静定平面桁架双语

1、桁架桁架A truss：由直杆组成的铰接体系由直杆组成的铰接体系assemblage of straight members connected at their ends by hinged joints主桁架主桁架纵梁纵梁 横梁横梁stringertrussFloor beam trusses （simple trusses）（compound trusses）（complex trusses）Girder trusses according to stressing properties 例例1. 1. 求以下桁架各杆的内力求以下桁架各杆的内力 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当内力未知杆件都为斜杆时，可列力矩平衡方程计算未知内力。当内力未知杆件都为斜杆时，可列力矩平衡方程计算未知内力。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而每个结点可列出两个独立平衡方程，共有而每个结点可列出两个独立平衡方程，共有2j2j个独立方程。个独立方程。则桁架共有则桁架共有 b + r 个未知力（杆件轴力和支反力）。个未知力（杆件轴力和支反力）。由桁架为静定结构，计算自由度由桁架为静定结构，计算自由度w = 0，既，既W = 2

5、j - ( b + r ) = 0由此可知，未知力数目与独立方程数目相同，既方程有唯一解，由此可知，未知力数目与独立方程数目相同，既方程有唯一解，既唯一确定全部反力与内力。既唯一确定全部反力与内力。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截面单杆截面单杆(): 截面法取出的隔离体，不管其上有几个轴力，截面法取出的隔离体，不管其上有几个轴力，如果某杆的轴力可以通过列一个平衡方程求得，如果某杆的轴力可以通过列一个平衡方程求得，则此杆称为截面单杆则此杆称为截面单杆 () 可能的截面

8、单杆通常有相交型和平行型两种可能的截面单杆通常有相交型和平行型两种形式。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、况平行情况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结点法结点法 Method of jointsfor the calculation of simple trusses 简单桁架，求全部杆件内力。简单桁架，求全

10、部杆件内力。截面法截面法Method of section for calculation of forces of desired members 求指定杆件内力，求指定杆件内力，联合桁架联系杆内力。联合桁架联系杆内力。（When 2 methods are required to determine the internal forces of members, we have combined method）Example Example 试求下页图示试求下页图示K K式桁架指定杆式桁架指定杆1 1、2 2、3 3的轴力的轴力 ED杆内力如何求杆内力如何求? ?hMFN0M M0 0 简

11、支梁弯矩简支梁弯矩h h 桁架高桁架高0QNFF FP链杆链杆links受弯杆受弯杆bending members链杆链杆: :二力杆，只有轴力二力杆，只有轴力links two-force members are subjected to axial forces.受弯杆受弯杆: :有弯矩、剪力有弯矩、剪力flexural member are mainly subjected to bending moment, sometimes shearing forces4m4m4m2m2m2m8kNCBADEFG解解Solution：计算反力计算反力 The calculation of rea

12、ctions.5kN3kN0（思路（思路method：先计算链杆内力，再计算受弯杆内力：先计算链杆内力，再计算受弯杆内力At first calculate the axial forces, then calculate the internal forces of bending members ）（分析：由几何构造分析知，结构上部可看成由结点（分析：由几何构造分析知，结构上部可看成由结点C C和杆和杆DEDE联结两刚片联结两刚片组成，可截断联系，取刚片为隔离体，由平衡条件求联系杆件内力（联组成，可截断联系，取刚片为隔离体，由平衡条件求联系杆件内力（联系未知力不超过系未知力不超过3 3个）

13、个）由截面由截面m-m截开联系，取左边为隔离体。截开联系，取左边为隔离体。mm4m2m2m2m8kNADF5kN0CFNDEFCXFCY 0CM085282NDEFkNFNDE12 0XF052NDENDAFFkNkNFFNDENDA4 .135625 0XF051NDFNDAFFkNFNDF6FNDE=12kNFNDFFNDADkNFkNFCYCX3;128kN12kN3kN6kN13.4kN5kNFACkNMF42843（上面受拉）3kN6kN13.4kNCGB12kN3kNkNMG1243（上面受拉）4m4m4m2m2m2m8kNCBADEFG5kN3kN04612M图（kNm）13.4

14、13.4-6-612-12FN图（kN）1.基本假定基本假定 Basic assumptions2.零杆的确定零杆的确定 The determination of zero-force members;3.两种解题方法两种解题方法:结点法，截面法结点法，截面法2 analysis methods ：method of joints, section method.4.几种桁架的比较；几种桁架的比较；the comparison of several trusses5.两种方法的联合应用：两种方法的联合应用：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截面单杆截面单杆()对计算自由度等于零的杆件体系，其几何不变性对计算自由度等于零的杆件体系，其几何不变性可由零载法来判别：可由零载法来判别：原理：计算自由度为零时，若体系为几何不变时，原理：计算自由度为零时，若体系为几何不变时，必为静定结构，由满足平衡条件的解答唯一性，必为静定结构，由满足平衡条件的解答唯一性，则反力和内力必然为零。则反力和内力必然为零。方法：设荷载为零，判别体系的反力和内力是否方法：设荷载为零，判别体系的反力和内力是否一定为零，若所有内力均为零，体系几何不变，一定为零，若所有内力均为零，体系几何不变，若存在非零反力或内力则体系为几何可变（常变若存在非零反力或内力则体系为几何可变（常变或瞬变）。或瞬变）。对计算自由度等于零的杆件体系，其几何不变性对计算自由度等于零的杆件体系，其几何不变性可由零载法来判别：可由零