具有体外预应力索的快速施工群钉式钢-混组合小箱梁自振特性分析

为了明确体外预应力索对快速施工钢-混组合小箱梁自振频率的影响,基于铁木辛柯梁理论和组合梁相对滑移对典型梁段及群钉的变形与受力进行了分析,同时,引入平面内梁体预应力变化量与振动位移之间的关系,运用达朗贝尔原理导出其平衡方程组,针对3种典型的体外预应力束布置型式给出快速施工钢-混组合小箱梁动力特性分析的解析公式,并将所提出方法的理论值与有限元数值分析进行了比较。在此基础上,详细分析了预应力筋布置位置(偏心距)、预应力筋初始应力大小、钢梁与混凝土板间抗剪连接刚度等参数对结构动力性能的影响。研究结果表明:所提出的方法及公式在分析体外预应力快速施工组合梁的动力特性方面具有较高的精度,其最大误差不超过2%;同时,在不考虑预应力对组合梁相对滑移影响的情况下,体外预应力筋初始应力的大小及抗剪连接刚度对结构本身的动力特性影响很小,最大不超过1%,可忽略不计;而预应力索布置的偏心距对结构自振频率影响相对较大,尤其是在低阶其频率约增加4%。因此,在实际工程中,使用体外预应力快速施工钢-混组合小箱梁或者采用体外预应力进行加固维修时,除应满足静力设计要求外,必须考虑偏心距对结构动力特性的影响。

Analytical Approach for the Free Vibration of Accelerated Construction Steel-concrete Composite Small Box Girders with External Prestressed Tendons and Group Studs

To study the effects of external prestressed tendons on the free vibration frequency of a rapid construction steel-concrete composite small box girder (SCCSBG) with external prestressed tendons, a typical micro beam segment and group studs were employed as research objects based on Timoshenko beam theory and the slip of the composite beam. By considering the relationship between the deformation and applied forces, and introducing the relation between the increment of external prestressed tendon forces and vibration displacement of box girders in plane, the corresponding equilibrium equations were established according to D'alembert's principle. Aiming to three typical types of external prestressing tendon arrangements in SCCSBG, analytical expressions for a natural frequency calculation of SCCSBGs with group studs and external prestressing tendons were deduced. A comparison of the theoretical values derived from the proposed method and analytical results obtained from the corresponding numerical finite element method was conducted. Based on the aforementioned research, the influences of the prestressed layout position (eccentricity), different initial prestress, shear joint stiffness between the steel beam and concrete slab of the SCCSBG on the dynamic performance of the structure were analyzed in detail. The results show that the effectiveness and correctness of the proposed method are verified and that the maximum error does not exceed 2%. Without the relative slip of composite beams caused by prestress being considered, the different initial prestress and shear joint stiffness of the SCCSBG has little impact on the vibration property of SCCSBG with group studs, and the maximum difference is no more than 1% and thus can practically be neglected. However, the eccentricity of the prestressed tendon has a relatively considerable influence on frequencies, especially for lower frequencies. For the 1st order vibration of SCCSBG, the frequency will increase by approximately 4%. Therefore, in practical engineering, the influence of eccentricity on the dynamic characteristics of the structure must be considered in addition to meeting the requirements of static design when using the rapid construction SCCSBG with external prestress tendons or external prestress tendons to strength the steel-concrete composite beams.