均质简支梁简化为单自由度系统条件研究

On the Conditions for Simplifying a Uniform Simply Supported Beam into a Single-Degree-of-Freedom System

简支梁是土木工程中的常见结构形式,工程计算中常将其简化为单自由度系统进行初步分析和计算.本文系统地讨论了简谐荷载作用下将简支梁简化为单自由度系统进行竖向位移计算的限定条件.对限定条件分析发现将梁上质量的一半集中到梁跨中处所得近似结果精度最好.给出公式可以通过单自由度系统的位移得到梁上任意点处的竖向位移.本文对结构力学教材中的集中质量法进行了进一步的分析和讨论,给出的近似计算公式对土木工程中简支梁在简谐力作用下竖向位移的快速估算具有一定的参考价值.

The simply supported beam is one of the common structures in civil engineering, which is usually simplified into a singledegree-freedom system for calculations in engineering applications. In this paper, the conditions under which a uniform simply supported beam subjected to a harmonic force can be approximated to a single-degree-of-freedom system are discussed. From the analysis, it is found that the approach of concentrating all the mass of the beam to its midspan leads to the highest precision for the estimation of the vertical displacement. A formula is given to calculate the vertical displacements of any point on the beam using the single-degree-of-freedom system. Further, the concentrated mass method in the textbooks of structural mechanics is evaluated and discussed. The formula presented in this paper is useful to make a rapid calculation for the vertical displacements of a uniform simply supported beam subjected to a harmonic force.