《矩陣位移法》

1、 8-1 概述 8-2 矩陣位移法的基本原理 8-3 單元剛度矩陣 8-4 直接剛度法 8-5 直接剛度法的另一種形式先處理法 8-6 等效結(jié)點荷載工程結(jié)構(gòu)的日趨復雜性對結(jié)構(gòu)分析提出更高的要求；計算機的飛速發(fā)展為復雜的結(jié)構(gòu)分析提供了可能性；位移法更容易用矩陣形式表示，適宜計算機分析。FK矩陣位移法是以位移法為基礎(chǔ)的結(jié)構(gòu)分析方法;以結(jié)點位移為基本未知量，以結(jié)點力平衡為基本方程矩陣位移法與位移法的區(qū)別：矩陣位移法一般考慮軸向變形；矩陣位移法不區(qū)分靜定和超靜定部分，將桿端所有變形都作為未知量；矩陣位移法的基本步驟1. 結(jié)構(gòu)標識。結(jié)點、單元編號，選擇局部和整體坐標；2. 計算各單元剛度矩陣ke；K0和

2、總剛度方程K0 D D0 =F0；4. 引入位移邊界條件，形成結(jié)構(gòu)剛度矩陣K和結(jié)構(gòu)剛度方程K D D =F ；5. 求解結(jié)構(gòu)剛度方程 ，得到結(jié)點位移D D ；6. 計算各單元桿端力和支座反力；4m3m20kN30kN1342xyyxo123452EI2EIEIEIijE AexyliuivjvjuyiFxiFxjFyjF()0()0eexijiyieexjjiyjEAFuulFEAFuulF 1010000010100000eeeixiiyijxjjyjuFvFEAuFlvF 8-3-1 桁架單元的剛度矩陣局部坐標系()eeNjiEAEAFluullD 材料力學中軸向拉壓桿的變形公式eejil

3、uuD xjNFFxiNFF NF llEAD 在小位移線性分析下，結(jié)點的位移不會引起y方向的反力1010000010100000eeeixiiyijxjjyjuFvFEAuFlvF exieiyiejxjyjFFFFFFFeieiiejjjuvuvDD1010000010100000eeEAlkeeeFk 局部坐標系中桁架單元的剛度矩陣局部坐標系中桁架單元的剛度矩陣局部坐標系中桁架單元局部坐標系中桁架單元的桿端位移向量的桿端位移向量局部坐標系中桁架單元的局部坐標系中桁架單元的桿端力向量桿端力向量局部坐標系中桁架單元的剛度方程局部坐標系中桁架單元的剛度方程結(jié)構(gòu)坐標系中桁架單元的剛度方程ixyy

4、xxiFyiFxiFyiFixycossinxixiyiFFFsincosyixiyiFFF cossinsincosxjxjyjyjxjyjFFFFFF cossin00sincos0000cossin00sincoseeexixiyiyixjxjyjyjFFFFFFFF cossin00sincos0000cossin00sincosTeeFTFeeT結(jié)構(gòu)坐標系桁架單元坐標轉(zhuǎn)換矩陣Tcossin00cossin00sincos00sincos0000cossin00cossin00sincos00sincos TT1000010000100001TTTI1TTTeeFTFeeTeeeFk

5、eeeTFk TTeeeFT k TTeekT k TeeeFk eeeFk 22222222eecsccscscsscsEAlcsccscscsscskcossincscossin001010cossin00sincos000000sincos0000cossin101000cossin00sincos000000sincoseeEAl kTeekT k T8-3-2 剛架單元的剛度矩陣2264262466126612ABABBAABQABABQBAABiMiiliMiiliiiFllliiiFlllDD D DABiBAjQAByiQBAyjMMMMFFFF AiBjijvv D ivij

6、jvE AexylyiFyjFjMiMijQBAFAQABFBAMABMBDl22642()624()6612()6612()iijijjijijyiijijyjijijiMiivvliMiivvliiiFvvllliiiFvvlll 順時針趨勢22642()624()6612()6612()iijijjijijyiijijyjijijiMiivvliMiivvliiiFvvllliiiFvvlll 222266426624612612612612iiijjjiijjyiiijjyjiijjiiMivivlliiMivivlliiiiFvvlllliiiiFvvllll 32322232322

7、212612664621261266264eeeiyiiijyjjjEIEIEIEIllllvFEIEIEIEIMllllvFEIEIEIEIllllMEIEIEIEIllll局部坐標系中局部坐標系中梁式梁式單元的剛度方程單元的剛度方程EIil局部坐標系中梁式單元的剛度方程局部坐標系中梁式單元的剛度方程32322232322212612664621261266264eeeiyiiijyjjjEIEIEIEIllllvFEIEIEIEIMllllvFEIEIEIEIllllMEIEIEIEIllll局部坐標系中梁式單元的剛度矩陣局部坐標系中梁式單元的剛度矩陣3232223232221261266

8、4621261266264eeEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk局部坐標系中桁架單元的剛度方程1010000010100000eeeixiiyijxjjyjuFvFEAuFlvF 00000000000000000000000000000000eeeixiiyiiijxjjyjjjEAEAuFllvFMuFEAEAllvFM32322232322212612664621261266264eeeiyiiijyjjjEIEIEIEIllllvFEIEIEIEIMllllvFEIEIEIEIllllMEIEIEIEIllll323222

9、3232220000001261260064620000000012612600626400eeixiiyiiijxjjyjjjEIEIEIEIuFllllvFEIEIEIEIMlllluFvFEIEIEIEIllllMEIEIEIEIlllle局部坐標系中梁式單元的剛度方程ijE AexyliuivjvjuyiFxiFxjFyjFivijjvEAexylyiFyjFjMiMij局部坐標系中剛架單元的剛度方程局部坐標系中剛架單元的剛度方程323222323222000012612600646200000012612600626400eeixiiyiiijxjjyjjEAEAllEIEIEIEI

10、uFllllvFEIEIEIEIMlllluFEAEAllvFEIEIEIEIMllllEIEIEIEIllllej00000000000000000000000000000000eeeixiiyiiijxjjyjjjEAEAuFllvFMuFEAEAllvFM3232223232220000001261260064620000000012612600626400eeixiiyiiijxjjyjjjEIEIEIEIuFllllvFEIEIEIEIMlllluFvFEIEIEIEIllllMEIEIEIEIlllle線性小位移范圍內(nèi)，軸力只與線性小位移范圍內(nèi)，軸力只與桿端軸向位移有關(guān)，而桿端剪桿

11、端軸向位移有關(guān)，而桿端剪力與彎矩只與桿端橫向位移和力與彎矩只與桿端橫向位移和轉(zhuǎn)角相關(guān)轉(zhuǎn)角相關(guān)局部坐標系中剛架單元的剛度矩陣局部坐標系中剛架單元的剛度矩陣323222323222000012612600646200000012612600626400eeEAEAllEIEIEIEIllllEIEIEIEIllllEAEAllEIEIEIEIllllEIEIEIEIllllkexiyieiiejxjyjjFFFMFFFM FeiieiiejjjjuvuvD DeeeFk 局部坐標系中剛架單元局部坐標系中剛架單元的桿端位移向量的桿端位移向量局部坐標系中剛架單元的局部坐標系中剛架單元的桿端力向量桿端力

12、向量0000000000100000000000000001eexixiyiyiiixjxjyjyjjjFFcsFFscMMFFcsFFscMM 0000000000100000000000000001eeiiiiiijjjjjjuucsvvscuucsvvsceeFTFeeTeeeFk eeeTFk TTeeeFT k TTeekT k T0000000000100000000000000001cssccsscTTTTI1TTTeeeFk 類似桁架單元，可以通過坐標變換將剛架單元的桿端力，桿端位移類似桁架單元，可以通過坐標變換將剛架單元的桿端力，桿端位移和單元剛度矩陣由局部坐標系轉(zhuǎn)換到結(jié)構(gòu)坐

13、標系下。剛架單元的坐和單元剛度矩陣由局部坐標系轉(zhuǎn)換到結(jié)構(gòu)坐標系下。剛架單元的坐標轉(zhuǎn)換矩陣僅需將桁架單元的轉(zhuǎn)換矩陣擴大而已，區(qū)別的是剛架結(jié)標轉(zhuǎn)換矩陣僅需將桁架單元的轉(zhuǎn)換矩陣擴大而已，區(qū)別的是剛架結(jié)點可以發(fā)生轉(zhuǎn)角，相應的桿端力包括桿端彎矩。點可以發(fā)生轉(zhuǎn)角，相應的桿端力包括桿端彎矩。考慮到轉(zhuǎn)角與彎矩考慮到轉(zhuǎn)角與彎矩在坐標轉(zhuǎn)換時不會發(fā)生變化在坐標轉(zhuǎn)換時不會發(fā)生變化8-3-3 單元的剛度矩陣的性質(zhì)與特點單元的剛度矩陣的性質(zhì)與特點323222323222000012612600646200000012612600626400eeixiiyiiijxjjyjjEAEAllEIEIEIEIuFllllvFEI

14、EIEIEIMlllluFEAEAllvFEIEIEIEIMllllEIEIEIEIllllejeeeiiiijijjijjj FkkFkkeeeeeiiiiijjeeeeejjiijjjFk k Fk k T()eeijjikkeeeFk ivijjvEAxylyiFyjFjMiMijiujuxiFxjF8-3-3 單元的剛度矩陣的性質(zhì)與特點單元的剛度矩陣的性質(zhì)與特點323222323222000012612600646200000012612600626400eeixiiyiiijxjjyjjEAEAllEIEIEIEIuFllllvFEIEIEIEIMlllluFEAEAllvFEIEI

15、EIEIMllllEIEIEIEIllllejeeeFk ivijjvEAxylyiFyjFjMiMijiujuxiFxjF120nFFFF120n1112111212222212nnnnnnnn kkkFkkkFkkkF1112121222012nnnnnnkkkkkkKkkkaaabaababbbb kkFkkFaaaabbabaabbbbkkFkkF1()aaaaabbkFkeeeFk 000FK xiiyiFFFiiiuva結(jié)點位移未知， 結(jié)點力已知。b結(jié)點位移已知， 結(jié)點力未知。aFbF例 8-14m3m20kN30kN13421. 結(jié)點、單元編號，建立結(jié)構(gòu)和局部坐標系；xy2. 建

16、立結(jié)點位移向量和結(jié)點力向量；53 10 kNEA iiiiijjjjijj FkkFkk13123400000000000000iiijjijj FkkFkk13iiiiijjjjijj FkkFkk12323400000000000000iiijjijj FkkFkk23123413FF23FF1234FFFFF3. 建立單元剛度矩陣；xiiyiFFFiiiuv例 8-14m3m20kN30kN13421. 結(jié)點、單元編號，建立結(jié)構(gòu)和局部坐標系；xy2. 建立結(jié)點位移向量和結(jié)點力向量；53 10 kNEA iiiiijjjjijj FkkFkk12433400000000000000jjji

17、ijiikkFkkF43iiiiijjjjijj FkkFkk14234200000000000000iiijjijjkkFkkF2443FF24FF12341234FFFFF3. 建立單元剛度矩陣；4m3m20kN30kN1342xy11222333344400000000FFFFFFFFFFFF33330FFFF3333FFFF11FF222FFF444FFF3F3F3F3F3F3F3F311222333344400000000FFFFFFFFFFFF12340000iiijiiiiijijjijijjjjjjjijiijiijj kkkkkkkkkkkkkkkkiiijjijjkkkk4

18、3iiijjijjkkkk13iiijjijjkkkk23iiijjijjkkkk241323432411233400000000000000iiijjijj FkkFkk12233400000000000000iiijjijj FkkFkk12334400000000000000jjjiijiikkFkkF12234400000000000000iiijjijjkkFkkF例 8-14m3m20kN30kN13421. 結(jié)點、單元編號，建立結(jié)構(gòu)和局部坐標系；xy2. 建立結(jié)點位移向量和結(jié)點力向量；111222034020kN30kN0 xyxyFFFFFFFFF1203343440000uv

19、uv53 10 kNEA 3. 建立單元剛度矩陣；4m3m20kN30kN1342xy5101000003 10kN/m101040000iiijjijjkkkkk22222222eecsccscscsscsEAlcsccscscsscsk53 10 kNEA 375037500000200kN/m375037500000 k311324240單元cos01sin 00csijijijcossincs3. 建立單元剛度矩陣；4m3m20kN30kN1342xy22222222eecsccscscsscsEAlcsccscscsscskcossincs53 10 kNEA 19214419214

20、4144108144108200kN/m1921441921441441081441083223單元cos4/5sin3/5cs516121612252525251691293 1025252525kN/m1612161252525252512912925252525iiijjijjkkkkk3. 建立單元剛度矩陣；4m3m20kN30kN1342xy22222222eecsccscscsscsEAlcsccscscsscskcossincs53 10 kNEA 單元cos/ 20sin/ 21cs/ 25000001013 10kN/m000030101iiijjijjkkkkk000005

21、000500200kN/m00000500050043344. 形成總剛度矩陣和總剛度方程1921441921441441081441081921441921441441081441083223430000050005000000050005003437503750000037503750000031132424375000375000375000375000192144144108192144144108192144144108192144144108000500000500000500000500375000375000375000375000123412340K總剛度矩陣11223344

22、0375037500000005671441921443750014410814410800200kN/m37501921445671440000014410814410805002037500037500005000500 xyxyFFFFuvuv kN30kN00375037500000567144192144375014410814410800200kN/m37501921445671440000144108144108050037500037500005000500K000K F桁架的總剛度方程5 建立桁架的結(jié)構(gòu)剛度方程3344567144000144608050020200kN/mk

23、N00375030050005000uvuv133445671440001446080500201m00375030200050005000uvuv30.35551.410m0.41.46 計算結(jié)點位移7 計算桿端力11113333375037500000200kN/m375037500000 xxiyyixxjyyjuvuv FFFFFFFF337503750026.67000000200kN/m10m=kN375037500.355526.6700001.40 4m3m20kN30kN1342xyeeeFk ijE AexyliuivjvjuyiFxiFxjFyjF7 計算桿端力31921

24、44192144026.67144108144108020.00200kN/m10m=kN1921441921440.355526.671441081441081.420.00 4m3m20kN30kN1342xy12123333192144192144144108144108200kN/m192144192144144108144108xyxyuvuv FFFFeeFTF0.80.60026.6733.330.60.80020.000kN=kN000.80.626.6733.33000.60.820.000 xiyixjyj FFFFeeeFk ixyyxxiFyiFxiFyiFixy8 計

25、算支座反力112233440375037500000005671441921443750014410814410800200kN/m37501921445671440000014410814410805002037500037500005000500 xyxyFFFFuvuv kN30kN01132237500.355526.67555001.40200kN/m10m=kN19214437500.43.33144108001.420 xyxyFFFF 9 校核112226.675550kN3.3320 xyxyFFFF4m3m20kN30kN1342xy2xF2yF1xF1yF12+30=26

26、.673.33300 xxxFFF12+20=020200yyyFFF整體平衡lll2pF1pFM123451D2D3D4D21324354vDDDD100pFMF2EI2EIEIEIyxo1 結(jié)構(gòu)標識2 建立結(jié)點位移向量和結(jié)點力向量32322232322212612664621261266264eeeiyiiijyjjjllllvFMllllEIvFllllMllll323222332322212612606462126126006264yiiyjjllllFMllllEIFllllMllll D34iEIMlD4kEIl32322243232122126126064620126126626

27、4yiiyjjllllFMllllEIFllllMllll DD414224ijMllEIMllDD4224llEIllk331414yxo123451D2D3D4D2EI2EIEIEIijxyiivjvjiMyiFyjFjM32322232322212612664621261266264eeeiyiiijyjjjllllvFMllllEIvFllllMllll3232222323232212612664620201261266264yiiyjjllllFMllllEIFllllMllllDD322322412128ijMllEIMllDD3222412128llEIllk32328448ll

28、EIllk3232223323242212612606462201261266264yiiyjjllllFMllllEIFllllMllll DD348448ijMllEIMllDD3443yxo123451D2D3D4D2EI2EIEIEIijxyiivjvjiMyiFyjFjM4EIl334224llEIll3222412128llEIll32328448llEIll3443322420024120012204024120llllEIllllllK14141322132442000241200122040024120pllFllEIlllMlllD DDD12113232211231224

29、14200214024120017411118122040276042824120pppppllF lMlF lMlFllF lMlEIEIlllF lMlMlllDDDDeeiyiiiejyjjjvFMvFMk21132212312412141741118276428ppppF lMlF lMlF lMlEIF lMlDDDD32323211221132322112212612617464620.580.05801201261262760.420.0581186264pyippipyjpjpllllFFF lMlF lMMllllEIFFEIF lMllllMF lMlllllyxo1234

30、51D2D3D4D2EI2EIEIEIijxyiivjvjiMyiFyjFjM2300yiiyjjFMFMDD例 8-3yxollllEIEIEI2EI2EI2EI2pF1pF3pF12345675D6D3D2D4D1D1 結(jié)構(gòu)標識2 建立結(jié)點位移向量和結(jié)點荷載向量4514253646576()vvvDDDDDD1230000pppFFFF例 8-3yxo12345675D6D3D2D4D1D3 計算單元剛度矩陣32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk1200120000

31、23020313000013453145135600600546004600ivjvjiivjvijEIEIEI2EI2EI2EIllllijxyiivjvjiMyiFyjFjM(4) 建立結(jié)構(gòu)剛度方程32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk120012000023020313000013453145135600600546004600123456123456yxo12345675D6D3D2D4D1DEIEIEI2EI2EI2EI312l26l26l4lEIK(4) 建

32、立結(jié)構(gòu)剛度方程32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk120012000023020313000013453145135600600546004600123456123456yxo12345675D6D3D2D4D1DEIEIEI2EI2EI2EI312l26l26l4l4l2l2l4lEIK(4) 建立結(jié)構(gòu)剛度方程32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIll

33、llk120012000023020313000013453145135600600546004600123456123456yxo12345675D6D3D2D4D1DEIEIEI2EI2EI2EI312l26l26l4l4l2l2l4l212l324l212l8lEIK(4) 建立結(jié)構(gòu)剛度方程32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk120012000023020313000013453145135600600546004600123456123456yxo123456

34、75D6D3D2D4D1DEIEIEI2EI2EI2EI312l26l26l4l4l2l2l4l212l324l212l8l324l212l212l8l324l324l212l212l212l4l212l8l324l212l212l4lEIK(4) 建立結(jié)構(gòu)剛度方程123456123456yxo12345675D6D3D2D4D1DEIEIEI2EI2EI2EI312l26l26l4l4l2l2l4l212l324l212l8l324l212l212l8l324l324l212l212l212l4l212l8l324l212l212l4l4l2l2l4lEIK32322232322212612

35、664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk120012000023020313000013453145135600600546004600(4) 建立結(jié)構(gòu)剛度方程32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk120012000023020313000013453145135600600546004600123456123456yxo12345675D6D3D2D4D1DEIEIEI2EI2E

36、I2EI312l26l26l4l4l2l2l4l212l324l212l8l324l212l212l8l324l324l212l212l212l4l212l8l324l212l212l4l4l2l2l4l33l23l23l4lEIK(4) 建立結(jié)構(gòu)剛度方程32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk120012000023020313000013453145135600600546004600123456123456yxo12345675D6D3D2D4D1DEIEIEI2E

37、I2EI2EI312l26l26l4l4l2l2l4l212l324l212l8l324l212l212l8l324l324l212l212l212l4l212l8l324l212l212l4l4l2l2l4l33l23l23l4lEIK(4) 建立結(jié)構(gòu)剛度方程32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllk120012000023020313000013453145135600600546004600123456123456yxo12345675D6D3D2D4D1DEIEIE

38、I2EI2EI2EI2l2l8lEIK360l26l0324l212l026l0324l212l08l2l2l20l212l000000212l4l4l00327l212l212l23l23l12l323321122342332322563226062412006820000220124000241227123001241212200328000pppllllFlllllllFFlllllllllllllDDDD DD結(jié)構(gòu)剛度方程例8-4EA30kNEIEI1m1m3m40.01radkADBC1 結(jié)構(gòu)標識12343D2D1Dyx2 建立結(jié)點位移向量和結(jié)點荷載向量212233vDDD300kN

39、0F =I=1.510-6m4, A=6.2510-5m2211=2 10 kNm/rad, =2 10 PakE3 計算單元剛度矩陣EA30kNEIEI1m1m3m40.01radkADBC32322232322212612664621261266264eEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllEIEIEIEIllllkI=1.510-6m4, A=6.2510-5m2211=2 10 kNm/rad, =2 10 PakE23618361818121861036183618186181222=3 10 kNmEI3D2D1Dyx3sin5sijiuivjuj

40、v22222222eecsccscscsscsEAlcsccscscsscskiviujvjuiuivjujv222222125 103( )36105/ 45EAksl2=125 10 kNEA1234113 計算單元剛度矩陣EA30kNEIEI1m1m3m40.01radkADBC12343D2D1Dyx0112011210231203236183618181218610361836181861812ekivjvjiivjvij210K12312311I=1.510-6m4, A=6.2510-5m2211=2 10 kNm/rad, =2 10 PakE2223610k183618121

41、2181866123411ijxyiivjvjiMyiFyjFjM2210k333 計算單元剛度矩陣EA30kNEIEI1m1m3m40.01radkADBC12343D2D1Dyx210K12312311I=1.510-6m4, A=6.2510-5m2211=2 10 kNm/rad, =2 10 PakE2223610k183618121218186636181818121861261234112210k330112011210231203236183618181218610361836181861812ekivjvjiivjvij3 計算單元剛度矩陣EA30kNEIEI1m1m3m40

42、.01radkADBC12343D2D1Dyx210K1231231136I=1.510-6m4, A=6.2510-5m2211=2 10 kNm/rad, =2 10 PakE1836181212181866361818181218612622223610k11332210k0112011210231203236183618181218610361836181861812ekivjvjiivjvij3 計算單元剛度矩陣EA30kNEIEI1m1m3m40.01radkADBC12343D2D1Dyx210K1231231136I=1.510-6m4, A=6.2510-5m2211=2 1

43、0 kNm/rad, =2 10 PakE18361812121818663618181812186126221218601810801810602460186142223610k11332210k0112011210231203236183618181218610361836181861812ekivjvjiivjvij4 建立結(jié)構(gòu)剛度方程122213108018301810024601061861400DDD1112231218601810801830106024600186140MDDD10.01rad 112223108018480.55851002466100.07895 m1861

44、400.6842DDD48605 計算結(jié)點位移1122123121860181080183010106024600186140MDDD6 計算桿端力1120yiiyjjFMFMDDk12343D2D1Dyx36183618018121861361836180.558518618120.07895 12230.5585100.078950.6842DDD236183618181218610361836181861812ek3.5261.4743.5265.00010.01rad 1230yiiyjjFMFMDDDk361836180.558518121860.078953618361801861

45、8120.6842 6.3685.0006.36841.368eeiyiiiejyjjjvFMvFMkijxyiivjvjiMyiFyjFjM12343D2D1Dyx7 結(jié)構(gòu)彎矩圖3.5261.4743.5265.000yiiyjjFMFM6.3685.0006.36841.368yiiyjjFMFM1.4745.0001.368ijxiFyiFxjFyjF22222222eexiiyiixjjyjjFucsccscFvscsscsEAFulcsccscFvscsscs3sin5s4cos5c4-21612161201291290.55851010161216120251291290eexiy

46、ixjyjFFFF =1.25ml2=125 10 kNEA26.8120.1126.8120.1126.8133.51cos4/5xjNFFijxyiivjvjiMyiFyjFjM|結(jié)構(gòu)的荷載 結(jié)點荷載與非結(jié)點荷載 原荷載換成與之相應的結(jié)點荷載|等效的原則：要求兩種荷載在基本結(jié)構(gòu)中產(chǎn)生相同的結(jié)點約束反力。eFeePF TeePT P局部坐標系下的單元等效結(jié)點荷載記住上冊記住上冊181頁中幾種經(jīng)典荷載所引起的固端約束頁中幾種經(jīng)典荷載所引起的固端約束力力 ，（兩端是固定端），（兩端是固定端） 將固端約束力反號，即得單元等效結(jié)點荷載結(jié)構(gòu)坐標系下單元的等效結(jié)點荷載整體結(jié)構(gòu)的等效結(jié)點荷載將結(jié)構(gòu)坐標系下單元的等效結(jié)點荷載對號入座，集成整體結(jié)構(gòu)的等效結(jié)點荷載1pF2pF2ql212ql212ql2ql12pF12pF18pF l18pF l22pF22pF/ 2