經(jīng)典材料力學(xué)結(jié)構(gòu)力學(xué)彎矩圖（課堂PPT）

1、.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=qLMLLqLLLL

2、2PPLLLqLPLLPP=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.2(15)(14)(13)(

3、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=qLMLLqLLLL2PPLLLqLPLLPP=2qLLqLPL2PLPLLL/22M=qLqL(15)(14)(13)(12)(11

4、)(10)(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=qLMLLqLLLL2P

5、PLLLqLPLLPP=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=qLMLLqLLLL2PPLLLqL

6、PLLPP=2qLLqLPL2PLPLLL/22M=qLqL(7)(8)(9)利用對稱性作M圖：221qL221qL281qL利用反對稱性作M圖：M21M21先計(jì)算支反力，再作M圖：qL41241qL281qL.3(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)(

7、2)(1)一、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

8、.4(16)(17)(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.5aaaaaaam(22)從附屬部分開始，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=2qaqa2aa2m2m2m15

9、60q=102mM=PL(23)從附屬部分開始，用“局部懸臂梁法”直接作M圖：2481aq24qa相切28qa216qa215qa25 . 8 qa2381aq.6(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)2PL9qL22PL34pL5pL3qL22M

10、2qL2qL22+pLpL22qL225qL3qL2222qLqL2882qL5qL2323225qL8qL2斜梁各截面彎矩值與所對應(yīng)簡支梁一樣，作M圖：所對應(yīng)簡支梁為：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+

11、pLpL22qL225qL3qL2222qLqL2882qL5qL2323225qL8qL2.7(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力通過截面以上部分還有力偶，所以彎矩不為0：用“局部

12、懸臂梁法”直接作M圖，P力通過截面彎矩為0.8(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力通過截面彎矩為0用“局部懸臂梁法”直接作M圖.9(31)(32)用“局部懸臂梁法”直接

13、作M圖：Pl21注：P力通過點(diǎn)彎矩為0Pl21Pl21PlPl2Pl2Pl注：P力通過點(diǎn)彎矩為0用“局部懸臂梁法”直接作M圖：.10(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：.11(35)(36)(28)(27)(26)(25)(24)(2

14、3)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2PL2PLPL3(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa22qa221qa281qa.12(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/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2

15、221qa221qa2qa.132m2m2m(34)(33)(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.14(41)(42)22qaqa222qa

16、2cos2qL2+2qL22cosqL2qL2222qL90901008060100100PaPa2m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa3315.15(43)(44)415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35)三、簡支式剛架aaqq2aqa2a2qaa2qaqaaqq/2a/2qaaaa/2PLPPaaa/2a2Pa2Paqa227qa4.16(45

17、)(46)(47)支座B無反力，AB段無變形2m2m2m(34)(33)(32)(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 .2284515.17(48)(49)415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35)三、簡支式剛架aaqq2aqa2a2qaa2qaqaaqq/2a/2qaaaa/2PLPPaaa

18、/2a2Pa2Paqa227qa4計(jì)算A支座水平反力，即可作M圖ABABA、B支座無水平反力，直接作M圖.18(51)(50)415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35)三、簡支式剛架aaqq2aqa2a2qaa2qaqaaqq/2a/2qaaaa/2PLPPaaa/2a2Pa2Paqa227qa4無水平支反力，直接作M圖無水平支反力，直接作M圖.19(52)(53)(46)2.595q7qL24qL24223qL345453904806906904Pa334Pa4Pa2qa225qaqa22

19、qa22qa22(45)(44)(43)(42)(41)3m4m4mqqLqLLL40kN10kN/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.20(54)(55)(46)2.595q7qL24qL24223qL345453904806906904Pa334Pa4Pa2qa225qaqa22qa22qa22(45)(44)(43)(42)(41)3m4m4mqqLqLLL40kN10kN/m3m3m3m3m3m4Paaaa2aqaqaa2a2M=qaqa/2a/2a3qa22先

20、計(jì)算支反力，再作M圖先計(jì)算支反力，再作M圖.21(57)(56)(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.22MM2Pa2PP2無彎矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPP

21、L2LLqLLMPa2先計(jì)算支反力，再作M圖無支反力，直接作M圖(58)(59).23(60)(61)MM2Pa2PP2無彎矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPLLL1.5LLLLqLPPL2LLqLLMPa2AA處無支反力，直接作M圖利用反對稱性，直接作M圖105105105105.24(62)(63)先計(jì)算A或B處支反力，再作M圖AB、CD段沒有彎曲變形，直接作M圖MM2Pa2PP2無彎矩N=P/222qL2qL2PLPL2qLqL22(52)(53)(50)(51)(48)(47)aaaaMaa2aPPL

22、LL1.5LLLLqLPPL2LLqLLMPa2ABABCD.25APLMM/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).26(66)(67)MM2Pa2PP2無彎矩N=P/222qL2qL2PLPL2qLqL22(52)(

23、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、三鉸式剛架B、A處無水平支反力，直接作M圖AABB、A處無水平支反力，AC、DB無彎曲變形，EC、ED也無彎曲變形ABCDE.27A圖。支座水平反力，即可作計(jì)算出段

24、彎矩為常數(shù)。點(diǎn)為直線，彎矩圖過向相反；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)算出處彎矩為圖對稱，荷載，特點(diǎn)：對稱結(jié)構(gòu)，對稱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)ABCDEABCPL41PL41.28A圖。支座水平反力，即可作計(jì)算出形。為二力

25、折桿，有彎曲變形；為二力桿，沒有彎曲變特點(diǎn)：MBCBAC22qa/32qa2qa/2PL(65)(64)(63)(62)(61)(60)(59)qaaaaq1.5aaaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/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)算出處彎矩為圖對稱，荷載，特點(diǎn)：對稱結(jié)構(gòu)，對稱MBACM0C.29A22qa/32qa2qa/2PL(65)(64)(63)(62)(61)(60)(59)qaaaaq1.5a

26、aaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/22qa/222qa/2MMMMqa2qa2/8MMMM/82qaqa2/82qa/322qa/3222qa/3qa/22PL2MMMqa(72)(73)ABCABC圖。即可直接作。處彎矩為。也反對稱，稱荷載，反力特點(diǎn)：對稱結(jié)構(gòu)，反對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MCXXAB000.30圖。，即可直接作彎矩為、。彎矩圖對稱。也對稱，荷載，反力特點(diǎn)：對稱結(jié)構(gòu)，對稱MBAYC00圖。，即可直接作彎矩為處、彎矩圖對稱。荷載，特點(diǎn)：對稱結(jié)構(gòu)，對稱MCBA022qa/32qa2qa

27、/2PL(65)(64)(63)(62)(61)(60)(59)qaaaaq1.5aaaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/22qa/222qa/2MMMMqa2qa2/8MMMM/82qaqa2/82qa/322qa/3222qa/3qa/22PL2MMMqaABCABC(74)(75).3122qa/32qa2qa/2PL(65)(64)(63)(62)(61)(60)(59)qaaaaq1.5aaaM1.5aaaq1.5aaaaa1.5aq2aaaPLLqa/22qa/222qa/2MMMMqa2qa2/8MMMM/82qaqa2/82qa/322qa/3222

28、qa/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)：MCXAXYCBBBB0.32(77)(78)M/43M/4M/2M/2M/2M/236kN.m36kN.m2q2q對稱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/

29、2qq2q2qABCABC圖。即可直接作的水平反力，或，計(jì)算出彎矩為、。彎矩圖對稱。也對稱，荷載，反力特點(diǎn)：對稱結(jié)構(gòu)，對稱MBABAYC00圖。即可直接作的水平反力，或計(jì)算出，彎矩為、特點(diǎn)：MBACBA0830031003100.33A(80)(79)M/43M/4M/2M/2M/2M/236kN.m36kN.m2q2q對稱23qa/82qa/82qa/2100kN.m200kN.m300kN.m300kN.m3m1.5m1.5m(71)(70)(69)(68)(67)(66)aaaaL/2L/2L/2L/23m2m3m12kN2mq2q2m2m2m2mqa/2a/2a2aa1.5m5m3m6

30、0kN100kN.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力，、計(jì)算出，彎矩為、特點(diǎn)：MBACBA0.34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對稱23qa/82qa/82qa/2100kN.m200kN.m300kN.m300kN.m3m1.5m1.5m(71)(70)(69)(68)(67)(66)aaa

31、aL/2L/2L/2L/23m2m3m12kN2mq2q2m2m2m2mqa/2a/2a2aa1.5m5m3m60kN100kN.mqa/22qa/823qa/82M/2M/2M/2qq2q2qABCABCM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)：MCBAXAXYCBBBB02.35(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/222

32、qaqa2ABCDEABCDEE圖。即可直接作段沒有彎曲變形，、形，為二力桿，沒有彎曲變。彎矩圖對稱。也對稱，荷載，反力特點(diǎn)：對稱結(jié)構(gòu)，對稱MCEDCABYC0圖。即可直接作水平反力，內(nèi)力、支座計(jì)算出段沒有彎曲變形。形，為二力桿，沒有彎曲變特點(diǎn)：MDABBEAB.36圖。即可直接作為斜梁。沒有彎曲變形，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(8

33、5)(86)ABCABC圖。即可直接作桿如同簡支梁。，處彎矩為、特點(diǎn)：MACCBA0.372qa22qa2qa2qL/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/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，基本部分為簡支梁，附屬部分，特點(diǎn)：BBABCDAB0.38E三處反力是必須的。、。計(jì)算處彎

34、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/m2m2m2m2m4m4m(78)(79)(80)(81)(82)Pa/2Pa/2對稱qa222qa2qa/23qa24Pa6Pa4P-8Pa12kN.m4kN.m8kN.m80kN.m24kN.m56kN.m(89)(90)2qa /82qaPa/2Pa/2Pa/2Pa/2PaaaaaPaaaaqqaa2a2aaqaqaaaaaP2kNq=10kN/m2m2m2m2m4m4m(78)(

35、79)(80)(81)(82)Pa/2Pa/2對稱qa222qa2qa/23qa24Pa6Pa4P-8Pa12kN.m4kN.m8kN.m80kN.m24kN.m56kN.mABCDABCDE四處反力是必須的。、。計(jì)算處彎矩為、為基本部分為附屬部分，特點(diǎn)：ECBAECBAABCDBE0,.39。處彎矩為、懸臂梁為基本部分為二力桿，梁，桿為附屬部分，為簡支特點(diǎn)：0,CBACDBCAB2qa /82qaPa/2Pa/2Pa/2Pa/2PaaaaaPaaaaqqaa2a2aaqaqaaaaaP2kNq=10kN/m2m2m2m2m4m4m(78)(79)(80)(81)(82)Pa/2Pa/2對稱q

36、a222qa2qa/23qa24Pa6Pa4P-8Pa12kN.m4kN.m8kN.m80kN.m24kN.m56kN.m(92)(91)ABCDABCDEF。處彎矩為、荷載的簡支梁，為中間有集中。再計(jì)算先計(jì)算，為二力桿，容易判斷、特點(diǎn)：0,0FBAFBXXYCDEFABB.40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圖。為簡支梁，直接作彎矩為二力桿，、特點(diǎn)：C,CEFBADBABEADCFCEDEPa4PaPa2Pa2qa2qa/22qa/4220k

37、N.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-10kNPa4PaPa2Pa2qa2qa/22qa/4220kN.m8kN.m(86)(85)(83)2m2m2aaaaaa2aPqa/2aqaaa/210kN1mq=4kN/m1m2m2m21.82kN.m21.82kN.m(84)5kN5kN5k

38、N4X3m=12m3m8m-3.536kN2.27kN2.27kN-5kN-10kN10.61kN2.27kN2.27kN-5kN10.61kN-3.536kN-10kN(94)(93)ABCABCDEF.41Pa4PaPa2Pa2qa2qa/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

39、.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,.42P/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.m2P

40、(96)ABCDEFG力都是必不可少的。算各處支反部分開始作彎矩圖，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.43(97)(98)P/2PPP/280kN.mP3P80kN.m100kN.m60kN.m30kN.m70kN.m10kN.m40kN.m30kN.m2m2m2m2m2m2m2m2m2m2m(90)(89)(88)(87)P2m2m2m2m1.5m20kN/m40kN2m2m4m4m22PP2m4m4m2m10kN/mm40kN20kN20kN10kN/m10kN/m10kN/m20k

41、N.m20kN.m40kN.m80kN.m80kN.m2PABCDE彎矩圖?？紤]為簡支梁，直接作點(diǎn)。到出發(fā)作彎矩圖，可一直從然簡支梁為附屬部分，顯三鉸剛架為基本部分，特點(diǎn)：DEACXBCABDEB0ABCDE即可。再計(jì)算出、可計(jì)算出為矩心部分，以考慮容易判斷為二力桿，、為基本部分，特點(diǎn)：BEEEEXXYCCDEXYDECDAB,22.44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

42、點(diǎn)：MYXHBCGABEFDEBB,(99)(100)P/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

43、)(91)aaaaaaaaPaaaaaP2m4m4m2m4m030030PPL/2L/2LLqLLLMMM4P4P4P4P4PPL/2MABCDEFGHIJKABCDEFGH.45P21P21P21P21Pa21Pa21P21P21P21P21P21P21無彎曲變形部分無需計(jì)算反力。即段當(dāng)然也無彎曲變形。桿無彎曲變形彎矩圖對稱，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,ABABCDE.465 . 75 . 711301130kNm11240kNm1124055101061.1061.1054. 354. 3228. 0228. 0228.

44、 0228. 0彎矩、軸力對稱。桁架部分得解。處對桁架作用了，由此以及處反力，桿，計(jì)算梁式桿彎矩圖?？紤]繪制支座反力先計(jì)算三鉸，看成三鉸結(jié)構(gòu)，特點(diǎn)：由EDAEAEAABCABCDE.47qL23qL23qL25qL25qL25qL212qL212qL230qL225。各桿軸力順利計(jì)算出來反力后、，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FC0FDDECBABABCDEF.482qL212qL21ABCD0DABDCBAC內(nèi)力為桿部分為二元體，特點(diǎn)：.49P4ABCD征直接作彎矩圖可由剛架彎矩圖基本特處都沒有水平反力、特點(diǎn)：DCBA.50P21P21P21P21曲變形。忽略軸向變

45、形時(shí)，無彎，彎矩圖反對稱。結(jié)構(gòu)對稱，荷載反對稱Pa21的。第二層、第三層是一樣后，做完第一層剛架彎矩圖Pa21Pa21.51有彎曲變形。忽略軸向變形時(shí)，只有ABCPABCPa2.52于計(jì)算支座反力。為二力桿，此題關(guān)鍵在、BCABABCDE.53BCBYCYCX, 0X 0XC, 0MC0604Y1210620BkN20YB桿彎矩圖可順利作出）（DEBDBYBCNDYDX, 0MD04N2Y420BCBkNNBC10, 0Y 0YD, 0X kNXD10kN20kN10kNm604020202060.54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，10055.55P2P4PP3P6P2P4圖可直接作出先計(jì)算支座反力，彎矩PLPL2PL4PL3P2P4P6.56計(jì)算支座反力是關(guān)鍵ABCDEGFAYBYCY, 0MA0Ma4Ya3YCB, 0Y 0YYYACBAED考慮ADEAYDGNEXEY, 0ME0aYa5 . 0NADGGFBC考慮BCG