divided into two main categories: Chuan-Dou (Figure 1) and Dei-Dou timber structures. Large quantities of
2 170 Structural Studies, Repairs and Maintenance of Heritage Architecture IX Chuan-Dou timber structures still exist in Taiwan so far, thus it is an urgent need to establish a safety evaluation method for these timber structures. In the past, the timber joints were assumed as pin connection, due to lack of knowledge of mechanical behavior of these timber joints. For advanced analyses, however, the mechanical performances, such as rotational stiffness, of these timber joints should be obtained, as they will affect the load transfer of the global structure. Much effort has been devoted on studying the mechanical behavior in the past decades, such as Brungraber [1], Kessel and Augustin [2], Inayama [3], Chang and Hsu [4]. This paper aims at proposing a new method for evaluating the rotational performance of beam-to-column timber joints of traditional Chuan- Dou timber structures as illustrated in Figure 1. Beam-to-column joints Figure. 1: Traditional Chuan-Dou Timber structures of Taiwan. 2 Dismantled survey A total of five historic timber structures were dismantled and investigated. One of the cases is illustrated in Figure 2. The dismantled survey indicated that beamto-column joints can be divided into three various types: (1) continuous type, (2) flat cut type and (3) dovetail connected type; as shown in Figure 2 and schematized in Figure 3. However we should notice that these various types of timber joints have the same appearances and cannot be visually identified outside these joints. Although the reasons why three various types of timber joints exist in these timber joints are still in question. The results of interviews of master carpenters show that: (1) The beam would be cut into several pieces so that it will be easier to compose the global structures. (2) Once the beam is too long to find an appropriate wood material, the beam might be composed by two different wood materials and connected by dovetail connections. The questions opened herein includes: (1) How can we classify the joint type nondestructively in case the mechanical performances of these various joints are quite different? (2) How can we evaluate the mechanical performances of these various types joints in the future?
3 Structural Studies, Repairs and Maintenance of Heritage Architecture IX 171 Figure. 2: Three different types of timber joints exist in a timber structure. Continuous type Connection Dovetail type Connection Flat cut type Connection Figure 3: Illustration of three types of timber joint. 3 Classification of timber joints A nondestructive method, considering the stress wave velocity and energy transmission, was developed to classify the joint types. Figure 4 demonstrates the instrumentation of the nondestructive testing. Two piezoelectric transducers, called starter sensor and receiver sensor, were used to calculate the stress wave velocity in material. The two sensors aforementioned are positioned on beam element at two sides of the column element with space of 30cm. A hammer was employed to strike the starter sensor. The time-history records were recorded simultaneously by High-speed data acquisition system at the sampling rate of 5KHz. A factor represents energy transmission is defined as the ratio of the maximum pulse amplitude found in starter and receiver sensor, and illustrated in figure 5: H R ATR = (1) H S
4 172 Structural Studies, Repairs and Maintenance of Heritage Architecture IX 2D Tomograph 30cm Data Logger Computer Figure 4: Nondestructive testing setup. Figure 5: Time-history records of starter and receiver sensors. A total of 72 full-scale specimens, each join type consists of 24 specimens, were tested. Analysis of variance (ANOVA) was used to analyze the experimental results. The results are shown in Figure 6 and 7, which indicates that stress wave velocity should be measured to distinguish the continuity of the beam. In the other hand, if the stress wave velocity in beam element is high, the joint should be continuous type; by contrast, the joint could be flat cut or dovetail connected. Furthermore, once the stress wave velocity in beam element is low, amplitude transmission ratio (ATR) in beam elements should be calculated afterward. If the ATR is high, the joint type should be dovetail connected, in contrast, low ATR exist in the cases that joint types are flat cut.
5 Structural Studies, Repairs and Maintenance of Heritage Architecture IX 173 Figure 6: Experimental results of stress wave velocity distribution of three various types of timber joints. Figure 7: Experimental results of amplitude transmission ratio distribution of three various types of timber joints. 4 Mechanical experiments of timber joints The bending tests were conducted on the 72 full-scale specimens mentioned in the previous section. The experimental installation was illustrated in Figure 8. Monotonic loading was applied on the specimens.
6 174 Structural Studies, Repairs and Maintenance of Heritage Architecture IX LVDT Load Cell Amplifier Data Logger Figure 8: Experimental installation. 4.1 Initial bending-slip characteristics All over the world, the typical moment-rotation relationship of traditional timber joints consist of the initial slip, and this is one of the significant characteristics of timber joints. As illustrated in Figure 9, the initial slip is resulted from two parts, including slip due to rigid body motion and due to limited compression length in the early stage. The slip due to rigid body motion is directly related to gap between beam and slot of column. The structural behavior of timber joints in initial slip stage means that the joints behave as a pin connection without any moment resistance capacity, and usually can be regarded as hinge connections. The global behavior of timber joints should behave as pin connection in the early stage and as semi-rigid connection afterward the early stage. To estimate the initial slip can help us to understand the range that the joint behave as a hinge connection. The initial slip can be evaluated by slip due to rigid body motion, and expressed as follows [5]: For continuous type: Si = S r (2) For flat cut type: Si = S r (3) For dovetail connected type: S i = 1.68 Sr (4) where S i and S r respectively represent the initial slip and slip due to rigid body motion. The slip due to rigid body motion can be obtained by measuring the clearance between beam and slot of column divided by the column width.
7 Structural Studies, Repairs and Maintenance of Heritage Architecture IX 175 Figure 9: Typical moment-rotational relationship of timber joints. 4.2 Initial rotational stiffness The rotational stiffness in the elastic stage is an important factor that should be obtained to analyze the timber structures. The theoretical models of continuous type timber joints were proposed by the author [6]. However, in order to propose simpler models for engineers to predict the initial rotational stiffness, statistical approach were employed in this section. The results of statistical analyses of three various types of timber joints can be expressed as follows: For continuous type joints: 3 Cw Bw E K i, C = (5) Bd 2 R a = For flat cut type joints: 3 Cw Bw E K i, FC = (6) Bd R 2 = For dovetail connected joints: K i, DC = Bw E (7) R 2 = where K i,c (kg-m), Cw (m), Bw (m), Bd (m) and E (kg/cm 2 ) are, respectively, initial rotational stiffness, width of column, width of beam, beam depth and modulus of elasticity of wood perpendicular to grain. Good agreements can be found between predicted and experimental results in three various types of
8 176 Structural Studies, Repairs and Maintenance of Heritage Architecture IX timber joints. The results of the analyses further indicate that we can evaluate the initial rotational stiffness of timber joints by using their dimensions and material properties in the future. Previous section pointed out that two different portions would compose the beam if the carpenters cannot find out an appropriate wood material. To discuss effect of this treatment, Figure 10 was plotted. The Y-axes of Figure 10 represent the ratio of initial rotational stiffness between flat cut type joints and continuous type joints. It can be found that the ratio decrease incorporated with increase of 3 parameter Cw Bw E / Bd. Thus the rotational stiffness of flat cut joints is only approximately 15% of the continuous type joints with identical geometrical and material conditions. This treatment will significantly degrade the initial rotational stiffness. The phenomenon described in previous paragraph is obvious and easy to understand. The initial rotational stiffness of timber joints degrades significantly if the continuous beam was cut into two separate portions without any mechanical connection K K i, FC i, C Cw Bw E Bd Figure 10: Comparison of initial rotational stiffness of a continuous type joints with flat cut type joints. 5 Establishment of evaluation procedure for rotational stiffness of timber joints Previous discussions enable us to establish an evaluation procedure for rotational stiffness of timber joints. As the rotational performances of various timber joints are different, it is important to classify the joint type prior to evaluation of the rotational performance of timber joints. The bending slip characteristics and initial rotational stiffness are two of the important factors of interest, thus after
9 Structural Studies, Repairs and Maintenance of Heritage Architecture IX 177 the joint type has been determined, the bending slip characteristics and initial rotational stiffness can be evaluated by using equation (2) to (4) and (5) to (7), respectively. The evaluation procedure is shown in Figure 11. Stress wave velocity Yes Fast No Amplitude transmission ratio Nondestructive testing High No Yes Continuous type Flat cut type Dovetail connected type Evaluating Bending Slip Evaluating Rotational Stiffness Equation (2) Equation (3) Equation (4) Equation (5) Equation (6) Equation (7) Figure 11: Evaluation procedures for rotational stiffness of timber joints. 6 Conclusions A novel method for evaluation of rotational stiffness has been presented in this paper, which consists of nondestructive testing method and measurement of dimensions and material properties of timber joints. From the discussions in this paper, following conclusions can be drawn: 1. The stress wave velocity and amplitude transmission ratio can be employed to classify the joint type for intact materials. Further study should be concentrated on the deteriorated materials. 2. Measuring the dimensions and material properties, such as elastic modulus of wood perpendicular to grain, can help us to evaluate the bending slip characteristics and rotational stiffness of timber joints.
10 178 Structural Studies, Repairs and Maintenance of Heritage Architecture IX 3. The method proposed in the paper can be used for evaluation of rotational stiffness of traditional beam-to-column timber joints in Chuan-Dou timber structures. Acknowledgement This paper was supported by Grant-in-Aid from National Science Council ( E ) of Taiwan. The authors would like to appreciate these supports. References [1] Brungraber, R. L. Traditional Timber Joinery: A Modern Analysis. Ph.D. Dissertation, Department of Civil Engineering of Stanford University, Palo Alto, California [2] Kessel, M. H. and R. Augustin. Load bearing capacity of timber connections with wood pegs. Timber Framing, Journal of the Timber Framers Guild. 39: [3] Inayama, M. Design of compressive strain resistance connections (Nuki). Kenchiku-Gijutu 547: (In Japanese) [4] Chang, W. S. and M. F. Hsu. Mechanical characteristics of traditional Go- Dou and Stepped Dovetail timber connections in Taiwan. Taiwan Journal of Forestry Science (in press). [5] Chang, W. S. On rotational performance of traditional Chuan-Dou timber joints in Taiwan. PhD dissertation, Department of Architecture of National Cheng Kung University, Taiwan [6] Chang, W. S., M. F. Hsu, and K. Komatsu. Rotational performance of traditional Nuki joints with gap I: theory and verification. Journal of Wood Science (in press)
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