平面體系的機動分析PPT（雙語71頁）

1、（Geometric Construction Analysis of Plane Systems）第二章 Chapter II平面體系的機動分析2-1 引 言 Introduction結構：由桿件、結點和支座組成的桿件體系Structure consists of members, joints and supports.結構必須是在不考慮材料變形的條件下能保持幾何形狀和位置不變的桿件體系。 Structure must maintain its geometric shape and positions without consideration of the deformation of

2、 materials. 在不考慮材料變形的條件下，桿件體系可分為如下兩種類型 If the deformation of materials is neglected, then framed systems can be classified into two categories：幾何不變體系 ( geometrically stable system )幾何可變體系( geometrically unstable system )幾何不變體系 ( geometrically stable system )在任意荷載作用下，幾何形狀及位置均保持不變的體系。（不考慮材料的變形）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.幾何可變體系( geometrically unstable system )在一般荷載作用下，幾何形狀及位置將發(fā)生改變的體系。（不考慮材料的變形） 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.結構機構幾何不變體系geometrically stable system幾何可變體系geometrically unstable system體系組成分析的目的The purpose of geometric Construction analysis： 1.判定體系是否幾何不變to estimate whether or not a system is geometrically stable；2.研究幾何不變體系的組成規(guī)則to discuss the geometric construction rules o

5、f stable systems；3. 區(qū)分靜定和超靜定的組成distinguish statically determinate structures and statically indeterminate structures 。剛片(rigid body)平面剛體。形狀可任意替換may be replaced by body of any shape.桿件，幾何不變部分均可視為剛片members or stable parts may be looked at as rigid bodies2-1 平面體系的自由度(degrees of freedom of planar system

6、)自由度- 確定物體位置所需要的獨立坐標數(shù)目或體系運動時可獨立改變的幾何參數(shù)數(shù)目Degrees of freedom of a system are the numbers of independent movements or coordinates which are required to locate the system fully.xy平面內(nèi)一點for a point in plane n=2AxyBFor plane rigid body平面剛體 n=3聯(lián)系或約束(link or restraint)一根鏈桿為一個約束 one link is equivalent to one

7、restraint聯(lián)系（約束）-減少自由度的裝置。link or restraint devices or connections reducing the degrees of a system平面剛體剛片n=31個單鉸 = 2個聯(lián)系one simple joint equivalent to 2 restraints單鉸聯(lián)后n=4xy每一自由剛片3個自由度for ecery body n=3兩個自由剛片共有6個自由度2 bodies have 6 degrees單鉸simple jointxyBAC兩剛片用兩鏈桿連接,兩相交鏈桿構成一虛鉸2 rigid bodies are connect

8、ed by 2 links which form one virtual hingen=41連接n個剛片的復鉸 = (n-1)個單鉸One multiple joint connecting n bars is equivalent to (n-1) simple joints n=5復鉸等于多少個單鉸？A復剛結點multiple rigid joint =(n-1 ) simple rigid joints連接n個桿的復剛結點等于多少個單剛結點？單剛結點相當于3個聯(lián)系one rigid joint=3 restraints n=3 W = 3m-(2h+b) m-剛片數(shù)the numbers

9、 of rigid bodies（excluding foundation不包括地基） h-單鉸數(shù)the numbers of simple joints b-單鏈桿數(shù)（含支桿）the numbers of links體系的計算自由度：計算自由度等于剛片總自由度數(shù)減總聯(lián)系數(shù) The computed degrees of freedom=the total numbers of degrees of freedom of rigid bodies total numbers of restraints鉸結鏈桿體系-完全由兩端鉸結的桿件所組成的體系link system connected by

10、 hinges system of bars connected by hinges at the ends of the bars. 鉸結鏈桿體系的計算自由度The computed degrees of freedom ： W=2j-bj-結點數(shù)the numbers of hinges;b-鏈桿數(shù),含支座鏈桿the numbers of links including the links at the supports例1：計算圖示體系的自由度 Determine the numbers of degrees of freedom of the following systemGW=38

11、-(2 10+4)=0ACCDBCEEFCFDFDGFG32311有幾個剛片？ 有幾個單鉸？例2：計算圖示體系的自由度Determine the numbers of degrees of freedom of the following systemW=3 9-(212+3)=0 332112 按剛片計算9根桿,9個剛片有幾個單鉸？3根單鏈桿另一種解法another solutionW=2 6-12=0按鉸結計算6個鉸結點12根單鏈桿W=0,體系是否一定幾何不變呢？討論W=3 9-(212+3)=0體系W等于多少？可變嗎？322113有幾個單鉸？ 能夠減少體系的自由度的聯(lián)系稱為必要聯(lián)系Res

12、traints which reduce the degrees of freedom is named as necessary restraints, otherwise they are called redundant restraints.因為除去圖中任意一根桿，體系都將有一個自由度，所以圖中所有的桿都是必要的聯(lián)系。Because the removal of any bar in the system will increase one degree of freedom, therefore all bars are necessary restraints 除去聯(lián)系后，體系的自

13、由度并不改變，這類聯(lián)系稱為多余聯(lián)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桿，除去都不增加自由度，都可看作多余的聯(lián)系。 圖中上部四根桿和三根支座桿都是必要的聯(lián)系。 例3：計算圖示體系的自由度W=3 9-(212+3)=0W=0,但布置不當幾何可變。上部有多余聯(lián)系，下部缺少聯(lián)系。W=2 6-12=0W=2 6-13=-10例4：計算圖示體系的自由度W0,體系是否一定幾何不變呢？上部具有多余聯(lián)系W=3 10-(214

14、+3)=-10, 缺少足夠聯(lián)系，體系幾何可變 Restraints are not enough, unstable。 W=0, 具備成為幾何不變體系所要求的最少聯(lián)系數(shù)目has the minimum necessary numbers of restraints for stable system。 W 0體系幾何可變unstableW0 時，體系一定是可變的。但W0僅是體系幾何不變的必要條件 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. 速度圖法：參見結構力學，河海大 學結構力學教研室編，水利 水電出版社出版，1983年2. 計算機分析：參見程序結構力學， 袁駟編著，高等教育出版社出版3. 零載法：在第二章介紹 詞匯 Vocabulary幾何組成分析Geometric Construction Analysis 幾何不變體系 ( geometrically stable systems )幾何可變體系( geometrically unstable systems)瞬變體系(Instantaneously unstable systems)剛片(rigid body)自由度(degrees of