一端外伸梁置换法挠度转角方程关系的完备性  

Relational Integrity between Deflection and Slope Equations of One End Overhanging Beam Based on Conversion Method

作　　者：喻晓今[1] 

机构地区：[1]华东交通大学土木建筑学院,江西南昌330013

出　　处：《华东交通大学学报》2015年第4期73-77,共5页Journal of East China Jiaotong University

基　　金：江西省高等学校教学改革研究课题(JXJG-14-5-31)

摘　　要：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 deflectionof 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 thedeflection 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 endoverhanging（at left or at right） through conversion method is verified and the property of the derivative relation ofequations of deflection and slope is proved. Owing to the loose and comfortable condition, the accurate outcomeand the preservation of the original nature of deflection curve, the displacement equation of conversion methodcould be used in theoretical analysis and engineering practice.

关 键 词：梁挠度和转角 约束反力 置换法 悬臂梁 外伸梁 

分 类 号：TU321[建筑科学—结构工程] TU323.3