剪切变形和剪力滞对混凝土简支箱梁挠度的影响
发布时间：2018-08-19 14:02
【摘要】：为分析剪切变形和剪力滞效应对混凝土简支箱梁挠度的影响情况，参照我国高速铁路32m箱梁尺寸，选取等截面简支梁为研究对象，采取解析与有限元数值相结合的方法进行计算。以经典Euler-Bernoulli梁理论、Timoshenko梁理论以及基于能量变分原理的剪力滞理论为基础，从理论上对剪切变形及剪力滞效应对箱梁挠度的影响机理进行了深入探讨。按照弯曲变形、考虑剪切变形、同时考虑剪切变形和剪力滞效应三种情况，计算了自重、均布荷载及集中荷载作用下箱梁的挠度解析值。采用ANSYS中的beam4、beam189、solsh190单元建立模型，得到了荷载作用下箱梁挠度的数值解。以有限元数值解为基础，对比分析了剪切变形和剪力滞效应对箱梁挠度影响的大小。通过保持截面几何参数不变，，改变箱梁跨径大小，分析了随着高跨比的变化剪切变形对挠度的影响规律，得到了箱梁考虑剪切变形影响的高跨比门槛值。依据Timoshenko梁理论对剪切修正系数的定义，通过有限元数值解进行逆推，得到了同一截面类型箱梁的剪切修正系数。结论如下： （1）针对本文算例，自重作用下箱梁弯曲变形挠度解析解与数值解相同，为8.1666mm。考虑剪切变形影响后挠度解析解为9.0187mm，数值解为9.0936mm，误差为0.82%，原因是解析解中计算剪切修正系数时腹板面积近似取值引起的。同时考虑剪切变形及剪力滞效应影响后挠度数值解为9.8492mm。 （2）相对于弯曲变形挠度，自重作用下考虑剪切变形及剪力滞效应影响后挠度增大20.60%，其中考虑剪切变形影响的挠度增大率为11.35%，考虑剪力滞效应影响的挠度增大率为9.25%，剪力滞效应对挠度的影响略小于剪切变形的影响。 （3）按照本文计算结果，当高跨比小于1/16时，剪切变形附加挠度占弯曲变形挠度的百分比才开始小于5%，即在工程上可忽略不计。当高跨比等于1/5时，考虑剪切变形产生的附加挠度占弯曲变形挠度的50%以上。因此，实心截面是否考虑剪切变形影响的高跨比门槛值1/5对于箱梁而言是不合适的，本文采用箱梁截面其高跨比门槛值为1/16。 （4）对于本文所研究箱梁截面，其剪切修正系数可参考取值0.2326。即腹板计算高度可取顶板与腹板交汇中心到底板上表面的距离，其结果是偏于安全的。 （5）对箱梁进行力学分析时假定其约束是施加在中性轴上的，但实际工程中通过支座对梁体进行约束，当约束施加在支座位置时，其腹板中性轴处跨中挠度增大值为0.4288mm，相当于弯曲变形挠度的5.25%。所以实际挠度应该在考虑剪切变形、剪力滞效应影响的基础上再加上因实际约束位置的不同而产生的附加挠度。
[Abstract]:In order to analyze the influence of shear deformation and shear lag effect on the deflection of simply supported concrete box girder, referring to the size of 32 m box girder of high-speed railway in China, a simple supported beam with equal section is selected as the research object. The analytical method combined with finite element method is used to calculate. Based on the classical Euler-Bernoulli beam theory and the shear lag theory based on the energy variational principle, the influence mechanism of shear deformation and shear lag effect on box girder deflection is discussed theoretically. According to the bending deformation, the shear deformation and the shear lag effect, the deflection of the box girder under the action of gravity, uniform load and concentrated load is calculated. The model is established by using the element Beam4 Beam189 and solsh190 in ANSYS, and the numerical solution of box girder deflection under load is obtained. Based on the finite element numerical solution, the effects of shear deformation and shear lag on the deflection of box girder are compared and analyzed. By keeping the geometric parameters of the section unchanged and changing the span size of the box girder, the influence of shear deformation on the deflection with the change of the ratio of height to span is analyzed, and the threshold value of the high span ratio of the box girder considering the effect of shear deformation is obtained. According to the definition of shear correction coefficient based on Timoshenko beam theory, the shear correction coefficient of box girder of the same section type is obtained by the inverse deduction of finite element numerical solution. The conclusions are as follows: (1) for the example of this paper, the analytical solution of bending deflection of box girder subjected to self-gravity is the same as the numerical solution, which is 8.1666 mm. After considering the effect of shear deformation, the analytical solution of deflection is 9.0187mm, the numerical solution is 9.0936mm, and the error is 0.82mm, which is caused by the approximate value of web area when calculating the shear correction coefficient in the analytical solution. Considering the effects of shear deformation and shear lag effect, the numerical solution of deflection is 9.8492mm. (2) relative to bending deflection, The deflection increases 20.60% after considering the effect of shear deformation and shear lag under gravity, in which the increase rate of deflection considering the effect of shear deformation is 11.35, the increase rate of deflection considering the effect of shear lag is 9.25, and the effect of shear lag is shadow of deflection. The response is slightly smaller than the effect of shear deformation. (3) according to the results of this paper, When the ratio of height to span is less than 1 / 16, the percentage of additional deflection of shear deformation to bending deflection begins to be less than 5, that is, it is negligible in engineering. When the ratio of height to span is equal to 1 / 5, the additional deflection due to shear deformation accounts for more than 50% of the deflection of bending deformation. Therefore, it is not appropriate for box girder that the threshold value of high span ratio of solid section considering shear deformation is 1 / 5. In this paper, the threshold value of high span ratio of box girder section is 1 / 16. (4) for the box girder section studied in this paper, the ratio of height to span is 1 / 16. (4) for the box girder section studied in this paper, The shear correction coefficient can be referred to as 0.2326. That is, the web can calculate the distance between the top plate and the center of the web, and the result is safety. (5) the constraint of the box girder is assumed to be imposed on the neutral axis when the box girder is subjected to mechanical analysis. But in the actual engineering, the beam body is restrained by the support. When the constraint is applied to the support position, the increasing value of the midspan deflection at the neutral axis of the web plate is 0.4288mm, which is equivalent to 5.2525mm of the bending deformation deflection. Therefore, the actual deflection should be taken into account the shear deformation, shear lag effect and the additional deflection caused by the difference of the actual constraint position.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U441;U448.213
[Abstract]:In order to analyze the influence of shear deformation and shear lag effect on the deflection of simply supported concrete box girder, referring to the size of 32 m box girder of high-speed railway in China, a simple supported beam with equal section is selected as the research object. The analytical method combined with finite element method is used to calculate. Based on the classical Euler-Bernoulli beam theory and the shear lag theory based on the energy variational principle, the influence mechanism of shear deformation and shear lag effect on box girder deflection is discussed theoretically. According to the bending deformation, the shear deformation and the shear lag effect, the deflection of the box girder under the action of gravity, uniform load and concentrated load is calculated. The model is established by using the element Beam4 Beam189 and solsh190 in ANSYS, and the numerical solution of box girder deflection under load is obtained. Based on the finite element numerical solution, the effects of shear deformation and shear lag on the deflection of box girder are compared and analyzed. By keeping the geometric parameters of the section unchanged and changing the span size of the box girder, the influence of shear deformation on the deflection with the change of the ratio of height to span is analyzed, and the threshold value of the high span ratio of the box girder considering the effect of shear deformation is obtained. According to the definition of shear correction coefficient based on Timoshenko beam theory, the shear correction coefficient of box girder of the same section type is obtained by the inverse deduction of finite element numerical solution. The conclusions are as follows: (1) for the example of this paper, the analytical solution of bending deflection of box girder subjected to self-gravity is the same as the numerical solution, which is 8.1666 mm. After considering the effect of shear deformation, the analytical solution of deflection is 9.0187mm, the numerical solution is 9.0936mm, and the error is 0.82mm, which is caused by the approximate value of web area when calculating the shear correction coefficient in the analytical solution. Considering the effects of shear deformation and shear lag effect, the numerical solution of deflection is 9.8492mm. (2) relative to bending deflection, The deflection increases 20.60% after considering the effect of shear deformation and shear lag under gravity, in which the increase rate of deflection considering the effect of shear deformation is 11.35, the increase rate of deflection considering the effect of shear lag is 9.25, and the effect of shear lag is shadow of deflection. The response is slightly smaller than the effect of shear deformation. (3) according to the results of this paper, When the ratio of height to span is less than 1 / 16, the percentage of additional deflection of shear deformation to bending deflection begins to be less than 5, that is, it is negligible in engineering. When the ratio of height to span is equal to 1 / 5, the additional deflection due to shear deformation accounts for more than 50% of the deflection of bending deformation. Therefore, it is not appropriate for box girder that the threshold value of high span ratio of solid section considering shear deformation is 1 / 5. In this paper, the threshold value of high span ratio of box girder section is 1 / 16. (4) for the box girder section studied in this paper, the ratio of height to span is 1 / 16. (4) for the box girder section studied in this paper, The shear correction coefficient can be referred to as 0.2326. That is, the web can calculate the distance between the top plate and the center of the web, and the result is safety. (5) the constraint of the box girder is assumed to be imposed on the neutral axis when the box girder is subjected to mechanical analysis. But in the actual engineering, the beam body is restrained by the support. When the constraint is applied to the support position, the increasing value of the midspan deflection at the neutral axis of the web plate is 0.4288mm, which is equivalent to 5.2525mm of the bending deformation deflection. Therefore, the actual deflection should be taken into account the shear deformation, shear lag effect and the additional deflection caused by the difference of the actual constraint position.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U441;U448.213
【参考文献】
相关期刊论文 前10条
1 郑健;;中国高速铁路桥梁建设关键技术[J];中国工程科学;2008年07期
2 刘世忠,吴亚平,夏e
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