单箱双室不等壁厚箱梁受弯与约束受扭的有限节线法分析
Analysis on single-box double-cells unequal-wall-thickness girder due to bending and restrained torsion by finite nodal-line method

为了分析单箱双室不等壁厚箱梁非对称受弯、约束受扭时其横截面的变形特征与应力分布规律，采用统一分析梁模型和有限节线法对其进行研究。统一分析梁模型不仅不对梁横截面的面外变形规律或应力分布规律作任何假定，而且对梁的长细比也不作任何限制；梁的位移场是用有限个单变量基本未知函数通过数值逼近来确定；梁的应力场通过与位移场相对应的应变场及梁材料的本构关系来确定；给出单箱双室不等壁厚箱梁受弯与约束受扭时的整体变形特征、横截面翘曲特点以及应力分布规律，并讨论扭转中心位置的确定方法，给出确定扭转中心位置的计算公式。研究结果表明：只要单箱双室不等壁厚箱梁承受非对称面内的横向荷载作用（横向力或扭矩），整个箱梁在非对称面内不存在单纯弯曲变形的问题，弯曲变形和横截面绕轴线转动的扭转变形总是耦合在一起，箱梁横截面不仅产生翘曲变形，而且其上的正应力、剪应力均为非线性分布；正应力、扭转剪应力的最大值、扭转中心的位置均随横截面翼缘板与各箱室尺寸，特别是箱室壁厚而变化。提出的方法适用于解决长细比小于3的短箱梁的力学分析问题，对于中长箱梁和长箱梁非约束扭转以外的力学分析问题，该方法可分别退化为Timoshenko梁和Bernoulli-Euler梁的相关问题，其还可以解决这2类传统箱梁理论不能解决的约束扭转问题。
In order to investigate the mechanics characteristics such as deformation and stress distributions of a real single-box double-cells unequal-wall-thickness girder subjected to bending in its asymmetric plane and restrained torsion around its axis, a unified analytical beam model and a finite nodal-line method were employed. The unified analytical beam model neither make any assumptions about the out-of-plane deformation or stress distribution of the beam, nor limit the aspect ratio of the beam. Displacement field of the whole beam was determined by the numerical approximation using finite single-variable basic unknown functions. Stress field of the beam was determined by the strain field corresponding to the displacement field and the constitutive relation of beam material. The exemplar study of a box girder revealed the global deformation features, the cross-section warping characteristics, and the stress distribution of girder. Torsional center of the cross section was determined as well, and the formula for obtaining the location of torsional center was developed. The results show that as long as a single-box double-cells unequal-wall-thickness girder is subjected to transverse loading (transverse force or torque) in its asymmetric plane, the whole box girder does not have the problem of pure bending deformation in the asymmetric plane. Bending deformation and torsional deformation of the cross section about the axis of rotation are always coupled together. Cross section of the box girder produces warping deformation, and the normal stress and shear stress induced by lateral loading are nonlinearly distributed on the cross section. Location of the torsional center and the maximum values of both normal stress and torsional shearing stress of the cross section change with the size of flange and cells, especially the wall thickness of cells. The method proposed is especially suitable for solving the mechanical analysis problems of short box girders with aspect ratio less than 3. For the mechanical analysis