多重抗侧力结构体系二阶效应及串并联模型
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摘要
多重抗侧力结构体系很好得利用了框架的抗剪性能和剪力墙、支撑、筒体的抗弯性能,两者通过各楼层楼板的横隔板的作用使他们变形一致,达到协同工作的状态,发生对框架有利的相互作用。
现行的双、多重抗侧力结构体系研究中,通常将剪力墙(或支撑、筒体)等效为一个仅受弯曲的悬臂柱,不发生剪切变形；将框架等效为一个连续受剪的悬臂柱,不发生弯曲变形,即框架柱的竖向刚度无限大；连接杆件由水平刚性连接介质代替,它仅传递水平力并且使得受弯和受剪两部分变形协调。而实际工程中广泛采用的框架—剪力墙结构体系、框架—核芯筒结构体系等多种双重抗侧力体系中的剪力墙结构、筒体结构与普通实腹式构件不同,通常采用空腹式、格构式,在水平荷载作用下发生侧向变形,或在竖向荷载作用下发生整体屈曲,其自身的剪切变形所占总的变形的比例是很大的,对于某些钢桁架、支撑框架,甚至剪切变形的比例大于弯曲变形。如此看来,对这样的结构体系,传统结构理论的简化会造成一定的误差。
本文同时考虑弯曲变形和剪切变形,将双、多重抗侧力结构体系的所有子结构等效为弯剪型结构,并在此基础上对双、多重抗侧力结构体系子结构间的相互作用、整体结构的侧移、二阶效应等进行了深入的研究,提出了一系列模型和计算方法。
根据Timoshenko弹性稳定理论,对由子结构等效成的悬臂构件由简到繁得进行研究。提出了一系列不同荷载方式和不同截面变化模型的弯矩二阶效应系数表达式,并通过ANSYS有限元程序检验了其计算精度。这些表达式不但简化了弯矩二阶效应系数的计算,而且为后续的研究带来了便利。
推导了等截面双重抗侧力结构在顶部集中力作用下的解析式,分析了双重抗侧力结构中子结构间相互作用原理,提出刚度放大系数的概念,并给出计算方法。并由此提出双重抗侧力结构二阶效应系数的简化计算方法。
研究了变刚度变轴力双、多重抗侧力结构体系,提出了刚度与荷载的等效方法。对等效后的结构,采用等截面等轴力时的计算方法计算二阶效应,对比大量有限元结果,证明提出的简化计算方法对截面、荷载沿高度变化的多重抗侧力结构体系均适用。
刚度放大系数描述了子结构间的相互支持作用。以此为基础,可考虑两个子结构具有不同的二阶效应这一因素,结合叠加原理,提出了二阶侧移的串并联模型。利用刚度与荷载的等效方法,将一阶、二阶侧移的串并联模型推广至更接近实际工程的变刚度变轴力多重抗侧力结构体系。
基于同时考虑弯曲变形和剪切变形的多重抗侧力结构体系,二阶效应系数、侧移等一系列公式与有限元分析结构吻合较好,简单实用、适用范围更广、概念明确。
Shearing property of frames and bending property of shear walls, bracing and tube structures are fully used in multiple structures system. Connected with diaphragm of the slabs, these structures are sharing the same horizontal deformation, and the interaction between them is advantageous to the steel frame.
The present research of dual or multiple structures usually consider shear wall (or bracing, tube structure) as a flexural type cantilever, whose shear deformation is ignored. And ignoring its flexural deformation, frame is considered as a shear type cantilever, which means the gravity stiffnesses of frame columns are infinite. The interaction is provided by rigid links between these cantilevers, and their deformations are compatible. Different from plain solid web structure, vierendeel structure and lattice structure are wildly used in shear wall and tube structure of dual structure system, such as steel frame-shear wall structure and steel frame-core structure in practical engineering. The shear deformations for vierendeel and lattice structure occupy a high proportion of total deformation, when the structure deforms laterally under horizontal load or buckles integrally under vertical load. The shear deformations are even proportionately larger than bending deformations in some steel trusses and braced frames. That means errors are bound to produced when simplification is taken in traditional theory of structure to these structures.
Both bending and shear deformations were considered, and the substructures of dual, multiple structures were considered as flexural-shear structures in this thesis. Based on these, interaction among substructures, total horizontal deformations of the structure, second-order effect were studied intensively. A series of models and computational methods were proposed in this thesis.
Based on Timoshenko elastic stability theory, substructures were equal to Timoshenko cantilevers considering both bending and shear deformations. From constant to varied, these equivalent cantilevers were studied, and a series of moment second-order factors formulas were proposed for models with multifarious cross-sections under multifarious loads. The accuracy of these formulas was proved to be suitable by finite element method. These proposed formulas not only simplified the calculation in moment second-order factors, but also provides convenience for follow-up researches.
Second-order elastic analytical equations were deduced for constant cross-section dual structures under lateral and vertical loads at the top of the structure. By analyzing the interaction between the substructures of dual structure, the concept of stiffness amplification factor and its computational method are proposed. According to these, simplified method for second-order factors of dual structures is also proposed.
By studying dual and multiple structure systems with varied cross-section stiffnesses and axial forces along the height, equivalent methods are proposed for both stffnesses and loads. With the proposed method for second-order factors under constant cross-section stiffnesses and axial forces, the second-order factors for the equivalent structures are obtained. The comparisons with finite element method show that, after equivalent, the proposed method is acceptable for multiple structure systems with varied cross-section stiffnesses and axial forces along the height.
Based on stiffness amplification factor which describes the interaction between two substructures, the difference between two second-order factors for both substructures is considered. According to the superposition principle, the series-parallel-circuit model for second-order horizontal deformation of dual structures is proposed. With the equivalent method used in calculating second-order factor, the series-parallel-circuit models for both linear elastic and second-order horizontal deformations of dual structures can be extend to multiple structures with varied cross-section stiffnesses and axial forces, which is more close to the structures in practical engineering.
Considering the multiple structures with both bending and shear stiffness, the results for second-order factors and horizontal deformations, obtained by the series of proposed and finite element method, have good agreements. And these formulas are simple, having wider application and clear meaning.
现行的双、多重抗侧力结构体系研究中,通常将剪力墙(或支撑、筒体)等效为一个仅受弯曲的悬臂柱,不发生剪切变形；将框架等效为一个连续受剪的悬臂柱,不发生弯曲变形,即框架柱的竖向刚度无限大；连接杆件由水平刚性连接介质代替,它仅传递水平力并且使得受弯和受剪两部分变形协调。而实际工程中广泛采用的框架—剪力墙结构体系、框架—核芯筒结构体系等多种双重抗侧力体系中的剪力墙结构、筒体结构与普通实腹式构件不同,通常采用空腹式、格构式,在水平荷载作用下发生侧向变形,或在竖向荷载作用下发生整体屈曲,其自身的剪切变形所占总的变形的比例是很大的,对于某些钢桁架、支撑框架,甚至剪切变形的比例大于弯曲变形。如此看来,对这样的结构体系,传统结构理论的简化会造成一定的误差。
本文同时考虑弯曲变形和剪切变形,将双、多重抗侧力结构体系的所有子结构等效为弯剪型结构,并在此基础上对双、多重抗侧力结构体系子结构间的相互作用、整体结构的侧移、二阶效应等进行了深入的研究,提出了一系列模型和计算方法。
根据Timoshenko弹性稳定理论,对由子结构等效成的悬臂构件由简到繁得进行研究。提出了一系列不同荷载方式和不同截面变化模型的弯矩二阶效应系数表达式,并通过ANSYS有限元程序检验了其计算精度。这些表达式不但简化了弯矩二阶效应系数的计算,而且为后续的研究带来了便利。
推导了等截面双重抗侧力结构在顶部集中力作用下的解析式,分析了双重抗侧力结构中子结构间相互作用原理,提出刚度放大系数的概念,并给出计算方法。并由此提出双重抗侧力结构二阶效应系数的简化计算方法。
研究了变刚度变轴力双、多重抗侧力结构体系,提出了刚度与荷载的等效方法。对等效后的结构,采用等截面等轴力时的计算方法计算二阶效应,对比大量有限元结果,证明提出的简化计算方法对截面、荷载沿高度变化的多重抗侧力结构体系均适用。
刚度放大系数描述了子结构间的相互支持作用。以此为基础,可考虑两个子结构具有不同的二阶效应这一因素,结合叠加原理,提出了二阶侧移的串并联模型。利用刚度与荷载的等效方法,将一阶、二阶侧移的串并联模型推广至更接近实际工程的变刚度变轴力多重抗侧力结构体系。
基于同时考虑弯曲变形和剪切变形的多重抗侧力结构体系,二阶效应系数、侧移等一系列公式与有限元分析结构吻合较好,简单实用、适用范围更广、概念明确。
Shearing property of frames and bending property of shear walls, bracing and tube structures are fully used in multiple structures system. Connected with diaphragm of the slabs, these structures are sharing the same horizontal deformation, and the interaction between them is advantageous to the steel frame.
The present research of dual or multiple structures usually consider shear wall (or bracing, tube structure) as a flexural type cantilever, whose shear deformation is ignored. And ignoring its flexural deformation, frame is considered as a shear type cantilever, which means the gravity stiffnesses of frame columns are infinite. The interaction is provided by rigid links between these cantilevers, and their deformations are compatible. Different from plain solid web structure, vierendeel structure and lattice structure are wildly used in shear wall and tube structure of dual structure system, such as steel frame-shear wall structure and steel frame-core structure in practical engineering. The shear deformations for vierendeel and lattice structure occupy a high proportion of total deformation, when the structure deforms laterally under horizontal load or buckles integrally under vertical load. The shear deformations are even proportionately larger than bending deformations in some steel trusses and braced frames. That means errors are bound to produced when simplification is taken in traditional theory of structure to these structures.
Both bending and shear deformations were considered, and the substructures of dual, multiple structures were considered as flexural-shear structures in this thesis. Based on these, interaction among substructures, total horizontal deformations of the structure, second-order effect were studied intensively. A series of models and computational methods were proposed in this thesis.
Based on Timoshenko elastic stability theory, substructures were equal to Timoshenko cantilevers considering both bending and shear deformations. From constant to varied, these equivalent cantilevers were studied, and a series of moment second-order factors formulas were proposed for models with multifarious cross-sections under multifarious loads. The accuracy of these formulas was proved to be suitable by finite element method. These proposed formulas not only simplified the calculation in moment second-order factors, but also provides convenience for follow-up researches.
Second-order elastic analytical equations were deduced for constant cross-section dual structures under lateral and vertical loads at the top of the structure. By analyzing the interaction between the substructures of dual structure, the concept of stiffness amplification factor and its computational method are proposed. According to these, simplified method for second-order factors of dual structures is also proposed.
By studying dual and multiple structure systems with varied cross-section stiffnesses and axial forces along the height, equivalent methods are proposed for both stffnesses and loads. With the proposed method for second-order factors under constant cross-section stiffnesses and axial forces, the second-order factors for the equivalent structures are obtained. The comparisons with finite element method show that, after equivalent, the proposed method is acceptable for multiple structure systems with varied cross-section stiffnesses and axial forces along the height.
Based on stiffness amplification factor which describes the interaction between two substructures, the difference between two second-order factors for both substructures is considered. According to the superposition principle, the series-parallel-circuit model for second-order horizontal deformation of dual structures is proposed. With the equivalent method used in calculating second-order factor, the series-parallel-circuit models for both linear elastic and second-order horizontal deformations of dual structures can be extend to multiple structures with varied cross-section stiffnesses and axial forces, which is more close to the structures in practical engineering.
Considering the multiple structures with both bending and shear stiffness, the results for second-order factors and horizontal deformations, obtained by the series of proposed and finite element method, have good agreements. And these formulas are simple, having wider application and clear meaning.
引文
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