基于曲梁理论的弧形钢闸门纵向主梁正应力计算

Calculation of normal stress in longitudinal girder of radial steel gate using curved beam theory

弧形钢闸门纵向主梁实为曲梁,其截面正应力仍沿用直梁理论进行计算。本文从曲梁挠曲线微分方程出发提出了一种基于曲梁理论的计算方法。通过对应力计算中结构特征系数公式的推导,提出了弧门箱形截面纵向主梁偏心距e的计算方法,分析了曲率对曲梁截面弯曲正应力分布的影响,并对曲梁理论和直梁理论计算结果进行详尽的误差分析。分别运用曲梁理论及直梁理论对工程实例进行计算,直梁理论相对有限元方法计算结果的误差达到14.23%,而曲梁理论相对有限元方法计算结果的误差仅为2.23%,可见基于曲梁理论的计算精度显著优于直梁理论,采用基于曲梁理论的计算方法更加安全可靠。本文方法可为相关工程设计提供参考和理论依据。

The longitudinal main girder of a radial steel gate is essentially a curved beam, but the straight beam theory is commonly used for calculation of normal stress at its cross section up to the present. This article presents a new calculation method using curved beam theory and corresponding flexural differential equations. By deriving a formula of characteristic coefficient for stress calculation, we have formulated a method for calculating the eccentricity of the girder of a radial steel gate with box section, analyzed the influence of curvature on the distribution of bending normal stress over the curved beam section, and compared the accuracies of the two theories. Application to case studies shows an error of 14.23% in the calculation results by straight beam theory relative to the FEM calculation, which is only 2.23% in the curved beam theory. Thus, the curved beam theory is much superior and its Calculation results should be more reliable.