体外预应力连续梁动力特性的等效刚度分析法

Equivalent stiffness method for analyzing dynamic behavior of externally prestressed continuous beam

在已有的体外预应力连续梁动力特性分析中,采用了正比假设和面积等效假设。本文指出了这两个假设存在的问题,放弃了这两个假设,提出了等效刚度法,同时引入两个新的假设:计算第1对称振型自振频率时,体外筋拉力增量产生的综合弯矩图等效为该振型的2阶导数的比例图,将体外预应力梁转化为具有等效刚度的受压梁,体外筋的效应体现为梁刚度的增加;忽略了体外筋对其他自振频率的效应。与已有算法相比,由于假设更为合理,梁的自振频率的计算结果更为准确,与数值解吻合良好。计算表明:已有算法低估了体外筋对第1对称振型自振频率的效应;随着体外筋面积和偏心距的增加,梁的第1对称振型自振频率也随之增加,其他频率的变化很小;体外筋线形的线性变换不影响梁的自振频率。

In the existent analysis of dynamic behavior of externally prestressed continuous beam, the proportional assumption and the equivalent area assumption were adopted. The problems of these two assumptions were pointed out. The equivalent stiffness method was put forward, which gave up two old assumptions and introduced two new assumptions. In calculation of 1st natural frequency of symmetric vibration mode. The resultant bending moment di- agram caused by the tension increment of external tendon was equivalent to the diagram proportional to the 2nd order derivative of this mode. The externally prestressed beam was transformed into the compressive beam with equivalent stiffness. The effect of external tendon was regarded as the increment of beam stiffness and the effect of external tendon on the other natural frequencies was neglected. Compared with the existent method, due to more rational assumptions, the calculation results of natural frequencies were more accurate, and conformed well to the numerical results. The calculation results show： the effect of external tendon on 1 st natural frequency of symmetric vibration mode is underestimated by the existent method. With increasing the area and the eccentricity of external tendon, the 1 st natural frequency of symmetric vibration mode increases, and other frequencies change slightly. The linear transformation of external tendon configuration doesn ＇ t influence the natural frequency.