基于三角级数解的波形钢腹板组合梁弯曲行为分析

发布时间：2019-01-05 08:53

【摘要】：波形钢腹板组合梁是一种新型组合结构,具有结构自重轻、预应力效率高、施工性能良好等优点而得到广泛应用,其区别于传统预应力混凝土箱梁的特点在于钢腹板显著的剪切变形。因此在分析波形钢腹板组合梁的弯曲变形时,必须考虑钢腹板的剪切性能。本文主要工作如下:1.分析了波形钢腹板组合梁的变形特点,结合其刚度特征,将现有波形钢腹板组合梁挠度的计算方法总结为4种方法:初等梁理论、Timoshenko梁理论、弹性剪切变形弯曲理论及有效刚度法,对比分析得出这4种方法的理论差异在于:(1)截面变形假定不同;(2)钢腹板剪力承担比例不同;(3)关键影响参数不同。最后通过建立空间有限元模型总结出波形钢腹板组合梁各挠度计算方法的不同跨高比适用范围。2.引入三角级数法,以三角级数形式表示三个基本的位移函数:钢腹板剪切变形转角函数、顶底板转角函数、组合梁挠度,基于最小势能原理,分别推导了简支和悬臂波形钢腹板组合梁弯曲变形计算模型。通过建立空间有限元模型,并与初等梁理论、Timoshenko梁理论进行对比,验证了三角级数法的合理性和适用性;最后总结得出三角级数法用于集中力和均布力作用下的简支梁挠度、悬臂梁挠度的跨高比适用范围。3.采用三角级数法对集中力和均布力作用下波形钢腹板组合梁的内力、应力进行了分析,并与空间有限元计算结果进行对比,结果表明:(1)波形钢腹板组合梁的抗弯主要由混凝土顶底板承担,比例高达99%;(2)抗剪主要由钢腹板承担,比例高达85%以上;(3)组合梁截面变形满足"拟平截面假定";(4)混凝土顶底板的剪应力很小,波形钢腹板的剪应力沿梁高呈等值均匀分布。所得到的研究成果可为波形钢腹板组合梁的设计和计算提供理论依据。
[Abstract]:Corrugated steel web composite beam is a new type of composite structure, which has the advantages of light weight, high prestress efficiency and good construction performance. It is distinguished from the traditional prestressed concrete box girder by the obvious shear deformation of the steel web. Therefore, the shear behavior of the steel web must be considered when analyzing the bending deformation of the corrugated steel web composite beam. The main work of this paper is as follows: 1. In this paper, the deformation characteristics of corrugated steel web composite beams are analyzed. Combined with the stiffness characteristics, the existing methods for calculating the deflection of corrugated steel web composite beams are summarized into four methods: elementary beam theory, Timoshenko beam theory, and so on. The theory of elastic shear deformation bending and the effective stiffness method are compared and analyzed. The theoretical differences of the four methods are as follows: (1) the assumption of cross-section deformation is different; (2) the shear bearing ratio of steel web plate is different; (3) the key influence parameters are different. Finally, through the establishment of the spatial finite element model, the application range of the different span height ratio of each deflection calculation method of the corrugated steel web composite beam is summarized. 2. 2. The triangular series method is introduced to represent three basic displacement functions in the form of trigonometric series: steel web shear deformation angle function, top and bottom plate rotation function, composite beam deflection, based on the principle of minimum potential energy. The bending deformation calculation models of simply supported and cantilever corrugated steel web composite beams are derived respectively. By establishing the spatial finite element model and comparing with the elementary beam theory and the Timoshenko beam theory, the rationality and applicability of the triangular series method are verified. Finally, it is concluded that the triangle series method is applied to the deflection of simply supported beam under the action of concentrated force and uniform force, and the applicable range of span to height ratio of deflection of cantilever beam is 3. 3. The internal force and stress of corrugated steel web composite beam under the action of concentrated force and uniform force are analyzed by means of triangle series method, and the results are compared with the results of spatial finite element method. The results show that: (1) the bending resistance of corrugated steel web composite beams is mainly carried by the concrete roof and bottom slab, and the ratio is as high as 99%; (2) the shear resistance is mainly carried by the steel web, the proportion is as high as 85%, (3) the section deformation of the composite beam meets the "pseudo-plane section assumption"; (4) the shear stress of concrete roof and bottom slab is very small, and the shear stress of corrugated steel web plate distributes uniformly along the beam height. The results can provide theoretical basis for the design and calculation of corrugated steel web composite beams.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：U441

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