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静定结构弯矩图百题练习(15)(14)(13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)一、梁L/2L/4L/4qLqLqL2M=qLP=qLLqLqLP=qLM=PL2PLLqLP=qLMLLqLLLL2PPLLLqLPLLPP=2qLLqLPL2PLPLLL/22M=qLqLqLL(22)(21)(20)(19)二、悬臂式刚架(18)(17)(16)PPLLL/2L/2L/2L/2030PLL2M=qaP=qaP=2qaqq4a2aaa2a2aa3aM=2qaqa2aa2m2m2m1560q=102mM=PL(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa22m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa(40)(39)(38)(37)L(36)(35)三、简支式刚架aaqq2aqa2a2qaaqaaqq/2a/2qaaaa/2PLPPaaa/2aqa2(46)(45)(44)(43)(42)(41)3m4m4mqqLqLLL40kN10kN/m3m3m3m3m3maaa2aqaqaa2a2M=qaqa/2a/2a4Pa(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLLq(49)qqqqa/2a/2aa(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLL(58)(57)L/2L/28L/2L/2四、三铰式刚架(56)LM50kN0.5m4m50kN0.5m4m2mL/2LP(55)3a3a2a(54)qaqq=20kN/maa/2a/2a/2a/2PMMLLPaa2aq1.5aaaMaa1.5aqaa1.5aMaa1.5aqaaaaq2qa(59)(60)(61)(62)(63)(64)(65)(66)10L/2(70)L/2L/22q(68)2m2mL/2q2m2ma(71)aa2ma(69)2m12kN3m3m1.5m5m3m3m1.5m1.5m60kNa/2(67)aaqa/22a五、复杂刚架aLqPaa/211a/2a(76)aqqa(77)2a2a2aqLL(74)La/2(72)aPL/2(75)qL/2L/2(73)aaaPaqa2q(79)4mPq=10kN/m2m12(82)2m2m2m4m2kN2aa(80)a2aqaqaa(78)aaaaaaa(81)aaaPqaa13a2a(86)aaaa2aP(84)4X3m=12m5kN5kN5kN2m(83)2maa8m3ma/2(85)a/2qa1m1m2m2m10kNq=4kN/mq(87)2m1.5mP2m4m224m(88)P2m2m2m2m2mP2m2m2m20kN10kN/m10kN/m2m(90)2m20kN/m4m(89)4m2m40kN2m2m2m10kN/m2m2mm40kN20kN10kN/ma(95)aaa15aaaa(94)(93)2maaaaP4m2ma4mP4mL(91)LLqL(92)L003030PL/2L/2PMa16(100)aaa(98)10kN/m2m2m2mLm100kN50kN2m2m20kN2m(96)2m60kNm2m2m60kN2mm2ma2a10kN/ma/2a/2L(99)LLPLa(97)aaPM静定结构弯矩图百题练习答案22qL8qL222qLqL2482qL2qL8PL42qL2qL/8LqM=qL2L/2LLP2PLPLLqLP=2qLPLLPLqLLLP2PLLLLqLLMP=qLLqLL2PM=PLP=qLLqLqLP=qLM=qL2LqLqLqL/4L/4L/2一、梁(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)2PL9qL22PL34pL5pL3qL22M2qL2qL22+pLpL22qL225qL3qL2222qLqL2882qL5qL2323225qL8qL2qa223qa2282qa829qaPL223PL3PL3PL2PL22PLPL2mq=1060152m2m2ma2aaqM=2qa3aa2a2aaa2a4aqqP=2qaP=qaM=qa2LM=PLLP300L/2L/2L/2L/2LLPP(16)(17)(18)二、悬臂式刚架(19)(20)(21)305552022qaPL2PL22qa4qa228qa16qa215qa217qa22qL(22)22qLqa2qa2222qa22qa2qa3PL2PLPL3PLPaPa(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaqaa/2aqqaaa2PLPL2LLLLP2LLLPPaaa2Paqa/822qa/2qa22qa2qa2qa/82qaPL222qaqa222qa2cosα2qL2+2qL22cosαqL2qL2222qL90901008060100100PaPa2m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35)三、简支式刚架aaqq2aqa2a2qaa2qaqaaqq/2a/2qaaaa/2PLPPaaa/2a2Pa2Paqa227qa4(46)2.595q7qL24qL24223qL345453904806906904Pa334Pa4Pa2qa225qaqa22qa22qa22(45)(44)(43)(42)(41)3m4m4mqqLqLLL40kN10kN/m3m3m3m3m3m4Paaaa2aqaqaa2a2M=qaqa/2a/2a3qa22MM2Pa2PP2无弯矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLLMPa285qa22qa82qa88qa22qa8qqq8qa225qa8qq(49)MM2Pa2PP2无弯矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLLMPa2PLMM/2M/2M/225kN.m25kN.mPa/25qa/29qa/2(58)(57)(56)(55)(54)LL/2L/2PL/2L/2LML/2q=20kN/m50kN50kN0.5m0.5m2m4m4ma/2a/2Pa/2a/2a3a3a2aqqa2qaPa/265kN.m25kN.m25kN.mPLPLPL四、三铰式刚架22qa/32qa2qa/2PL(65)(64)(63)(62)(61)(60)(59)qaaaaq1.5aaaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/22qa/222qa/2MMMMqa2qa2/8MMMM/82qaqa2/82qa/322qa/3222qa/3qa/22PL2MMMqaM/43M/4M/2M/2M/2M/236kN.m36kN.m2q2q对称23qa/82qa/82qa/2100kN.m200kN.m300kN.m300kN.m3m1.5m1.5m(71)(70)(69)(68)(67)(66)aaaaL/2L/2L/2L/23m2m3m12kN2mq2q2m2m2m2mqa/2a/2a2aa1.5m5m3m60kN100kN.mqa/22qa/823qa/82M/2M/2M/2qq2q2q2qa22qa2qa2qL/2PaPa/4Pa/4(77)(76)(75)(74)(73)(72)五、复杂刚架qa2a2aqa/2aaaqL/2L/2L/2qLLLLaaaPaPPa/2a/2aaPaPaqL/822qL/322qa/8qa/222qaqa22qa/82qaFpa/2PaaaaaFpaaaaqqaa2a2aaqaqaaaaaP2kNq=10kN/m2m2m2m2m4m4m(78)(79)(80)(81)(82)Fpa/2对称qa222qa2qa/23qa24Pa6Pa4P-8Pa12kN.m4kN.m8kN.m80kN.m24kN.m56kN.mPa4PaPa2Pa2qa2qa/22qa/4220kN.m8kN.m(86)(85)(83)2m2m2aaaaaa2aPqa/2aqaaa/210kN1mq=4kN/m1m2m2m21.82kN.m21.82kN.m(84)5kN5kN5kN4X3m=12m3m8m-3.536kN2.27kN2.27kN-5kN-10kN10.61kN2.27kN2.27kN-5kN10.61kN-3.536kN-10kNP/2PPP/280kN.mP3P80kN.m100kN.m60kN.m30kN.m70kN.m10kN.m40kN.m30kN.m2m2m2m2m2m2m2m2m2m2m(90)(89)(88)(87)P2m2m2m2m1.5m20kN/m40kN2m2m4m4m22PP2m4m4m2m10kN/mm40kN20kN20kN10kN/m10kN/m10kN/m20kN.m20kN.m40kN.m80kN.m80kN.m2PMPa/2Pa/2Pa/2Pa/2Pa/2Pa/24P4PPL/22qL/223qL/2(95)(94)(93)(92)(91)aaaaaaaaPaaaaaP2m4m4m2m4m030030PPL/2L/2LLqLLLMMM4P4P4P4P4PPL/2M20kN.m20kN.m40kN.m20kN.m60kN.m100kN.mM-2P6P4P2PL3PLPL2Pa2m(100)(99)(98)(97)(96)aaaa/2a/2aPLLLLL10kN/m2mm2m50kN100kN2m2m2mPaaa2aa60kNmm60kN10kN/m20kN2m2m2m2m2mM5kN.m5kN.m4PL2Pa