曲杆预应力平面内效应偏差分析及修正方法

Deviation analysis and correction method for prestressing in-plane effects of curved beam

预应力混凝土(PC)曲线梁桥在工程中常采用曲杆有限元模型进行分析和设计,曲杆模型由于无法考虑曲率半径沿径向的变化,因此在计算预应力平面内效应时会产生偏差,进而导致PC曲线梁桥上、下部结构受力状态与实际不符。文章基于虚功原理,给出了曲杆模型计算预应力平面内效应产生偏差的原因;通过在功能方程中引入曲率变化函数,推导并提出了可准确计算曲梁预应力平面内效应的修正方法;采用2个PC曲梁示例对该修正方法的准确性和适用性进行了验证,结果表明:采用修正后曲杆模型计算的预应力平面内效应与根据虚功原理推导的解析解、实体有限元模型的结果均一致。文章提出的修正方法可适用于对称或非对称截面形式、任意结构和边界形式的PC曲线梁桥,具有较好的工程应用性。

Prestressed concrete(PC)curved girder bridges are often analysed and designed with the curved beam element model in practice.The curved beam element model cannot consider the variation in the radius of curvature along the radial direction.Hence,the prestressing in-plane effect calculated from the curved beam model may yield inaccurate results,which consequently leads to the discrepancy between the calculated and actual structural behaviours for both superstructure and substructure of PC curved girder bridges.Based on the principle of virtual work,the reasons for the discrepancy of the prestressing in-plane effect in the curved beam model are given.A correction calcualtion method for the accurate prestressing in-plane effect in curved girders is deduced by introduing the function of curvature variation into the work-energy equations.The accuracy and feasibility of the proposed correction method are verified using two PC curved girder bridge examples.The analysis results show that the corrected curved beam models can yield results consistent with the analytic solution based on the principle of virtual work and also the results from solid element models.In addition,the proposed method is applicable to curved girder bridge with symmetry or asymmetry cross-sectional forms and arbitrary structural and boundary conditions.