1、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=
2、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
3、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)AR21FSALMALFSAR
4、dl1dlABEDdMALABED1FSALABED22 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/3
5、dddddBGH28ME2d/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 F0
6、FMABEF6d/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
7、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 411
8、Z ()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=1
9、ABCDl/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
10、，。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-
11、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=3
12、7.8kN/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 1239
13、0 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()0RPcrRRPcrRccFFFa
14、bccFFFab 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 0.7583538.312
15、46.07784.38RBFkN 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
16、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 /CDABqABCDayCyD
17、dxdxa)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.
18、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 Mc
19、r 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-1FRAb1biFP1F
20、PcrAxDFPiFRAb1biMD86(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 ，。FP2FP
21、cr 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 2ma
22、x1 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
23、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=1EFAKBCDEF11MCMCABCDEFAK11MKMK97
24、BCDEFAK11FSKFSKBCDEFA11FSCRFSCRBCDEFA11FSCLFSCLBCDEFA11FRBFRB98 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)
