曲线薄壁箱梁桥的空间静力与时效分析
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摘要
曲线箱形梁桥具有抗扭刚度大、经济性好、外形美观等优点,是高速公路立交匝道、城市高架桥常用的结构型式。由于曲率的存在,曲线梁桥的力学行为比直线梁桥复杂,计算难度也较直线梁桥大。随着大跨度曲线箱梁桥的日益增多,截面构造呈现出变曲率、变高度的特点,迫切需要一个能充分反映曲线箱梁拉、压、弯、扭、翘曲和畸变等复杂受力状态,同时又能计算桥梁结构逐步施工过程和收缩徐变效应的分析理论和计算程序。本文针对变曲率、变梁高的曲线箱梁桥,深入系统地开展了空间静力分析和混凝土收缩徐变时效分析的研究,建立了复杂受力状态下曲线箱梁的计算模型,编制了能实现混凝土收缩徐变效应分析的曲线箱梁桥有限元程序。主要研究内容如下:
1.针对具有竖直对称轴的矩形断面变曲率箱梁,考虑了挠曲剪切应变和曲梁剪心和形心分离的影响,推导了变曲率箱梁的平衡方程;通过箱梁内任一点的位移方程和内力-位移关系,推导了考虑曲梁剪心和形心分离的变曲率箱梁的挠曲扭转控制微分方程。研究结果表明,曲率半径越小,剪心和形心分离对扭转角的影响越大。
2.分析了引起曲线桥梁正应力在横桥向分布不均匀的原因:除了翘曲和畸变引起正应力分布不均匀以外,由于宽度方向的曲率变化对箱梁竖向挠曲转角的影响,弯曲变形后的曲线箱梁的截面已不再符合平截面假定,截面上各点的弯曲正应力与该点的曲率半径的平方成反比,内侧纵向弯曲正应力大于外侧正应力。弯曲和翘曲扭转引起的内外侧应力分布不均匀通常是相反的。当曲轴线半径与箱梁宽度比小于10时,必须考虑曲率沿横向变化的影响。
3.建立适合于变高度曲线箱梁的曲线坐标系,推导了变曲率、变高度箱梁弯曲、翘曲扭转和畸变的位移方程和应变-位移关系式,提出了具有一个竖直对称轴的变高度变曲率曲线箱梁的薄壁曲梁空间分析有限元方法。推导中除考虑曲率变化、截面形心和剪切中心分离、梁的横向剪切变形影响等因素外,还考虑了曲率沿横向变化对竖向挠转角的影响。为了计算单元内的曲率和梁高,有限元的形函数也同时作为曲率和梁高在单元内变化的插值函数。
4.根据积分中值定理,推导了增量时间段中点时刻徐变系数等效弹性模量的计算式;将徐变和收缩应变视为强迫应变,推导了强迫应变法计算混凝土梁桥的徐变、收缩效应的分析方法,写出了混凝土桥梁的徐变、收缩时效分析有限元列式,并将此方法应用到曲线箱梁桥的时效分析中。
5.在上述研究结果的基础上,编制了能同时开展桥梁施工过程分析和混凝土收缩徐变时效分析的曲线箱梁桥有限元程序。通过算例证实了本文计算理论和分析程序的正确性。
Due to the excellence of torsional stiffness, economy and aesthetic appearance, curved box-girders are widely used in modern highway bridges, interchanges and urban viaduct systems. Because of curvature, the mechanical behavior and the calculation of curved girder are more complex compared to the straight girder. Box-girder bridge has become increasingly popular in construction of curved bridge, the conformation of it has been presented the characteristic of variable curvature and variable height. Practical design of curved box-girder bridges requires an analytical method which can be applied to analysis of construction process and the finite element formulas about analysis of creep effect and shrinkage effect. In this dissertation, spatial static linearity analysis and time effec(tcreep effect and shrinkage effect) for curved thin-walled box-girder bridge were studied. According to those, the main contents and results are as follows:
1. In this dissertation, considering the influence of transverse shearing deflection and noncoincidence of torsion center and gravity center, the equilibrium formulas of variable-curvature box-girder with rectangular cross section were established. Based on deformation expression of arbitrary point on the girder and relationship between inner forces and displacement equations, considering noncoincidence of torsional center and gravity center, the governing differential equations for variable-curvature box-girders were generalized. The results of research indicates: the shorter the radius is, the greater influence of the noncoincidence of the torsion center and gravity center for torsion angle will be.
2.The causes why normal stress of curved-box girder vary with transverse axis are as follows。Besides the normal stress of torsion and distortional warping,bending normal stress brings asymmetrical distributing. Because curvature varying on width of curved girders have effects on the vertical bending deflection angle, the displacement assumption which plane surfaces of girder remain plane after bending is canceled. The bending normal stress of arbitrary point on the cross section are in inverse proportion to square of radius of this point. And the inner portrait bending stress of curved box-girder are stronger than outer portrait stress. The effects of above-mentioned are usually opposite. If the ratio of axis-radius to width is less than 10, the effect of curvature varying on width of curved girders must be considered.
3. A curve coordinate system which is suitable for variable height curved box-girder were established. The flexure, torsion and distortional warping displacement functions were established, and the strain-deformation equations were obtained, a spatial finite element analysis method of trapeziform cross section variable-curvature box-girder with vertical symmetrical axis was also presented. During the process, following were considered:the effects of variable radius of cross section on the vertical bending deflection angle, noncoincidence of torsional center and gravity center, the effect of transverse shearing strain on energy of strain. In order to calculating the curvature and height in the element, the shape functions were also used for the variable expression of curvature and height.
4. Applying integral intermediate value theorem, new effective elasticity modulus expressions were presented, which creep aging coefficient can be calculated by the creep coefficient of intermediate time of incremental time segment. Creep and shrinkage strain were treated as a kind of compulsive strain. Compulsive strain methods were used for the analysis of creep effect and shrinkage effect about concrete curved box-girder bridge. A group of finite element formulas about analysis of creep effect and shrinkage effect were deduced.
5. Based on the facts mentioned above, the curved boxed-girder bridge program was programmed, which can be applied to the analysis of bridge construction process. Some examples were proved to the validity and the accuracy of these proposed methods and analysis programs.
1.针对具有竖直对称轴的矩形断面变曲率箱梁,考虑了挠曲剪切应变和曲梁剪心和形心分离的影响,推导了变曲率箱梁的平衡方程;通过箱梁内任一点的位移方程和内力-位移关系,推导了考虑曲梁剪心和形心分离的变曲率箱梁的挠曲扭转控制微分方程。研究结果表明,曲率半径越小,剪心和形心分离对扭转角的影响越大。
2.分析了引起曲线桥梁正应力在横桥向分布不均匀的原因:除了翘曲和畸变引起正应力分布不均匀以外,由于宽度方向的曲率变化对箱梁竖向挠曲转角的影响,弯曲变形后的曲线箱梁的截面已不再符合平截面假定,截面上各点的弯曲正应力与该点的曲率半径的平方成反比,内侧纵向弯曲正应力大于外侧正应力。弯曲和翘曲扭转引起的内外侧应力分布不均匀通常是相反的。当曲轴线半径与箱梁宽度比小于10时,必须考虑曲率沿横向变化的影响。
3.建立适合于变高度曲线箱梁的曲线坐标系,推导了变曲率、变高度箱梁弯曲、翘曲扭转和畸变的位移方程和应变-位移关系式,提出了具有一个竖直对称轴的变高度变曲率曲线箱梁的薄壁曲梁空间分析有限元方法。推导中除考虑曲率变化、截面形心和剪切中心分离、梁的横向剪切变形影响等因素外,还考虑了曲率沿横向变化对竖向挠转角的影响。为了计算单元内的曲率和梁高,有限元的形函数也同时作为曲率和梁高在单元内变化的插值函数。
4.根据积分中值定理,推导了增量时间段中点时刻徐变系数等效弹性模量的计算式;将徐变和收缩应变视为强迫应变,推导了强迫应变法计算混凝土梁桥的徐变、收缩效应的分析方法,写出了混凝土桥梁的徐变、收缩时效分析有限元列式,并将此方法应用到曲线箱梁桥的时效分析中。
5.在上述研究结果的基础上,编制了能同时开展桥梁施工过程分析和混凝土收缩徐变时效分析的曲线箱梁桥有限元程序。通过算例证实了本文计算理论和分析程序的正确性。
Due to the excellence of torsional stiffness, economy and aesthetic appearance, curved box-girders are widely used in modern highway bridges, interchanges and urban viaduct systems. Because of curvature, the mechanical behavior and the calculation of curved girder are more complex compared to the straight girder. Box-girder bridge has become increasingly popular in construction of curved bridge, the conformation of it has been presented the characteristic of variable curvature and variable height. Practical design of curved box-girder bridges requires an analytical method which can be applied to analysis of construction process and the finite element formulas about analysis of creep effect and shrinkage effect. In this dissertation, spatial static linearity analysis and time effec(tcreep effect and shrinkage effect) for curved thin-walled box-girder bridge were studied. According to those, the main contents and results are as follows:
1. In this dissertation, considering the influence of transverse shearing deflection and noncoincidence of torsion center and gravity center, the equilibrium formulas of variable-curvature box-girder with rectangular cross section were established. Based on deformation expression of arbitrary point on the girder and relationship between inner forces and displacement equations, considering noncoincidence of torsional center and gravity center, the governing differential equations for variable-curvature box-girders were generalized. The results of research indicates: the shorter the radius is, the greater influence of the noncoincidence of the torsion center and gravity center for torsion angle will be.
2.The causes why normal stress of curved-box girder vary with transverse axis are as follows。Besides the normal stress of torsion and distortional warping,bending normal stress brings asymmetrical distributing. Because curvature varying on width of curved girders have effects on the vertical bending deflection angle, the displacement assumption which plane surfaces of girder remain plane after bending is canceled. The bending normal stress of arbitrary point on the cross section are in inverse proportion to square of radius of this point. And the inner portrait bending stress of curved box-girder are stronger than outer portrait stress. The effects of above-mentioned are usually opposite. If the ratio of axis-radius to width is less than 10, the effect of curvature varying on width of curved girders must be considered.
3. A curve coordinate system which is suitable for variable height curved box-girder were established. The flexure, torsion and distortional warping displacement functions were established, and the strain-deformation equations were obtained, a spatial finite element analysis method of trapeziform cross section variable-curvature box-girder with vertical symmetrical axis was also presented. During the process, following were considered:the effects of variable radius of cross section on the vertical bending deflection angle, noncoincidence of torsional center and gravity center, the effect of transverse shearing strain on energy of strain. In order to calculating the curvature and height in the element, the shape functions were also used for the variable expression of curvature and height.
4. Applying integral intermediate value theorem, new effective elasticity modulus expressions were presented, which creep aging coefficient can be calculated by the creep coefficient of intermediate time of incremental time segment. Creep and shrinkage strain were treated as a kind of compulsive strain. Compulsive strain methods were used for the analysis of creep effect and shrinkage effect about concrete curved box-girder bridge. A group of finite element formulas about analysis of creep effect and shrinkage effect were deduced.
5. Based on the facts mentioned above, the curved boxed-girder bridge program was programmed, which can be applied to the analysis of bridge construction process. Some examples were proved to the validity and the accuracy of these proposed methods and analysis programs.
引文
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