基于微分方程法的季冻区桥梁墩台内力计算分析

本文以Maple计算软件为平台,利用其求解微分方程组的强大功能,提出了一种对季冻区桥梁墩台进行内力计算的新方法。本方法通过对切向冻胀力作用下的桥梁墩台进行受力分析,划分结构计算单元,建立各墩台的微分方程组表达式,并根据混凝土的收缩、徐变以及温度影响力作用下,整桥各墩台之间及墩台各计算单元之间协同变形确定方程组的边界条件,求解出桥梁各墩台在切向冻胀力作用下的弯矩、剪力与位移的函数解析式。通过与桥梁博士分析软件的计算结果相对比,验证了本方法可以作为季冻区桥梁墩台内力计算分析方法的一种有效补充,并在实际工程中应用推广。

Calculation and Analysis on Internal Force of Bridge Abutment in Seasonal Frozen Region based on Differential Equation

The article proposes a new method of calculating the internal force of the bridge abutment in seasonal frozen region, using powerful function of solving differential equations of Maple software. This method analyzes the stress of bridge abutment under the action of tangential frost heaving force, and divides the computing unit of structure, then establishes the differential equations expression of each abutment and ensures the boundary determination conditions of differential equation set according to coordination deformation between abutments and units under the action of the concrete shrinkage, creep and temperature influence. Finally it solves the function analytic formula of bending moment, shear force and displacement of bridge abutment under the action of tangential frost heaving force. Comparing with the results calculated by Dr. bridge analysis software, it proves that the method can be used as an effective supplement for internal force calculation of bridge abutment in seasonal frozen region, and can be used and popularized in practical engineering.