STRUTURAL PERFORMANE OF DOU-GONG BRAKETS OF YINGXIAN WOOD PAGODA UNDER VERTIAL LOADING Enchun Zhu 1, Zhiyong hen 2, Jinglong Pan 3, Frank Lam 4 ABSTRAT: Yingxian Wood Pagoda, built in 1056, is located in the town of Yingxian ounty, Shanxi Province, hina. It is the oldest and highest standing ancient wood structure in hina. The pagoda is octagon-shaped in plan, with a total height of 67.31m and a base diameter of 30.27m. It appears as a five-storeyed structure, but actually consists of nine storeys, with four shorter but stiffer storeys hidden between the five apparent storeys. Yingxian wood pagoda was built without any metal connectors like nail, screw, or bolt. Instead, Dou-Gong brackets and Tenon-Mortise joints were used to connect all posts and beams. The Dou-Gong brackets and Tenon-Mortise joints have been playing a vital role for the pagoda to resist severe winds, earthquakes and some human-induced disasters for nearly a thousand years. To evaluate the safety of the pagoda, it is, therefore, useful to investigate the structural performance of Dou-gong brackets. In this paper, a test model of typical Dou-Gong brackets of Yingxian Wood Pagoda was manufactured with a ratio of 1:3.4. The structural performance in terms of the load-carrying capacity, stiffness, load transfer paths and the failure modes of Dou-Gong brackets under monotonic vertical load was investigated both experimentally and numerically. The test and FE modelling correlated closely, the structural performance of the Dou-Gong brackets was thus revealed. Results of this study provides basis of numerical analysis of overall structure of the pagoda and reference for evaluation of the safety of the pagoda. KEYWORDS: ancient wood structure, wood pagoda, Dou-Gong brackets, structural performance 1 INTRODUTION 123 Yingxian Wood Pagoda [1], as shown in Figure 1, is located in the town of Yingxian ounty, Shanxi Province, hina. Built in 1056, it is the oldest and highest standing ancient wood structure in hina, and has been being dedicated to Buddhism [2]. The pagoda is octagon-shaped in plan, with a total height of 67.31m and a base diameter of 30.27m. It appears as a fivestoreyed structure, but actually consists of nine storeys, with four shorter but stiffer storeys hidden between the five apparent storeys. It was built without any metal connectors like nail, screw, or bolt. Instead, Dou-Gong Brackets (Dou-Gong for short, hereafter) and Tenon- Mortise joints were used to connect all posts and beams. The Dou-Gong and Tenon-Mortise joints have been playing a vital role for the pagoda to resist severe winds, earthquakes and some other human-induced disasters for nearly a thousand years. To evaluate the safety of the pagoda, it is, therefore, useful to investigate the structural performance of Dou-Gong. 1 Enchun Zhu, School of civil Engineering, Harbin Institute of Technology, P.O. box 2453, 73 Huanghe Road, Nangang Distract, Harbin 150090, hina. Email: e.c.zhu@hit.edu.cn 2 Zhiyong hen, School of civil Engineering, Harbin Institute of Technology, P.O. box 2453, 73 Huanghe Road, Nangang Distract, Harbin 150090, hina. Email: zhiyong_chen@hit.edu.cn 3 Jinglong Pan, School of civil Engineering, Harbin Institute of Technology, P.O. box 2453, 73 Huanghe Road, Nangang Distract, Harbin 150090, hina. Email: Jinglong_Pan@hotmail.com 4 Frank Lam, Department of Wood Science, University of British olombia, 4 th Floor, Forest Sciences entre, 4026-2424 Main Mall, Vancouver, B.. anada V6T 1Z4. Email: franklam@interchange.ubc.ca Figure 1: Yingxian Wood Pagoda
This study is the continuance of the work reported in reference [3]. A test model of typical Dou-Gong of Yingxian Wood Pagoda was manufactured with a geometrical ratio of 1:3.4 to the prototype. The structural performance in terms of the load-carrying capacity, stiffness, load transfer paths and the failure modes of Dou-Gong under monotonic vertical load was investigated both experimentally and numerically. The test and FE modelling correlated closely, the structural performance of the Dou-Gong was thus revealed. Results of this study provide basis of numerical analysis of overall structure of the pagoda and reference for evaluation of the safety of the pagoda. Architecturally, they are classified into 54 types, with differences between them, major or minor [1], while they are categorized into 9 types from a structural point of view [4]. According to the position in the column ring, as shown in Figure 2, Dou-Gong of Yingxian Wood Pagoda can be divided into 3 groups: 1) Dou-Gong on top of a corner column, 2) Dou-Gong on top of an intermediate column along an octagon side, and 3) Dou- 2 TEST PROGRAM 2.1 TEST MODEL Yingxian Wood Pagoda is regarded as a Dou-Gong museum with totally 480 of such connections [3]. Prototype of test (a) Perspective view of Dou-Gong 1 3 2 3 (a) Outward overhanging of Dou-Gong on the outer column ring (b) Formation of Dou-Gong 3 1 (b) Outward overhanging of Dou-Gong on the inner column ring 1 - Dou-Gong on top of a corner column; 2 Dou-Gong on top of an intermediate column; 3 - Dou-Gong on Lan-E. Figure 2: Dou-Gong of Yingxian Wood Pagoda 1 - An-Xiao (a hidden wood dowel to fix the Lu-Dou on the top of column), 2 - Lu-Dou, 3 - An-Xiao (a hidden wood dowel to fix Dou on Gong), 4 - Nidao-Gong (N1), 5 - The 1st rise Hua-Gong (H1), 6 - San-Dou, 7 - Jiaohu- Dou, 8 - An-Xiao (between Gong and Tou), 9 - Guazi- Gong, 10 - Man-Gong (N2), 11 - The 2nd rise Hua-Gong (H2), 12 - Ling-Gong, 13 - Zhutou-Fang (N3 and N4), 14 - The 3rd rise Hua-Gong (H3), 15 - Luohan-Fang, 16 - Liaoyan-Fang, 17 - Shua-Tou (H4), 18 - olumn. Figure 3: Formation of the Dou-Gong with a section of column on top of an intermediate column from the second hidden floor
Gong on a beam (Lan-E). Dou-Gong on top of a column transfers vertical load down to the pagoda base, and Dou-Gong on a beam serves as supporting the overhanging eaves and decorating the building. Similar to reference [3], the typical Dou-Gong on top of the column in the outer column ring of the second hidden floor, as indicated in Figure 2a, was selected as the prototype. A test model of Dou-Gong, as shown in Figure 3a, was manufactured using Northeast hina red pine [4], with a ratio of 1:3.4. Figure 3 gives a perspective view and a detailed description of the formation of the Dou-Gong test model. The formation and structure of the model shown in the figure are derived from the on-site survey by the authors of this paper and from reference made to Ying Zao Fa Shi (Specifications for manufacture and construction, published in 1103 AD, hinese Song Dynasty) [5] and the related literature [6]. The overall dimensions of the Dou- Gong model with a section of column are 600 mm high, 830 mm long in Hua-Gong direction, and 685 mm wide in Nidao-Gong direction. All components of the test model were manufactured following the dimension module a, being equal to 5mm, which was derived from Ying Zao Fa Shi by the ratio of 1:3.4. The crosssectional dimensions of wood used to fabricate Hua- Gong and Shua-Tou were thus 10a 21a (width depth), and 10a 15a for other Gong, Fang and Tou components. Lu-Dou was cut from wood with dimensions of 32a 32a 20a (length width depth), and 18a 16a 10a for Jiaohu-Dou and 14a 16a 10a for San-Dou. An-Xiao fixing Lu-Dou on top of column was 8a 4a 4a (length width thickness), while 4a 2a 2a was for An- Xiao between Dou and Gong, and 8a 2a 4a was for An-Xiao between Hua-Gong 5 and 11, between Hua- Gong 11 and 14, and between Hua-Gong 14 and Shua- Tou 17. The column was 500 mm in height and 175mm in diameter, which was forked and went through Dou- Gong from the top down to Lou-Dou. All components were notched and cut according to Ying Zao Fa Shi. 2.2 TEST SETUP As shown in Figure 4, the model of Dou-Gong was installed on a steel plate with a thickness of 20mm, and the steel plate was placed on the top of a screw jack. Another steel plate of 30mm thick and a load cell with a capacity of 100kN were placed on top of the column. The load cell touched the bottom of the fixed steel beam of the loading frame. The test model was held in place by applying small vertical load via the screw jack, while all ends of Gong and Fang were free of any restriction. The Dou-Gong model was loaded manually via the screw jack, and the load was measured with the load cell. Fourteen linear variable displacement transducers (LVDT) were employed to capture the displacement of the test model. They were applied to the two ends of Shua-Tou 17, Nidao-Gong 4, Man-Gong 10 and Zhutou- Fang 13, and applied to two opposite points on the column at a height level paralleling the top of Shua-Tou 17, and finally, to the two diagonally opposite corners of the bottom of the steel plate below Lu-Dou 2. The load and displacement of the test model were collected and recorded via a WS-3811 data acquisition system. Ninety-two electrical resistance strain gauges were attached, respectively, to the column 18, Lu-Dou 2, Gong and Fang for measuring strain of the key points. The strain of the test model was recorded via a DH3816 static strain measuring system. Figure 4: Model of Dou-Gong under testing 2.3 TEST PROEDURES The model of Dou-Gong was loaded following a way of load-control first and then a way of displacement-control. At the beginning, load was applied at a constant rate of 1kN/min, when the load-displacement curve deviated significantly from the initial trend, load was then applied at a rate of 0.1mm/min, until the vertical displacement reached 15mm. To this point, components of Dou-Gong yielded or failed, but the loaddisplacement still ascended with a lower slop similar to the behaviour of wood under compression perpendicular to grain. As is well known, there is not specific ultimate load for wood under compression perpendicular to grain, the test model was thus loaded to the full capacity of the load cell, at a constant rate of 1mm/min. 3 TEST RESULTS AND THE FE ANALYSIS 3.1 TEST RESULTS 3.1.1 Load-displacement curve The load-displacement curve of the Dou-Gong model is shown in Figure 5. It can be seen that the load increased linearly with displacement in the initial stage, the stiffness was about 11.1kN/mm. The relationship
between load and displacement changed into the nonlinear stage after Lu-Dou 2 fractured and yielded perpendicularly to grain. Nidao-Gong 4, Man-Gong 10 and column 18 fractured perpendicularly to grain Load(kN) 100 80 60 40 20 A B A - Failure perpendicular to grain of Lu-Dou 2; B - Yield perpendicular to grain of Lu-Dou 2; - Failure perpendicular to grain of Nidao-Gong 4; D - Failure perpendicular to grain of Man-Gong10; E-Failure perpendicular to grain of column 18; F - breaking of Nidao-Gong 4. Figure 5: Load-displacement curve D 0 0 10 20 30 40 E Displacement(mm) F progressively, and finally Nidao-Gong 4 broken. The test model of Dou-Gong carrying vertical load up to 100kN with large compression deformation was shown in Figure 6, indicating the potential to carry higher load, in a way similar to wood under compression perpendicular to grain. 3.1.2 Failure modes As shown in Figure 7, five failure modes of components of the test model were identified. Those include Lu-Dou 2 yielded and fractured perpendicularly to grain(figure 7a), Nidao-Gong 4 fractured perpendicularly to grain first and then broke finally(figure 7b), Man-Gong 10 fractured perpendicularly to grain(figure 7c), Hua-Gong 5 fractured parallel to grain(figure 7b), and olumn 18 fractured perpendicularly to grain(figure 7e). (a) Lu-Dou 2 yield and fractured perpendicularly to grain (b) Nidao-gong 4 fractured perpendicularly to grain and broken (c) Man-Gong 10 fractured perpendicularly to grain (a) Side elevation along Hua-Gong direction (d) Hua-Gong 5 fractured parallel to grain (e) olumn 18 fractured perpendicularly to grain Figure 7: Failure modes of Dou-Gong test model (b) Side elevation along Nidao-Gong direction Figure 6: Deformation of Dou-Gong test model under 100kN 3.2 FE ANALYSIS OF THE BEHAVIOUR OF DOU-GONG 3.2.1 Refined FE model of Dou-Gong A three-dimensional finite element model of typical Dou-Gong of the pagoda shown in Figure 8, with its true geometric structure, complex constitutive relationship [7]
and friction formulation between components, was developed based on ABAQUS [8,9]. All components of the refined FE model are same with the Dou-Gong test model. The whole Dou-Gong is modelled with eight-node brick element 3D8R [8], totally about 50,000 elements (70000 nodes) are used, with a typical element size of 10mm 10mm 10mm, two times of the module a. In the FE model, all components are contacted each other, following the ONTAT technique of frictiontype in ABAQUS and with a coefficient of friction (both static and kinetic) being equal to 0.5 [4]. 3.2.2 FE analytical results Vertical load is applied to the top of the column, and the base of Lu-Dou is restrained in vertical directions. The load-displacement curve and the deformed shape of the Dou-Gong are shown in Figures 9 and 10, respectively. 80 60 Load (kn) 40 20 Test data FE result 0 0 5 10 15 20 25 30 Displacement (mm) Figure 8: FE model of typical Dou-Gong Figure 9: Load-displacement curves Wood is an anisotropic material. In order to simulate accurately the behaviour of Dou-Gong, a constitutive model of wood [7], in consideration of the orthotropic elasticity, Yamada-Sun strength criterion, yield flow rule and hardening rule for compression and strain softening for post-peak stress behaviour, was proposed and encoded into the user-defined subroutine (VUMAT) in ABAQUS. Some mechanical properties of Northeast hina red pine [4], as listed in Table 1, are used to evaluate the structural performance of the test model. Table 1: Mechanical properties of Northeast hina red pine [4] (MPa) Property Value Property Value E 13743 ν 11 13 0.341 E 434 X 22 T 81.2 E 434 X 33 52.4 G 935 Y 12 T 2.2 G 76.5 Y 23 4.4 G 935 Z 31 T 2.2 ν 0.341 Z 12 4.4 ν 0.011 S 21 XY 8.3 ν 0.578 S 23 YZ 2.0 ν 0.578 S 32 ZX 8.3 ν 0.011 31 (a) Side elevation along Hua-Gong direction (b) Side elevation along Hua-Gong direction Figure 10: Deformation of Dou-Gong FE Model under vertical load
It can be seen from Figure 9 that the behaviour of the Dou-Gong FE model is very similar to the test model. The vertical load on the FE model also increases linearly with displacement in the initial stage. The relationship between load and displacement changes into a nonlinear stage after Lu-Dou 2 fractures and yields perpendicularly to grain. Nidao-Gong 4, Man-Gong 10, Hua-Gong 5, and olumn 18 fractures perpendicularly to grain progressively, and finally Nidao-Gong 4 is broken, as shown in Figure 10 and Figure11. (a) Lu-Dou 2 yields and fractures perpendicularly to grain (b) Nidao-gong 4 fractures perpendicularly to grain and is broken (c) Man-Gong 10 fractures perpendicularly to grain (d) Hua-Gong 5 fractures parallel to grain Both test and FE analysis showed that, under vertical load, Dou-Gong transferred load down mainly via column 18, Shua-Tou 17, Hua-Gong (14, 11, and 5), Gong-Fang (13, 10, and 4), San-Dou 6 and Lu-Dou 2. The structural behaviour is basically similar to wood under compression perpendicular to grain, and coupled with bending of Gong-Fang as beams. 4 ONLUSIONS A test model of typical Dou-Gong of the pagoda, with a geometrical ratio of 1:3.4 to the prototype, has been fabricated. Test and FE analysis of the structural performance of Dou-Gong under monotonic vertical loading have been conducted. The structural performance of the Dou-Gong under short-term vertical loading was thus revealed. The study aims to provide useful reference, from a structural point of view, for the preservation of cultural relics like Yingxian Wood Pagoda. The investigation, both numerically and experimentally, of structural performance of Dou-Gong under long-term loading is to be conducted. REFERENES [1] M. D. hen: Yingxian Wood Pagoda. ultural Relic Press, Beijing, 2001. [2] J. L. Pan, and E.. Zhu. Wood structures design principles. hina Architecture and Building Press, Beijing, 2009. [3] E.. Zhu, Z. Y. hen, and J. L. Pan. Finite element modelling of the structural performance of Dou- Gong brackets of Yingxian Wood Pagoda. In 11th World onference on Timber Engineering, 2010. [4] Z. Y. hen: Behaviour of typical joints and the structure of Yingxian Wood Pagoda. PhD thesis, Harbin Institute of Technology, Harbin, hina, 2011. [5] J. Li: Ying Zao Fa Shi. hina Bookstore Press, Beijing, 2006. [6] D. H. Pan: Dou-Gong Brackets. Southeast University Publishing ompany, Nanjing, 2004. [7] Z. Y. hen, E.. Zhu, J. L. Pan. Numerical simulation of mechanical behaviour of wood under complex stress. hinese Journal of omputational Mechanics, 28(04):629-634, 2011. [8] Hibbitt, Karlsson & Sorensen, Inc.: ABAQUS theory manual Version 6.1. (2000a). Pawtucket, R.I. 2000. [9] Hibbitt, Karlsson & Sorensen, Inc.: ABAQUS theory manual Version 6.1. (2000b). Pawtucket, R.I. 2000. (e) olumn 18 fractures perpendicularly to grain Figure 11: Failure modes of Dou-Gong FE model