组拼式拱结构平面外弹塑性稳定性设计计算方法研究

With the increase of arch-span and the application of the high strength materials, the stability of arch structures becomes more and more important. But until now, the out-of-plane stability theory and design method of the widely used assembling arches are not well established and not available for practical use. In this project, theoretic derivation, numerical simulation and model test will be adopted to study the out-of-plane elasto-plastic stability design method of the assembling arches. The following studies will be carried out:.(1) The axial displacement model considering compression effect of arches and the buckling model of lateral displacement and torsion angle are proposed as triangle composite functions. Based on Ritz method, the analytical solution of the out-of-plane buckling critical load of the assembling arch is derived. .(2) Using large deflection elasto-plastic finite element method, a great number of numerical simulations will be carried out. Refer to the stability design and calculation method of columns, the theoretical calculation formula of the out-of-plane elasto-plastic stability coefficient of assembling arches are established by utilizing the normalized arch slenderness, which is introduced to unify different rise-to-span ratios and boundary conditions and so on..(3) A great number of experiments will be conducted on all kinds of arch models to study the effect of the design parameters, including section type, boundary condition, lateral brace etc., on the assembling arches’ critical load of the out-of-plane elasto-plastic stability. The theoretical calculation formula proposed in this project are verified and improved in comparison with the results obtained from model tests..(4) Based on the above researches, the design method and procedure of the out-of-plane elastic-plastic stability of assembling arches are aimed to be established. All kinds of buckling curves with different design parameters will be derived and provided to engineers for their convenient design of arch structures.

随着跨度的增大及高强度材料的应用，拱结构的稳定性问题日益突出，但对于组拼拱，目前其平面外弹塑性稳定设计方法尚不成熟。本项目拟采用理论推导、数值计算和试验研究相结合的方法，对组拼拱平面外弹塑性稳定设计计算方法展开系列创新研究：(1)提出考虑拱肋压缩变形的轴向位移模式和接近于拱肋面外失稳真实变形的复合三角函数失稳模式，基于Ritz法，推导组拼拱平面外弹性屈曲临界荷载解析计算公式，可破解以往侧倾临界荷载只适用于浅拱的局限性。(2)采用大挠度弹塑性有限元法进行大量数值计算，借鉴柱子的稳定设计方法，基于正则化长细比，提出组拼拱平面外弹塑性稳定系数的设计计算公式。(3)进行大量模型试验，研究截面类型、边界条件、横撑布置等设计参数对组拼拱平面外弹塑性失稳临界荷载的影响，验证并改进上述计算公式。(4)通过上述研究，建立组拼拱平面外弹塑性稳定设计方法和流程，绘制便于工程人员使用的各类稳定曲线图，指导工程设计。

本项目采用理论推导、数值计算和试验研究相结合的方法，对组拼拱平面外弹塑性稳定设计计算方法展开研究，完成了以下研究工作：.(1) 采用能量法，基于卡式定理和力法方程，在直角坐标系下建立拱顶集中力作用下固接抛物线拱模型，提出了考虑剪切变形的抛物线拱屈曲失稳前弯矩和轴力计算公式。采用Rayleigh-Ritz法，提出采用幂级数形式的面外位移函数和面外转角函数来构建拱顶集中力作用下固接抛物线拱平面外失稳能量方程，进而求解得到了固接抛物线拱在拱顶集中力作用下平面外失稳临界屈曲荷载解析解。.(2) 使用正则化长细比代替换算长细比，借助中国钢结构规范中轴压柱子稳定系数曲线，提出了圆弧组拼双拱平面外弹塑性稳定承载力计算方法和流程。并综合考虑横撑各影响因素的情况，参考德国钢结构规范中组拼拱的弹塑性稳定承载力设计公式，提出了考虑横撑影响因素的屈曲长度因子与桥门高度比系数的计算公式，以及圆弧组拼拱平面外稳定承载力计算方法。.(3) 制作了多组不同参数的组拼拱模型，并设计了特定的五点径向加载装置，对试验模型进行了平面外弹塑性稳定加载试验。根据试验结果，系统研究了长细比、矢跨比、横撑刚度比等各设计参数对组拼拱模型平面外稳定性能的影响规律，验证了本项目提出的组拼拱平面外稳定承载力设计计算方法的正确性。.通过本项目研究，取得了如下成果：(1)以第一作者和通讯作者在《Steel and Composite Structures》、《Thin-walled Structures》、《Journal of Constructional Steel Research》等国际著名期刊发表论文12篇，发表中文期刊论文1篇；（2）申请国家发明专利1项，授权实用新型专利1项；（3）获软件著作权1项；（4）获得教育部科技进步二等奖和广州市科技进步一等奖各1项；（5）培养博士研究生2名，硕士研究生7名。