波形钢腹板组合梁弯曲变形的三角级数解

Trigonometric Series Solution of Bending Deformation for Composite Beam with Steel Corrugated Webs

为研究波形钢腹板剪切变形对波形钢腹板组合梁弯曲变形行为的影响,采用三角级数拟合简支波形钢腹板组合梁的变形曲线,各构件弯曲变形满足平截面假定,基于最小势能原理,推导了简支和悬臂波形钢腹板组合梁分别在均布荷载和集中荷载作用下的弯曲变形解析解和简化解;基于简化解推导出考虑剪切变形的波形钢腹板组合梁挠度增大系数,并给出对考虑剪切变形影响与否的高跨比界限;采用有限元方法验证了解析解和简化解的正确性和适用性.研究结果表明:所提方法边界条件明确、推导过程简单、结果可靠、适用性强,可为波形钢腹板组合梁的设计和变形计算提供可靠的依据.

In order to study the influence of shear deformation on the bending deformation of composite beams with steel corrugated steel webs,trigonometric series solution was introduced to simulate the deformation of the components(web and flange)of the beam according to the plane-section assumption,and a theoretical model was presented on the basis of the principle of minimum potential energy.Then,analytical solutions and respective simplified forms were derived for simply supported and cantilever corrugated steel web girder cases under uniform distribution and mid-span concentrated load.Furthermore,a limit value of depth-span ratio was suggested to estimate the influence of shear deformation with regard to magnifying coefficient of deflection.Validity and usability of the analytical solution and the model were determined by the finite element method.The results show that the presented method has advantages of ease in boundary condition and deduce,high reliability and universal applicability,and can be referred for deflection design of steel corrugated steel web beam.