Abstract
This study investigated the mechanical behaviour of Dou-Gong brackets with different structural forms, including Jixinzao and Touxinzao. Scaled Dou-Gong models were designed and fabricated at a 1:3.4 geometrical ratio. Vertical load tests were conducted to determine the failure modes, load-displacement response, stiffness degradation, and deformation capacity of the Dou-Gong models. Under vertical load, the primary failure modes of the Dou-Gong models were observed at the Lu-Dou, Nidao-Gong, and Hua-Gong component. The specimens demonstrated excellent load-bearing capacity and high deformation resistance. The Jixinzao Dou-Gong model exhibited a 15.0% higher ultimate load-carrying capacity than the Touxinzao Dou-Gong due to the presence of transverse arches. The number of transverse arches in the Dou-Gong models positively correlated with the compression stiffness, while their presence had a negligible effect on stiffness degradation rates. The Touxinzao Dou-Gong model exhibited superior ductility, characterized by a ductility coefficient 8.57% higher than that of the Jixinzao Dou-Gong model. Although the regular layering of the Dou-Gong models was disrupted by Ang component, the models remained stable in both the vertical and horizontal directions. The bi-linear model can effectively simulate the deformation behaviour of the Dou-Gong model under vertical load.
Download PDF
Full Article
Mechanical Behavior of Dou-Gong Brackets in Chinese Traditional Timber Structures: An Experimental Study
Ruyuan Yang,a,b Weidong Lu,b,* Longlong Zhao,c and Tao Li a,b
This study investigated the mechanical behaviour of Dou-Gong brackets with different structural forms, including Jixinzao and Touxinzao. Scaled Dou-Gong models were designed and fabricated at a 1:3.4 geometrical ratio. Vertical load tests were conducted to determine the failure modes, load-displacement response, stiffness degradation, and deformation capacity of the Dou-Gong models. Under vertical load, the primary failure modes of the Dou-Gong models were observed at the Lu-Dou, Nidao-Gong, and Hua-Gong component. The specimens demonstrated excellent load-bearing capacity and high deformation resistance. The Jixinzao Dou-Gong model exhibited a 15.0% higher ultimate load-carrying capacity than the Touxinzao Dou-Gong due to the presence of transverse arches. The number of transverse arches in the Dou-Gong models positively correlated with the compression stiffness, while their presence had a negligible effect on stiffness degradation rates. The Touxinzao Dou-Gong model exhibited superior ductility, characterized by a ductility coefficient 8.57% higher than that of the Jixinzao Dou-Gong model. Although the regular layering of the Dou-Gong models was disrupted by Ang component, the models remained stable in both the vertical and horizontal directions. The bi-linear model can effectively simulate the deformation behaviour of the Dou-Gong model under vertical load.
DOI: 10.15376/biores.18.4.7745-7768
Keywords: Traditional timber structure; Dou-Gong; Vertical loads; Failure modes; Mechanical properties
Contact information: a: College of Art & Design, Nanjing Tech University, Nanjing, 211816, P.R. China; b: College of Civil Engineering, Nanjing Tech University, Nanjing, 211816, P.R. China; c: College of Civil Engineering, Nanjing Forestry University, Nanjing, 210037, P.R. China;
*Corresponding author: ryyang@njtech.edu.cn
INTRODUCTION
Different from modern steel structures, reinforced concrete structures, and modern timber structures connected by mechanical fasteners, Chinese traditional timber structures have their own structural characteristics, forming a unique architectural style in the world (Lu and Deng 2012; Gao et al. 2022; Xu et al. 2022). Among them, the Hall-type timber structure is one of the most complex structural forms with the highest class (Fig. 1). It plays an important role in the history of Chinese architecture (Liu et al. 2021; Yang et al. 2023).
The Dou-Gong bracket is a prominent feature of the Hall-type timber structure, and it is also a symbolic element of Chinese traditional architectural culture, reflecting the essence of Chinese traditional construction techniques. It consists of several components, including Dou, Gong, Ang, and others. As a key structural member of the traditional timber structure, the Dou-Gong bracket, plays an important role in transferring the load of the roof-beam system to the column frame layer. It serves both structural load-bearing and decoration functions, and its mechanical properties affect structural safety. Therefore, it is of great significance to study the structural performance of Dou-Gong brackets for the protection of traditional timber structures. The structural decomposition of the Dou-Gong bracket can be shown in Fig. 2. It is worth noting that the horizontal direction, i.e. the orientation of Nidao-Gong and Hua-Gong, corresponds to the direction of the wood parallel to the grain.
Fig. 1. The typical Hall-type timber structure: (a) the Hall of Saintly Mother of Jinci Memorial Temple in Shanxi Province; (b) the Main Hall of Kaishan Temple in Hebei Province
Fig. 2. Split graph of different components on Dou-Gong bracket
The Dou-Gong bracket underwent a gradual evolution, leading to an increase in the number of its components. From 206 B.C. to 479 A.D. (the Han Dynasty to the Northern and Southern Dynasties), the Dou-Gong bracket was exclusively comprised of Dou and transverse Gong components. At that time, Dou-Gong brackets did not have the function of making the eaves overhang longer. They only played the role of reducing the internal force of the Yanling (eave purlin). Later, the emergence of Hua-Gong (overhanging beams) and Ang required that the Dou-Gong bracket also take on the function of overhanging eaves. Throughout the Tang Dynasty to the Yuan Dynasties, which spanned from 618 to 1368 A.D., the Dou-Gong bracket underwent significant development, resulting in the establishment of a comprehensive system. Based on the roles and functions of the Dou-Gong bracket in the structure, it can be divided into three categories, i.e., column set (Dou-Gong bracket at column top), corner set (Dou-Gong bracket at the corner), and intermediate set (Dou-Gong bracket at intermediate position). Moreover, the structural form of the Dou-Gong bracket differs between Jixinzao (Dou-Gong bracket with transverse arch) and Touxinzao (Dou-Gong bracket without transverse arch) (Pan 2004).
The two structural forms of the Dou-Gong bracket described above were extensively discussed in the book Yinzao Fashi (Building Regulation) (Li 1982) published by the Northern Song Dynasty government in 1103 A.D. It is reported that Hua-Gong and Ang as the longitudinal components that project outward in the Dou-Gong bracket. In the Jixinzao structural form of the Dou-Gong bracket, the transverse arch is typically positioned above the Hua-Gong and Ang, while in the Touxinzao structural form, the San-Dou is placed on the Hua-Gong and Ang without the transverse arch. The Dou-Gong bracket at the top of the column in the East Hall of Foguang Temple is a representative Dou-Gong structure of the Chinese Tang Dynasty, and the differences between the two construction methods are illustrated in Fig. 3. From 1368 to 1912 A.D., corresponding to the Ming and Qing Dynasties, a gradual increase in the number of transverse arches on both the Hua-Gong and Ang was implemented. This adjustment was made with the primary objective of enhancing the overall structural stability. Consequently, the structural configuration of the Dou-Gong bracket underwent a gradual transformation, transitioning from the Touxinzao to the Jixinzao form.
Fig. 3. The Dou-Gong bracket at column top in the East Hall of Foguang Temple: (a) exterior photo; (b) the structural form of Jixinzao and Touxinzao Dou-Gong bracket
Wood exhibits a series of advantages, including energy conservation, environmental friendliness, high strength-to-weight ratio, as well as cost effectiveness. However, it also possesses anisotropic properties, thus introducing complexity to its mechanical behavior. In recent decades, several scholars have conducted extensive studies on the mechanical properties of the Dou-Gong bracket. Zhou et al. (2015, 2017) conducted experimental studies on three different types of Qing-style Dou-Gong bracket in the first and second floors of the Taihe Hall of the Forbidden City. The failure modes, internal forces, and deformation characteristics of different Dou-Gong brackets under vertical load were discussed, and the vertical stiffness calculation model of the Dou-Gong bracket was investigated. Liu et al. (2020a,b) used the Dou-Gong bracket between the columns of the Main Hall of Huishan Temple as the research object and fabricated the full-scale model specimens. Through the vertical monotonic load test, the deformation capacity and force transmission mechanism of the Dou-Gong bracket under the vertical load were considered, and the mechanical model of the vertical bearing capacity was obtained. Test results showed that under the vertical load, shear, and load-bearing failure were easy to occur at the intersection of Lu-Dou, Ang, and Nidao-Gong, which was the weak part of the Dou-Gong bracket. The ultimate bearing capacity of the Dou-Gong bracket was about 383 kN, and the residual deformation was about 22.3 mm, which showed the good vertical bearing and deformation capacity of the Dou-Gong bracket. The vertical stiffness calculation model of the Dou-Gong bracket in the Main Hall of Huishan Temple can be simplified to the trilinear model under the vertical load. Yeo et al. (2016, 2018) carried out pseudo-static tests on Taiwanese traditional Dieh-Dou timber structures. The load-displacement relationship of the Dieh-Dou timber structure under the vertical and horizontal loads was obtained, and a hysteretic model was established. Wang (2016) simulated the mechanical properties of the Jixinzao and Touxinzao Dou-Gong bracket under the vertical static load and the horizontal low-cycle repeated load by the finite element (FE) software, and obtained the calculation models of the Dou-Gong bracket. The results showed that the vertical ultimate bearing capacity and lateral stiffness of Jixinzao Dou-Gong bracket is better compared with the Touxinzao Dou-Gong bracket, and the Jixinzao Dou-Gong bracket is more beneficial to the seismic energy consumption of traditional timber structures than the Touxinzao Dou-Gong bracket. Pan et al. (2017) used the Jixinzao and Touxinzao Dou-Gong bracket of the Great Buddha Hall of Raoyi Temple as the research object and established the finite element models (FEM), the mechanical properties of the two kinds of Dou-Gong brackets under vertical load and horizontal low-cycle repeated load were analyzed. The results showed that under the vertical load, the Jixinzao Dou-Gong bracket experienced a strength hardening stage, with the ultimate bearing capacity 29.9% higher than that of Touxinzao Dou-Gong bracket, and the additional structural member (transverse arch) in Jixinzao Dou-Gong bracket contributed to the higher bearing capacity. Under the horizontal low-cycle repeated load, the two kinds of Dou-Gong brackets behaved equally well in terms of energy dissipation performance, and both exhibited relatively plump hysteresis loops.
To date, existing research has primarily focused on the mechanical properties of Dou-Gong brackets fabricated according to the book of Yinzao Fashi (Building Regulation) (Li 1982) or some Dou-Gong brackets in typical northern official traditional structures of the Ming and Qing dynasties. However, the quantitative influence of the structural form on the structural performance of the Dou-Gong bracket has been relatively limited, with a lack of systematic theoretical and experimental research. This study presents the results of an experimental investigation into the structural performance of two Dou-Gong models i.e. Jixinzao Dou-Gong model DG-1 and Touxinzao Dou-Gong model DG-2, with a geometrical ratio of 1:3.4 under monotonic static vertical load. The structural performance of the Dou-Gong bracket in terms of failure modes, load-carrying capacity, stiffness, and ductility was investigated. Through this work, the evolution of the Dou-Gong bracket from the perspective of mechanics is interpreted, and the results can serve as a reference for the protection and maintenance of Chinese traditional timber structures.
EXPERIMENTAL
Materials
The selection of materials for Chinese traditional timber structures follows the principle of “utilizing local and nearby materials”. Building materials for Chinese traditional timber structures often include widely distributed wood species such as pine (Pinus sp.), China fir (Cunninghamia sp.), cedarwood (Cupressaceae), and poplar (Populus sp.). For example, in the Yingxian Wood Pagoda in Shanxi Province, larch (Larix gmelinii) is mostly used as the timber frame material, and in the Main Hall of Beiyue Temple in Hebei Province, spruce (Picea asperata) is used as the column material (Ni and Li 1994, Yuan et al. 2021). In this study, Pinus sylvestris was used as the model material, which was obtained from the same batch of logs to minimize the effects of various factors, including wood density, moisture content, and maturity, on the mechanical properties of the material. Material tests were conducted on the raw material following ASTM D143 (2014), GB/T 1931 (2009), and GB/T 1933 (2009). The basic material properties are listed in Table 1.
Table 1. Basic Properties of Pinus sylvestris
Notes: The value in parentheses denotes the coefficient of variation. In the table, Ei denotes the elastic modulus (MPa); fc denotes the compression strength under all-area compression (MPa); The subscript ∥ and ⊥ denote the direction parallel to the grain and perpendicular to the grain, respectively; ρ denotes the air-dried density (g·cm-3); MC denotes the moisture content (%).
Fabrication of Specimens
Considering that the structural form and dimension of the Dou-Gong bracket are closely related to the class and function of the building, the Chinese Song-style Dou-Gong bracket with Ang was selected as the prototype in the current study, based on relevant literature (Li 1982; Chen 1991; Wang 1992).
Table 2. The Conversion Method for the Sectional Dimensions of Wood Used During the Song Dynasty
Note: In the unit system of the Song Dynasty, 1 cun was converted to 30.9 to 32.9 mm in metric system, and 30.9 mm is taken in the current study.
Initially, the wood used to fabricate the prototype Dou-Gong bracket underwent cutting with a band saw, resulting in cross-sectional dimensions of 255 mm × 170 mm (height × width), and the conversion method for the sectional dimensions of wood used during the Chinese Song Dynasty is presented in Table 2. Subsequently, skilled carpenters meticulously crafted each component by hand. Lastly, the bracket was meticulously polished to a smooth finish using sandpaper.
In light of the potential machining and assembly errors, two Dou-Gong models with a geometrical ratio of 1:3.4, i.e., the Jixinzao Dou-Gong model DG-1 and Touxinzao Dou-Gong model DG-2 were fabricated. The overall geometry of the 1:3.4 scale Dou-Gong model is characterized by dimensions of 450 mm × 840 mm × 490 mm in height, length (Hua-Gong direction) and width (Nidao-Gong direction), respectively, as shown in Fig. 5.
Fig. 4. Schematic diagram of Dou-Gong brackets: (a) the Jixinzao Dou-Gong model DG-1; (b) the Touxinzao Dou-Gong model DG-2
Fig. 5. Dimensions of Dou-Gong models (all dimensions are in mm): (a) specimen DG-1; (b): specimen DG-2
The prototype Dou-Gong bracket comprises components manufactured based on a dimension module of ap = 17 mm, as specified the book of Yinzao Fashi (Building Regulation) (Li 1982). Therefore, the dimensions of the wood used to fabricate the 1:3.4 scale Dou-Gong model are multiples of as = 17/3.4 = 5 mm. Specifically, the Lu-Dou has dimensions of 20a × 32a × 32a (height × length × width), and the Hua-Gong has dimensions of 21a × 72a × 10a (height × length × width). More detailed dimensional information on Dou-Gong components can be seen in Fig. 6. The cross-sectional dimension of other Gong and Fang is 15a × 10a (height × width), and the overall geometry dimensions of Jiaohu-Dou and San-Dou are 10a × 18a × 16a (height × length × width) and 10a × 14a × 16a (height × length × width), respectively. To connect partial components of the Dou-Gong model, hidden timber dowels with dimensions of 4a × 2a × 2a (height × length × width) are utilized. All internal hidden structures of the components, such as the slotting, are fabricated in accordance with the guidelines presented in the book of Yinzao Fashi (Li 1982) and relevant literature (Pan 2004).
The Dou-Gong bracket comprises numerous small components with a complex manufacturing process, as illustrated in Fig. 6. To economize on testing expenditures, a cost-efficient strategy that involved the replacement of failed components after each test was used. This method commenced with the disassembly of all Dou-Gong bracket components following testing. Subsequently, a meticulous inspection of each component took place, with particular attention devoted to averting any minor damage that might potentially compromise the mechanical performance of the Dou-Gong bracket. Finally, the failed components were substituted, and the Dou-Gong model was reassembled. This systematic method enabled the execution of three repeated tests for each Dou-Gong model. It should be noted that the Dou-Gong bracket serves both structural and decorative purposes. To simplify the manufacturing process, the decorative components that do not impact the structural performance were omitted in the current study, and the main simplified parts were as follows: (1) the Juan-Sha (the end of the component made into an arc shape) was replaced with a chamfer, and the volume of wood removed by both methods was equal; (2) the bottom of all types of Dou was cut into a pyramid-shaped frustum without making radians; (3) the Qinmian-Ang at the end of the Ang was simplified to a straight Pizhu-Ang. Each component was prefabricated in the factory and then assembled in the laboratory.
Fig. 6. Dimensions of partial components (all dimensions are in mm)
Arrangement of Measurement Points and Loading Protocol
Loading protocol
During the test, the Dou-Gong models were installed upside down on the steel base, and the geometric center of the loading block passed through the central points of Lu-Dou, which ensured that the vertical load was applied along the central axis of the Dou-Gong models. All ends of the Gong components were free from any restriction. To minimize the impact of uneven stress on displacement measurement, silver sand was used to ensure that the bottom surface of the Dou-Gong model had uniform contact with the testing platform. The test setup is illustrated in Fig. 7.
Under vertical load, the load-displacement curve of the Dou-Gong bracket showed similarity to that of wood under compression perpendicular to the grain without a clearly defined ultimate load. Therefore, the displacement-controlled loading method was employed in the current study. The Dou-Gong models were loaded as follows: (1) Initially, the preload was applied to reduce the assembly clearance. According to the research conducted by Gao et al. (2003), the internal force and deformation of the Dou-Gong bracket do not exceed 1/7 of its ultimate strength in the normal use stage, and it is always in the elastic stage. Therefore, the preload was increased to 8 kN for the Jixinzao Dou-Gong model DG-1, and 5 kN for the Touxinzao Dou-Gong model DG-2, respectively; (2) During the formal loading, the load was applied with a displacement rate of 1 mm·min-1 until some components of the Dou-Gong model either yielded or fractured. At this point, the Dou-Gong model was visibly damaged, yet the load-displacement curve continued to ascend with a smaller slope; (3) During the unloading stage, the unloading rate was maintained at 10 kN·min-1. The corresponding residual deformation of each specimen was recorded after unloading to 0. The laboratory temperature was 14 ± 3 °C, and the relative humidity was 58 to 65%. The entire test was conducted in a stable environment.
Fig. 7. Set up used for testing Dou-Gong models (taking DG-1 as an example)
Fig. 8. Loading and measurement of displacement and strain for testing Dou-Gong models: (a) Layout of displacement meters; (b) Layout of strain gauges
Test configurations and setup
The applied load was quantified using a load senser positioned at the top of Dou-Gong models. Vertical displacements of specific components were recorded using eight displacement meters (model: YHD-50, China), designated as LVDT 1 to 8. These were positioned to measure the displacements of Lu-Dou (LVDT 1), the end of Hua-Gong (LVDT 2 and 3), the 2nd rise Hua-Gong (LVDT 4 and 5), Shua-Tou (LVDT 6 and 7), and Ang (LVDT 8). An additional two displacement meters (model: YHD-30, China), designated as LVDT 9 and 10, were installed at the interfaces between the 2nd rise Hua-Gong and Ang to detect any relative slip due to the applied loading. The arrangement of LVDTs is illustrated in Fig. 8(a). Strain measurements were obtained using fourteen electrical resistance strain gauges (model: BX120-30AA, China) placed at specific locations on Nidao-Gong, Hua-Gong, Bineiman-Gong, Guazi-Gong, and Ling-Gong (as indicated by the black stripe in Fig. 8b). All experiments were performed using a microcomputer-controlled electro-hydraulic servo universal testing machine with a capacity of 2000 kN (model: SAN SHT4 206, China) and a data acquisition system (model: TDS-530, Japan).
RESULTS AND DISCUSSION
Failure Modes
The Jixinzao Dou-Gong model DG-1
The study investigated short-term load-displacement behaviour of Dou-Gong models. Initially, the Dou-Gong model DG-1 was compacted at a vertical displacement of approximately 2.18 mm, influenced by the processing accuracy of components. As the load increased to approximately 15 kN, a squeak was heard at the clearance of components due to the biting force between them, while no significant cracking was observed in other components. With continued loading, the Lu-Dou cracked (at a load of around 25 kN) at the corner of the precut slots, i.e., the root of a protuberance, and the crack gradually widened. Simultaneously, splitting cracks appeared on the end of Hua-Gong and Nidao-Gong, extending from the position of Juan-Sha to the intersection with the Lu-Dou, as shown in Fig. 9(a). At around 40 kN, the wood fibers at the surface of Hua-Gong tilted upwards, accompanied by frequent splitting sounds (Fig. 9b). Subsequently, the Lu-Dou collapsed at approximately 72 kN, and the protuberance on one side was almost severed from the root (Fig. 9c). Due to the local bending moment caused by the concentrated force, an accompanied uplift (Fig. 9d) of the far end of the Nidao-Gong was also observed. The cracks on the Nidao-Gong and Hua-Gong gradually developed into a through crack, and the splitting sound became low frequency and high-pitched. At a load of approximately 82 kN, the bending deformation of the Nidao-Gong was more evident, and the tenon pulling phenomenon occurred at both ends. The Nidao-Gong and Hua-Gong split at the intersection with the Lu-Dou (Fig. 9e). Finally, the loading was terminated due to excessive deformation, and no further decrease in stiffness was observed. At this point, the relative slip between the Ang and the 2nd rise Hua-Gong was small, not exceeding 1 mm. During unloading, the components with bending deformation tended to recover. The Dou-Gong model produced a dense sound caused by the loose bite between components as the load decreased.
Fig. 9. Typical failure modes of specimen DG-1: (a) Hua-Gong cracked; (b) peeling of wood fiber; (c) Lu-Dou cracked at the root of a protuberance; (d) bending deformation of Nidao-Gong; (e) Nidao-Gong and Huagong yielded locally and fractured
The damage of the model DG-1 was primarily concentrated on the Lu-Dou, Nidao-Gong, and Hua-Gong components, while the other components remained intact without obvious deformation. The Dou-Gong model DG-1 exhibited three failure modes, which were identified as: (і) yield of Lu-Dou, Nidao-Gong, and Hua-Gong under compression perpendicular to the grain; (іі) cracking of Lu-Dou, Nidao-Gong and Hua-Gong under tension perpendicular to the grain; and (ііі) shear failure of Nidao-Gong and Hua-Gong. The yield and cracking of the components were the result of multiple micro-deformation that slowly accumulated over time.
The Touxinzao Dou-Gong model DG-2
The mortise-tenon joint is a semi-rigid connection method that combines timber components through concave and convex parts, effectively limiting relative slip between components under loading. In the Dou-Gong model DG-2, there are fewer transverse arches, and the combination of components is not as tight as in model DG-1. At a vertical displacement of approximately 3.16 mm, the model DG-2 was essentially compacted. As the load increased to approximately 13 kN, the Dou-Gong model emitted a noticeable creaking sound, and no obvious deformation of each component was observed. Subsequently, the Nidao-Gong and Hua-Gong components displayed bending deformation at a load around 20 kN. Additionally, local plastic embedding deformation was observed on the surface of the Lu-Dou, with the protuberance gradually uplifting outward. At approximately 30 kN, a longitudinal crack appeared on the Nidao-Gong, beginning from the intersection with the Lu-Dou and extending to the end of the Nidao-Gong (Fig. 10a). Simultaneously, the Lu-Dou cracked perpendicular to the wood grain near the protuberance due to stress concentration at the precuts, as shown in Fig. 10(b). At approximately 43 kN, bending deformation of the Nidao-Gong and Hua-Gong was observed (Fig. 10c). At this point, a relatively apparent relative slip between the Ang and the 2nd rise Hua-Gong was observed, as shown in Fig. 10(d). As the load increased to approximately 60 kN, 45-degree diagonal cracks appeared on the surface of the end of the Hua-Gong, with a crisp sound. The intersection of the Nidao-Gong and Hua-Gong experienced yield failure, and the Hua-Gong broke off due to combined shear and bending forces at approximately 72 kN (Fig. 10e). After loading, deformation was clearly observed on the Lu-Dou, Nidao-Gong, and Hua-Gong components, similar to DG-1 but with more components yielding. In contrast, the cracks at the end of the Nidao-Gong and Hua-Gong in DG-2 were notably fewer than those in DG-1. Additionally, the Jiaohu-Dou placed on the Shua-Tou cracked due to the relative slip of the Ang in the Dou-Gong model DG-2, and the hidden dowel on the Ang deformed. During the unloading process, at a load of approximately 16 kN, a “bang” was emitted from the specimen due to component deformation recovery.
Fig. 10. Typical failure modes of specimen DG-2: (a) Hua-Gong cracked; (b) Lu-Dou cracked; (c) bending deformation of Nidao-Gong and Hua-Gong; (d) inter-layer slippage of Ang; (e) breaking-off of Hua-Gong
Four failure modes of the Dou-Gong model DG-2 were identified. These modes included (і) yield of Lu-Dou, Nidao-Gong, and Hua-Gong under compression perpendicular to the grain; (іі) cracking of Lu-Dou, Nidao-Gong, and Hua-Gong under tension perpendicular to the grain; (ііі) shear failure of Lu-Dou, Nidao-Gong, Hua-Gong, Jiaohu-Dou, and Ang; and (іv) breaking-off of Hua-Gong under bending.
Comparison with related literature
Chen et al. (2014) conducted an experimental study on the structural performance of Dou-Gong brackets in Yingxian Wood Pagoda, and the test model was manufactured using Northeast China red pine (Pinus koraiensis) with a geometrical ratio of 1:3.4. Yield of Lu-Dou, and fractures of Nidao-Gong and Hua-Gong were observed during their tests, which were similar to the failure modes of components of DG-1 (Fig. 9e) and DG-2 (Fig. 10a and 10e). Xue et al. (2022) investigated the vertical mechanical performance of the Dou-Gong at column tops through a vertical monotonic loading test and numerical simulation. The failure observations of their compression specimens were cracks of Lu-Dou, Nidao-Gong, and Hua-Gong, similar to DG-1 (Fig. 9a-d) and DG-2 (Fig. 10a-b). Cheng et al. (2019) fabricated 1:3.52 scaled China fir models of Song-style Dou-Gong brackets at the column top with Ang and carried out vertical load tests, showing that Lu-Dou was the first to be destroyed under different loads.
These studies serve as validation for the current study, which establishes that the transmission of vertical loads in the Dou-Gong bracket occurs sequentially from top to bottom, utilizing the following components: Shua-Tou, Ang, Hua-Gong, Nidao-Gong, San-Dou, and Lu-Dou. Due to the gradual increase in internal force from top to bottom, Lu-Dou is more susceptible to crushing and splitting failures as a weak member compared to other components of the Dou-Gong bracket. In future research endeavors, an intriguing and promising avenue for exploration resides in the enhancement of the mechanical performance of the Dou-Gong bracket through the reinforcement or alteration of the dimensions of these vulnerable components.
Load-displacement Response
The vertical displacement of the Dou-Gong model is the sum of two parts i.e. stress deformation of each component in the vertical direction and compression deformation of the assembly clearance between the components in each layer. This composite displacement reflects the overall vertical compression deformation characteristics of the Dou-Gong model and can be simplified as the vertical displacement of the actuator. The load-displacement curves of the tested Dou-Gong model are presented in Fig. 11 and can be divided into four distinct stages.