靜定梁與靜定剛架雙語

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、浮淺學(xué)習(xí)（一知半解、浮淺學(xué)習(xí))of )of knowledgeknowledge.常見單跨梁常見單跨梁 The most common single span beams ：簡支梁簡支梁Simplysupported beam 伸臂梁伸臂梁Overhanging beam懸臂梁懸臂梁Cantilever beam 單跨梁都是由粱和地基按兩剛片規(guī)則組成的單跨梁都是由粱和地基按兩剛片規(guī)則組成的靜定結(jié)構(gòu)靜定結(jié)構(gòu)，因而其，因而其支座反力都只有三個(gè)支座反力都只有三個(gè)，可

3、取，可取全梁為隔離體，由平面一般力系的全梁為隔離體，由平面一般力系的三個(gè)平衡方三個(gè)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內(nèi)力圖內(nèi)力圖- -表示結(jié)構(gòu)上各截面內(nèi)力值的圖形表示結(jié)構(gòu)上各截面內(nèi)力值的圖形, ,橫坐標(biāo)橫坐標(biāo)-截截面位置；縱坐標(biāo)面位置；縱坐標(biāo)-內(nèi)力的值內(nèi)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 ( (豎標(biāo)）豎標(biāo)） denote the internal force values.注：注：當(dāng)外力效果與內(nèi)力正方向一致時(shí)，當(dāng)外力效果與內(nèi)力正方向一致時(shí)，彎矩圖彎矩圖-習(xí)慣繪在桿件受拉的一側(cè)，不需標(biāo)正負(fù)號習(xí)慣繪在桿件受拉的一側(cè)，不需標(biāo)正負(fù)號 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.軸力和剪力圖軸力和剪力圖-可繪在桿件的任一側(cè)，但需標(biāo)明正負(fù)號可繪在桿件的任一側(cè)，但需標(biāo)明正負(fù)號 Shear and axial force diagram can be depicted on any side of the member, but sign indication must be made FNBAFNABFSBAFSABMABMBABFP lFPlABABlqql2 2復(fù)雜的內(nèi)力圖是由若干簡單的內(nèi)力圖疊加而成。復(fù)雜的內(nèi)力圖是由若干簡單的內(nèi)力圖疊加而成。Complex internal force diagrams are comp

9、osed of simple internal force diagrams應(yīng)熟記常用單跨梁的彎矩圖應(yīng)熟記常用單跨梁的彎矩圖BAFlabFab lBAqlql2 8mBAablm l a lm b lmm lFPFN+d FNFNFS+dFSFSMM+dMdxdxq)(dd )(dd ddNSSxpxF,xqxF,FxM拋物線拋物線( (下凸下凸) ) 彎矩圖彎矩圖MomentMoment梁上梁上情況情況集中力偶集中力偶M M作作用處用處Concentratedmoment鉸處鉸處hinges)(dd )(dd ddNSSxpxF,xqxF,FxM4 4、疊加法作彎矩圖、疊加法作彎矩圖meth

10、od of superposition簡支梁彎矩圖簡支梁彎矩圖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：外力不連續(xù)點(diǎn)作為分點(diǎn)、分段：外力不連續(xù)點(diǎn)作為分點(diǎn) partitioning of beams3 3、定點(diǎn)：選定控制截面，求截面的內(nèi)力值，用豎標(biāo)繪出，定、定點(diǎn)：選定控制截面，求截面的內(nèi)力值，用豎標(biāo)繪出，定出內(nèi)力圖上的各控制點(diǎn)出內(nèi)力圖上的各控制點(diǎn) Sel

11、ect controlling sections and determine the internal forces at these sections. 4 4、聯(lián)線：利用微分關(guān)系分別用直線或曲線將控制點(diǎn)相聯(lián)，即、聯(lián)線：利用微分關(guān)系分別用直線或曲線將控制點(diǎn)相聯(lián)，即得內(nèi)力圖得內(nèi)力圖 Using differential relationships to link the controlling points of the diagrams。作圖示梁的彎矩圖和剪力圖作圖示梁的彎矩圖和剪力圖FA=58 kNFB=12 kN164618201826MEqMFFQFFQE10單位單位: kN m.FS

12、 圖圖( 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：圖示多跨靜定梁全長受均布荷載例：圖示多跨靜定梁全長受均布荷載 q q，各跨長度均為，各跨長度均為 l l。欲使梁上最大正、負(fù)彎矩的絕對值相等，試確。欲使梁上最大正、負(fù)彎矩的絕對值相等，試確 定鉸定鉸 B B、E E 的位置。的位置。多跨多跨簡

13、支梁簡支梁例：作圖示多跨靜定梁的內(nèi)力圖，并求出各支座的反力例：作圖示多跨靜定梁的內(nèi)力圖，并求出各支座的反力1m4m1m4m4mFS簡支剛架簡支剛架三鉸剛架三鉸剛架懸臂剛架懸臂剛架剛架剛架-具有剛結(jié)點(diǎn)的由直桿組成的結(jié)構(gòu)具有剛結(jié)點(diǎn)的由直桿組成的結(jié)構(gòu)。Rigid frames - systems of several members connected by rigid joints ABCDDE剛結(jié)點(diǎn)處的變形特點(diǎn)剛結(jié)點(diǎn)處的變形特點(diǎn)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只有兩桿匯交的剛結(jié)點(diǎn)，若結(jié)點(diǎn)上無外力偶作只有兩桿匯交的剛結(jié)點(diǎn)，若結(jié)點(diǎn)上無外力偶作用，則兩桿端彎矩必大小相等，且同側(cè)受拉。用，則兩桿端彎矩必大小相等，且同側(cè)受拉。FAyFByFBx40 kN80 kN30 kNDE30FNEDFNEB30FNDCFNDEFQFN4080FAyFByFBxFBxFQFN附屬部分附屬部分Subsidiaryportion基本部分基本部分main portion3-43-4少求或不求反力繪

16、制彎矩圖少求或不求反力繪制彎矩圖Construct internal force diagrams without or withlittle computation of reactions MMMM1M2集中力偶作用的桿端處，集中力偶作用的桿端處，桿端彎矩與集中力偶相同；桿端彎矩與集中力偶相同；無集中力偶作用的桿端處，桿無集中力偶作用的桿端處，桿端彎矩為零。端彎矩為零。剛結(jié)點(diǎn)剛結(jié)點(diǎn)rigid joints ：兩桿結(jié)點(diǎn)無外力偶兩桿結(jié)點(diǎn)無外力偶MMMMM1M2M3213MMMFPFPFPFPFPaFPaFPaFPaFPaFPa2FPFByFAyFAx602401804040 M圖圖kN mFP

17、aaaaaFPaFPaFPaFPa2FPa2FP 5kN304020207545a/2a/2aFPa /2FPaFPaFPaFP a/2FP2 FP4 m4 m2 m2 m888628已知結(jié)構(gòu)的彎矩圖，試?yán)L出其荷載已知結(jié)構(gòu)的彎矩圖，試?yán)L出其荷載determine the external forcesBy the given M-diagram。反反 問問 題題3-5 3-5 靜定結(jié)構(gòu)的特性靜定結(jié)構(gòu)的特性 Properties of statically determinate structures（1） 滿足全部平衡條件的解答是靜定結(jié)構(gòu)的唯一解答滿足全部平衡條件的解答是靜定結(jié)構(gòu)的唯一解答So

18、lutions satisfying all equilibrium conditions are the unique solutions of the problem. 證明的思路：證明的思路： 靜定結(jié)構(gòu)是無多余聯(lián)系的幾何不變體系，用剛體虛靜定結(jié)構(gòu)是無多余聯(lián)系的幾何不變體系，用剛體虛位移原理求反力或內(nèi)力解除約束以位移原理求反力或內(nèi)力解除約束以“力力”代替后，體代替后，體系成為單自由度系統(tǒng)，一定能發(fā)生與需求系成為單自由度系統(tǒng)，一定能發(fā)生與需求“力力”對應(yīng)對應(yīng)的虛位移，因此體系平衡時(shí)由主動力的總虛功等于零的虛位移，因此體系平衡時(shí)由主動力的總虛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。靜定結(jié)構(gòu)派生性質(zhì)靜定結(jié)構(gòu)派生性質(zhì)The d