曲线波形钢腹板箱梁竖向弯曲自振特性

Vertical Bending Natural Vibration Characteristics of Curved Box Girder with Corrugated Steel Webs

为精确计算曲线波形钢腹板简支箱梁的竖向弯曲自振特性,考虑箱梁剪力滞和剪切变形双重效应,在假设箱梁翼板纵向位移函数的基础上,运用能量变分法和哈密顿原理推导了曲线波形钢腹板简支箱梁的弯曲自由振动微分方程,得到其竖向弯曲自振频率的解析解;建立有限元模型,将分析结果与推导的理论公式计算结果加以对比,并分析了跨径比、宽跨比和高跨比对竖向弯曲基频的影响。研究结果表明:本文竖向弯曲自振频率公式的计算结果与有限元分析结果差值在9%以内,且比初等梁理论计算精度高;剪力滞效应和剪切变形均削减了曲线波形钢腹板简支箱梁的刚度,使其竖向弯曲自振频率与初等梁理论的计算结果相比有所降低,同时考虑2种效应可能使竖向弯曲基频降低25%以上。剪力滞效应对竖向弯曲基频的影响随着跨径比和宽跨比的增大而增大,而高跨比变化时影响略有减小;剪切变形对竖向弯曲基频的影响随着宽跨比和高跨比的增大而增大,而跨径比变化时影响保持不变。对于不同参数取值的曲线波形钢腹板简支箱梁,竖向弯曲基频的剪切变形影响系数变化范围为5%~25%,而剪力滞效应的影响系数一般小于10%。在分析曲线波形钢腹板箱梁动力性能时应考虑剪切变形;当跨径比小于0.4,宽跨比小于0.1时,可忽略剪力滞效应的影响。

To study the vertical bending natural vibration characteristics of simply supported curved box girders withcorrugated steel webs,the double effects of shear lag and shear deformation of box girder were considered. Based on theassumption of longitudinal displacement function of box girder flange,the differential equation of the bending vibrationfor simply supported curved box girder with corrugated steel webs was deduced by the energy variational method and theHamilton principle. The analytical solution of the vertical bending vibration frequency was obtained. The finite elementmodels were established,and the results were compared with that obtained from the deduced theoretical formula. Then,the influences of span-radius ratio,width-span ratio and height-span ratio of simply supported curved box girder withcorrugated steel webs on the vertical bending fundamental frequency were analyzed. The results show that the errorsbetween the calculation results of vertical bending natural vibration frequency formula and the finite element analysisresults are less than 9%,the calculation accuracy is higher than that of the elementary beam theory. Both the shear lageffect and the shear deformation may reduce the stiffness of the box girder with corrugated steel webs,and the verticalbending vibration frequency of the structure are lower than that calculated by elementary beam theory. Considering botheffects simultaneously,the vertical bending fundamental frequency reduce by more than 25%. The effect of shear lag onthe vertical bending fundamental frequency of simply supported curved box girder with corrugated steel webs increasesas the increase of span-radius ratio and width-span ratio,and decreases slightly as the increase of height-span ratio. Theeffect of shear deformation on the vertical bending fundamental frequency increases as the increase of width-span ratioand height-span ratio,and remains unchanged as the increase of span-radius ratio. The influence coefficient of sheardeformation on the vertical bending fundamental frequency of the simply supported curved composite box girder withcorrugated steel webs is 5%~25%,while the influence coefficient of shear lag effect is generally less than 10%. Theeffect of the shear deformation should be taken into account when analyzing the dynamic performance of simplysupported curved box girder with corrugated steel webs. When the span-radius ratios is less than 0.4 and the width-spanratios is less than 0.1,the shear lag effect can be neglected.