刚性与弹性支承圆弧钢拱的平面内稳定性及设计方法研究
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摘要
拱形钢结构以其优美的造型、合理的受力性能和相对良好的经济指标而在工程实践中得到广泛的使用。当拱圈上部有铺板密铺或是设置横向支承构件对其提供侧向约束时,钢拱主要发生平面内的失稳破坏。目前,国内外学者对拱的平面内稳定极限承载力的设计方法主要采用相关公式法。但是,这些公式的适用性和归一性有待进一步检验。
本文对工字形截面三铰、两铰和无铰圆弧拱的平面内稳定性与极限承载力进行了系统的研究。根据有限元数值分析的结果,拟合得到了轴压拱的线弹性临界屈曲轴力,并与根据传统的经典理论得到的临界值进行了比较。利用临界轴力定义了圆弧拱的正则化长细比,采用Perry-Robertson公式的形式建立了以正则化长细比为变量的轴压拱稳定设计曲线。由于几何大变形的影响,轴力的二阶效应会导致截面上弯矩的增大,本文以三铰拱为例对弯矩放大系数进行了研究并给出了相应的计算公式。根据有限元分析结果,本文提出了压弯拱平面内稳定承载力设计的N-M相关公式,与以往学者研究成果不同的是：(1)轴力和弯矩数值采用一阶线弹性分析得到的控制截面的内力,而不是最大轴力与最大弯矩,因为这两个最大内力不一定出现在同一个截面上,这更符合工程设计的习惯；(2)公式中通过特定的系数考虑了支承条件、弯矩分布、几何二阶效应以及截面塑性开展能力等因素的影响。同时本文还对已有的设计公式进行了验证比较。
钢拱常支承于其他结构上,拱脚在水平方向很难做到完全的刚性支承,拱的支座约束可以用拱脚处的水平弹簧进行等效替代。由于水平弹性约束的影响,拱脚会出现水平位移,拱的力学行为会发生显著改变。本文由圆弧拱线性平衡微分方程出发得到了水平弹性支承拱在面内竖向对称荷载作用下的内力及位移的解析解,并构造了一个反映支座约束程度的无量纲化系数——弹性柔度系数。根据拱与拱形梁在跨中轴力上的区别,提出了在线性计算范围内划分拱与拱形梁的标准。分析了支座弹簧刚度对扁度不同的拱内力分布的影响。利用有限元程序,在线弹性分析的范围内确定了拱由反对称屈曲转变为对称屈曲时弹性柔度系数的界限值,提出了临界荷载和跨中临界轴力与弹性柔度系数的关系表达式。
本文利用有限元程序,在考虑了几何缺陷、残余应力和材料非线性的基础上,采用大挠度变形理论对水平弹性支承拱进行了弹塑性研究,分析了其平面内失稳特征和极限承载力。针对工字型截面,研究了不同荷载工况下支座刚度对拱的承载力和极限状态下拱脚位移的影响,并以弹性柔度系数为变量,分别拟合了无量纲化极限荷载以及极限状态下支座水平位移的计算公式。使用已有的两铰圆弧拱设计公式对弹性支承拱进行了验算,并提出了实用的简化设计准则。
对考虑初始缺陷和材料塑性性能的双轴对称工字形截面压杆,采用大变形理论自编程序3D-Steel-Struct对其屈曲前后的变形曲线和受力性能进行了研究。利用解析方法分别对压杆进行了二阶弹性和二阶塑性的理论分析,推导了相应阶段轴压力与变形之间的关系。通过与有限元解的比较,构造了轴力与跨中挠度以及轴力与轴向位移之间的解析表达式,与数值解非常吻合。
对轴压杆的延性进行了定义,利用有限元程序研究工字形截面绕强轴和绕弱轴、圆管截面以及单角钢截面绕弱轴和绕平行轴受压弯曲后的延性性能；同时提出了延性与长细比之间的计算表达式。
对考虑初始缺陷和材料塑性性能的双轴对称工字形截面受弯及压弯杆件,利用解析方法分别得到二阶弹性和二阶塑性的荷载—位移关系,并通过与有限元解的比较,构造公式得到受弯及压弯杆件受荷全过程曲线的解析表达式。
Steel arches, with their elegant shapes, reasonable mechanical characteristics and relatively good economic have been widely used in engineering projects. When a slab encases the top flange of the arch and is mechanically anchored to it, or there are some lateral supports to provide restraints, in-plane stability of steel arches is needed to be concerned. Until recently, the in-plane ultimate load-carrying capacity of steel arches has been studied by several researchers, and the strength design methods with interaction equation are established. The applicability and normalization of these formulas need to be further examination.
In this thesis, in-plane inelastic stability behavior and strength design of three-hinged, two-hinged and fixed steel circular arches with I-section are studied systematically. Based on the results of finite element method (FEM), fitted values of linear elastic critical compression when arches subject to hydrostatic load are presented, and the obtained results are compared with classic buckling theory. The relationship between the arch stability coefficients and the normalized slenderness ratio which is defined using the critical compression is established in the form of Perry-Roberson formula. Second-order effect of axial compression due to the large displacement will lead to the increase of moment. This thesis studies the moment amplification factor of three-hinged arches and proposes the corresponding formulas. The interaction formula composed of compression and bending which are obtained by a first order analysis is proposed for the in-plane strength design of circular arches. Compared to other research, innovations of this thesis are:(1) axial compression and bending moment are internal forces of controlling section using first-order linear elastic analysis, rather than the maximum compression and maximum bending which dose not necessarily appear in the same cross-section. This approach is consistent with the habits of the engineering design.(2) in the formula, supporting condition, distribution of moment, geometric second-order effect and plastic capacity of cross-section are considered by some factors. Moreover, existing design formulas proposed by other researchers are verified in the thesis.
An arch is often connected with other structures that provide elastic restraints to the arch. It can be considered to be supported elastically at both ends by horizontal springs. These elastic restraints significantly influence its behavior. Analytical solutions of horizontally elastically supported arches that are subjected to several vertical symmetric uniformly distributed loads are obtained based on linear equilibrium equations. A dimensionless elastic flexibility factor is introduced. By analyzing the linear analytical solutions and using the flexibility factor, criterions that distinguish between arches and arched beams are suggested. The effects of the stiffness of the horizontal end restraint on the distribution of internal forces are studied. By FEM, a limiting flexibility factor that distinguishes between in-plane linear elastic anti-symmetric bifurcation mode and symmetric snap-through mode is presented, and formulas for critical load and mid-span axial forces in term of elastic flexibility factor are proposed.
In this thesis, an elasto-plastic finite element model is established to study the in-plane stability behavior and ultimate strength of steel circular arches with horizontal elastic restraints using large deformation theory by FEM. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. In six load cases, the effects of the stiffness of end restraints on the bearing capacity of arches with I-section and horizontal displacement of supports in the limit state of load-carrying are studied. Based on the numerical results, formulas for dimensionless ultimate strength and displacement of supports in terms of elastic flexibility factor are proposed. The design formulas for pin-ended arches proposed by other researches are used for elastically supported arches, and a simplified design criterion is presented.
This thesis investigates the deformation characteristics and mechanical properties of compressed bars with biaxial symmetric I-section. Based on the large deformation theory, a finite-element program of3D-Steel-Struct developed by the authors is used in the analysis. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. Second order elastic and second order rigid-plastic analysis are carried out for imperfect members, and relation between axial compression and deformation are deduced. Analytical expressions of axial compression and deflection at mid-span and of axial compression and axial shortening are presented, and comparison shows the excellent agreement between the proposed explicit expressions and the numerical results.
The axial ductility of compressed members is defined. This thesis studies the ductility of compressed bars with I-section revolving round the maximum and the minimum principal axes of inertia of an area, with tube section, and with L-section revolving round the minimum principal axis of inertia of an area and parallel axis respectively. Formulas relating the ductility to the slenderness are proposed.
Second order elastic and second order rigid-plastic analysis are carried out for imperfect beams and beam-columns with biaxial symmetric I-section, and relation between load and deformation are deduced. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. Based on the results of FEM, analytical expressions with good accuracy of relationship between load and deformation of beams and beam-columns are presented.
本文对工字形截面三铰、两铰和无铰圆弧拱的平面内稳定性与极限承载力进行了系统的研究。根据有限元数值分析的结果,拟合得到了轴压拱的线弹性临界屈曲轴力,并与根据传统的经典理论得到的临界值进行了比较。利用临界轴力定义了圆弧拱的正则化长细比,采用Perry-Robertson公式的形式建立了以正则化长细比为变量的轴压拱稳定设计曲线。由于几何大变形的影响,轴力的二阶效应会导致截面上弯矩的增大,本文以三铰拱为例对弯矩放大系数进行了研究并给出了相应的计算公式。根据有限元分析结果,本文提出了压弯拱平面内稳定承载力设计的N-M相关公式,与以往学者研究成果不同的是：(1)轴力和弯矩数值采用一阶线弹性分析得到的控制截面的内力,而不是最大轴力与最大弯矩,因为这两个最大内力不一定出现在同一个截面上,这更符合工程设计的习惯；(2)公式中通过特定的系数考虑了支承条件、弯矩分布、几何二阶效应以及截面塑性开展能力等因素的影响。同时本文还对已有的设计公式进行了验证比较。
钢拱常支承于其他结构上,拱脚在水平方向很难做到完全的刚性支承,拱的支座约束可以用拱脚处的水平弹簧进行等效替代。由于水平弹性约束的影响,拱脚会出现水平位移,拱的力学行为会发生显著改变。本文由圆弧拱线性平衡微分方程出发得到了水平弹性支承拱在面内竖向对称荷载作用下的内力及位移的解析解,并构造了一个反映支座约束程度的无量纲化系数——弹性柔度系数。根据拱与拱形梁在跨中轴力上的区别,提出了在线性计算范围内划分拱与拱形梁的标准。分析了支座弹簧刚度对扁度不同的拱内力分布的影响。利用有限元程序,在线弹性分析的范围内确定了拱由反对称屈曲转变为对称屈曲时弹性柔度系数的界限值,提出了临界荷载和跨中临界轴力与弹性柔度系数的关系表达式。
本文利用有限元程序,在考虑了几何缺陷、残余应力和材料非线性的基础上,采用大挠度变形理论对水平弹性支承拱进行了弹塑性研究,分析了其平面内失稳特征和极限承载力。针对工字型截面,研究了不同荷载工况下支座刚度对拱的承载力和极限状态下拱脚位移的影响,并以弹性柔度系数为变量,分别拟合了无量纲化极限荷载以及极限状态下支座水平位移的计算公式。使用已有的两铰圆弧拱设计公式对弹性支承拱进行了验算,并提出了实用的简化设计准则。
对考虑初始缺陷和材料塑性性能的双轴对称工字形截面压杆,采用大变形理论自编程序3D-Steel-Struct对其屈曲前后的变形曲线和受力性能进行了研究。利用解析方法分别对压杆进行了二阶弹性和二阶塑性的理论分析,推导了相应阶段轴压力与变形之间的关系。通过与有限元解的比较,构造了轴力与跨中挠度以及轴力与轴向位移之间的解析表达式,与数值解非常吻合。
对轴压杆的延性进行了定义,利用有限元程序研究工字形截面绕强轴和绕弱轴、圆管截面以及单角钢截面绕弱轴和绕平行轴受压弯曲后的延性性能；同时提出了延性与长细比之间的计算表达式。
对考虑初始缺陷和材料塑性性能的双轴对称工字形截面受弯及压弯杆件,利用解析方法分别得到二阶弹性和二阶塑性的荷载—位移关系,并通过与有限元解的比较,构造公式得到受弯及压弯杆件受荷全过程曲线的解析表达式。
Steel arches, with their elegant shapes, reasonable mechanical characteristics and relatively good economic have been widely used in engineering projects. When a slab encases the top flange of the arch and is mechanically anchored to it, or there are some lateral supports to provide restraints, in-plane stability of steel arches is needed to be concerned. Until recently, the in-plane ultimate load-carrying capacity of steel arches has been studied by several researchers, and the strength design methods with interaction equation are established. The applicability and normalization of these formulas need to be further examination.
In this thesis, in-plane inelastic stability behavior and strength design of three-hinged, two-hinged and fixed steel circular arches with I-section are studied systematically. Based on the results of finite element method (FEM), fitted values of linear elastic critical compression when arches subject to hydrostatic load are presented, and the obtained results are compared with classic buckling theory. The relationship between the arch stability coefficients and the normalized slenderness ratio which is defined using the critical compression is established in the form of Perry-Roberson formula. Second-order effect of axial compression due to the large displacement will lead to the increase of moment. This thesis studies the moment amplification factor of three-hinged arches and proposes the corresponding formulas. The interaction formula composed of compression and bending which are obtained by a first order analysis is proposed for the in-plane strength design of circular arches. Compared to other research, innovations of this thesis are:(1) axial compression and bending moment are internal forces of controlling section using first-order linear elastic analysis, rather than the maximum compression and maximum bending which dose not necessarily appear in the same cross-section. This approach is consistent with the habits of the engineering design.(2) in the formula, supporting condition, distribution of moment, geometric second-order effect and plastic capacity of cross-section are considered by some factors. Moreover, existing design formulas proposed by other researchers are verified in the thesis.
An arch is often connected with other structures that provide elastic restraints to the arch. It can be considered to be supported elastically at both ends by horizontal springs. These elastic restraints significantly influence its behavior. Analytical solutions of horizontally elastically supported arches that are subjected to several vertical symmetric uniformly distributed loads are obtained based on linear equilibrium equations. A dimensionless elastic flexibility factor is introduced. By analyzing the linear analytical solutions and using the flexibility factor, criterions that distinguish between arches and arched beams are suggested. The effects of the stiffness of the horizontal end restraint on the distribution of internal forces are studied. By FEM, a limiting flexibility factor that distinguishes between in-plane linear elastic anti-symmetric bifurcation mode and symmetric snap-through mode is presented, and formulas for critical load and mid-span axial forces in term of elastic flexibility factor are proposed.
In this thesis, an elasto-plastic finite element model is established to study the in-plane stability behavior and ultimate strength of steel circular arches with horizontal elastic restraints using large deformation theory by FEM. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. In six load cases, the effects of the stiffness of end restraints on the bearing capacity of arches with I-section and horizontal displacement of supports in the limit state of load-carrying are studied. Based on the numerical results, formulas for dimensionless ultimate strength and displacement of supports in terms of elastic flexibility factor are proposed. The design formulas for pin-ended arches proposed by other researches are used for elastically supported arches, and a simplified design criterion is presented.
This thesis investigates the deformation characteristics and mechanical properties of compressed bars with biaxial symmetric I-section. Based on the large deformation theory, a finite-element program of3D-Steel-Struct developed by the authors is used in the analysis. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. Second order elastic and second order rigid-plastic analysis are carried out for imperfect members, and relation between axial compression and deformation are deduced. Analytical expressions of axial compression and deflection at mid-span and of axial compression and axial shortening are presented, and comparison shows the excellent agreement between the proposed explicit expressions and the numerical results.
The axial ductility of compressed members is defined. This thesis studies the ductility of compressed bars with I-section revolving round the maximum and the minimum principal axes of inertia of an area, with tube section, and with L-section revolving round the minimum principal axis of inertia of an area and parallel axis respectively. Formulas relating the ductility to the slenderness are proposed.
Second order elastic and second order rigid-plastic analysis are carried out for imperfect beams and beam-columns with biaxial symmetric I-section, and relation between load and deformation are deduced. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. Based on the results of FEM, analytical expressions with good accuracy of relationship between load and deformation of beams and beam-columns are presented.
引文
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