基于板元分析法的梯形截面箱梁畸变效应研究

为揭示梯形截面箱梁的畸变效应,以箱梁腹板和底板交点处的夹角改变为未知量,用图乘法推导板元横向板端弯矩和箱梁畸变角之间的关系,采用板元分析法推导箱梁的四阶畸变控制微分方程。给出方程的初参数解,通过算例验证所推公式的正确性,并分析梁高、腹板倾角的变化对梯形截面箱梁畸变角和畸变双力矩的影响。结果表明:基于该法推导出的畸变控制微分方程可精确计算箱梁的畸变效应,且本文推导板元横向板端弯矩和箱梁畸变角关系的过程较为简单,算例验证了本文解和相关文献解、有限元解吻合良好;随着梁高逐渐增大,跨中截面畸变角逐渐减小,而畸变双力矩逐渐增大;腹板倾角逐渐增大时,跨中截面畸变角先增大后减小,畸变双力矩则逐渐减小。

Research on Distortion Effect of Box Girder with Trapezoidal Cross Section Based on Plate Element Analytic Method

In order to reveal the distortion effect of box girder with trapezoidal cross section,the variable angle of intersection point at the web and bottom slab of the box girder was used as an unknown quantity.The relationship between the transverse bending moment of the plate element and the distortion angle of the box girder was derived by the graph multiplication method.The fourth-order distortion governing differential equation of the box girder was derived by employing the plate element analytic method.According to the derived initial parameter solutions to the equation and the example verification of the correctness of the equation,the influence of variation of beam height and web inclination on the distortion angle and distortion bi-moment of the box girder with trapezoidal cross section was analyzed.The results show that the distortion governing differential equation based on the proposed method can calculate the distortion effect of box girder accurately.The process of the proposed method deducing the relationship between transverse bending moment of plates and box girder distortion angle is simple.The verification of examples shows that the results of the proposed method are in good agreement with those of the relevant literature and the finite element.With the increase of the beam height,the distortion angle of the middle span section decreases gradually,while the distortion bi-moment of the middle span section increases gradually.With the gradual increase of the web inclination,the distortion angle of middle span section increases first then decreases,while the distortion bi-moment in middle span section decreases gradually.