开口薄壁截面弯曲中心 [开口薄壁杆的板件面内拉弯综合抗力体系]

　　作者简介：金声(1975)，男，博士，主要从事薄壁钢结构计算理论研究，（Email）jsatcq@163.com。摘要：针对薄壁杆件力学分析较为复杂的问题，讨论了一种把开口薄壁杆的分析拆分为2个较简单部分的方法。针对薄壁中面内荷载效应的分析问题，首先在适当简化基本应力应变条件的基础上，按平面应力问题分析单肢板件面内荷载效应，然后对其进行向量综合，得到反映开口薄壁杆轴向伸缩、弯曲及翘曲性质的“板件面内拉弯综合抗力体系”及其变形方程；探讨了刚度方程的建立及其计算特点，并与经典理论进行对比。分析表明，在板件面内弯矩定义中引入板件间纵向相互作用力，可简化该体系分析过程和结论，使之具备与平面弯曲问题一致的形式。作为应用举例，推导了求解薄壁截面主轴方向、主轴惯性矩、弯心坐标、主扇性惯性矩的线性方程组，剖析了经典理论中这些截面几何特性对于计算的意义及其效率。
　　关键词：薄壁结构；单肢解析化方法；翘曲；扭转；扇性惯性矩；刚度矩阵
　　中图分类号：TU392.5; O342文献标志码：A文章编号：16744764（2012）03005807
　　Slabs Inplane Tensionbending Resistance System
　　of Thinwalled Openprofile
　　JIN Shenga,b , LI Kaixia , DAI Guoxina,b
　　(a. College of Civil Engineering; b. Key Laboratory of New Technology for Construction of Cities in Mountain Area,
　　Ministry of Education, Chongqing University, Chongqing 400045, P. R. China)
　　Abstract:In order to simplify the analyses of thinwalled openprofile bars, a thinwalled bar was split into two parts which were dominated by inplane and outplane loading effects respectively. The inplane loading effects were focused. On the basis of appropriate simplified stress and strain conditions, each plate was analyzed and the results were integrated into vectors, resulting in the slabs inplane tensionbending resistance system of thinwalled openprofile bars, which reflects their axial stretch/compression, bending and warping properties. And then the deformation equation and the stiffness equation were set up. Because longitudinal interaction forces between plates were introduced in the definition of the plates inplane bending moments, the deduction and conclusions here were consistent in form with those in bending theory. Principal axes directions, shear centers coordinates, principal inertia moments and sectorial inertia moment of thinwalled open sections can be deduced by the slabsdisassembled method proposed here. Lateral deformed bars analysis based on those sectional parameters in classical theory is proved to be inefficient, where additional “rigid contour hypothesis” has to be introduced.
　　Key words:thinwalled structures; slabsdisassembled method; warping; torsion; sectorial inertia moment; stiffness matrix
　　Vlasov［1］针对开口薄壁杆件所提出的经典理论通过引入扇性几何特性和广义力（双力矩），反映不均匀翘曲对扭转的显著影响，未考虑翘曲剪应变及截面的畸变。包世华等［2］，Benscoter［3］，Kollbrunner等［4］采用翘曲函数θ(z)代替扭率φ′(z)表征翘曲沿杆长的分布，以计及翘曲剪应变对扭转的的影响，对闭口截面杆件而言，该修正是必要的。文献［5］研究了薄壁几何特征参数对Уманский理论准确性的影响。文献［6］基于KollbrunnerHajdin理论，提出薄壁杆件扭转刚度矩阵，其扭角位移为双曲函数。文献［7］考虑沿壁厚均匀分布的正应变、剪应变（弯曲、翘曲及Bredt剪应变）以及沿壁厚线性分布的St. Venant剪应变，推导了弯扭联合作用下不对称截面薄壁梁四阶变形微分方程，并建立有限元模型。文献［8］通过构造位移函数列向量，对薄壁杆件的复杂变形微分方程进行降阶，并利用求系数矩阵特征值和特征向量的方法求解方程，得到位移的精确插值函数。文献［9］基于薄壁杆件理论，通过构建相容于Timoshenko梁理论（转角位移与侧向位移相互独立）、相容于KollbrunnerHajdin假定（扭转位移与翘曲位移相互独立）的插值多项式，建立薄壁杆件单元的刚度矩阵。文献［10］研究了开口薄壁型钢檩条在偏心横向荷载及复杂约束条件下考虑扭转的杆件内力简化计算方法。文献［11］将图论引入薄壁杆件结构计算，导出了计算扇性坐标、Bredt剪应力流、二次剪应力流及弯曲剪应力流的矩阵方程式。文献［12］据此编制计算程序，验证了其结论的正确性。上述研究均假设横截面周线不变形，近年来，考虑截面畸变的计算理论，如广义梁理论［13］、有限条法［14］等发展迅速。因薄壁杆件的变形及力因素均较多，不论考虑畸变与否，分析理论的建立过程均较复杂、抽象，例如通常需引入新的广义力，需采用能量法建立变形方程等。分析理论的抽象性不利于对薄壁杆件力学特点的深入把握，限制了其应用水平［15］。对于薄平板，可以将其所受到的一般荷载分解为作用在中面之内的荷载和垂直于中面的荷载，分别按平面应力问题和薄板弯曲问题进行计算［16］。〖=D(〗金声，等：开口薄壁杆的板件面内拉弯综合抗力体系〖=〗