钢—混凝土组合肋壳非线性分析
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摘要
本文提出一种新型组合空间结构体系——组合肋壳，由U型截面钢肋和浇注于其内的混凝土肋构成组合肋，以组合肋为支架浇注混凝土薄壳，最终完成组合肋壳施工。在整个施工过程中，建成构件依次作为后者施工时的模板和支架，避免混凝土薄壳施工中支模拆摸等繁琐工作，大大缩短工期，降低造价，是一种具有很好工程应用前景的新型壳体结构形式。为深入探讨组合肋壳的受力机理，弥补新型结构研究空白，本文依照施工先后顺序，分别对单根钢肋、组合肋及组合肋壳的受力性能、承载力影响因素等进行研究，主要内容有：
1．对单根钢肋圆拱稳定性及承载力进行理论研究和数值分析，探讨了钢肋的稳定性，拟合了钢肋平面内屈曲和侧倾屈曲临界荷载计算公式。
首次对U型截面钢肋圆拱进行分析，利用APDL语言，分别建立不带隔板、带隔板两种模型，对30种不同截面尺寸，180余例单根钢肋在平面内屈曲及侧倾失稳时的极限承载力、失稳形态进行了研究，考察隔板设置对钢肋受力性能的影响，并探讨了不同截面尺寸、半跨荷载作用以及初始缺陷对钢肋稳定性的影响，为全面了解钢肋圆拱力学性能提供了资料。
2．对组合肋截面构件进行了几何非线性和材料非线性分析，推导了组合肋正截面受压、受拉和受弯时承载力计算公式。
对组合截面承载力研究方法进行讨论，着重论述了非线性有限单元法与软件分析相结合的实用分析方法，并以标准混凝土抗压试块、钢筋混凝土梁及钢管混凝土短柱为例，进行验证。对组合肋截面构件在正截面受压、受拉、受弯三种不同受力情况进行有限元模拟，同时考虑几何、材料非线性影响，在有限元分析基础上，依据极限平衡理论，推导了组合肋截面构件承载力计算公式。对不同混凝土强度下不同截面尺寸组合肋承载力进行参数分析，证明所推导的承载力计算公式的可靠性。
3．通过组合肋壳弹塑性分析，对组合肋壳承载能力、变形特点进行了全面探讨。
采用更新拉格朗日格式，基于增量虚功原理建立了组合肋壳非线性增量平衡方程，利用空间梁单元和层合曲边壳单元，考虑组合肋与混凝土薄壳间的偏心影响，建立了组合肋壳刚度矩阵；研究了在自重和均布压力荷载作用下，组合肋壳内力分布特点、荷载传递方式、结构内部力流分布，以及材料进入塑性后，结构变形特点、内力分布特点等；最后与普通的钢筋混凝土带肋壳受力性能进行比较。
4．在组合肋壳稳定性分析中，探讨了结构的失稳形态和后屈曲特性，结论可供设计参考。
提出线搜索和弧长法相结合的稳定性分析方法，通过典型例题进行验证；由组合肋壳受力全过程跟踪，判断结构稳定性，并对不同影响因素进行大规模参数分析，研究了不同肋格数、不同矢跨比、不同截面尺寸、不同边界条件及不同荷载作用下，组合肋壳极限承载力变化和失稳区域分布情况等，可供该新型结构设计参考。
本文创新之处：
1．提出了一种新型结构形式——钢—混凝土组合肋壳，对其承载能力、弹塑性和稳定性进行了全面研究，发现这种结构能克服混凝土薄壳施工繁琐缺陷，同时具有承载能力高，稳定性能优越等特点。
2．通过对钢肋稳定性研究，分别拟合了单根钢肋平面内失稳、侧倾失稳时临界荷载计算公式，并对此进行检验，为U型截面圆拱临界荷载数值计算提供参考；对两种不同模型的钢肋极限承载力和失稳形态比较发现，带有隔板的钢肋承载力是不带隔板的2-3倍，在添加隔板后，不仅可以有效防止浇注过程中混凝土沿钢肋轴线下滑，同时可大大提高钢肋的承载能力；对承载力影响因素进行分析发现，钢肋板厚度是重要影响因素，其次是钢肋截面高度，宽度和隔板间距。
3．在有限元模拟结果的基础上，根据极限平衡理论，推导出组合肋截面轴心受压、轴心受拉及正截面受弯承载力计算公式，并对组合肋三种受力状态下承载力进行计算，计算结果与非线性有限元分析结果吻合较好，两者相差仅2％左右，所提出的U型截面计算公式可为设计提供参考。
4．组合肋壳弹塑性分析发现，经过组合肋壳中心的两条正交组合肋是重要传力构件，结构传力路线明确、流畅；钢肋不仅可以作为浇注混凝土肋模板使用，一定程度上也改善了结构的受力性能，调节组合肋轴向压力和弯矩变化幅度，可使结构内力分布趋于均匀，结构受力性能比钢筋混凝土带肋壳优越。稳定性分析发现在组合肋壳局部失稳后，承载能力仍有所提高，与网壳结构受力性能不同，结构表现出一定的屈曲后强度，因此对于组合肋壳而言，取第一个临界点作为临界荷载是不合理的，应该考虑并充分利用结构的后屈曲强度。
Steel-concrete composite ribbed shell is described in this paper, which is a new kind of space structure for enclosing large spaces. This kind of shell is made of composite rib and concrete shell: steel rib is formed by three thin steel plates welded in U shape, then concrete is poured to build composite ribs; those composite ribs are used as the formworks to make RC shell, finally the whole composite ribbed shell is completed. During the whole construction process, the founded members are used as the formworks and brackets to the latter. The new structure retains all the benefits of thin concrete shells, while eliminates the need for temporary formwork and minimises the required falsework, declines construction cost, so it is a kind of spatial structural system with good developing prospect.
To grasp the structure mechanics and remedy blank of research, the factors to mechanics and bearing capability of single steel rib, composite rib and the whole structure are discussed according to construction order. The main content is described as follows:
1. Theory and numerical study on stability and bearing capability of single steel rib, critical bearing capability formula are made.
Steel rib arch with U section is presented, the models with and without clapboard are made separately by using APDL language, 30 groups of different sections and more than 180 steel arch examples are researched, the ultimate bearing capability and instable form are investigated, the influence factors including clapboard, different section dimension, half span loading and initial imperfection are discussed in detail, all the above provides abundant information to master the mechanics of steel arch.
2. Bearing capability of composite rib members is analyzed considering geometry and material nonlinear, bearing capability formula of composite rib is concluded.
Bearing capability analysis methods of composite section are discussed, especially the applied method which is combined by nonlinear finite element method and software analysis, standard concrete compress member, RC beam and steel tube concrete puncheon are validated. The mechanics capability of composite rib section members are simulated by finite element method, which including press, pull and bend. Based on the analysis, the calculation formula of bearing capability is put forward which considering the effects of geometry and material nonlinear and using limit continuum equation. Under different concrete intension, parameter analysis of various section dimension is made, which provides data support for calculation formula of bearing capability.
3. Elastic-plastic analysis of composite ribbed shell is made completely, which includes ultimate bearing capability and characteristic of deformation.
Based on the virtual work, the composite ribbed shell nonlinear incremental continuum equation is made by using space beam element and layer curved shell element, stiffness matrix is founded considering the eccentricity influence; then internal force distributing, loading transfer fashion and characteristic deformation are researched under the load of deadweight and equal pressure; finally a comparison with RC ribbed shell is made.
4. During the stability analysis of composite ribbed shell, stable deformation and post-buckling characteristic are discussed in detail. The conclusions can be resulted in structure design.
A new stability analysis method is put forward, which is combined line research and arc-length, and is validated by representative examples; structure stability is judged by tracing the whole process analysis. In order to grasp the bearing capability variation and instable area distribution, a great deal of parameter analysis of influence factors are made, which including rib number, rise to span ratio, section dimension and different loading, all of the conclusions can be consulted to new structure design.
The originality of the thesis lies in:
1. A new spatial structure named steel-concrete composite ribbed shell is presented, the bearing capability, elastic-plastic mechanics and stability of this structure are studied thoroughly, it has many advantages such as good mechanics of bearing capability and stability, it also can overcomes the trivial objection in RC shell construction.
2. From single steel rib stability research, bearing capability formula of single steel rib arch under in plane and out plane buckling are obtained separately, which is valuable to the limit bearing calculation of U section arch; from two different models analysis, it is found that: the bearing capability of steel rib with clapboard is 2 or 3 more than the none one, the appended clapboard can not only avoid concrete sliding along the steel rib axes, but also improve the carrying capability; from influence factor research, the main factor is the steel board thickness, then the section dimension of height and width, the influence of clapboard is the smallest.
3. The bearing calculation formula under 3 loading condition are obtained based on the nonlinear finite element research, a comparison between formula calculation and nonlinear finite element are made, the discrepancy of them is only 2%, which is proved that the formula can be used to U section member.
4. From the elastic-plastic analysis of composite ribbed shell, it is found that: two composite ribs through structure mid are the main members which transfer loading to other parts, the whole loading path is definitely and smoothly; for the existing of steel ribs, mechanics of the structure is improved in a certain extent, the variety range of axial pressure and moment in composite ribs is adjusted, the internal force distribution goes to uniformity. After local instable area appeared, the bearing capability can be improved yet, the whole structure behaves certain post-buckling strength, and it is distinct to lattice shell structures. So to composite ribbed shell, it is unreasonable to take the first limit point as critical load, post buckling strength should be considered and used.
1．对单根钢肋圆拱稳定性及承载力进行理论研究和数值分析，探讨了钢肋的稳定性，拟合了钢肋平面内屈曲和侧倾屈曲临界荷载计算公式。
首次对U型截面钢肋圆拱进行分析，利用APDL语言，分别建立不带隔板、带隔板两种模型，对30种不同截面尺寸，180余例单根钢肋在平面内屈曲及侧倾失稳时的极限承载力、失稳形态进行了研究，考察隔板设置对钢肋受力性能的影响，并探讨了不同截面尺寸、半跨荷载作用以及初始缺陷对钢肋稳定性的影响，为全面了解钢肋圆拱力学性能提供了资料。
2．对组合肋截面构件进行了几何非线性和材料非线性分析，推导了组合肋正截面受压、受拉和受弯时承载力计算公式。
对组合截面承载力研究方法进行讨论，着重论述了非线性有限单元法与软件分析相结合的实用分析方法，并以标准混凝土抗压试块、钢筋混凝土梁及钢管混凝土短柱为例，进行验证。对组合肋截面构件在正截面受压、受拉、受弯三种不同受力情况进行有限元模拟，同时考虑几何、材料非线性影响，在有限元分析基础上，依据极限平衡理论，推导了组合肋截面构件承载力计算公式。对不同混凝土强度下不同截面尺寸组合肋承载力进行参数分析，证明所推导的承载力计算公式的可靠性。
3．通过组合肋壳弹塑性分析，对组合肋壳承载能力、变形特点进行了全面探讨。
采用更新拉格朗日格式，基于增量虚功原理建立了组合肋壳非线性增量平衡方程，利用空间梁单元和层合曲边壳单元，考虑组合肋与混凝土薄壳间的偏心影响，建立了组合肋壳刚度矩阵；研究了在自重和均布压力荷载作用下，组合肋壳内力分布特点、荷载传递方式、结构内部力流分布，以及材料进入塑性后，结构变形特点、内力分布特点等；最后与普通的钢筋混凝土带肋壳受力性能进行比较。
4．在组合肋壳稳定性分析中，探讨了结构的失稳形态和后屈曲特性，结论可供设计参考。
提出线搜索和弧长法相结合的稳定性分析方法，通过典型例题进行验证；由组合肋壳受力全过程跟踪，判断结构稳定性，并对不同影响因素进行大规模参数分析，研究了不同肋格数、不同矢跨比、不同截面尺寸、不同边界条件及不同荷载作用下，组合肋壳极限承载力变化和失稳区域分布情况等，可供该新型结构设计参考。
本文创新之处：
1．提出了一种新型结构形式——钢—混凝土组合肋壳，对其承载能力、弹塑性和稳定性进行了全面研究，发现这种结构能克服混凝土薄壳施工繁琐缺陷，同时具有承载能力高，稳定性能优越等特点。
2．通过对钢肋稳定性研究，分别拟合了单根钢肋平面内失稳、侧倾失稳时临界荷载计算公式，并对此进行检验，为U型截面圆拱临界荷载数值计算提供参考；对两种不同模型的钢肋极限承载力和失稳形态比较发现，带有隔板的钢肋承载力是不带隔板的2-3倍，在添加隔板后，不仅可以有效防止浇注过程中混凝土沿钢肋轴线下滑，同时可大大提高钢肋的承载能力；对承载力影响因素进行分析发现，钢肋板厚度是重要影响因素，其次是钢肋截面高度，宽度和隔板间距。
3．在有限元模拟结果的基础上，根据极限平衡理论，推导出组合肋截面轴心受压、轴心受拉及正截面受弯承载力计算公式，并对组合肋三种受力状态下承载力进行计算，计算结果与非线性有限元分析结果吻合较好，两者相差仅2％左右，所提出的U型截面计算公式可为设计提供参考。
4．组合肋壳弹塑性分析发现，经过组合肋壳中心的两条正交组合肋是重要传力构件，结构传力路线明确、流畅；钢肋不仅可以作为浇注混凝土肋模板使用，一定程度上也改善了结构的受力性能，调节组合肋轴向压力和弯矩变化幅度，可使结构内力分布趋于均匀，结构受力性能比钢筋混凝土带肋壳优越。稳定性分析发现在组合肋壳局部失稳后，承载能力仍有所提高，与网壳结构受力性能不同，结构表现出一定的屈曲后强度，因此对于组合肋壳而言，取第一个临界点作为临界荷载是不合理的，应该考虑并充分利用结构的后屈曲强度。
Steel-concrete composite ribbed shell is described in this paper, which is a new kind of space structure for enclosing large spaces. This kind of shell is made of composite rib and concrete shell: steel rib is formed by three thin steel plates welded in U shape, then concrete is poured to build composite ribs; those composite ribs are used as the formworks to make RC shell, finally the whole composite ribbed shell is completed. During the whole construction process, the founded members are used as the formworks and brackets to the latter. The new structure retains all the benefits of thin concrete shells, while eliminates the need for temporary formwork and minimises the required falsework, declines construction cost, so it is a kind of spatial structural system with good developing prospect.
To grasp the structure mechanics and remedy blank of research, the factors to mechanics and bearing capability of single steel rib, composite rib and the whole structure are discussed according to construction order. The main content is described as follows:
1. Theory and numerical study on stability and bearing capability of single steel rib, critical bearing capability formula are made.
Steel rib arch with U section is presented, the models with and without clapboard are made separately by using APDL language, 30 groups of different sections and more than 180 steel arch examples are researched, the ultimate bearing capability and instable form are investigated, the influence factors including clapboard, different section dimension, half span loading and initial imperfection are discussed in detail, all the above provides abundant information to master the mechanics of steel arch.
2. Bearing capability of composite rib members is analyzed considering geometry and material nonlinear, bearing capability formula of composite rib is concluded.
Bearing capability analysis methods of composite section are discussed, especially the applied method which is combined by nonlinear finite element method and software analysis, standard concrete compress member, RC beam and steel tube concrete puncheon are validated. The mechanics capability of composite rib section members are simulated by finite element method, which including press, pull and bend. Based on the analysis, the calculation formula of bearing capability is put forward which considering the effects of geometry and material nonlinear and using limit continuum equation. Under different concrete intension, parameter analysis of various section dimension is made, which provides data support for calculation formula of bearing capability.
3. Elastic-plastic analysis of composite ribbed shell is made completely, which includes ultimate bearing capability and characteristic of deformation.
Based on the virtual work, the composite ribbed shell nonlinear incremental continuum equation is made by using space beam element and layer curved shell element, stiffness matrix is founded considering the eccentricity influence; then internal force distributing, loading transfer fashion and characteristic deformation are researched under the load of deadweight and equal pressure; finally a comparison with RC ribbed shell is made.
4. During the stability analysis of composite ribbed shell, stable deformation and post-buckling characteristic are discussed in detail. The conclusions can be resulted in structure design.
A new stability analysis method is put forward, which is combined line research and arc-length, and is validated by representative examples; structure stability is judged by tracing the whole process analysis. In order to grasp the bearing capability variation and instable area distribution, a great deal of parameter analysis of influence factors are made, which including rib number, rise to span ratio, section dimension and different loading, all of the conclusions can be consulted to new structure design.
The originality of the thesis lies in:
1. A new spatial structure named steel-concrete composite ribbed shell is presented, the bearing capability, elastic-plastic mechanics and stability of this structure are studied thoroughly, it has many advantages such as good mechanics of bearing capability and stability, it also can overcomes the trivial objection in RC shell construction.
2. From single steel rib stability research, bearing capability formula of single steel rib arch under in plane and out plane buckling are obtained separately, which is valuable to the limit bearing calculation of U section arch; from two different models analysis, it is found that: the bearing capability of steel rib with clapboard is 2 or 3 more than the none one, the appended clapboard can not only avoid concrete sliding along the steel rib axes, but also improve the carrying capability; from influence factor research, the main factor is the steel board thickness, then the section dimension of height and width, the influence of clapboard is the smallest.
3. The bearing calculation formula under 3 loading condition are obtained based on the nonlinear finite element research, a comparison between formula calculation and nonlinear finite element are made, the discrepancy of them is only 2%, which is proved that the formula can be used to U section member.
4. From the elastic-plastic analysis of composite ribbed shell, it is found that: two composite ribs through structure mid are the main members which transfer loading to other parts, the whole loading path is definitely and smoothly; for the existing of steel ribs, mechanics of the structure is improved in a certain extent, the variety range of axial pressure and moment in composite ribs is adjusted, the internal force distribution goes to uniformity. After local instable area appeared, the bearing capability can be improved yet, the whole structure behaves certain post-buckling strength, and it is distinct to lattice shell structures. So to composite ribbed shell, it is unreasonable to take the first limit point as critical load, post buckling strength should be considered and used.
引文
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