关键词: 道路工程, 主应力, 方向余弦, 计算公式法, 雅可比方法, 特征值, 特征向量

Abstract: Up to now, there are two methods for calculating principal stresses and their direction cosines at home and abroad: calculating formulation method and Jacobi method. Firstly, the calculation of characteristic value and characteristic vector in linear algebra and the calculation of principal stresses and their direction cosines in elasticity were introduced. By comparing the two calculation processes, the mathematical origin of the two methods was discussed. It is found that in the process that calculating formulation method or Jacobi method is used to calculate the direction cosines of principal stresses at present, in fact, only one set of solutions of two sets of direction cosine solutions of principal stresses are calculated. Only when the other set of solutions is complemented, the complete calculation results can be obtained. Secondly, some dozens of numerical examples under various mechanical conditions were calculated by using the calculating formulation method in NESCP (N-layer Elastic System Computer Program) computer program compiled by author and Jacobi method in BISAR（BItumen Structures Analysis in Roads）computer program well-known in the world, and four examples were listed. The calculation results show that the calculation results of the above two methods are very close under various mechanical conditions. Whether the calculating formulation method or Jacobi method is used, the calculation results of the principal stresses and their direction cosines can be obtained accurately enough.

Key words: highway engineering, principal stress, direction cosine, calculating formulation method, Jacobi method, characteristic value, characteristic vector