## A NEW METHOD FOR GEOMETRIC CONSTRUCTION ANALYSIS OF COMPLEX PLANAR SYSTEMS1)

WANG Mengfu,2)

College of Civil Engineering, Hunan University, Changsha 410082, China

 基金资助: 1)国家自然科学基金资助项目(51578225)

Abstract

It is well known that the zero-load method is generally used to analyze the geometric construction of complex plane systems in structural mechanics. However, the zero-load method needs involved calculation, and the analysis process is cumbersome. In order to simplify the analysis of geometric construction of complex plane system, based on the substitute member method and the zero-load method, a new method for geometric construction analysis of complex plane systems is developed, and the basic rule of geometric construction analysis of complex plane system is presented. Finally, the feasibility and superiority of this method are demonstrated by several examples.

Keywords： substitute member method; zero-load method; complex plane system; analysis of geometric construction

WANG Mengfu. A NEW METHOD FOR GEOMETRIC CONSTRUCTION ANALYSIS OF COMPLEX PLANAR SYSTEMS1). Mechanics in Engineering, 2022, 44(2): 404-408 DOI:10.6052/1000-0879-21-330

## 1 平面体系几何组成分析的零载法

(1) 求体系的计算自由度$W$,$W$应等于零。

(2) 去掉肯定为零的轴力杆简化体系。

(3) 设某内力或反力为非零值$X$,分析在满足全部平衡条件时$X$的值。

(4) 如果$X$等于零,则体系为静定结构;如果存在非零值$X$,则体系为几何可变。

## 2 复杂静定平面结构计算的杆件替代法

### 图3

$F_{NEF} =3.6F_{P} +3X=0$

$X=-1.2F_{P}(\downarrow)$

## 3 复杂平面体系的几何组成分析规则

### 图4

(2) 与零载法判断平面体系需要计算体系全部内力与反力不同,本文提出的判断平面体系几何组成的基本规则只需要计算替换支座链杆反力或体系中替换链杆轴力。由于可以根据简便计算需要选择替换杆件的位置,从而大幅度地提高了平面体系几何组成分析的效率,减少了因计算量大而可能出现的错误判断。

(3) 算例分析表明,本文提出的判断平面体系几何组成的基本规则是高效可行的,可编入结构力学教材供学生学习应用。

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

Yang Fukang, Li Jiabao, Hong Fanwen, et al. Structural Mechanics, 6th edn. Beijing: Higher Education Press, 2016 (in Chinese)

Long Yuqiu, Bao Shihua, Yuan Si. Structural Mechanics I (Basic Course), 4th edn. Beijing: Higher Education Press, 2019 (in Chinese)

Zhu Cimian, Zhang Weiping. Structural Mechanics, 3rd edn. Beijing: Higher Education Press, 2016 (in Chinese)

Hibbeler RC, Kiang T.

Structural Analysis, 9th revised edn

Upper Saddle River: Pearson Prentice Hall, 2014

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