Download gong model

Original Article Open access Published: 26 November 2024 Journal of Wood Science volume 70, Article number: 54 (2024) Cite this article AbstractDou-gong is important component of ancient timber buildings in China, Japan, and South Korea, etc. It has important decoration and load transferring functions. Due to its complex structure, Dou-gong is difficult to be fully analyzed in large-scale structured. Therefore, it is necessary to establish a reliable and simplified Dou-gong calculation model. In this study, some traditional Chinese timber buildings built in the Song and Yuan dynasties (960–1368 AD) are investigated, and the characteristics of the typical Dou-gong model are obtained. Experimental study and refined finite-element analysis of the typical Dou-gong model is then carried out to study the load transferring mechanism under horizontal load. Then, the load path is extracted from the force-flow perspective to establish a simplified beam element model. The simplified model is then numerically and experimentally verified. The results show that the simplified model has a good consistency with the experimental model, and it is suitable for large-scale structural analysis of ancient timber buildings. IntroductionDou-gong (Fig. 1) plays an important role in the overall structure of ancient timber buildings in China, Japan, and South Korea. It has a great decoration function, but also transfers the roof and horizontal loads [1]. However, Dou-gong has a special form and complex structural composition. Its mechanical properties are very different from the mechanical properties of a timber column, a timber beam, and a beam–column joint. Therefore, obtaining mechanical properties of Dou-gong is important for evaluating the structural performance of ancient timber buildings. In recent years, some scholars have used experimental research to determine typical failure modes of Dou-gong [2, 3], and studied its energy dissipation characteristics [4,5,6,7], joint stiffness [8, 9] and other characteristics. On the other hand, some scholars have studied the mechanical properties of Dou-gong through theoretical derivation and refined finite-element model analysis. According to the coordination of rocking and racking deformation and the existing method on backbone characterization of traditional timber elements, Wu et al. [10] established an analytical model on the lateral load–displacement relationship of Dou-gong joints. Based on the three-dimensional elastic–plastic damage constitutive model of wood, Wang et al. [11] carried out the finite-element model analysis on hysteretic behavior of Dou-gong. Due to the complex structure of Dou-gong, the calculation speed of the refined finite-element model analysis of Dou-gong is very slow, which is not suitable for large-scaled structural analysis. Therefore, some scholars [12,13,14,15] have tried to find a simplified method. Most of them used spring elements to simulate the semi-rigid characteristics of Dou-gong, but this method ignored the specific geometric structure of Dou-gong. Li et al. [16] used Euler beam to simulate the horizontal component of Dou-gong, and used multiple elastic links and multiple plastic links to simulate the vertical component. Although the geometric characteristics of Dou-gong were taken into account, the model was not optimized, making the simplified model too complex.Fig. 1Dou-gong layer in the main hall of the Tian-ning templeFull size imageAs

Shown in Fig. 1c, Dou-gongs in the Dou-gong layer are categorized according to the different constraints: the Dou-gong located above the corner column is called Zhuan-jiao, the Dou-gong located above the side column is called Zhu-tou, and the Dou-gong located above the Fang between columns is called Bu-jian. Bu-jian is the most numerous Dou-gong in the Dou-gong layer, so the study of a typical Dou-gong is carried out based on its features, constraints and loading conditions.As shown in Fig. 2, in this study, a simplified modeling method of Dou-gong is proposed through four stages. In stage I, a typical Dou-gong is designed based on real features by conducting a research on Dou-gongs’ feature in the Chinese traditional timber buildings built in the Song and Yuan Dynasties (960–1368 AD). In stage II, the experimental study and refined finite-element model analysis are carried out to analyze the load transferring mechanism of Dou-gong. The experimental study provides the basis for verification of the simplified model in stage IV, while finite-element analysis provides the basis for the force flow analysis in stage III. In stage III, the simplified method is proposed, which includes extracting simplified model members through force flow analysis, calculating member dimensions and setting constraints and loading conditions. In stage IV, the simplified method is verified by comparing the simplified model with the experimental model. Through this study, for the Dou-gong that is similar in real features to the typical Dou-gong designed in stage I, the simplified method in stage III can be used to establish a reliable and efficient finite-element calculation model.Fig. 2Flow chart of the studyFull size imageTypical Dou-gong model designThis section explores some Chinese traditional timber buildings built in the Song and Yuan dynasties (960–1368 AD). The characteristics of Dou-gongs are sorted out to summarize the typical Dou-gong model.The basic structure of Dou-gongDou-gongs of traditional timber buildings built in the Song and Yuan dynasties are the classic Dou-gongs. They are similar to those in Japanese and South Korean traditional timber buildings. They mainly consist of Dou, Gong, Ang and other additional components (Fig. 3).Fig. 3Dou-gong componentsFull size imageGong can be divided into two types according to position. One is Hua-gong in the x-direction used as a load-bearing member; the other is Heng-gong in the y-direction which plays the stabilization role. Dou is divided into four types, including Lu-dou at the bottom of Dou-gong, Jiao-hu-dou at the end of Gong and Ang, Qi-xin-Dou at the middle of Heng-gong, and San-dou at the end of Heng-gong. Ang is an inclined member, including Xia-Ang and Shang-ang. The other members mainly include Shua-tou, Xue-xie, Hua-tou-zi, Dian mu, and Fang.The progressing layers of Dou-gong’s overhanging are achieved by Hua-gong and Ang. The overhanging from Lu-dou to the inside or outside of Hua-gong or Ang is called a Tiao. Each layer of Dou-gong is called Pu-zuo. It shows the overlapping relationship between Dou, Gong, and other members. In general, the number of Tiao is equal to the number of Hua-gong plus the number of Ang,

LoadFull size imageThe differences in structural stiffness between the simplified model and the test are then compared. The load–displacement curves of the simplified and experimental models under horizontal load are shown in Fig. 31. The simplified model fits well with the experimental results in the early stage of loading. The relative error between the results of the experiment and the simplified model is less than 10% for displacements ranging from 4 to 32 mm. As possible and late damages to the material are not considered in the finite-element analysis, a significant reduction in the stiffness of the simplified model does not occur at a later stage. Overall, the results of the finite-element analysis of the simplified model are in good agreement with the experimental results of structural stiffness (Table 4).Fig. 31Comparison diagram of the lateral stiffnessFull size imageTable 4 Comparison of simplified model result and experiment result in lateral stiffnessFull size tableBy comparing the deformation and lateral stiffness of the experimental model and simplified under horizontal load, it can be found that the simplified model reflects the displacement patterns of the experimental model relatively well. In conclusion, the simplified model is in good consistency with the experimental model. On the one hand, because the simplified model uses the beam element for modeling and analysis, the computational efficiency is significantly improved. On the other hand, in the large-scale finite-element calculations of traditional timber structures, the beam element is often used for simulation, so the simplified model of Dou-gong is unified in the use of elements. Therefore, the simplified model proposed in this study is a suitable method for large-scale finite-element calculations of traditional timber structure.ConclusionIn this study, the simplified model of Dou-gong under horizontal load is studied. First, the typical Dou-gong style is summarized based on the investigation of some classic traditional timber buildings in China built in the Song and Yuan Dynasties (960–1368 AD). The refined finite-element modeling of the typical Dou-gong is performed to analyze its displacement pattern, stress distribution and force flow paths under horizontal load. Based on the results of the finite-element analysis, a simplified model for the typical Dou-gong is proposed, and the calculation methods of the section size of each member are given on the basis of equivalent stiffness. Finally, the reliability of the simplified model is verified based on experimental results. The main conclusions are as follows: (1) The typical Dou-gong style in the Song and Yuan dynasties has the following characteristics. Six Pu-zuo is the main form of Dou-gong used in the traditional hall timber buildings. The overhanging is achieved using Hua-gong and Xia-Ang in the outer part, and using Hua-gong and other members in the inner part. The form in the middle is the overlap of Gong and Fang. In terms of selecting members, some members may be omitted, or a single member may be used to replace a group of members to simplify the structure. (2) In the simplified model of Dou-gong, the section size should be adjusted according to the

Stress state of each member. For the second type of members in the y-direction, the unit composed of Dou and Gong is simplified into three beam elements on the basis of equivalent stiffness principle. The section size reduction factor varies from 0.39 to 0.47 according to the grade of Cai. (3) For the third type of members, the section size should be defined by considering the stress state of each member. For the first kind, namely O-2, the section size reduction factor can be 0.71–0.85. For the other two kinds, the section size can be determined by the projection area on the force transmission paths. (4) The simplified model of Dou-gong retains good consistency with the experimental model under horizontal load. In general, the simplified model can simulate the mechanical behavior of Dou-gong and is a suitable method for the large-scale structural analysis of the ancient timber buildings in China, Japan, and South Korean. (5) In further research, simplification method for other Dou-gong types, such as Zhu-tou and Zhuan-jiao types will be studied. Availability of data and materialsThe data sets used and/or analyzed during the current study are available from the corresponding author on reasonable request.ReferencesWu YJ, Song XB, Li K (2018) Compressive and racking performance of eccentrically aligned Dou-gong connections. Eng Struct 175:743–752Article Google Scholar Chen Z, Zhu E, Lam F, Pan J (2014) Structural performance of Dou-Gong brackets of Yingxian Wood Pagoda under vertical load—an experimental study. Eng Struct 80:274–288Article Google Scholar Wu C, Xue J, Song D, Ren G, Zhang J (2022) Mechanical performance of inclined Dougong bracket sets under vertical load : experimental tests and finite element calculation. J Build Eng 45:103555Article Google Scholar Cao J, Zhao Y, Liu Y, Lu H, Wang W (2021) Load-carrying capacity analysis of traditional Chinese Dou-gong joints under monotonic vertical and reversal lateral loading. J Build Eng 44:102847Article Google Scholar Meng X, Li T, Yang Q (2019) Lateral structural performance of column frame layer and Dou-Gong layer in a timber structure. Ksce J Civ Eng 23:666–677Article Google Scholar Sha B, Xie L, Yong X, Li A (2021) Hysteretic behavior of an ancient Chinese multi-layer timber substructure : a full-scale experimental test and analytical model. J Build Eng 43:103163Article Google Scholar Sui Y, Zhao HT, Xue JY, Zhang XC (2012) Experimental study on stiffness of Dougong in Chinese ancient buildings. 4th International Conference on Technology of Architecture and Structure (ICTAS 2011)Wu C, Xue J, Song D, Zhang Y (2022) Seismic performance evaluation of a roof structure of a historic Chinese timber frame building. Int J Arch Herit 16:1474–1495Article Google Scholar Xie Q, Wang L, Zhang L, Xiang W, Hu W (2020) Rotational behaviors of fork-column Dou-Gong : experimental tests and hysteresis model. J Perform Constr Fac 34:04020032Article Google Scholar Wu Y, Song X, Gu X (2020) Lateral load-displacement model of Dou-Gong connections based on rocking and racking coordination. J Build Struct 43:197–202+211CAS Google Scholar Wang M, Xu Q, Zhou Q, Chen X, Leng Y, Zhang F (2021) Analysis on hysteretic performance