介绍一端外伸梁置换法位移方程,其主要由自变量梁长、中间变量左置换梁自由端挠度、中间变量右置换梁自由端挠度等等构成.作其相应的置换法图像,即让所述变量几何关系图形化.对挠度方程求关于自变量梁长的一阶导数.对求导过程中出现的一个新的变量组合进行几何分析,指出它为置换梁挠度导数的协和,证明此协和的值为零.用归纳的方法证明向左、向右外伸梁置换法位移方程的完备性,即证实其挠度方程与转角方程的一阶导数的关系性质.置换法位移方程建立的条件宽松,结果精确,保存挠曲线原有特性,故可应用于理论分析和工程实践.%This study presents the displacement equations of the beam with one end overhanging through conver-sion method. The equations consist of the argument of longitudinal size and intermediate variables of the deflection of the left conversion beam, the deflection of the right conversion beam, etc. The relevant pictures of the conver-sion method are made, which reveal the geometric relations of those variables. Then, it gives the derivatives of the deflection equation of conversion method with respect to the longitudinal size. A new component of variables in ge-ometry is analyzed, which refers to the harmony sum of the derivative of deflection of conversion method beam. And it proves the sum has the value 0. The relational integrity of displacement equations of beam with one end overhanging (at left or at right) through conversion method is verified and the property of the derivative relation of equations of deflection and slope is proved. Owing to the loose and comfortable condition, the accurate outcome and the preservation of the original nature of deflection curve, the displacement equation of conversion method could be used in theoretical analysis and engineering practice.
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