下承式拱桥合理拱轴线的解析解与计算方法

为了得到下承式拱桥合理拱轴线的解析解与计算方法，建立了恒载作用模式和合理拱轴线微分方程，得到合理拱轴线的解析解；在解析解的基础上，定义了主拱恒载占比系数，得到了基于矢跨比和主拱恒载占比系数的合理拱轴线快速求解计算方法；采用拱桥设计规范、工程案例与相关研究成果，验证了本文方法的可靠性。研究结果表明:下承式拱桥的恒载作用模式可等效为连续均布恒载+主拱恒载的形式，合理拱轴线为悬链线，相应的拱轴系数由矢跨比和主拱恒载占比系数共同决定；拟合出的不同矢跨比下的拱轴系数与主拱恒载占比系数的函数关系式为线性相关关系，决定系数大于0.99，说明拟合公式准确；工程中下承式拱桥矢跨比范围为1/3~1/8，相应的拱轴系数范围为1.000~1.792，常见的矢跨比范围为1/4~1/5，相应的拱轴系数范围为1.000~1.465，与工程案例中拱轴系数统计结果的吻合度较高，说明计算结果可靠；工程中常见主拱恒载占比系数范围为0.1~0.5，对应的拱轴系数范围为1.102~1.364，与拱桥设计规范中的取值范围接近，证明了规范取值的合理性；当主拱恒载占比系数小于0.5且矢跨比小于1/7，或主拱恒载占比系数小于0.1时，拱轴系数接近于1.000，即合理拱轴线可采用二次抛物线；利用查表法或简化公式法，可以快速求得合理拱轴线方程；与已有研究成果相比较，主拱截面弯矩、偏心距和偏心距平方和的偏差均在5%以内，证明了本文计算方法的正确性。 

Analytical solution and calculation method of reasonable arch axis of through arch bridge

To obtain the analytical solution and calculation method of the reasonable arch axis of through arch bridge, the dead load action mode and differential equation of the reasonable arch axis were established, and the analytical solution of the reasonable arch axis was determined. Based on the analytical solution, the dead load ratio of main arch was defined. Based on the rise-span ratio and dead load ratio of main arch, a quick calculation method of the reasonable arch axis was obtained. The reliability of the proposed method was confirmed by arch bridge design specifications, engineering cases, and related research achievements. Research results show that the dead load action mode of through arch bridge can be equivalent to the combination of continuous uniform dead load and arch dead load, the reasonable arch axis is catenary, and the corresponding arch axis coefficient is determined by the rise-span ratio and dead load ratio of main arch. The fitted functional relationships between the arch axis coefficients and dead load ratios of main arch under different rise-span ratios are a linear correlation, and the determination coefficients are greater than 0.99, indicating that the fitted equations are accurate. The rise-span ratio of through arch bridge is between 1/3 and 1/8 in engineerings, and the range of the corresponding arch axis coefficient is between 1.000 and 1.792. The common rise-span ratio ranges from 1/4 to 1/5, and the corresponding arch axis coefficient ranges from 1.000 to 1.465. The calculation results are in good agreement with the statistical results of arch axis coefficients of engineering cases, indicating that the calculation results are reliable. The common dead load ratio of main arch ranges from 0.1 to 0.5, and the corresponding arch axis coefficient ranges from 1.102 to 1.364. The calculation results are close to the value ranges in the arch bridge design specification, which proves the rationality of value range in the arch bridge design specification. When the dead load ratio of main arch is less than 0.5 and the rise-span ratio is less than 1/7, or the dead load ratio of main arch is less than 0.1, the arch axis coefficient is close to 1.000. As a result, the quadratic parabola can be used as reasonable arch axis. The reasonable arch axis equation can be obtained quickly by the look-up table method and simplified formula method. Compared with the mature research achievements, the deviations of bending moments, eccentricities and sums of squared eccentricities of main arch cross-section are within 5%, which proves the correctness of the solution method.