共轭梁比拟方法及在变截面梁计算中的应用

Conjugate beam method and application for calculating variable cross-section beams

为了探寻变截面梁静动力特性和静动力反应的解法,从梁的弯矩与所受分布力关系的方程和梁的挠度与弯矩/抗弯刚度关系的方程具有相似性出发,将待求解梁的弯矩/抗弯刚度当作与该梁共轭的虚梁的虚荷载,进而根据静力等效的原则,将连续分布的虚荷载转换成虚集中力后计算虚集中力作用下虚梁的虚剪力、虚弯矩。依据实梁与虚梁的对应关系,虚剪力与虚弯矩就是实梁的截面转角和挠度,得到了原来实梁问题的解答。结果表明,该方法概念明确、计算工作量较小,可以推广应用于变截面连续梁与刚架等结构的静动力反应分析。

In order to seek a new way to solve problems in static/dynamic characteristics and in static/dynamic responses of a variable cross-section beam, due to the similarity of moment-distributive force relation to displace-ment-ratio of moment to flexural rigidity （ RMF） relation, the RMF of a real beam was treated as virtual distrib-utive force of corresponding virtual beam.According to statically equivalent principle, the virtual distributive force was hence converted to virtual concentrated force, thus virtual shear forces, virtual bending moments un-der virtual concentrated force can be easily calculated.Following analogical relations, the virtual shear forces and the virtual bending moments are section rotation angles and displacements of the real beam, respectively. Results show that this approach has both clear concepts and lower calculating cost , and can also be used in sol-ving variable continuous beams and rigid frames.