靜定平面桁架雙語(yǔ)

1、桁架桁架A truss：由直桿組成的鉸接體系由直桿組成的鉸接體系assemblage of straight members connected at their ends by hinged joints主桁架主桁架縱梁縱梁 橫梁橫梁stringertrussFloor beam trusses （simple trusses）（compound trusses）（complex trusses）Girder trusses according to stressing properties 例例1. 1. 求以下桁架各桿的內(nèi)力求以下桁架各桿的內(nèi)力 Determine the interna

2、l forces of the members of the following trussABllxlyFNABXNABYNABNAByxNABYllXNAByNABFllYNABxNABFllXNABxyNABXllY-3334.819190kNYCDADFNADNAD8 .34kN 11 ; 0NADYYkN 333NNNADADADYYCDACXkN 33; 0NACFXkNFAy19kNFBy19kNFAx0求反力：求反力：Free body diagram of joint A-3334.819190-33-8Free body diagram of joint C-3334.8-

3、33-819190- -8 kN5 . 075. 0 CECDXYDEDE37.5-5.4Free body diagram of joint D-3334.8-33-837.5-5.419190-5.4-8-33-3334.8FN2=0FN1=0FN=0FN=0FP/2FP/2FPFPFP當(dāng)內(nèi)力未知桿件都為斜桿時(shí)，可列力矩平衡方程計(jì)算未知內(nèi)力。當(dāng)內(nèi)力未知桿件都為斜桿時(shí)，可列力矩平衡方程計(jì)算未知內(nèi)力。When the desired members are inclined members, may use moment equilibrium equations to determine t

4、he internal forces.ABNACFNACFNACYNACXNBCFNBCYNBCXm1m3m3ABCkN100CkN100NBCFkNXXMNACNACB75; 010034; 0kNXXMNACNBCA75; 010034; 0kNXFNACNAC105 .37210kNXFNBCNBC2752而每個(gè)結(jié)點(diǎn)可列出兩個(gè)獨(dú)立平衡方程，共有而每個(gè)結(jié)點(diǎn)可列出兩個(gè)獨(dú)立平衡方程，共有2j2j個(gè)獨(dú)立方程。個(gè)獨(dú)立方程。則桁架共有則桁架共有 b + r 個(gè)未知力（桿件軸力和支反力）。個(gè)未知力（桿件軸力和支反力）。由桁架為靜定結(jié)構(gòu)，計(jì)算自由度由桁架為靜定結(jié)構(gòu)，計(jì)算自由度w = 0，既，既W = 2

5、j - ( b + r ) = 0由此可知，未知力數(shù)目與獨(dú)立方程數(shù)目相同，既方程有唯一解，由此可知，未知力數(shù)目與獨(dú)立方程數(shù)目相同，既方程有唯一解，既唯一確定全部反力與內(nèi)力。既唯一確定全部反力與內(nèi)力。Therefore the number of unknown forces and the number of equations are identical, i.e. the equations have unique solution, and all reactions and internal forces are uniquely determined. 截面法截面法力矩平衡方程力矩平

6、衡方程moment equilibrium equations力平衡方程力平衡方程Force equilibrium equations123mm842m2ABCDkN20kN20m2123mm842m2ABCDkN20kN20kNFAy25kNFBy150mm1NF3NF2NFCkNFAy25AD20kNkNFFFMNAyNC30;042202;011kNFFMNND25;02252;033kNFFFNNy25;0202521;022m2ABmm842m2kN10kN10kN20123CDEFGHABmm842m2kN10kN10kN20123CDEFGHkN30kN10AkN10kN20C

7、DFGkN301NF2NF3NFmm 0FM023021013NFkNFN4031NF1NXAkN10kN20CDFGkN301NF2NF3NF1NY 0DM022041043021NXkNXN201kNXFNN5102511AkN10kN20CDFGkN301NF2NF3NF2NF2NX2NY 0AM022042NYkNYN101kNYFNN510522截面單桿截面單桿(): 截面法取出的隔離體，不管其上有幾個(gè)軸力，截面法取出的隔離體，不管其上有幾個(gè)軸力，如果某桿的軸力可以通過列一個(gè)平衡方程求得，如果某桿的軸力可以通過列一個(gè)平衡方程求得，則此桿稱為截面單桿則此桿稱為截面單桿 () 可能的截面

8、單桿通常有相交型和平行型兩種可能的截面單桿通常有相交型和平行型兩種形式。形式。 FPFPFPFPFPFP2 special cases3 members are 3 members are concurrent to joint concurrent to joint K, by summing K, by summing the moments the moments about K ,we can about K ,we can determine the determine the axial force of axial force of member member a a. .平行情

9、況平行情況FPFP4 members are parallel each other, by summing the force components in the direction perpendicular to the axial lines of the parallel members we can determine the axial force of member b.FPFPFPFP12FPFN2FN1FN3FAy結(jié)點(diǎn)法結(jié)點(diǎn)法 Method of jointsfor the calculation of simple trusses 簡(jiǎn)單桁架，求全部桿件內(nèi)力。簡(jiǎn)單桁架，求全

10、部桿件內(nèi)力。截面法截面法Method of section for calculation of forces of desired members 求指定桿件內(nèi)力，求指定桿件內(nèi)力，聯(lián)合桁架聯(lián)系桿內(nèi)力。聯(lián)合桁架聯(lián)系桿內(nèi)力。（When 2 methods are required to determine the internal forces of members, we have combined method）Example Example 試求下頁(yè)圖示試求下頁(yè)圖示K K式桁架指定桿式桁架指定桿1 1、2 2、3 3的軸力的軸力 ED桿內(nèi)力如何求桿內(nèi)力如何求? ?hMFN0M M0 0 簡(jiǎn)

11、支梁彎矩簡(jiǎn)支梁彎矩h h 桁架高桁架高0QNFF FP鏈桿鏈桿links受彎桿受彎桿bending members鏈桿鏈桿: :二力桿，只有軸力二力桿，只有軸力links two-force members are subjected to axial forces.受彎桿受彎桿: :有彎矩、剪力有彎矩、剪力flexural member are mainly subjected to bending moment, sometimes shearing forces4m4m4m2m2m2m8kNCBADEFG解解Solution：計(jì)算反力計(jì)算反力 The calculation of rea

12、ctions.5kN3kN0（思路（思路method：先計(jì)算鏈桿內(nèi)力，再計(jì)算受彎桿內(nèi)力：先計(jì)算鏈桿內(nèi)力，再計(jì)算受彎桿內(nèi)力At first calculate the axial forces, then calculate the internal forces of bending members ）（分析：由幾何構(gòu)造分析知，結(jié)構(gòu)上部可看成由結(jié)點(diǎn)（分析：由幾何構(gòu)造分析知，結(jié)構(gòu)上部可看成由結(jié)點(diǎn)C C和桿和桿DEDE聯(lián)結(jié)兩剛片聯(lián)結(jié)兩剛片組成，可截?cái)嗦?lián)系，取剛片為隔離體，由平衡條件求聯(lián)系桿件內(nèi)力（聯(lián)組成，可截?cái)嗦?lián)系，取剛片為隔離體，由平衡條件求聯(lián)系桿件內(nèi)力（聯(lián)系未知力不超過系未知力不超過3 3個(gè)）

13、個(gè)）由截面由截面m-m截開聯(lián)系，取左邊為隔離體。截開聯(lián)系，取左邊為隔離體。mm4m2m2m2m8kNADF5kN0CFNDEFCXFCY 0CM085282NDEFkNFNDE12 0XF052NDENDAFFkNkNFFNDENDA4 .135625 0XF051NDFNDAFFkNFNDF6FNDE=12kNFNDFFNDADkNFkNFCYCX3;128kN12kN3kN6kN13.4kN5kNFACkNMF42843（上面受拉）3kN6kN13.4kNCGB12kN3kNkNMG1243（上面受拉）4m4m4m2m2m2m8kNCBADEFG5kN3kN04612M圖（kNm）13.4

14、13.4-6-612-12FN圖（kN）1.基本假定基本假定 Basic assumptions2.零桿的確定零桿的確定 The determination of zero-force members;3.兩種解題方法兩種解題方法:結(jié)點(diǎn)法，截面法結(jié)點(diǎn)法，截面法2 analysis methods ：method of joints, section method.4.幾種桁架的比較；幾種桁架的比較；the comparison of several trusses5.兩種方法的聯(lián)合應(yīng)用：兩種方法的聯(lián)合應(yīng)用：the joint use of 2 methods. Popular vocabula

15、ryPopular vocabulary1. 4.（simple truss）8.（compound truss）9.（complex truss）10.Beam-like trusses 11.Popular vocabularyPopular vocabulary12.13. 力矩法力矩法moment method,投影投影法法projection method截面單桿截面單桿()對(duì)計(jì)算自由度等于零的桿件體系，其幾何不變性對(duì)計(jì)算自由度等于零的桿件體系，其幾何不變性可由零載法來判別：可由零載法來判別：原理：計(jì)算自由度為零時(shí)，若體系為幾何不變時(shí)，原理：計(jì)算自由度為零時(shí)，若體系為幾何不變時(shí)，必為靜定結(jié)構(gòu)，由滿足平衡條件的解答唯一性，必為靜定結(jié)構(gòu)，由滿足平衡條件的解答唯一性，則反力和內(nèi)力必然為零。則反力和內(nèi)力必然為零。方法：設(shè)荷載為零，判別體系的反力和內(nèi)力是否方法：設(shè)荷載為零，判別體系的反力和內(nèi)力是否一定為零，若所有內(nèi)力均為零，體系幾何不變，一定為零，若所有內(nèi)力均為零，體系幾何不變，若存在非零反力或內(nèi)力則體系為幾何可變（常變?nèi)舸嬖诜橇惴戳騼?nèi)力則體系為幾何可變（常變或瞬變）?；蛩沧儯?duì)計(jì)算自由度等于零的桿件體系，其幾何不變性對(duì)計(jì)算自由度等于零的桿件體系，其幾何不變性可由零載法來判別：可由零