弯矩图100解答

(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图：qL2q作用下的M图：221qL223qLP与q作用下的M图：(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(2)P作用下的M图：qL2q作用下的M图：221qLP与q作用下的M图：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图：q作用下的M图：221qL24qL25.4qLP与q作用下的M图：直线与曲线相切22qL(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=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(4)(5)(6)从右向左作M图：PLPL从右向左作M图：223qL225qL221qL281qL从右向左作M图：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=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)(9)(8)(7)(6)(5)(4)(3)(2)(1)一、梁L/2L/4L/4qLqLqL2M=qLP=qLLqLqLP=qLM=PL2PLLqLP=qLMLLqLLLL2PPLLLqLPLLPP=2qLLqLPL2PLPLLL/22M=qLqL(7)(8)(9)利用对称性作M图：221qL221qL281qL利用反对称性作M图：M21M21先计算支反力，再作M图：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、梁L/2L/4L/4qLqLqL2M=qLP=qLLqLqLP=qLM=PL2PLLqLP=qLMLLqLLLL2PPLLLqLPLLPP=2qLLqLPL2PLPLLL/22M=qLqL(10)(11)(12)叠加法作M图：1.先考虑力偶作用PL2PL2.再叠加P的作用PL41先计算支反力，再作M图：P34P35PL34PL35先计算支反力，再作M图：kN4.1kN6.04.26.11.06.1(13)(14)(15)作M图,只需计算C截面弯矩Fl21作M图,只需计算C截面弯矩221qa曲线在B点与水平线相切281qa不用计算支反力，可快速作M图3030(16)(17)(18)先计算支反力，再作M图：F31FaFa31直接作M图：2qa289qa直接作M图：601020(19)(20)(21)CD段直接作M图，AC段采用叠加法：2qa221qa相切力偶只影响BD段,直接用叠加法作M图：2qa2qa力偶只影响BC段,力只影响AC段,作M图：22qa2qa不与水平线相切aaaaaaam(22)从附属部分开始，直接作M图：mmmmqLL(22)(21)(20)(19)二、悬臂式刚架(18)(17)(16)PPLLL/2L/2L/2L/2030PLL2M=qaP=qaP=2qaqq4a2aaa2a2aa3aM=2qaqa2aa2m2m2m1560q=102mM=PL(23)从附属部分开始，用“局部悬臂梁法”直接作M图：2481aq24qa相切28qa216qa215qa25.8qa2381aq(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+pLpL22qL225qL3qL2222qLqL2882qL5qL2323225qL8qL2斜梁各截面弯矩值与所对应简支梁一样，作M图：所对应简支梁为：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+pLpL22qL225qL3qL2222qLqL2882qL5qL2323225qL8qL2(27)(28)qL22(22)Lq2217qa215qa216qa8qa224qa2qa2PL2PL23qaqa222055530(21)(20)(19)二、悬臂式刚架(18)(16)PPLLL/2L/2L/2L/2030PLM=PLL2M=qaP=qaP=2qaqq4a2aaa2a2aa3aM=2qaq2m2m2m1560q=102mPLPL22PL23PL3PL3PL22PL9qa28a2aa228qa(17)用“局部悬臂梁法”直接作M图，P力通过截面以上部分还有力偶，所以弯矩不为0：用“局部悬臂梁法”直接作M图，P力通过截面弯矩为0(29)(30)qL22(22)Lq2217qa215qa216qa8qa224qa2qa2PL2PL23qaqa222055530(21)(20)(19)二、悬臂式刚架(18)(16)PPLLL/2L/2L/2L/2030PLM=PLL2M=qaP=qaP=2qaqq4a2aaa2a2aa3aM=2qaq2m2m2m1560q=102mPLPL22PL23PL3PL3PL22PL9qa28a2aa228qa(17)与杆件轴线相切用“局部悬臂梁法”直接作M图，P力通过截面弯矩为0用“局部悬臂梁法”直接作M图(31)(32)用“局部悬臂梁法”直接作M图：Pl21注：P力通过点弯矩为0Pl21Pl21PlPl2Pl2Pl注：P力通过点弯矩为0用“局部悬臂梁法”直接作M图：(33)(34)(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2PaPaPa2AB注：AB段弯矩为常数。(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2PLPLPL3用“局部悬臂梁法”直接作M图：用“局部悬臂梁法”直接作M图：(35)(36)(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2PL2PLPL3(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa22qa221qa281qa(37)(38)(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa22qa2qa221qa与杆件轴线相切(28)(27)(26)(25)(24)(23)qq2aaaa/2qqaa/2aqqaaaPL2LLLLP2LLLPPaaa2PLqa2221qa221qa2qa2m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa8010060100(39)有疑惑(40)22qaqa222qa2cosα2qL2+2qL22cosαqL2qL2222qL90901008060100100PaPa2m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa(41)(42)22qaqa222qa2cosα2qL2+2qL22cosαqL2qL2222qL90901008060100100PaPa2m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaa3315(43)(44)415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35)三、简支式刚架aaqq2aqa2a2qaa2qaqaaqq/2a/2qaaaa/2PLPPaaa/2a2Pa2Paqa227qa4(45)(46)(47)支座B无反力，AB段无变形2m2m2m(34)(33)(32)(31)(30)(29)qqaaaaaLqLL/2L/2qL3m30kN20kN/m3m3m3m40kN10kN/mP=40kN2m2m2maPaaBAPaPa180180不用计算支反力，直接作M图AB计算A支座水平反力，即可作M图155.2284515(48)(49)415qa221qa2822qa22qaqa2qa22qa2qa2PLPLPa22Pa2PaPa(40)(39)(38)(37)L(36)(35