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1、(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=qLqL(1)P作用下的M圖:qL2q作用下的M圖:221qL223qLP與q作用下的M圖:(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=qLMLLqLLLL2P
2、PLLLqLPLLPP=2qLLqLPL2PLPLLL/22M=qLqL(2)P作用下的M圖:qL2q作用下的M圖:221qLP與q作用下的M圖:221qL(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=qLqL(3)P作用下的M圖:q作用下的M圖:221qL24qL25 . 4 qLP與q作用下的M圖:直線與曲線相切22qL(15)(14)(13)(12)(
3、11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)一、梁L/2L/4L/4qLqLqL2M=qLP=qLLqLqLP=qLM=PL2PLLqLP=qLMLLqLLLL2PPLLLqLPLLPP=2qLLqLPL2PLPLLL/22M=qLqL(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=qLqL(15)(14)(13)(12)(11)(10
4、)(9)(8)(7)(6)(5)(4)(3)(2)(1)一、梁L/2L/4L/4qLqLqL2M=qLP=qLLqLqLP=qLM=PL2PLLqLP=qLMLLqLLLL2PPLLLqLPLLPP=2qLLqLPL2PLPLLL/22M=qLqL(4)(5)(6)從右向左作M圖:PLPL從右向左作M圖:223qL225qL221qL281qL從右向左作M圖:PLPL(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=qLMLLqLLLL2PPLLL
5、qLPLLPP=2qLLqLPL2PLPLLL/22M=qLqL(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=qLqL(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=qLMLLqLLLL2PPLLLqLPLLP
6、P=2qLLqLPL2PLPLLL/22M=qLqL(7)(8)(9)利用對(duì)稱性作M圖:221qL221qL281qL利用反對(duì)稱性作M圖:M21M21先計(jì)算支反力,再作M圖:qL41241qL281qL(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=qLqL(15)(14)(13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)一
7、、梁L/2L/4L/4qLqLqL2M=qLP=qLLqLqLP=qLM=PL2PLLqLP=qLMLLqLLLL2PPLLLqLPLLPP=2qLLqLPL2PLPLLL/22M=qLqL(10)(11)(12)疊加法作M圖:1.先考慮力偶作用PL2PL2.再疊加P的作用PL41先計(jì)算支反力,再作M圖:P34P35PL34PL35先計(jì)算支反力,再作M圖:kN4 . 1kN6 . 04 . 26 . 11 . 06 . 1(13)(14)(15)作M圖,只需計(jì)算C截面彎矩Fl21作M圖,只需計(jì)算C截面彎矩221qa曲線在B點(diǎn)與水平線相切281qa不用計(jì)算支反力,可快速作M圖3030(16)(1
8、7)(18)先計(jì)算支反力,再作M圖:F31FaFa31直接作M圖:2qa289qa直接作M圖:601020(19)(20)(21)CD段直接作M圖,AC段采用疊加法:2qa221qa相切力偶只影響B(tài)D段,直接用疊加法作M圖:2qa2qa力偶只影響B(tài)C段,力只影響AC段,作M圖:22qa2qa不與水平線相切aaaaaaam(22)從附屬部分開(kāi)始,直接作M圖:mmmmqLL(22)(21)(20)(19)二、懸臂式剛架(18)(17)(16)PPLLL/2L/2L/2L/2030PLL2M=qaP=qaP=2qaqq4a2aaa2a2aa3aM=2qaqa2aa2m2m2m1560q=102mM=
9、PL(23)從附屬部分開(kāi)始,用“局部懸臂梁法”直接作M圖:2481aq24qa相切28qa216qa215qa25 . 8 qa2381aq(24)(25)(26)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+pLp
10、L22qL225qL3qL2222qLqL2882qL5qL2323225qL8qL2斜梁各截面彎矩值與所對(duì)應(yīng)簡(jiǎn)支梁一樣,作M圖:所對(duì)應(yīng)簡(jiǎn)支梁為: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+pLpL22qL225q
11、L3qL2222qLqL2882qL5qL2323225qL8qL2(27)(28)qL22(22)Lq2217qa215qa216qa8qa224qa2qa2PL2PL23qaqa222055530(21)(20)(19)二、懸臂式剛架(18)(16)PPLLL/2L/2L/2L/2030PLM=PLL2M=qaP=qaP=2qaqq4a2aaa2a2aa3aM=2qaq2m2m2m1560q=102mPLPL22PL23PL3PL3PL22PL9qa28a2aa228qa(17)用“局部懸臂梁法”直接作M圖,P力通過(guò)截面以上部分還有力偶,所以彎矩不為0:用“局部懸臂梁法”直接作M圖,P力通
12、過(guò)截面彎矩為0(29)(30)qL22(22)Lq2217qa215qa216qa8qa224qa2qa2PL2PL23qaqa222055530(21)(20)(19)二、懸臂式剛架(18)(16)PPLLL/2L/2L/2L/2030PLM=PLL2M=qaP=qaP=2qaqq4a2aaa2a2aa3aM=2qaq2m2m2m1560q=102mPLPL22PL23PL3PL3PL22PL9qa28a2aa228qa(17)與桿件軸線相切用“局部懸臂梁法”直接作M圖,P力通過(guò)截面彎矩為0用“局部懸臂梁法”直接作M圖(31)(32)用“局部懸臂梁法”直接作M圖:Pl21注:P力通過(guò)點(diǎn)彎矩為
13、0Pl21Pl21PlPl2Pl2Pl注:P力通過(guò)點(diǎn)彎矩為0用“局部懸臂梁法”直接作M圖:(33)(34)(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2PaPaPa2AB注:AB段彎矩為常數(shù)。(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2PLPLPL3用“局部懸臂梁法”直接作M圖:用“局部懸臂梁法”直接作M圖:(35)(36)(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaP
14、L2LLLLP2LLLPPaaa2PLqa2PL2PLPL3(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa22qa221qa281qa(37)(38)(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa22qa2qa221qa與桿件軸線相切(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2221qa221qa2qa2m2m2m(34)(33)
15、(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa8010060100(39)(40)22qaqa222qa2cos2qL2+2qL22cosqL2qL2222qL90901008060100100PaPa2m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa(41)(42)22qaqa222qa2cos2qL2+2qL22cosqL2qL2222qL90901
16、008060100100PaPa2m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa3315(43)(44)415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35)三、簡(jiǎn)支式剛架aaqq2aqa2a2qaa2qaqaaqq/2a/2qaaaa/2PLPPaaa/2a2Pa2Paqa227qa4(45)(46)(47)支座B無(wú)反力,AB段無(wú)變形2m2m2m(34)(33)(32
17、)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaaBAPaPa180180不用計(jì)算支反力,直接作M圖AB計(jì)算A支座水平反力,即可作M圖155 .2284515(48)(49)415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35)三、簡(jiǎn)支式剛架aaqq2aqa2a2qaa2qaqaaqq/2a/2qaaaa/2PLPPaaa/2a2Pa2Paqa227qa4計(jì)算A支座水平反力,即可作M圖ABABA、B支座無(wú)
18、水平反力,直接作M圖(51)(50)415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35)三、簡(jiǎn)支式剛架aaqq2aqa2a2qaa2qaqaaqq/2a/2qaaaa/2PLPPaaa/2a2Pa2Paqa227qa4無(wú)水平支反力,直接作M圖無(wú)水平支反力,直接作M圖(52)(53)(46)2.595q7qL24qL24223qL345453904806906904Pa334Pa4Pa2qa225qaqa22qa22qa22(45)(44)(43)(42)(41)3m4m4mqqLqLLL40kN10k
19、N/m3m3m3m3m3m4Paaaa2aqaqaa2a2M=qaqa/2a/2a3qa22先計(jì)算A支座水平支反力,再作M圖ABAB先計(jì)算B支座水平支反力,再作M圖(54)(55)(46)2.595q7qL24qL24223qL345453904806906904Pa334Pa4Pa2qa225qaqa22qa22qa22(45)(44)(43)(42)(41)3m4m4mqqLqLLL40kN10kN/m3m3m3m3m3m4Paaaa2aqaqaa2a2M=qaqa/2a/2a3qa22先計(jì)算支反力,再作M圖先計(jì)算支反力,再作M圖(57)(56)(46)2.595q7qL24qL24223
20、qL345453904806906904Pa334Pa4Pa2qa225qaqa22qa22qa22(45)(44)(43)(42)(41)3m4m4mqqLqLLL40kN10kN/m3m3m3m3m3m4Paaaa2aqaqaa2a2M=qaqa/2a/2a3qa22先計(jì)算支反力,再作M圖先計(jì)算支反力,再作M圖MM2Pa2PP2無(wú)彎矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLLMPa2先計(jì)算支反力,再作M圖無(wú)支反力,直接作M圖(58)(59)(60)(61)MM2Pa2PP2
21、無(wú)彎矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLLMPa2AA處無(wú)支反力,直接作M圖利用反對(duì)稱性,直接作M圖105105105105(62)(63)先計(jì)算A或B處支反力,再作M圖AB、CD段沒(méi)有彎曲變形,直接作M圖MM2Pa2PP2無(wú)彎矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLLMPa2ABABCDAPLMM/2M/2M/225kN.m25kN.mPa/25qa/
22、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、三鉸式剛架AAB以B為矩心,計(jì)算A處水平支反力,再作M圖計(jì)算A處支反力為0,直接作M圖(64)(65)(66)(67)MM2Pa2PP2無(wú)彎矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLLMPa2PLMM/2M/2M/225
23、kN.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、三鉸式剛架B、A處無(wú)水平支反力,直接作M圖AABB、A處無(wú)水平支反力,AC、DB無(wú)彎曲變形,EC、ED也無(wú)彎曲變形ABCDEA圖。支座水平反力,即可作計(jì)算出段彎矩為常數(shù)。點(diǎn)為直線,彎矩圖過(guò)向相反;支座反力大小相等,方、特點(diǎn):MADECBA圖。即可作支座水平反力,或。計(jì)算出處彎矩為圖對(duì)稱,荷載,特點(diǎn):對(duì)
24、稱結(jié)構(gòu),對(duì)稱MBACM0PLMM/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、三鉸式剛架(68)(69)ABCDEABCPL41PL41A圖。支座水平反力,即可作計(jì)算出形。為二力折桿,有彎曲變形;為二力桿,沒(méi)有彎曲變特點(diǎn):MBCBAC22qa/32qa2qa/2PL(65)(64)(63)(62)(61)(60)(59)qaa
25、aaq1.5aaaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/22qa/222qa/2MMMMqa2qa2/8MMMM/82qaqa2/82qa/322qa/3222qa/3qa/22PL2MMMqa(70)(71)ABABC圖。即可作支座水平反力,或。計(jì)算出處彎矩為圖對(duì)稱,荷載,特點(diǎn):對(duì)稱結(jié)構(gòu),對(duì)稱MBACM0CA22qa/32qa2qa/2PL(65)(64)(63)(62)(61)(60)(59)qaaaaq1.5aaaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/22qa/222qa/2MMMMqa2qa2/8MMMM/82qaqa2/82qa/322
26、qa/3222qa/3qa/22PL2MMMqa(72)(73)ABCABC圖。即可直接作。處彎矩為。也反對(duì)稱,稱荷載,反力特點(diǎn):對(duì)稱結(jié)構(gòu),反對(duì)MCXXBA00圖。即可直接作處彎矩為。,列平衡方程計(jì)算得力很重要,特點(diǎn):計(jì)算支座水平反MCXXAB000圖。,即可直接作彎矩為、。彎矩圖對(duì)稱。也對(duì)稱,荷載,反力特點(diǎn):對(duì)稱結(jié)構(gòu),對(duì)稱MBAYC00圖。,即可直接作彎矩為處、彎矩圖對(duì)稱。荷載,特點(diǎn):對(duì)稱結(jié)構(gòu),對(duì)稱MCBA022qa/32qa2qa/2PL(65)(64)(63)(62)(61)(60)(59)qaaaaq1.5aaaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/22qa/2
27、22qa/2MMMMqa2qa2/8MMMM/82qaqa2/82qa/322qa/3222qa/3qa/22PL2MMMqaABCABC(74)(75)22qa/32qa2qa/2PL(65)(64)(63)(62)(61)(60)(59)qaaaaq1.5aaaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/22qa/222qa/2MMMMqa2qa2/8MMMM/82qaqa2/82qa/322qa/3222qa/3qa/22PL2MMMqa(76)ABC圖。,即可直接作彎矩為,計(jì)算出方程,為矩心,列寫力矩平衡。以征得為二力折桿,由幾何特特點(diǎn):MCXAXYCBBBB0(77
28、)(78)M/43M/4M/2M/2M/2M/236kN.m36kN.m2q2q對(duì)稱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/2qq2q2qABCABC圖。即可直接作的水平反力,或,計(jì)算出彎矩為、。彎矩圖對(duì)稱。也對(duì)稱,荷載,反力特點(diǎn):對(duì)稱結(jié)構(gòu),對(duì)稱MBABAYC00圖。即可直接作的水平反力,或計(jì)算出
29、,彎矩為、特點(diǎn):MBACBA0830031003100A(80)(79)M/43M/4M/2M/2M/2M/236kN.m36kN.m2q2q對(duì)稱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/2qq2q2qABCABC圖。即可直接作的水平反力,、計(jì)算出,彎矩為、特點(diǎn):MBACBA0圖。即可直接作的水平反
30、力,、計(jì)算出,彎矩為、特點(diǎn):MBACBA0圖。即可直接作,彎矩為、,計(jì)算出方程,為矩心,列寫力矩平衡。以征得為二力折桿,由幾何特特點(diǎn):MCBAXAXYCBBBB0(82)(81)M/43M/4M/2M/2M/2M/236kN.m36kN.m2q2q對(duì)稱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/2qq
31、2q2qABCABCM圖。即可直接作,彎矩為、,計(jì)算出方程,為矩心,列寫力矩平衡。以征得為二力折桿,由幾何特特點(diǎn):MCBAXAXYCBBBB02(84)(83)2qa22qa2qa2qL/2PaPa/4Pa/4(77)(76)(75)(74)(73)(72)五、復(fù)雜剛架qa2a2aqa/2aaaqL/2L/2L/2qLLLLaaaPaPPa/2a/2aaPaPaqL/822qL/322qa/8qa/222qaqa2ABCDEABCDEE圖。即可直接作段沒(méi)有彎曲變形,、形,為二力桿,沒(méi)有彎曲變。彎矩圖對(duì)稱。也對(duì)稱,荷載,反力特點(diǎn):對(duì)稱結(jié)構(gòu),對(duì)稱MCEDCABYC0圖。即可直接作水平反力,內(nèi)力、支
32、座計(jì)算出段沒(méi)有彎曲變形。形,為二力桿,沒(méi)有彎曲變特點(diǎn):MDABBEAB圖。即可直接作為斜梁。沒(méi)有彎曲變形,為二力桿,、特點(diǎn):MACBCABE2qa22qa2qa2qL/2PaPa/4Pa/4(77)(76)(75)(74)(73)(72)五、復(fù)雜剛架qa2a2aqa/2aaaqL/2L/2L/2qLLLLaaaPaPPa/2a/2aaPaPaqL/822qL/322qa/8qa/222qaqa2(85)(86)ABCABC圖。即可直接作桿如同簡(jiǎn)支梁。,處彎矩為、特點(diǎn):MACCBA02qa22qa2qa2qL/2PaPa/4Pa/4(77)(76)(75)(74)(73)(72)五、復(fù)雜剛架qa
33、2a2aqa/2aaaqL/2L/2L/2qLLLLaaaPaPPa/2a/2aaPaPaqL/822qL/322qa/8qa/222qaqa2E(87)(88)ABCDEABCD。處彎矩為、為二力桿,為懸臂剛架,基本部分為外伸梁,附屬部分,特點(diǎn):0CAACCDEAB相切,彎矩圖在處彎矩為、。為懸臂剛架,基本部分為簡(jiǎn)支梁,附屬部分,特點(diǎn):BBABCDAB0E三處反力是必須的。、。計(jì)算處彎矩為、為懸臂剛架,基本部分為二力桿,附屬部分,、特點(diǎn):DBABAABDBCAC0,2qa /82qaPa/2Pa/2Pa/2Pa/2PaaaaaPaaaaqqaa2a2aaqaqaaaaaP2kNq=10kN/
34、m2m2m2m2m4m4m(78)(79)(80)(81)(82)Pa/2Pa/2對(duì)稱qa222qa2qa/23qa24Pa6Pa4P-8Pa12kN.m4kN.m8kN.m80kN.m24kN.m56kN.m(89)(90)2qa /82qaPa/2Pa/2Pa/2Pa/2PaaaaaPaaaaqqaa2a2aaqaqaaaaaP2kNq=10kN/m2m2m2m2m4m4m(78)(79)(80)(81)(82)Pa/2Pa/2對(duì)稱qa222qa2qa/23qa24Pa6Pa4P-8Pa12kN.m4kN.m8kN.m80kN.m24kN.m56kN.mABCDABCDE四處反力是必須的。
35、、。計(jì)算處彎矩為、為基本部分為附屬部分,特點(diǎn):ECBAECBAABCDBE0,。處彎矩為、懸臂梁為基本部分為二力桿,梁,桿為附屬部分,為簡(jiǎn)支特點(diǎn):0,CBACDBCAB2qa /82qaPa/2Pa/2Pa/2Pa/2PaaaaaPaaaaqqaa2a2aaqaqaaaaaP2kNq=10kN/m2m2m2m2m4m4m(78)(79)(80)(81)(82)Pa/2Pa/2對(duì)稱qa222qa2qa/23qa24Pa6Pa4P-8Pa12kN.m4kN.m8kN.m80kN.m24kN.m56kN.m(92)(91)ABCDABCDEF。處彎矩為、荷載的簡(jiǎn)支梁,為中間有集中。再計(jì)算先計(jì)算,為二
36、力桿,容易判斷、特點(diǎn):0,0FBAFBXXYCDEFABB可直接作彎矩圖。處彎矩為為外伸梁,為外伸斜梁,為二力桿,特點(diǎn):0CCBACAB為矩心列方程。以和分別取水平反力即可。、的簡(jiǎn)支梁,計(jì)算布荷載為中間受集中荷載和分支梁,為中間受集中荷載的簡(jiǎn)圖。為簡(jiǎn)支梁,直接作彎矩為二力桿,、特點(diǎn):C,CEFBADBABEADCFCEDEPa4PaPa2Pa2qa2qa/22qa/4220kN.m8kN.m(86)(85)(83)2m2m2aaaaaa2aPqa/2aqaaa/210kN1mq=4kN/m1m2m2m21.82kN.m21.82kN.m(84)5kN5kN5kN4X3m=12m3m8m-3.5
37、36kN2.27kN2.27kN-5kN-10kN10.61kN2.27kN2.27kN-5kN10.61kN-3.536kN-10kNPa4PaPa2Pa2qa2qa/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-10kN(94)(93)ABCABCDEFPa4PaPa2P
38、a2qa2qa/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-10kN(95)ABCDE部分彎矩圖。可進(jìn)一步作,點(diǎn)。容易判斷一直到點(diǎn)開(kāi)始直接作彎矩圖,附屬部分,從為基本部分,其它都為特點(diǎn):ABPYPXBEABBB,P/2PPP/280kN.mP3P80kN.m100kN.m6
39、0kN.m30kN.m70kN.m10kN.m40kN.m30kN.m2m2m2m2m2m2m2m2m2m2m(90)(89)(88)(87)P2m2m2m2m1.5m20kN/m40kN2m2m4m4m22PP2m4m4m2m10kN/mm40kN20kN20kN10kN/m10kN/m10kN/m20kN.m20kN.m40kN.m80kN.m80kN.m2P(96)ABCDEFG力都是必不可少的。算各處支反部分開(kāi)始作彎矩圖,計(jì)部分,從處集中力作用在復(fù)雜剛架。以此增加二元體,完成三鉸剛架為基本部分,特點(diǎn):FGDEFFABC90kNm50kNm70kNm110kNm(97)(98)P/2PP
40、P/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.m2PABCDE彎矩圖??紤]為簡(jiǎn)支梁,直接作點(diǎn)。到出發(fā)作彎矩圖,可一直從然簡(jiǎn)支梁為附屬部分,顯三鉸剛架為基本部分,特點(diǎn):DEACXBCABDEB0ABCDE即可。再計(jì)算出、可計(jì)算出為矩心部
41、分,以考慮容易判斷為二力桿,、為基本部分,特點(diǎn):BEEEEXXYCCDEXYDECDAB,22圖可順利作出。變形,。只有中間矩形有彎曲處彎矩為、處只有水平反力,去掉不影響計(jì)算,也為二元體,、為二元體,、處反力都為、特點(diǎn):容易判斷MKHKIEEFCGCDBA0, 0圖。,即可作和可計(jì)算出為矩心,列寫方程。桿,以考慮為矩心,列寫方程;桿,以考慮為二力桿、特點(diǎn):MYXHBCGABEFDEBB,(99)(100)P/2PPP/280kN.mP3P80kN.m100kN.m60kN.m30kN.m70kN.m10kN.m40kN.m30kN.m2m2m2m2m2m2m2m2m2m2m(90)(89)(8
42、8)(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/2MABCDEFGHIJKABCDEFGHP21P21P21P21Pa21Pa21P21P21P21P21P21P
43、21無(wú)彎曲變形部分無(wú)需計(jì)算反力。即段當(dāng)然也無(wú)彎曲變形。桿無(wú)彎曲變形彎矩圖對(duì)稱,容易判斷逐段繪制彎矩圖。結(jié)構(gòu)法,力,再按照局部懸臂梁特點(diǎn):應(yīng)先計(jì)算支座反ABCDECE,ADBC,ABABCDE5 . 75 . 711301130kNm11240kNm1124055101061.1061.1054. 354. 3228. 0228. 0228. 0228. 0彎矩、軸力對(duì)稱。桁架部分得解。處對(duì)桁架作用了,由此以及處反力,桿,計(jì)算梁式桿彎矩圖。考慮繪制支座反力先計(jì)算三鉸,看成三鉸結(jié)構(gòu),特點(diǎn):由EDAEAEAABCABCDEqL23qL23qL25qL25qL25qL212qL212qL230qL22
44、5。各桿軸力順利計(jì)算出來(lái)反力后、,計(jì)算出桿軸力為容易判斷彎矩圖和桿內(nèi)力,就可作特點(diǎn):先計(jì)算FC0FDDECBABABCDEF2qL212qL21ABCD0DABDCBAC內(nèi)力為桿部分為二元體,特點(diǎn):P4ABCD征直接作彎矩圖可由剛架彎矩圖基本特處都沒(méi)有水平反力、特點(diǎn):DCBAP21P21P21P21曲變形。忽略軸向變形時(shí),無(wú)彎,彎矩圖反對(duì)稱。結(jié)構(gòu)對(duì)稱,荷載反對(duì)稱Pa21的。第二層、第三層是一樣后,做完第一層剛架彎矩圖Pa21Pa21有彎曲變形。忽略軸向變形時(shí),只有ABCPABCPa2于計(jì)算支座反力。為二力桿,此題關(guān)鍵在、BCABABCDEBCBYCYCX, 0X 0XC, 0MC0604Y1210620BkN20YB桿彎矩圖可順利作出)(DEBDBYBCNDYDX, 0MD04N2Y420BCBkNNBC10, 0Y 0YD, 0X kNXD10kN20kN10kNm604020202060彎矩圖可直接作出就不用計(jì)算支座反力,如果只做彎矩圖的話,10055P2P4PP3P6P2P4圖可直接作出先計(jì)算支座反力,彎矩PLPL2PL4PL3P2P4P6計(jì)算支座反力是關(guān)鍵ABCDEGFAYBYCY, 0MA0Ma4Ya3YCB, 0Y 0YYYACBAED考慮ADEAYDGNEXEY
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