高层结构体系弹性整体稳定性研究
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摘要
随着建筑物高度的不断增加以及建筑体型的不断复杂化,各国学者对高层超高层结构体系进行了大量的研究,相应的理论体系也日趋完善。然而高层结构设计构件太多,结构的整体稳定难以简单地把握,可喜的是,现在的计算机有限元程序可以相对容易的解决高层结构稳定性问题。本文分析各类结构的特点,对结构进行合理的简化,并对相应的结构体系进行了整体性分析,得到了四类高层结构稳定性的基本规律。
对伸臂位于顶部及中部任意高度的巨型结构整体稳定性进行了分析,提出了双伸臂巨型结构中模拟伸臂和柱子作用的独立弹簧和关联弹簧的模型。推导了核心筒及边框柱中轴力不同时结构整体失稳的临界方程,通过具体算例的计算分析,得出了双伸臂巨型结构失稳时,伸臂层总的临界荷载与荷载在核心筒与伸臂端柱子之间的分布基本无关的结论。通过算例分析揭示了巨型层层与层之间存在较大的相互作用。通过对比普通框架的合并解法,揭示了伸臂巨型结构与框架结构在稳定问题上的区别,通过对基于整体的和层的荷载负刚度概念的伸臂结构屈曲的近似分析,进一步揭示了伸臂巨型结构在性质上更加接近于框架结构,而偏离整体弯曲型结构更远的性质。
采用连续化模型,对双肢剪力墙结构平面内稳定性进行了研究,求得了顶部作用集中压力时临界荷载的精确显式表达式和显式屈曲波形。这个临界荷载公式表明,联肢剪力墙是一种双重抗侧力结构,并且可以采用串并联电路模型来表示两者之间的相互作用。串并联模型推广到线性分析的情况,得到顶部抗侧刚度的近似显式表达式,与精确解进行了比较。推导了顶部作用竖向集中荷载时,在不同水平荷载作用下结构的侧移、墙肢弯矩、墙肢轴力和连梁弯矩放大系数,并提供了近似计算公式。
基于对等截面等轴力的联肢剪力墙的稳定性研究成果,并运用串并联电路模型,研究了变截面变轴力联肢剪力墙结构的稳定性。运用能量法,构建弯曲型、剪切型曲线,考察了变刚度变轴力联肢剪力墙结构的失稳波形,得出结论,变截面变轴力联肢墙的屈曲问题比较复杂,不简单的等效于弯曲、剪切或简单的弯剪型。进而文章通过大量的算例拟合出了联肢墙的屈曲荷载表达式,有比较好的精确度。
用有限元的方法,通过建立多个巨型框架结构以及相关的巨型框架结构模型,分析了巨型框架结构失稳特性。揭示了单层和多层巨型框架失稳时,一级框架和二级框架共同工作、相互作用的机理。阐述了巨型框架与双重抗侧力结构稳定特性的相似性,从而得出简化的求解结构屈曲荷载的方法。对于巨型框架结构的设计研究,有一定的参考作用。
研究了单个吊挂荷载的悬挂结构的弹性屈曲,求得了解析解。对多层吊挂荷载的巨型悬挂结构,运用连续化模型,推导了稳定平衡微分方程。结果表明：悬挂结构的弹性稳定,等同于将竖向荷载直接作用于悬挂巨型柱相同高度处的变轴力巨型框架柱的稳定。运用能量法,求出了竖向均布荷载作用下两端转动约束柱的屈曲荷载表达式,有限元方法验证说明其具有良好的精度。对两个巨型层的悬挂结构,用初等代数方法阐述了考虑层与层相互作用的屈曲荷载求解方法,与有限元方法比较表明,初等代数方法也具有良好的精度。
As more and more high-rise structures were built in the past decades, researchers had done lots of studies on high-rise structural systems, and the theories are comparatively perfect. However, understanding the overall stability of a structure is not an easy task. Fortunately, current designers have computer software to analyze it. Based on reasonable simplification, this thesis analyzed the overall stability of several different high-rise structure systems, accurate or approximate buckling load expressions are obtained, the stability behaviors of these structures are illustrated.
The second chapter analyze a simplified model of double-outrigger-braced structure, a model composed of independent rotational spring and relative rotational spring is proposed for the outrigger-column systems. The critical buckling equation is presented where the axial force of the core and the exterior columns may be varied. By analyzing a specific example, the second chapter reveals the total buckling load of each mega-story is independent of the load distribution among the core and the exterior columns. The analysis reveals also the strong inter-story interaction of the double-outrigger braced structures. By comparing the buckling of the normal frame and the double-outrigger-braced structures, and also by using the approximate buckling analysis based on the negative stiffness concept of gravity loads, which is very successful in normal frame buckling analysis, it is concluded that the double-outrigger braced mega-structure is closer to a normal frame in its buckling behavior, although it has a stronger inter-storey interaction than normal frames.
Using the continuum model, the third chapter made a study on buckling of coupled shear walls. A closed form solution and an explicit formula for the buckling load are obtained. The form of the formula implies that the coupled shear wall is a kind of dual structural system, and the interaction between two structural components may be elucidated by a series-parallel circuit. Based on this circuit, an explicit expression for the lateral stiffness of coupled shear wall is found and compared with exact solution. Amplification factors of drift, bending moments and axial forces in walls and bending moments in the link beams due to the second order effect are studied and a simple formula for the amplification factor is also provided.
Based on the study of coupled shear walls in the third chapter, the forth chapter studies the stability problem on coupled shear walls with cross section and axial force varies uniformly through the height. Using energy method, shear and flexural deformation curve are assumed to simulate the real buckling deflection curve. It is proved that coupled wall structure behaviors more complicated than a single shear or flexural system. Then a fitted buckling load expression is given, which has a fine accuracy.
The fifth chapter pays attention on studies of mega frame structure. Several model are established to analyze and illustrate the nature of stability of mega frame structure. Mega frame structures with single and double storey are presented. The interaction behavior between mega stories are explained. Then a simplified method of solving buckling load of mega frame structure is proposed, which could be a estimation for design work.
The sixth chapter analyze at first the buckling of frames with one suspended storey, closed form solution was obtained. Mega-frames with multiple suspended storeys were then studied using the continuum method, equilibrium differential equation for buckling was established. It was found that the stability of suspension mega frames is the same as the frames supporting the gravity loads at the same level at the mega columns. Using the energy method, an approximate expression for the buckling load of columns rotationally restrained at two ends is presented, its accuracy was verified by EFM. For suspension frames with two mega storeys, an elementary algebra method is proposed to solve for the buckling loads an the interaction between two storeys, its accuracy is also verified using numerical analysis.
对伸臂位于顶部及中部任意高度的巨型结构整体稳定性进行了分析,提出了双伸臂巨型结构中模拟伸臂和柱子作用的独立弹簧和关联弹簧的模型。推导了核心筒及边框柱中轴力不同时结构整体失稳的临界方程,通过具体算例的计算分析,得出了双伸臂巨型结构失稳时,伸臂层总的临界荷载与荷载在核心筒与伸臂端柱子之间的分布基本无关的结论。通过算例分析揭示了巨型层层与层之间存在较大的相互作用。通过对比普通框架的合并解法,揭示了伸臂巨型结构与框架结构在稳定问题上的区别,通过对基于整体的和层的荷载负刚度概念的伸臂结构屈曲的近似分析,进一步揭示了伸臂巨型结构在性质上更加接近于框架结构,而偏离整体弯曲型结构更远的性质。
采用连续化模型,对双肢剪力墙结构平面内稳定性进行了研究,求得了顶部作用集中压力时临界荷载的精确显式表达式和显式屈曲波形。这个临界荷载公式表明,联肢剪力墙是一种双重抗侧力结构,并且可以采用串并联电路模型来表示两者之间的相互作用。串并联模型推广到线性分析的情况,得到顶部抗侧刚度的近似显式表达式,与精确解进行了比较。推导了顶部作用竖向集中荷载时,在不同水平荷载作用下结构的侧移、墙肢弯矩、墙肢轴力和连梁弯矩放大系数,并提供了近似计算公式。
基于对等截面等轴力的联肢剪力墙的稳定性研究成果,并运用串并联电路模型,研究了变截面变轴力联肢剪力墙结构的稳定性。运用能量法,构建弯曲型、剪切型曲线,考察了变刚度变轴力联肢剪力墙结构的失稳波形,得出结论,变截面变轴力联肢墙的屈曲问题比较复杂,不简单的等效于弯曲、剪切或简单的弯剪型。进而文章通过大量的算例拟合出了联肢墙的屈曲荷载表达式,有比较好的精确度。
用有限元的方法,通过建立多个巨型框架结构以及相关的巨型框架结构模型,分析了巨型框架结构失稳特性。揭示了单层和多层巨型框架失稳时,一级框架和二级框架共同工作、相互作用的机理。阐述了巨型框架与双重抗侧力结构稳定特性的相似性,从而得出简化的求解结构屈曲荷载的方法。对于巨型框架结构的设计研究,有一定的参考作用。
研究了单个吊挂荷载的悬挂结构的弹性屈曲,求得了解析解。对多层吊挂荷载的巨型悬挂结构,运用连续化模型,推导了稳定平衡微分方程。结果表明：悬挂结构的弹性稳定,等同于将竖向荷载直接作用于悬挂巨型柱相同高度处的变轴力巨型框架柱的稳定。运用能量法,求出了竖向均布荷载作用下两端转动约束柱的屈曲荷载表达式,有限元方法验证说明其具有良好的精度。对两个巨型层的悬挂结构,用初等代数方法阐述了考虑层与层相互作用的屈曲荷载求解方法,与有限元方法比较表明,初等代数方法也具有良好的精度。
As more and more high-rise structures were built in the past decades, researchers had done lots of studies on high-rise structural systems, and the theories are comparatively perfect. However, understanding the overall stability of a structure is not an easy task. Fortunately, current designers have computer software to analyze it. Based on reasonable simplification, this thesis analyzed the overall stability of several different high-rise structure systems, accurate or approximate buckling load expressions are obtained, the stability behaviors of these structures are illustrated.
The second chapter analyze a simplified model of double-outrigger-braced structure, a model composed of independent rotational spring and relative rotational spring is proposed for the outrigger-column systems. The critical buckling equation is presented where the axial force of the core and the exterior columns may be varied. By analyzing a specific example, the second chapter reveals the total buckling load of each mega-story is independent of the load distribution among the core and the exterior columns. The analysis reveals also the strong inter-story interaction of the double-outrigger braced structures. By comparing the buckling of the normal frame and the double-outrigger-braced structures, and also by using the approximate buckling analysis based on the negative stiffness concept of gravity loads, which is very successful in normal frame buckling analysis, it is concluded that the double-outrigger braced mega-structure is closer to a normal frame in its buckling behavior, although it has a stronger inter-storey interaction than normal frames.
Using the continuum model, the third chapter made a study on buckling of coupled shear walls. A closed form solution and an explicit formula for the buckling load are obtained. The form of the formula implies that the coupled shear wall is a kind of dual structural system, and the interaction between two structural components may be elucidated by a series-parallel circuit. Based on this circuit, an explicit expression for the lateral stiffness of coupled shear wall is found and compared with exact solution. Amplification factors of drift, bending moments and axial forces in walls and bending moments in the link beams due to the second order effect are studied and a simple formula for the amplification factor is also provided.
Based on the study of coupled shear walls in the third chapter, the forth chapter studies the stability problem on coupled shear walls with cross section and axial force varies uniformly through the height. Using energy method, shear and flexural deformation curve are assumed to simulate the real buckling deflection curve. It is proved that coupled wall structure behaviors more complicated than a single shear or flexural system. Then a fitted buckling load expression is given, which has a fine accuracy.
The fifth chapter pays attention on studies of mega frame structure. Several model are established to analyze and illustrate the nature of stability of mega frame structure. Mega frame structures with single and double storey are presented. The interaction behavior between mega stories are explained. Then a simplified method of solving buckling load of mega frame structure is proposed, which could be a estimation for design work.
The sixth chapter analyze at first the buckling of frames with one suspended storey, closed form solution was obtained. Mega-frames with multiple suspended storeys were then studied using the continuum method, equilibrium differential equation for buckling was established. It was found that the stability of suspension mega frames is the same as the frames supporting the gravity loads at the same level at the mega columns. Using the energy method, an approximate expression for the buckling load of columns rotationally restrained at two ends is presented, its accuracy was verified by EFM. For suspension frames with two mega storeys, an elementary algebra method is proposed to solve for the buckling loads an the interaction between two storeys, its accuracy is also verified using numerical analysis.
引文
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