应县木塔典型节点及结构受力性能研究
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摘要
应县木塔建于辽清宁二年(公元1056年),距今已有近千年历史,是我国现存最古老和最高的木构塔式建筑,也是唯一一座木结构楼阁式塔。木塔历经近千年沧桑,经受了多次强烈地震和人为破坏而巍然屹立,向世人展现着中国灿烂的文明。但也应看到,历经千年的木塔,其结构发生了明显压缩、倾斜与扭转变形,其中构件横纹承压破坏和受弯产生严重变形与损伤,木构件开裂和老化,尚有遭受炮击等人为损伤,且这些情况有随时间增长而恶化的趋势。木塔亟待进行结构安全评估和维修。然而应县木塔结构复杂,结构体系及其传力路径不甚明确、节点构造及传力机理不明晰。本文在全面结构调查的基础上,对木塔进行结构解读,开展其典型节点性能试验研究与有限元分析,并进行木塔整体结构精细化有限元分析,以对木塔结构的安全评估乃至维修加固提供重要依据。
基于现场调查结果,对应县木塔进行了结构体系分析。木塔为“层叠式半刚性连接多层超静定结构”。从结构角度对木塔斗栱、梁柱节点和柱脚节点进行了归类。用工程力学的观点,分析了古建筑木结构特有的“侧脚”和“生起”的结构作用。
通过竖向单调加载试验和水平低周循环加载试验,研究了应县木塔典型斗栱节点腜汀⒘褐诘愫椭沤诘隳P偷某性亓透斩取;谑匝榻峁拖嗨理论,估算了木塔典型斗栱原型、梁柱节点和柱脚节点原型的受力性能谑向荷载作用下,斗栱节点主要通过薓贰⒒獤怼龛省⑸⒍泛丸佣反莺稍兀其受力机理与木材横纹承压工作相似。在水平荷载作用下,斗栱节点主要以各道栱枋抗弯的形式传递荷载，其受力机理与木材受弯工作相似褐诘阒饕通过木柱卯口与阑额榫头间的横纹承压将水平荷载传至阑额上,使阑额受扭和横纹承压,并使木柱卯口处横纹受拉,普拍枋横纹承压。柱脚节点则主要通过木柱卯口与栱枋间的横纹承压将水平荷载传至栱枋上，使栱枋受弯和扭，并使木柱卯口处横纹受拉,栱枋和地栿横纹承压匝楸砻鳎窎斫诘恪⒘褐诘和柱脚节点抵抗水平荷载的性能皆随柱上竖向荷载的增大而提高。木柱经加固后节点抵抗水平荷载的性能亦皆有所提高。
针对木材各向异性的特点,建立了复杂应力状态下的本构关系模型,并结合ABAQUS编制了用户子程序VUMAT,模拟复杂受力情况下的木材力学性能。基于各节点的真实构造、所建立的木材本构关系模型和各构件间动摩擦接触关系模型,建立了的木塔典型斗栱节点、梁柱节点和柱脚节点的精细化有限元模型,并对这些节点的力学性能进行了计算分析,结果与试验吻合良好。在试验和计算分析的基础上,提出了斗栱在竖向荷载作用下的简化力学腜停确了传力路径。
基于ABAQUS建立了应县木塔整体结构无损和现状两种精细化有限元模型。通过动力特性分析,得到了木塔两种模型的自振频率和振型,其中现状模型的动力特性与文献实测结果吻合。通过对木塔整体结构有限元分析,分别研究了木塔在竖向(重力)荷载和水平(地震)荷载作用下的工作性能,明确了木塔竖向和水平方向的传力路径。经对木塔进行多遇地震作用下的有限元分析,得到了木塔的地震响应,并结合所提出的倾覆评判指标,对木塔的抗震安全进行了评估。对木塔的整体和局部倾斜、抗扭刚度低、明层抗侧移刚度低、局部抗侧移刚度低和节点横纹承压强度低等各薄弱环点进行了分析,提出了相应的加固增强设想。
Built in the 2nd year of Qingning, Liao Dynasty (1056 AD) of approximate a thousand years ago, the Yingxian Wood Pagoda is located in the Town of Yingxian County, Shanxi Province, China. It is the oldest and highest standing ancient wood structure and the only storeyed wood pagoda of China. With vicissitudes of nearly a thousand years, the pagoda has undergone times of severe earthquakes and some human-induced disasters. Yet it is still towering there with majesty, showing the world the glory of the ancient Chinese civilizations. Meanwhile, it should be noted that significant deformation of compression, both overall inclination and torsion of pagoda and local inclination of columns have happened. The situation is serious for some wood components with large deformation and even damage due to compression perpendicular to grain and bending, some with fractures and property-deteriorations due to aging, some even with damage from shelling in the war. The distortions of pagoda and deteriorations of wood are worsening and can become critical any time. It is, therefore, of urgent need to evaluate the structural safety of Yingxian Wood Pagoda and to undertake repairing accordingly. However, the structure of the pagoda is rather complicated, the structural system and the load-transfer paths are not quite clear, and the structure and load-carrying mechanism of joints and connections of the pagoda are not quite clear either. This study aims to undertake thorough on-site survey of the pagoda, undertake analysis and understanding of the structural system, conduct tests of structural performance of the typical joints, and finally conduct refined FE analysis of the whole structure of the pagoda, thus providing basis for evaluation of the structural safety and reinforcement and repairing of the pagoda.
By the on-site survey and the analysis and understanding of the structural system, the Yingxian Wood Pagoda can be regarded as a layered multi-storey structure with semi-rigid connections and high degrees of indeterminacy. The Dou-Gong Brackets, beam-column joints and column-base joints were classified from a structural point of view. The structural virtues of Column-Lean and Column-Raising, unique in ancient Chinese wood structures like the pagoda, were investigated by means of engineering mechanics.
Tests on models of the typical Dou-Gong Brackets, beam-column joints and column-base joints under monotonic vertical and cyclic lateral loads, respectively, were conducted, the structural performance in terms of load-carrying capacity, stiffness and failure modes of these joints were investigated. Based on the test results and the theory of similarity, the load-carrying capacity and stiffness of the prototype joints in the true pagoda were deduced. Under vertical load from the column, a Dou-Gong Bracket transfers load down mainly via Shua-Tou, Hua-Gong, Gong-Fang, San-Dou and Lu-Dou, the structural behaviour is basically similar to wood under compression perpendicular to grain. Under cyclic lateral load, a Dou-Gong Bracket transfers load mainly via bending of the several Gong-Fang’s, the structural behaviour is basically similar to wood under bending. A beam-column joint transfers lateral load to Lan-E via compression perpendicular to grain between tenon of Lan-E and mortise of column. Lan-E is thus under torsion and local compression perpendicular to grain, column under tension perpendicular to grain at the mortise and Pupai-Fang under compression perpendicular to grain. Whist a column-base joint transfers lateral load to the several Gong-Fang’s via compression perpendicular to grain between the mortise of column and Gong-Fang. Gong-Fang is thus under bending and torsion, column under tension perpendicular to grain at the mortise, Gong-Fang and Di-Fu under compression perpendicular to grain. Tests also showed that, the lateral resistance and stiffness of Dou-Gong Brackets, beam-column joints and column-base joints increase with the axial compressive load applied to the column. The lateral performances of all joints are enhanced with reinforcement of column to prevent propagation of the fracture perpendicular to grain.
In consideration of the anisotropy, constitutive relationships of wood under complex stresses, suitable for EF modelling of the structures, were developed and incorporated into ABAQUS via encoding a user-defined subroutine VUMAT. FE models of the Dou-Gong Brackets, beam-column joints and column-base joints were developed based on the true geometric structure of the joints, the complex constitutive relationships and the kinematic friction formulation between the components. The structural performance of these typical joints was simulated, and good agreement between FE modelling and tests was obtained. Based on the FE modelling and tests, simplified mechanics models of Dou-Gong Brackets transferring vertical load were developed, and the load-transferring paths clarified.
Two refined FE models of the structure of Yingxian Wood Pagoda, with and without considering damage, were developed incorporating ABAQUS, respectively. The natural vibration frequencies and modes of both FE models were obtained by the numerically dynamic analysis, and analytical results from the FE model with considering damage correlated with test reported by literature. The structural performance and load-transferring paths of the pagoda were investigated via conducting FE modelling of the structure under gravity and static lateral earthquake actions, respectively. FE modelling of the structure of the pagoda under frequently occurring earthquakes was also conducted, and the structural responses obtained. The index for evaluating the overturning of the pagoda was suggested, and the safety of Yingxian Wood Pagoda under earthquakes assessed. The structural weaknesses of the pagoda, such as inclinations both overall and local, poor torsional stiffness, poor inter-storey and local lateral stiffness of the apparent storeys and low compression strength perpendicular to grain, were reviewed and analysed, and measures to reinforce the structure of the pagoda and to alleviate detrimental effect of gravity were proposed.
基于现场调查结果,对应县木塔进行了结构体系分析。木塔为“层叠式半刚性连接多层超静定结构”。从结构角度对木塔斗栱、梁柱节点和柱脚节点进行了归类。用工程力学的观点,分析了古建筑木结构特有的“侧脚”和“生起”的结构作用。
通过竖向单调加载试验和水平低周循环加载试验,研究了应县木塔典型斗栱节点腜汀⒘褐诘愫椭沤诘隳P偷某性亓透斩取;谑匝榻峁拖嗨理论,估算了木塔典型斗栱原型、梁柱节点和柱脚节点原型的受力性能谑向荷载作用下,斗栱节点主要通过薓贰⒒獤怼龛省⑸⒍泛丸佣反莺稍兀其受力机理与木材横纹承压工作相似。在水平荷载作用下,斗栱节点主要以各道栱枋抗弯的形式传递荷载，其受力机理与木材受弯工作相似褐诘阒饕通过木柱卯口与阑额榫头间的横纹承压将水平荷载传至阑额上,使阑额受扭和横纹承压,并使木柱卯口处横纹受拉,普拍枋横纹承压。柱脚节点则主要通过木柱卯口与栱枋间的横纹承压将水平荷载传至栱枋上，使栱枋受弯和扭，并使木柱卯口处横纹受拉,栱枋和地栿横纹承压匝楸砻鳎窎斫诘恪⒘褐诘和柱脚节点抵抗水平荷载的性能皆随柱上竖向荷载的增大而提高。木柱经加固后节点抵抗水平荷载的性能亦皆有所提高。
针对木材各向异性的特点,建立了复杂应力状态下的本构关系模型,并结合ABAQUS编制了用户子程序VUMAT,模拟复杂受力情况下的木材力学性能。基于各节点的真实构造、所建立的木材本构关系模型和各构件间动摩擦接触关系模型,建立了的木塔典型斗栱节点、梁柱节点和柱脚节点的精细化有限元模型,并对这些节点的力学性能进行了计算分析,结果与试验吻合良好。在试验和计算分析的基础上,提出了斗栱在竖向荷载作用下的简化力学腜停确了传力路径。
基于ABAQUS建立了应县木塔整体结构无损和现状两种精细化有限元模型。通过动力特性分析,得到了木塔两种模型的自振频率和振型,其中现状模型的动力特性与文献实测结果吻合。通过对木塔整体结构有限元分析,分别研究了木塔在竖向(重力)荷载和水平(地震)荷载作用下的工作性能,明确了木塔竖向和水平方向的传力路径。经对木塔进行多遇地震作用下的有限元分析,得到了木塔的地震响应,并结合所提出的倾覆评判指标,对木塔的抗震安全进行了评估。对木塔的整体和局部倾斜、抗扭刚度低、明层抗侧移刚度低、局部抗侧移刚度低和节点横纹承压强度低等各薄弱环点进行了分析,提出了相应的加固增强设想。
Built in the 2nd year of Qingning, Liao Dynasty (1056 AD) of approximate a thousand years ago, the Yingxian Wood Pagoda is located in the Town of Yingxian County, Shanxi Province, China. It is the oldest and highest standing ancient wood structure and the only storeyed wood pagoda of China. With vicissitudes of nearly a thousand years, the pagoda has undergone times of severe earthquakes and some human-induced disasters. Yet it is still towering there with majesty, showing the world the glory of the ancient Chinese civilizations. Meanwhile, it should be noted that significant deformation of compression, both overall inclination and torsion of pagoda and local inclination of columns have happened. The situation is serious for some wood components with large deformation and even damage due to compression perpendicular to grain and bending, some with fractures and property-deteriorations due to aging, some even with damage from shelling in the war. The distortions of pagoda and deteriorations of wood are worsening and can become critical any time. It is, therefore, of urgent need to evaluate the structural safety of Yingxian Wood Pagoda and to undertake repairing accordingly. However, the structure of the pagoda is rather complicated, the structural system and the load-transfer paths are not quite clear, and the structure and load-carrying mechanism of joints and connections of the pagoda are not quite clear either. This study aims to undertake thorough on-site survey of the pagoda, undertake analysis and understanding of the structural system, conduct tests of structural performance of the typical joints, and finally conduct refined FE analysis of the whole structure of the pagoda, thus providing basis for evaluation of the structural safety and reinforcement and repairing of the pagoda.
By the on-site survey and the analysis and understanding of the structural system, the Yingxian Wood Pagoda can be regarded as a layered multi-storey structure with semi-rigid connections and high degrees of indeterminacy. The Dou-Gong Brackets, beam-column joints and column-base joints were classified from a structural point of view. The structural virtues of Column-Lean and Column-Raising, unique in ancient Chinese wood structures like the pagoda, were investigated by means of engineering mechanics.
Tests on models of the typical Dou-Gong Brackets, beam-column joints and column-base joints under monotonic vertical and cyclic lateral loads, respectively, were conducted, the structural performance in terms of load-carrying capacity, stiffness and failure modes of these joints were investigated. Based on the test results and the theory of similarity, the load-carrying capacity and stiffness of the prototype joints in the true pagoda were deduced. Under vertical load from the column, a Dou-Gong Bracket transfers load down mainly via Shua-Tou, Hua-Gong, Gong-Fang, San-Dou and Lu-Dou, the structural behaviour is basically similar to wood under compression perpendicular to grain. Under cyclic lateral load, a Dou-Gong Bracket transfers load mainly via bending of the several Gong-Fang’s, the structural behaviour is basically similar to wood under bending. A beam-column joint transfers lateral load to Lan-E via compression perpendicular to grain between tenon of Lan-E and mortise of column. Lan-E is thus under torsion and local compression perpendicular to grain, column under tension perpendicular to grain at the mortise and Pupai-Fang under compression perpendicular to grain. Whist a column-base joint transfers lateral load to the several Gong-Fang’s via compression perpendicular to grain between the mortise of column and Gong-Fang. Gong-Fang is thus under bending and torsion, column under tension perpendicular to grain at the mortise, Gong-Fang and Di-Fu under compression perpendicular to grain. Tests also showed that, the lateral resistance and stiffness of Dou-Gong Brackets, beam-column joints and column-base joints increase with the axial compressive load applied to the column. The lateral performances of all joints are enhanced with reinforcement of column to prevent propagation of the fracture perpendicular to grain.
In consideration of the anisotropy, constitutive relationships of wood under complex stresses, suitable for EF modelling of the structures, were developed and incorporated into ABAQUS via encoding a user-defined subroutine VUMAT. FE models of the Dou-Gong Brackets, beam-column joints and column-base joints were developed based on the true geometric structure of the joints, the complex constitutive relationships and the kinematic friction formulation between the components. The structural performance of these typical joints was simulated, and good agreement between FE modelling and tests was obtained. Based on the FE modelling and tests, simplified mechanics models of Dou-Gong Brackets transferring vertical load were developed, and the load-transferring paths clarified.
Two refined FE models of the structure of Yingxian Wood Pagoda, with and without considering damage, were developed incorporating ABAQUS, respectively. The natural vibration frequencies and modes of both FE models were obtained by the numerically dynamic analysis, and analytical results from the FE model with considering damage correlated with test reported by literature. The structural performance and load-transferring paths of the pagoda were investigated via conducting FE modelling of the structure under gravity and static lateral earthquake actions, respectively. FE modelling of the structure of the pagoda under frequently occurring earthquakes was also conducted, and the structural responses obtained. The index for evaluating the overturning of the pagoda was suggested, and the safety of Yingxian Wood Pagoda under earthquakes assessed. The structural weaknesses of the pagoda, such as inclinations both overall and local, poor torsional stiffness, poor inter-storey and local lateral stiffness of the apparent storeys and low compression strength perpendicular to grain, were reviewed and analysed, and measures to reinforce the structure of the pagoda and to alleviate detrimental effect of gravity were proposed.
引文
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