理论力学全套解疑04

F1F2FnABRAMARBMB4-1(a)RARBMAMB4-1R=ΣFΣFRA=RBOM)(FOOmM∑=AMB(F1F2Fn)=(RAMA)=(RBMB)MAMBMB=MA+mB(RA)ARAMABRAABBRB(RB=RA=ΣF)mB=mB(RA)MAB4-1(b)MAmB(RA)MBMB=MA+MB(RA)AB)(ABABmMMR+=MBMA0)(=ABmRRA0BRA4-3BRAAB4-3R=F=0OR=∑0)(==∑FOOmM∑F=0R=F=0∑4-4F1FnA)(FAAmM∑==0∑F=0ARA(F1Fn)=RARABRBAABBdmMRR±==)(RBRA=∑FdBRA4-4ABd0MB0MBdRA=0RA0R=∑F=0xAB∑mA(F)=012ARm∑B(F)=0ABR4-5xABX=0X=Rcosα=0αRxxxABα=90cosα=0R=0ABRxABα90cosα0∑∑X=Rcosα=0R=0000===)()()(∑∑∑FFFOBAmmmABC∑mA(F)=0∑mB(F)=0ABRm∑O(F)=0m∑C(F)=Rd=0dCAB4-6CABCR=0d=0ABCRABCd≠0B=04-8X=0∑Y=0X=0m∑∑∑A(F)=0AOxOA∑X=Rx=0∑mA(F)=mA(R)=0∑mA(F)=0AO4-8∑X=0∑X=Rcosα0α9°cosαR0∑mA=0m∑B=0ABO∑mA(F)=0R0AOR4-94-9∑mB(F)=0m∑B(F)=Rd=0OABd≠0R0xX0∑4-10∑Y=0m∑O(F)=0xy4-10∑X=0∑Y=0∑mO(F)=0xX=0X0∑Y=0∑m∑∑O(F)=04-10xαα≠9°X=0∑0coscos=⋅=⋅=∑∑∑FFXααα≠9°cosα≠0F=0∑∑Y=0α≠°sinα≠F=0X=0Y=0m0sinsin=⋅=⋅=∑∑∑FFYαα∑∑∑∑O(F)=012F1F2FnF2FnF14-12(a)4-12F2Fn1R123F2FnR1F1R1F1R1R4-12(b)F2FnmmF1R4-12(c)F2FnF1FnF1F1Fn1∑X=0∑Y=0∑mO(F)=0∑mA(F)=0∑mB(F)=0X=0∑23ADE4-131(a)F1=500(N)F2=1000(N)F3=800(N)α=45°DEADADADE4-131(b)4-1310131sin4,0)(321=×−×−×−×=∑FFFNmDAαFNDND=1038(N)XAYAN)(3160sin,0)N(4460cos,02131==+−−=−==+−=∑∑ADAAAYNFFYYXFFXXαα∑mA(F)=0∑mD(F)=00113sin4321=×−×+×+×−FFFYAαYA=316(N)∑X=0∑Y=0yAD∑mA(F)=0m∑D(F)=0011cos3sin14,0)(211=×+×−×+×+×−=∑FFFXYmAAEααFXA=-446(N)4-132(a)ABClF1F2F3FABCABC4-132(b)ABC4-13202223,0)(13=++=∑lFlFlSmCAFFSC332−=02223,0)(32=−+=∑lFlFlSmABFSA=002223,0)(12=−−=∑lFlFlSmBCFFSB332=ABCmNmNM=60(kN⋅m)CP=20(kN)AB4-151aAB4-151bABXAYANBAB4-152(a)BPP=20(kN)4-152(b)XAYAXDYD4-1514-152mNmn450(N)ABABABC4-153aAB=lAD=0.4lOAB4-153bc4-153ABOOABOAB2+3=5NENDXAYANBC5NDN′DABBCBA4-154(a)M=20(kN⋅m)q=15(kN/m)ABBCABBC4-154bc)ABBCXAYAmAXBYBXCYC4-154P=2(kN)4-155(a)AB=CDEGHCDFGIABGD=GB=DBABCD5-155bcABCDCD(1)0,0=′+−=∑XHEFGNNXX(2)0,0=′−+=∑HYGDNYNY(3)060cos60sin,0=⋅−⋅−⋅′−=∑DDGDNGENGHNmDEFHGAB(4)0,0=′−+′=∑IXFEGNNXX(5)0,0=′−′−=∑IYGBNYNY(6)060cos60sin,0=⋅+⋅+⋅=ΣDDGBNGFNIGNmBFEIG4-155(7)0,0=−=∑HXIXNNX(8)0,0=−+=∑PNNYHYIY(1)(4)(7)(7)HXIXNN=EFFEEFNN=(4)10=′−−′IXFEGXNXNEFNFENHXNIXGGHXXHXHEGXXNNNNX′=′==−−,(0(1)(1)(4)(7)X=0∑4-16(a)ACBC4-16(b)(c)1ABC4-162ACBCABABC3PACBCMBCACACACBCACBCABACDE4-171(a)DEEM=1(kN⋅m)AD=BD=0.5(m)BCDFBCABDEABACACDEDFABDEABAXDDEYDYFXF4-171b4-171)km(10,00,0)km(10,0)(−=−==+======−×=∑∑∑CBCBBCCBNYNYYXXBCΜNMBCNmFAB4-171c00,0)(==⋅+⋅=∑DDBAXADXABXmFDE4-171c)kN(20,0)kN(20,0)(00,0F===−====−⋅===+−=∑∑∑FDDFFFDFDYYYYYDFMYMDFYmXXXXF4-172(a)ACDFBFECABCDEFADBFECXAYAXDYD)ACDFDFACDFDF4-172b(1)01524062,0=⋅+×−=∑DAXmXD=5.34(kN)(2)0,0=+=∑ADXXXXA=−XD=−5.34(kN)(3)02,0=−+=∑DAYYYDF4-172c0203212032152,0=⎟⎠⎞⎜⎝⎛+−=∑DDGYXm(4)YD=1.33(kN)YD(3)YA=0.67(kN)4-1724-173(5)0coscos,0=−+=∑ααBFECDNNXX8.0765.1015.101cos22=+=α(6)0sinsin,0=++=∑ααBFECDNNYY6.0cos1sin2=−=αα56)kN(23.2)kN(45.4=−=BFECNN4-173aABCDTGABCD=2bCK=hAC=HFABaFXCYCNDBDFABACACABAC4-173bTHhXHXhTmAAC−==⋅+⋅=∑0,0)(FAB4-173c0,0=+=∑FXXATHhXFA=−=n2nmNmNmN2nmN2n14-19a24-19b34-19c4-194-20(a)AC1234(b)CD56(c)CD311E1181394-21(b)1(a)1(c)4-214-23(a)DDP12C34E564-23(b)NAA12C34E56D7891011121314154-23(a)4564564-23cP4564-23(d)678ABNANB6784-23d6784-23?4-241(a)F1=F2=F4=F5=30(kN)F3=40(kN)678NA4-24(b)05.765.435.19,012345=×−×−×−×−×−×=∑FFFFFNmABNA=80(kN)4-241m-m4-241(b)4-241(c)03sin35.1,0821=×−×−×−=∑βSFFmA2225.12sin+=βS8=56.3kN4-24205.435.12,0127=×−×+×+×=∑AFNFFSmS7=112.5(kN)0cos5.13,061=⋅−×+×−=∑DESFNmADα5.432,5.425.4cos22×=+=DEαS6=160(kN)4-242(a)ABABLNL4-242(b)ABKKSAB4-242(b)0322,0)(=⋅−⋅−⋅=∑aPaPaNmLJFPNL25=4-242(c)0323,0)(=⋅+⋅−⋅−⋅=∑aNaPaPaSmLABKFPSAB65=4-25(a)GECDACDEHGHHE1GECDCA4-25(b)4-25(c)04403804sin3cos,0)(=×+×−⋅−⋅−=∑ααGEGECSSmFSGE=−16.7(kN)040sin,0=−+=∑αGECDSSXSCD=50(kN)4-250cos80,0=−−−=∑αGEACSSYSAC=−66.7(kN)2DEE4-25(d)0sin,0=′−−=∑αGEDESSXSDE=−S′GEsinα=10.6(kN)