矩-面积定理的拟图乘法证明及局部图乘法导出  

The Proof of Moment-Area Theorems with Method of pseudo Graph Multiplication and the Derivation of Method of Local Graph Multiplication

作　　者：阙仁波 QUE Renbo(School of Civil Engineering,Xiamen University Tan Kah Kee College,Zhangzhou 363105)

机构地区：[1]厦门大学嘉庚学院土木工程分院,福建漳州363105

出　　处：《福建建筑》2020年第4期33-37,共5页Fujian Architecture & Construction

摘　　要：采用拟图乘法证明了矩-面积第一定理和第二定理,从一个新的视角说明了矩-面积定理亦可看作是图乘法的一种局部化应用。基于此,将两者思想融会,导出局部图乘法。相比通常的图乘法,由于图乘局部化,可减少一定的计算量。相比矩-面积定理,可减少为确定方向而要画变形示意图和建立局部坐标系的麻烦。若与力法或位移法相结合,还可用于求超静定梁和刚架的转角和挠度。First moment-area theorem and second moment-area theorem were proved herein with method of pseudo graph multiplication,and it was illustrated from a new perspective that moment-area theorems can also be regarded as the result of local application of method of graph multiplication. Under the inspiration of such a viewpoint,method of local graph multiplication is derived by the alliance of ways of thinking of moment-area theorems and method of graph multiplication. Compared with traditional graph multiplication method,computational effort can be saved to some degree because graph multiplication is only applied to part of the bending-moment diagram. Compared with moment-area method,it is unnecessary to construct a sketch of deflected shape,and to establish a local coordinate system for every element. Combined with force method or displacement method,it can also be applied to indeterminate beams and frames for determining slope and deflection.

关 键 词：矩-面积定理 局部图乘法 证明 导出 

分 类 号：TU311[建筑科学—结构工程]