静定梁与静定刚架双语

1、Using basic principles to determine the Using basic principles to determine the internal forces of different statically internal forces of different statically determinate structures skillfully and determinate structures skillfully and accurately.accurately.Avoiding or shunning being satisfied with

2、Avoiding or shunning being satisfied with smatteringsmattering（一知半解、浮浅学习（一知半解、浮浅学习)of )of knowledgeknowledge.常见单跨梁常见单跨梁 The most common single span beams ：简支梁简支梁Simplysupported beam 伸臂梁伸臂梁Overhanging beam悬臂梁悬臂梁Cantilever beam 单跨梁都是由粱和地基按两刚片规则组成的单跨梁都是由粱和地基按两刚片规则组成的静定结构静定结构，因而其，因而其支座反力都只有三个支座反力都只有三个，可

3、取，可取全梁为隔离体，由平面一般力系的全梁为隔离体，由平面一般力系的三个平衡方三个平衡方程求出。程求出。Single span beam is a statically determinate Single span beam is a statically determinate structure composed of beam and foundation structure composed of beam and foundation according to according to 2-body rule2-body rule, there are , there are 3

4、reaction3 reaction forcesforces which can be determined by which can be determined by isolating isolating free body free body andand solving the equilibrium equation solving the equilibrium equation of forces.of forces.FN+d FNFNFS+dFSFSMM+dMdxdxtensile as positiveclockwise as positiveMcausing tensio

5、n in the lower fibers-positiveaxial force =The algebraic sum of the projections of external forces on one side of the section to the axis.shear force =The algebraic sum of the projections of external forces on one side of the section to the axis perpendicular to axis.bending moment=The algebraic sum

6、 of the moments of external forces about the center of axis of section内力图内力图- -表示结构上各截面内力值的图形表示结构上各截面内力值的图形, ,横坐标横坐标-截截面位置；纵坐标面位置；纵坐标-内力的值内力的值 Internal force diagram Internal force diagram is the diagramis the diagram on which the variation law alone the location of member sections of the internal f

7、orce is clearly represented. The ordinates ( (竖标）竖标） denote the internal force values.注：注：当外力效果与内力正方向一致时，当外力效果与内力正方向一致时，弯矩图弯矩图-习惯绘在杆件受拉的一侧，不需标正负号习惯绘在杆件受拉的一侧，不需标正负号 The ordinates of bending moment diagrams have to be plotted on the sides where the fibers of the member are under tension, and no sign i

8、ndication is necessary.轴力和剪力图轴力和剪力图-可绘在杆件的任一侧，但需标明正负号可绘在杆件的任一侧，但需标明正负号 Shear and axial force diagram can be depicted on any side of the member, but sign indication must be made FNBAFNABFSBAFSABMABMBABFP lFPlABABlqql2 2复杂的内力图是由若干简单的内力图叠加而成。复杂的内力图是由若干简单的内力图叠加而成。Complex internal force diagrams are comp

9、osed of simple internal force diagrams应熟记常用单跨梁的弯矩图应熟记常用单跨梁的弯矩图BAFlabFab lBAqlql2 8mBAablm l a lm b lmm lFPFN+d FNFNFS+dFSFSMM+dMdxdxq)(dd )(dd ddNSSxpxF,xqxF,FxM抛物线抛物线( (下凸下凸) ) 弯矩图弯矩图MomentMoment梁上梁上情况情况集中力偶集中力偶M M作作用处用处Concentratedmoment铰处铰处hinges)(dd )(dd ddNSSxpxF,xqxF,FxM4 4、叠加法作弯矩图、叠加法作弯矩图meth

10、od of superposition简支梁弯矩图简支梁弯矩图M diagram for simple beams：Superposition is the superposition of the ordinates of the diagrams1 1、求反力、求反力 determine reactions of supports2 2、分段：外力不连续点作为分点、分段：外力不连续点作为分点 partitioning of beams3 3、定点：选定控制截面，求截面的内力值，用竖标绘出，定、定点：选定控制截面，求截面的内力值，用竖标绘出，定出内力图上的各控制点出内力图上的各控制点 Sel

11、ect controlling sections and determine the internal forces at these sections. 4 4、联线：利用微分关系分别用直线或曲线将控制点相联，即、联线：利用微分关系分别用直线或曲线将控制点相联，即得内力图得内力图 Using differential relationships to link the controlling points of the diagrams。作图示梁的弯矩图和剪力图作图示梁的弯矩图和剪力图FA=58 kNFB=12 kN164618201826MEqMFFQFFQE10单位单位: kN m.FS

12、 图图( kN )qqqlmain portionsindependentlyMaintain their stability independentlysubsidiary portionDepend Supported On main portions to Maintain Stability如何如何求支座求支座B反力反力?例例101810125例：图示多跨静定梁全长受均布荷载例：图示多跨静定梁全长受均布荷载 q q，各跨长度均为，各跨长度均为 l l。欲使梁上最大正、负弯矩的绝对值相等，试确。欲使梁上最大正、负弯矩的绝对值相等，试确 定铰定铰 B B、E E 的位置。的位置。多跨多跨简

13、支梁简支梁例：作图示多跨静定梁的内力图，并求出各支座的反力例：作图示多跨静定梁的内力图，并求出各支座的反力1m4m1m4m4mFS简支刚架简支刚架三铰刚架三铰刚架悬臂刚架悬臂刚架刚架刚架-具有刚结点的由直杆组成的结构具有刚结点的由直杆组成的结构。Rigid frames - systems of several members connected by rigid joints ABCDDE刚结点处的变形特点刚结点处的变形特点The deformation of rigid jointsStatically indeterminate Rigid framesMethods of drawin

14、g force diagrams:First, determine reactions, then determine the moments at Controlling sections, then constructdiagrams using superposition method.kNFFAXX4886, 0kNFMBA426/ ) 320486(, 0)(9224220, 0kNFFAYYkNmMCD482462kNmMCB192320642MCB20kN42kNCBMCA48kN22kNACkNmMCA1442/464482kNmMkNmMkNmMCACBCD144192480

15、14419248CMFSCB20kN42kNCBFNCBkNmFSCB2242200NCBFkNmFSCA244648kNmFNCA2248kN22kNACFSCAFNCA6kN/m只有两杆汇交的刚结点，若结点上无外力偶作只有两杆汇交的刚结点，若结点上无外力偶作用，则两杆端弯矩必大小相等，且同侧受拉。用，则两杆端弯矩必大小相等，且同侧受拉。FAyFByFBx40 kN80 kN30 kNDE30FNEDFNEB30FNDCFNDEFQFN4080FAyFByFBxFBxFQFN附属部分附属部分Subsidiaryportion基本部分基本部分main portion3-43-4少求或不求反力绘

16、制弯矩图少求或不求反力绘制弯矩图Construct internal force diagrams without or withlittle computation of reactions MMMM1M2集中力偶作用的杆端处，集中力偶作用的杆端处，杆端弯矩与集中力偶相同；杆端弯矩与集中力偶相同；无集中力偶作用的杆端处，杆无集中力偶作用的杆端处，杆端弯矩为零。端弯矩为零。刚结点刚结点rigid joints ：两杆结点无外力偶两杆结点无外力偶MMMMM1M2M3213MMMFPFPFPFPFPaFPaFPaFPaFPaFPa2FPFByFAyFAx602401804040 M图图kN mFP

17、aaaaaFPaFPaFPaFPa2FPa2FP 5kN304020207545a/2a/2aFPa /2FPaFPaFPaFP a/2FP2 FP4 m4 m2 m2 m888628已知结构的弯矩图，试绘出其荷载已知结构的弯矩图，试绘出其荷载determine the external forcesBy the given M-diagram。反反 问问 题题3-5 3-5 静定结构的特性静定结构的特性 Properties of statically determinate structures（1） 满足全部平衡条件的解答是静定结构的唯一解答满足全部平衡条件的解答是静定结构的唯一解答So

18、lutions satisfying all equilibrium conditions are the unique solutions of the problem. 证明的思路：证明的思路： 静定结构是无多余联系的几何不变体系，用刚体虚静定结构是无多余联系的几何不变体系，用刚体虚位移原理求反力或内力解除约束以位移原理求反力或内力解除约束以“力力”代替后，体代替后，体系成为单自由度系统，一定能发生与需求系成为单自由度系统，一定能发生与需求“力力”对应对应的虚位移，因此体系平衡时由主动力的总虚功等于零的虚位移，因此体系平衡时由主动力的总虚功等于零一定可以求得一定可以求得“力力”的唯一解答。的唯一解答。静定结构派生性质静定结构派生性质The d