平面体系的机动分析PPT（双语71页）

1、（Geometric Construction Analysis of Plane Systems）第二章 Chapter II平面体系的机动分析2-1 引 言 Introduction结构：由杆件、结点和支座组成的杆件体系Structure consists of members, joints and supports.结构必须是在不考虑材料变形的条件下能保持几何形状和位置不变的杆件体系。 Structure must maintain its geometric shape and positions without consideration of the deformation of

2、 materials. 在不考虑材料变形的条件下，杆件体系可分为如下两种类型 If the deformation of materials is neglected, then framed systems can be classified into two categories：几何不变体系 ( geometrically stable system )几何可变体系( geometrically unstable system )几何不变体系 ( geometrically stable system )在任意荷载作用下，几何形状及位置均保持不变的体系。（不考虑材料的变形）Under t

3、he action of any loads, the system still maintain its shape and remains its location if the deformations of the members are neglected.几何可变体系( geometrically unstable system )在一般荷载作用下，几何形状及位置将发生改变的体系。（不考虑材料的变形） Under the action of any loads, the system will change its shape and its location if the def

4、ormations of the members are neglected.结构机构几何不变体系geometrically stable system几何可变体系geometrically unstable system体系组成分析的目的The purpose of geometric Construction analysis： 1.判定体系是否几何不变to estimate whether or not a system is geometrically stable；2.研究几何不变体系的组成规则to discuss the geometric construction rules o

5、f stable systems；3. 区分静定和超静定的组成distinguish statically determinate structures and statically indeterminate structures 。刚片(rigid body)平面刚体。形状可任意替换may be replaced by body of any shape.杆件，几何不变部分均可视为刚片members or stable parts may be looked at as rigid bodies2-1 平面体系的自由度(degrees of freedom of planar system

6、)自由度- 确定物体位置所需要的独立坐标数目或体系运动时可独立改变的几何参数数目Degrees of freedom of a system are the numbers of independent movements or coordinates which are required to locate the system fully.xy平面内一点for a point in plane n=2AxyBFor plane rigid body平面刚体 n=3联系或约束(link or restraint)一根链杆为一个约束 one link is equivalent to one

7、restraint联系（约束）-减少自由度的装置。link or restraint devices or connections reducing the degrees of a system平面刚体刚片n=31个单铰 = 2个联系one simple joint equivalent to 2 restraints单铰联后n=4xy每一自由刚片3个自由度for ecery body n=3两个自由刚片共有6个自由度2 bodies have 6 degrees单铰simple jointxyBAC两刚片用两链杆连接,两相交链杆构成一虚铰2 rigid bodies are connect

8、ed by 2 links which form one virtual hingen=41连接n个刚片的复铰 = (n-1)个单铰One multiple joint connecting n bars is equivalent to (n-1) simple joints n=5复铰等于多少个单铰？A复刚结点multiple rigid joint =(n-1 ) simple rigid joints连接n个杆的复刚结点等于多少个单刚结点？单刚结点相当于3个联系one rigid joint=3 restraints n=3 W = 3m-(2h+b) m-刚片数the numbers

9、 of rigid bodies（excluding foundation不包括地基） h-单铰数the numbers of simple joints b-单链杆数（含支杆）the numbers of links体系的计算自由度：计算自由度等于刚片总自由度数减总联系数 The computed degrees of freedom=the total numbers of degrees of freedom of rigid bodies total numbers of restraints铰结链杆体系-完全由两端铰结的杆件所组成的体系link system connected by

10、 hinges system of bars connected by hinges at the ends of the bars. 铰结链杆体系的计算自由度The computed degrees of freedom ： W=2j-bj-结点数the numbers of hinges;b-链杆数,含支座链杆the numbers of links including the links at the supports例1：计算图示体系的自由度 Determine the numbers of degrees of freedom of the following systemGW=38

11、-(2 10+4)=0ACCDBCEEFCFDFDGFG32311有几个刚片？ 有几个单铰？例2：计算图示体系的自由度Determine the numbers of degrees of freedom of the following systemW=3 9-(212+3)=0 332112 按刚片计算9根杆,9个刚片有几个单铰？3根单链杆另一种解法another solutionW=2 6-12=0按铰结计算6个铰结点12根单链杆W=0,体系是否一定几何不变呢？讨论W=3 9-(212+3)=0体系W等于多少？可变吗？322113有几个单铰？ 能够减少体系的自由度的联系称为必要联系Res

12、traints which reduce the degrees of freedom is named as necessary restraints, otherwise they are called redundant restraints.因为除去图中任意一根杆，体系都将有一个自由度，所以图中所有的杆都是必要的联系。Because the removal of any bar in the system will increase one degree of freedom, therefore all bars are necessary restraints 除去联系后，体系的自

13、由度并不改变，这类联系称为多余联系Restraints, removal of which doesnt change the degrees of freedom, is named as redundant restraints . 下部正方形中任意一根杆，除去都不增加自由度，都可看作多余的联系。 图中上部四根杆和三根支座杆都是必要的联系。 例3：计算图示体系的自由度W=3 9-(212+3)=0W=0,但布置不当几何可变。上部有多余联系，下部缺少联系。W=2 6-12=0W=2 6-13=-10例4：计算图示体系的自由度W0,体系是否一定几何不变呢？上部具有多余联系W=3 10-(214

14、+3)=-10, 缺少足够联系，体系几何可变 Restraints are not enough, unstable。 W=0, 具备成为几何不变体系所要求的最少联系数目has the minimum necessary numbers of restraints for stable system。 W 0体系几何可变unstableW0 时，体系一定是可变的。但W0仅是体系几何不变的必要条件 When the computed numbers of freedom W 0 , then system is certainly unstable. Condition W0 is only t

15、he necessary condition for stable system, but is not the sufficient condition.其它分析方法：1. 速度图法：参见结构力学，河海大 学结构力学教研室编，水利 水电出版社出版，1983年2. 计算机分析：参见程序结构力学， 袁驷编著，高等教育出版社出版3. 零载法：在第二章介绍 词汇 Vocabulary几何组成分析Geometric Construction Analysis 几何不变体系 ( geometrically stable systems )几何可变体系( geometrically unstable systems)瞬变体系(Instantaneously unstable systems)刚片(rigid body)自由度(degrees of