结构力学影响线解析ppt课件.ppt
12 3FP1FP2FP3FP4a1a3a2ba4qCMC M , FS , FN, 4AB F = 1 5F = 1xlFRA,(0)0RABMlxFFxll 。 F = 1A FRA (0)RAlxFxll FRA FFRAlxl RAFOxBA6 x y RAF xFRA RAFxyFRA1yOBA7FP1FP21122RAPPFyFyF 。 FRA xFRA1y1y2yOBABA8ZZF ZZF ，。Z F Z Z F Z F = 1 Z Z Z 9FN ：M ：FS 10 Zx Z11FRA1BAFRB1BAx0(0)RBAlFxlMxl 。，0(0)RABxFlMxl ，。F = 1xlabCRAFRBFOBA12 F = 1 SCFCMRAFaCA00()()CRASCRACyMFMFaaxlFFaxl 。，。，F = 1CMSCFRBFbBC(0)00()0CRBSCRBCyMFMFbxaFFxa ，。13MC abablBACFSCal11blBAC14xF = 1ACablBablMCACB x=aF = 1ACablBablM ACBblalFSCACBblalFS ABC15x xxyy F = 1y F = 1 16C F = 1 FSCF = 1FSCLFSCRblalFSCL=AblblCBFSCR= al CalFSC 11blalCBA17 FRA及及FRB。()RARBlxxFFlldxl d ，。00BAMM 由由及及得得：lxF = 1ACabBddEDRAFRBFx1FRA 1dl dlABED1dl dl1FRB ABED18F = 10()0()CCRBySCRBMMFbdxaFFFdxa ，。，。 F = 10()0()CCRAySCRAMMF aaxldFFFaxld ，。，。CMSCFRBFbBCdEa)dADaCb)RAFSCFCM19 MCFSCFSARA FSARMC adlbdlablABEDFSC dlblaldlABED20FSAR(0)SARRAFFxld ， F = 1 F = 1 0SARRBFFdx ，ARdDARMSARFRAFb)lBdERBFSARFARMa)AR21FSALMALFSARdl1dlABEDdMALABED1FSALABED22 ABF = 1ABZ KZ MK F = 1ACDKxBxO23MK F = 1CD,KKMyMy。F = 1C, DMKAKBa)yDyCCDdCDKF = 1x dxd xd b)BA24DCKCDCyydxxMyyyxdddfx （）。 x MK C，DKMx MK MKACKDByCyDc)25K Z FSKFSKACKDBycyd26BF = 1ACDxFEd/2d/22d/3dddddGHd/23d/4MCd/2d/21/31/2FSC1/31/31/2275d/6d/35d/12MDFSD1/61/35/62/3d/2d/2F = 1ACDxFE2d/3dddddBGH28ME2d/31/32/3FSFR1/3FSFL1/31/32/31/3Bd/2F = 1ACDxFEd/22d/3dddddGH29 F = 1 F = 1 301, 2FN1 , , FN2 FRA , , FRBF = 1F = 1RAFRBFAEF21BCD5dIIh3101(/013 )NRBFFFFdMMhh ，。011(02 )/ NRAFFFFdMMhh ，。FN1 F = 1CI-I F = 1DI-I F。0FMABCD2d/h3d/h0.9d/hd/hFN16d/5h3201(/013 )NRBFFFFdMMhh ，。011(02 )/ NRAFFFFdMMhh ，。FN1 F = 1EI-I F = 1FI-I F0FMABEF6d/5hFN12d/h3d/h6d/10h33FN2 F = 1CI-I2222040NyRBFFhFhd ，2222024422NRBSCDhdhdFFFhh 。0SCDFCDhd/22242hd 342222040NyRAFFhFhd ，2222024422NRASCDhdhdFFFhh 。 F = 1 DI-Ihd/22242hd 0SCDFCDABCD223 420hdh 2242hdh FN22242hdh 2244hdh 35FN2 F = 1EI-I22220244220NRBSEyFhdhdFFFFhh ，。22220244220yNRASEFhdhdFFFhhF ，。 F = 1 EI-I0SEFFEFABEFFN22242hdh 2242hdh 22410hdh 223 410hdh 36F = 1xl/4l/4lAB ABFRB 37 Z Z 0ZPZFx （ ）。P 图图F = 1xZ ()Px 14Z 54Z ABRBZF RBF RBZF F ZZ Px （ ）PFx （ ）Px （ ）38( )PZxZ 。1Z ，( )PZx 。Z1Z P P 1454AB1FRB39CMCFSC F = 1ABC2ddddxMC CCCMP CM40: : ( )( )00)0( )()CPPPPCCCZCZMMFxFxFxxMMM ，。2Zd Z3d Z 23Zd 23Zd ( )Px CMP 图图ABC1F 411Z ()CPMx 。1Z P MCFSC CCP SCFSCFMC23d23d3dCBA42: : 12()3300( )( )( )SCZZSCPPZSCZPFxFFxFFx ，。Z 13Z ( )Px SCFP 图图13Z ABC1F 23Z 13Z Z SCFSCFCC431Z P FSC 1Z P( )SCFx 2313FSC1313ABC44xF = 1ABCDl / 2l / 2l / 2l / 2E1/21FRAABEDCABZ 12Z RAF( )Px P 图图DEC45MB/ 2lACBDE11/2FSBLACBLEDACDZ BBMP 图图/ 2Zl EDABLZ /2Z /Zl SBLF/Zl P 图图EC46xF = 1ABCDl / 2l / 2l / 2l / 2EFSBR1DEBRCASBRFZ ADBRCP 图图E47 Z ZCMC MC 0.253m1mA1m 1mB0.750.75MCC480.3750.7501015203.75.2511.25 520CMkN m ：131.12502.75BBCCCBCMqydxqydxqdqqq 0.250.3750.253m1mA1m 1mB0.750.75MCCqCBC0.5m2m20kN15kN10kNB49 我们ZmaxZmin Z Zmax Zmin FSC FP Ca/lFSCABb/lC50 MC FPCEmaxmaxminmin()()CPCPMFyMFy ，。 ZmaxZminmaxmin(),()SCLPSCRPbaFFFFll 。ADBymaxyminMCCE51max1min23()()()CCMqMq ，。q(MC) max(MC) minqq132ADBMCCE52 Z53 FP1FP2FR1FP3FP4FR2FP5FP6FR3Z Z xxxx1y 1y2y 3y 2y3yZy 1 2 3 5411223366.PPPPPiiZF yF yF yF yF y 112233RRRRiiZFyFyFyF y xZ xxiyiyiiyxtg Z 3311RiiRiiiiZFyxF tg 31RiiiZF tgx 1230,0,0 55 Z xZ-x Z/xZ/xxZ+-+00-xZ-+-00+ Z x00RiiF tg x0，即即稍稍向右移，向右移， 。0RiiF tg 当当x0，即即稍稍向左移，向左移， 。0RiiF tg ZFRiFRi FPcr FPcr FRi RiiF tg R iiFtg itg 57112RPPPcrFFFF 245RPPFFF112RPPFFF245RPcrPPFFFF FP1FP2FR1FPcrFP4FP5FR2 FPcr RiiZF tgx FP5FP1FP2FR1FPcrFP4FR258 RiiZF tgx FPcr FPcr FPcr R iiFtg Z Z Zmax Zmin PcrF59Z q=37.8kN/m, FP1=FP2=FP3=FP4=FP5=90kNFP1FP2FP3FP4FP5qaaaaaa=1.5m30mZ 6m4m8m1310.75260FP4 。12310.250.75,84()6tgtgtg RiiF tg Z 6m4m8m10.750.810.9063 2 1 FP1FP2FP3FP4FP5qaaaaaa=1.5m6m3.5m16112390 3270,90 237.8 1217.8,37.8 6226.8,10.250.75270217.8226.88.20846RRRRiiFkNFkNFkNF tgkN 。12310.250.75,846tgtgtg 12390 43609037.8 1127.837.8 6226.810.250.75360127.8226.88.70846RRRRiiFkNFkNFkNF tgkN ，。62 FP4RiiF tg Z 3.556.590(1)900.9068880.810.750.75637.8(1)22258.7581.54114.53454.82ZkN FP463 ZZ0R iiFtg 0R iiFtg ()0RPcrRFtgFFtg 左左右右()0RPcrRFFtgFtg 左左右右FP1FP2FR左左FPcrFP4FP5FR右右abc64tg =c/atg = -c/b()0()0RPcrRRPcrRccFFFabccFFFab 左左右右左左右右PcrRRRRPcrFFFabFFFab 右右左左右右左左FPcr FPcr()0RPcrRFtgFFtg左左右右()0RPcrRFFtgFtg左左右右65FRBFP1=FP2=478.5kN，FP3=FP4=324.5kN。FRBFP2FPcr 0.75mFP1FP2FP3FP45.25m1.45m4.55m0.25mFRB0.1256m6m1ABC0.7583662 478.5324.5(159.554.08)66478.5478.5 324.5(79.75 133.83)66 ，。，。FP2478.5 (10.125)324.5 0.7583538.31246.07784.38RBFkN 67478.5324.5324.5(133.8354.08)66478.52 324.5(79.75108.17)66 ，。，。FP3FPcrFRB0.26m6m1ABC0.75830.70mFP1FP2FP3FP44.55m1.45m4.80m1.20m68max()784.38RBFkN 。FP3478.5 0.7583324.5 (10.2)362.85389.40752.25RBFkN。69MCq=92kN/m， FP1=FP2=FP3=FP4=FP5=220kN。FP1FP5q18.5m51.5m10ABC20m20mMC70FP5FPcr5 22092 18.5, (5585.1)2020220 422092 18.5(4496.1)2020。，。FP571max5220929220,1100921840,8.042020()22053.73928.047.999220 10/ 241035910920019213CxxxmMkN m 。FP1FP5q20m51.5mx=8.04m4.46m10ABC20m20m3.735.98MC72 CDyDdxyCdxa）aqABCDyCyD73所以所以 ()()DCDCdZq y dxy dxdZq yydx ，。令令 0dZdx ，()0,DCDCq yyyy 。即即故故 /CDABqABCDayCyDdxdxa)qABCDaaEb)74 b)75 Z Zmax Zmin ZmaxZmin76 Zmax Zmin ZZmax Zmin Zmax Zmin 77(FS)max=82(0.7+0.575+0.283-0.0083)=127.07kN12m3.5m3.5m82kN82kN82kN82kN1.5m3.5m3.5m82kN82kN82kN82kN3.4m1.5m0.1m8.4m3.6m0.70.5750.30.2830.008378(FS)min= -82(0.3+0.0083)= -25.28kN3.5m82kN82kN0.1m82kN8.4m3.6m0.70.5750.30.2830.008379kN17915394.31272126541.725.316.48.2017915394.31272126541.725.316.48.2080kNm5.625m6.375m21536646555957457821536646555957881 82FRFPcr()0)0(RARRABRF lFlxaFFlxlMa ，。AD1 11 1(.)()(.)0DRAPPiiRcrcrPPiiDMFxF bF bFlxa xMlMF bF bM ，。b1FP1FPcrFRFPnl/2l/2ACxBa/2a/2DFPiFPn-1FRAbiFP1FPcrAxDFPiFRAb1biMD83 Mcr D D (2)0DRdMFlx adxl 2lax MD FPcr FR a FPcr aDCFPcr FPcr FPcr FR a84max2()()()22()2RDcrRcrRcrFMlxa xMlFlalalaMlFlaMl 2max2(),RDcrFMxMallx 。 FR FPcr a0。2lax 85() 0)0(RARRABRF lF lx aFFlxlMa ，。AD1 11 1(.)()(.)0DRAPPiiRcrcrPPiiDMFxF bF bFlxa xMlMF bF bM ，。FP1FPcrFRFPnl/2l/2ADxBa/2a/2CFPiFPn-1FRAb1biFP1FPcrAxDFPiFRAb1biMD86(2)0DRdMFlxadxl 。2lax a0 2lax max2()()()22()2RDcrRcrRcrFMlxa xMlFlalalaMlFlaMl 。2max)2(RDcrFMxMllax ，。87FPcr FPcr FR FR FPcr (MD)max 88例例5-5-1 求求图示简支梁图示简支梁的的绝对最大弯矩，绝对最大弯矩，已知已知: : FP1=FP2=FP3=FP4= 280280kN。合力合力为为:280 41120RFkN 荷载位置荷载位置如如图示，图示，FR FPcr0.72()/2(120.72)/25.64amxlam ，。FP2FPcr FP1FP3FRFP46m6mADB0.36m0.36mCFP2 =FPcr0.84m4.8m4.8m0.12m0.72m 8921 max1120()5.64280 4.82968.91344121624.9DMkN m。 FP2 图所示。此时图所示。此时 FP4 已已移到移到梁外。梁外。280 3840RFkN 。840280 4.8280 1.441.12ddm ，。d 为为FR FP2 FP1FP3FRFP46m6mADB0.56m0.56mCFP2 =FPcr1.76m4.8m4.0m0.8m1.44m 9022max840()6.562804.8121668.35DMkN m 2max1 max()()DDMM max1668.35MkN m FR FPcr 1.12 ,()/2(121.12)/26.56amxlam 。915-6 92 Z1=FRC ABCDxFP =1ABDxFP =1Z1 =FRCCFRCZ1=FRCn-1=29311110PZZ1=1Z1FP=1Z1ABDxFP =11PCABD11CP1Z1 =FRC =1P194于是力法方程成为：11111111( )0PPxZZ 上式中P1是x的函数，是Z1=1引起的在移动荷载FP=1方向上的位移。与FP=1同向为正，反向为负，见图b)。11为常数。11PP3) 由位移互等定理可得： 。ABD11CP1Z1 =FRC =1P1图图ABDZ1 =FRCb)c)95则 。上式中，令 ，111)(11xZP 由上式可见，Z1影响线与P1(x)曲线形状相同，只是正负号相反。Z1影响线见上页图c)。小结：1）撤除与Z1相应的约束，使原结构成为n-1次超静定结构。2）使体系产生沿Z1的正方向产生位移，作结构在Z1=1作用下的挠度图，该图即为P1(x)图。Z1影响线形状与P1(x)图形相同，只是正负号相反。3）求出11与P1(x)，即可求得Z1-x的函数关系，也就求出了Z1的影响线。96例例5-6-1 画出画出图示连续梁影响线图示连续梁影响线的的形状。形状。BCDxFP =1EFAKBCDEF11MCMCABCDEFAK11MKMK97BCDEFAK11FSKFSKBCDEFA11FSCRFSCRBCDEFA11FSCLFSCLBCDEFA11FRBFRB98 99maxmaxminmin()()ZZZZZZ 恒恒活活恒恒活活100BCDFG =66kNAFGFGFGFGFG435621121.277.2131.633.3121.277.2131.6 (kNm)BCDFP =109.8kNAFP435621225.9177.3145.885.112.124.136.224.5 (kNm)101BCDAFP43562136.573.0109.5165.036.573.0109.5(kNm)FP =109.8kNBCDFP =109.8kNAFP435621225.9177.3145.885.112.124.136.224.5 (kNm)1021max1minmaxmin()121.2225.912.1359.2()121.236.584.7()131.636.295.4()131.6145.8109.5386.9BBMkNmMkNmMkNmMkNm BCDA435621359.2278.6386.9198.34.284.795.476.3 (kNm)
