静定平面桁架（双语46页）PPT

1、第五章 Chapter V,静定平面桁架 Statically determinate trusses,5-1 概述 Introduction,桁架A truss：由直杆组成的铰接体系assemblage of straight members connected at their ends by hinged joints,基本假设:Basic assumptions,1、各结点为理想铰；all hinges are frictionless,2、各杆轴线为直线,所有用铰联结的杆交于铰心；The centroidal axes are straight lines,those meeting

2、 at a hinge all intersect at the centre of hinge,3、荷载只作用于结点上。All loads are applied on truss only at its joints,导出特性：各杆截面上只受轴力作用，而没有弯矩和剪力，这样的杆称为二力杆。All members are subjected only to axial forces, but not subjected to bending moments and shear forces, these members are called two-force members,stringe

3、r,truss,Floor beam,注：轴力又称为主内力（axial forces are called primary internal forces,上弦杆top chords,下弦杆 Bottom chords,斜杆diagonal web members,弦杆chords,桁架各部分名称classification of the members,桁架结构的分类Classification of trusses,一、平面（二维）桁架（plane trusses） 所有组成桁架的杆件以及荷载的作用线都在同一平面内. All the members and the applied load

4、s lie in the a single plane,二、按外型分类Classification according to their forms,平行弦桁架 Parallel chord trusses,2. 三角形桁架Triangular trusses,3. 抛物线桁架（折线桁架）Parabolic trusses,4. 梯形桁架Trapezoidal trusses,简单桁架 （simple trusses,联合桁架 （compound trusses,复杂桁架（complex trusses,三、按几何组成分类Classification according to their Ge

5、ometric construction,梁式桁架 Girder trusses,四、按受力特点分类Classification according to stressing properties,2. 拱式桁架 Arch-like trusses,竖向荷载下将产生水平反力Under the action of vertical loads horizontal thrust will be developed,5-2 结点法（The method of joints,取结点为隔离体研究，用结点的平衡方程求解各杆内力的方法 Take joints as isolated free bodies

6、, use equilibrium conditions of joints to determine the internal forces of members.This method is suitable for analysis of simple trusses,例1. 求以下桁架各杆的内力 Determine the internal forces of the members of the following truss,斜杆内力的分解Resolution of the axial force,求反力,Free body diagram of joint A,Free body

7、 diagram of joint C,8 kN,Free body diagram of joint D,利用对称性可确定右半边各杆的内力。Use symmetry property to determine the internal forces of members on the right side portion,以结点作为隔离体，结点承受汇交力系作用。Take joints as isolated bodies, use equilibrium conditions of joints to determine the internal forces of members. 按与“

8、组成顺序相反”的原则，逐次建立各结点的平衡方程，求解各杆的内力。 Take analyzing sequence as the order which is opposite to that of the geometric construction, consecutively develop the Equilibrium equations of the joints to determine the internal forces of every members,小结summary,结点单杆：以结点为隔离体仅用一个平衡方程求出内力 的杆件，称为结点单杆（For isolated jo

9、int, if only one equilibrium equation is needed for the determination of axial force of the bar, then such a bar is called nodal single bar,结点单杆nodal single bar,利用这个概念，选择结点，使所考虑的杆件为接结点单杆，避免解联立方程，简化计算。This concept can be used to determine the axial forces of bars without solving simultaneous equation

10、s,3. 零杆 零内力杆简称零杆 (zero-force bar,FN=0,FN=0,利用结点单杆概念，根据荷载状况可判断杆件内力是否为零。Using the concept of nodal single bar we can identify zero-force bars,L型结点(无荷载) two non-collinear members,T型结点(无荷载) T-type joints,L型结点(有荷载) L-type joints,FP/2,FP/2,FP,FP,判断结构中的零杆Identify the zero-force members,当内力未知杆件都为斜杆时，可列力矩平衡方

11、程计算未知内力。 When the desired members are inclined members, may use moment equilibrium equations to determine the internal forces,A,B,讨论discussion：对静定桁架，利用结点平衡条件可以唯一确定全部反力与内力。For statically determinate trusses we can use Equilibrium equations to determine all forces,设：j 结点数，b 杆件数，r 支座链杆数,而每个结点可列出两个独立平衡方

12、程，共有2j个独立方程,则桁架共有 b + r 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w = 0，既,W = 2j - ( 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，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 de

13、termined,5-3 截 面 法 Method of sections,截取桁架的某一局部作为隔离体，由平面任意力系的平衡方程即可求得未知的轴力。Cutting the truss Into two portions by passing an imaginary section through the members whose forces are desired. Use the equilibrium equations of forces to determine all axial forces. 对于平面桁架，由于平面任意力系的独立平衡方程数为3，因此所截断的杆件数一般不宜超

14、过3.There are only 3 equilibrium equations are available, so the sections should be chosen that do not pass through more than 3 nonconcurrent(不共点的） and nonparallel（不平行的） members with unknown forces,截面法,力矩平衡方程moment equilibrium equations,力平衡方程Force equilibrium equations,1,2,3,A,B,C,D,例：求图示桁架1、2、3杆的内力

15、Determine the axial forces of members 1 through 3 of the shown truss,1,2,3,A,B,C,D,求支反力,m,m,C,用截面m-m截开1、2、3杆，取左侧为隔离体,列力矩平衡方程和投影平衡方程计算未知力,截面上有两个或两个以上内力未知杆件为斜杆时，要考虑斜杆对某点的力矩时，可用前面提到方法来处理。If there are 2 or more than 2 desired inclined members, then the above mentioned method may be used,例：求图示桁架1、2、3杆的内力

16、。 Determine the axial forces of members 1 through 3 of the shown truss,求反力,用截面m-m截开1、2、3杆，取左侧为隔离体,列力矩平衡方程和投影平衡方程计算未知力,截面单杆(section single bar): 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，则此杆称为截面单杆 (section single bar- the axial force of which can be determined by only one equation by section method) 可

17、能的截面单杆通常有相交型和平行型两种形式。 2 types of section single bars: concurrent type and parallel type,相 交情况concurrent type,FP,FP,FP,FP,FP,FP,a为截面单杆,2 special cases,3 members are concurrent to joint K, by summing the moments about K ,we can determine the axial force of member a,b为截面单杆,4 members are parallel each o

18、ther, 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,FP,FP,用截面法灵活截取隔离体,1,2,5-4结点法和截面法的联合应用,结点法 Method of jointsfor the calculation of simple trusses 简单桁架，求全部杆件内力,截面法Method of section for calculati

19、on of forces of desired members 求指定杆件内力，联合桁架联系杆内力,有时，需要同时应用结点法和截面法才能确定杆件内力。In some cases it is necessary to jointly use both methods to calculate the internal forces of members,当同时应用结点法和截面法才能确定杆件内力时，统称为联合法（When 2 methods are required to determine the internal forces of members, we have combined meth

20、od,Example 试求下页图示K式桁架指定杆1、2、3的轴力 Determine the axial forces of members 1 through 3 of the shown truss,ED杆内力如何求,5-5 几种梁式桁架的比较Comparison of several Girder trusses,M0 简支梁弯矩,h 桁架高,弦杆chords,腹杆web,FQ0 -简支梁剪力,5-6 组合结构的计算 The calculation of composite structures,FP,链杆links,受弯杆bending members,组合结构composite st

21、ructures,链杆:二力杆，只有轴力links two-force members are subjected to axial forces,受弯杆:有弯矩、剪力flexural member are mainly subjected to bending moment, sometimes shearing forces,静定组合结构 Statically determinate composite structures,特点properties: They are composed by two-force members and flexural members, and gene

22、rally have key links. 既有桁架杆，又有弯曲杆,一般有一些关键的联系杆 求解的关键点 The key points for the solution 选择恰当方法解决关键杆内力计算，Select appropriate methods to calculate the key links. 选择截面时，必须注意区分两类杆To identify two kinds of members when select sections. 从组成入手先解决关键杆计算 To calculate key links according the geometric construction,

23、例：分析图示组合结构的内力Determine the internal forces of the composite structure,4m,4m,4m,2m,2m,2m,8kN,C,B,A,D,E,F,G,解Solution：计算反力 The calculation of reactions,5kN,3kN,0,思路method：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C和

24、杆DE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（联系未知力不超过3个,由截面m-m截开联系，取左边为隔离体,上面受拉,上面受拉,Summary 小结,1.基本假定 Basic assumptions 2.零杆的确定 The determination of zero-force members; 3.两种解题方法:结点法，截面法 2 analysis methods ：method of joints, section method. 4.几种桁架的比较；the comparison of several trusses 5.两种方法的联合应用：the joint use of 2 methods,Popular v