各类梁的弯矩剪力计算汇总表

1、表1简单载荷下基本梁的剪力图与弯矩图梁的简图aIlF否息剪力Fs图弯矩M图2一、qqa(21-a)8122、qa(1-a)a(21二a)2111-3a-|M表2各种载荷下剪力图与弯矩图的特征某一段梁上的外力情况剪力图的特征弯矩图的特征无载荷11水平直线斜直线或集中力1FFL突变-F转折,集中力偶Me-无变化突变/Me均布载荷口qn斜直线抛物线L或零点极值表3各种约束类型对应的边界条件约束类型位移边界条件力边界条件（约束端无集中载荷）固定端w=0，6=0一间支端幺尸w=0M=0自由端11一M=0，FS=0注：力边界条件即剪力图、弯矩图在该约束处的特征。序号常用截面几何与力学特征表表2-5截面边缘

2、至.主轴的距离y对主轴的惯性矩11,y=TA2t=Th_i.(bj+2b)h*尸3(如+b)(b+2h"以=3+，)(乂+4加+")/336(6+bj截面抵抗也W回转半径11卬=而Dt=0.289ftW尸古妒W古而i=0.236h(M+4砧e+“)MWl2(b2b3+4助+bf)ML12(261+fr),Q.23独/,i.Akk4,2-b+bi5+4M#加注：1.I称为截面对主轴（形心轴）的截面惯性矩（mm4）。基本计算公式如下：I=y2dAAI2. W称为截面抵抗矩（mm3）,它表不截面抵抗弯曲变形能力的大小，基本计算公式如下：W=ymax3. i称截面回转半径（mm）,

3、其基本计算公式如下：i=4,上列各式中，A为截面面积（mm2）,y为截面边缘到主轴（形心轴）的距离（mm）,I为对主轴（形心轴）的惯性矩。5.上列各项几何及力学特征，主要用于验算构件截面的承载力和刚度。2.单跨梁的内力及变形表（表2-6表2-10）（1）简支梁的反力、剪力、弯矩、挠度表2-6序次图类图示项目计算式1荷载尸TJ反力J?A=Rh=剪力y网vs=-零短弯矩Ma=-Ef.剪力挠度_Fl3w-48£ihnwn2荷载月Jc反力Ra="F*=十F剪力F产Rr*Yr=-RbL上】弯矩一Fta>j-弯矩挠度若。小时，在上当J七（fl+SfT期力Mi山L_Ffr1(a22

4、ab)3w-9EkV33荷载上反力Ra=Rr=F="Zi1P一：剪力人；vB=-j?b弯矩穹矩Maj=Fa.：'Z的力nn.一，HillI挠度Wmoi=24El荷载LteJ3或反力Ra=b二年F剪力Fa=R小VB=-fi0TT*'-B1弯矩pr弯矩Ma=fFL剪力挠度19F-皿必一3B4E1血皿Lil5荷载反力R&=R®="醒ALLiLl.LTITLJr剪方Va=R*;Vb=-弯矩弯拒M*=/以，剪力挠度5金*a384E.序次图类图示项目it算式1荷载Xh反力剪力VB-/?B弯矩rrrrrnrrrfTnTI弯矩Ml-FkIMa=Mr=-F&

5、#163;穹矩_<rnTiiirnTi弯矩M*=-F(工rh工M,=-Fb剪力-nnmnnm挠度w*-6EII3i)序次图类图示项目计算式1荷载4:反力比a="eRb="f1：2剪力Va=Ka；vb=-j?b弯矩I一rfp弯矩琏;MB=-Fl“io剪力in山hi11I1JL1111挠度当工=0,447七时，Hg=0,Cl0932a上I2荷载jst4P反力R祟；3都-£)剪力3Ra；*自弯矩弯矩当工=以时，3-y-j剪力_挠度CH段；ua-Ra（3f。一工）一3FfcO+Fa）310总JIhllIIIJa3荷载AirLLpb反力RL（2-3宁+3Rl/（2+3

6、予-3/）：口一2"四力"E公Vb=-Rr弯矩7皿1山炉加弯矩Mc=Ra；-竽1-亍）剪力W挠度CD®；wK=Zr<7（jRa3产工工，）=3F（Z2"2al+2a.2）wCij&J+F（x-a）3II1!N1口ALILmi弯短时如FTTTW翦力nnnnni1bBS.荷载2弯矩tthizlfll剪力THjjT：lll1lllll项目计算式反力Ra=Re=/f剪力A-Ra3%=-Rb弯矩Mg=十9挠度Tt)=192EI反力w臂。冲竽)剪力=¥b=-Hr弯矩iw2Ed产,M皿二Me.3-t挠度±l_2aZ_u_t_2F若工乩

7、当±-3a+b此M"一羽a(3.+6*序次图类图示项目计算式1荷裁ra反力心二八+十年,口马-一节C/。/剪力Vc=-F;5-Rr-FA弯矩>fnTTnnmTT弯矩Mx=Ma=-Fa剪力(mi'ttu；挠度加广普(1+亍)当工=&+Q+5£时，卬面=-0.0642嘴£1川III2荷载LJ反力J?A工RB=F<T剪力¥尺=-Ra：/=Rb弯矩/ffUWIHHIIRK弯矩M产iVfB=-Fa剪力EBjmu挠度寓Ri亍当工=&+0.5!时，w猫尸一黑OjDI3 .等截面连续梁的内力及变形表（1）等跨连续梁的弯矩、剪

8、力及挠度系数表（表2-11表2-14）1）二跨等跨梁的内力和挠度系数表2-11序次荷载图鹿内最大弯矩支座弯短«力跨度中点挠度MiMiMbVAV酸1vcW1W2140.0700,070-0.1250.375-Q.6250.625-0,3750.5210,521匚：11,11111'11.11月4一L一j(A/i)(AA)2Allui'Ct0.096-0.0630.437-0.S630.063仇0630,912-03913A-+4八，Rr0.1560*1560.1880.312-0.6880.688-0,3120.9110.9114rTFBC0.203-0.094Q.4Q

9、6-0.5940.0940.0941.497-0+5864注：1.在均布荷载作用下：”=表中系数xql2；丫=表中系数xql；亚=表中系数父ql。100EIFl32.在集中荷载作用下：”=表中系数XFl;丫=表中系数XF;亚=表中系数父。100EI例1已知二跨等跨梁l=5m,均布荷载q=11.76kN/m,每跨各有一集中荷载F=29.4kN,求中间支座的最大弯矩和剪力。解1支=(-0.125X11.76X52)+(0.188X29.4X5)=(36.75)+(-27.64)=-64.39kN-mVb左=(-0.625X11.76X5)+(0.688X29.4)=(36.75)+(20.23)=

10、-56.98kN例2已知三跨等跨梁l=6m,均布荷载q=11.76kN/m,求边跨最大跨中弯矩。解M1=0.080X11.76X62=33.87kNm。2)三跨等跨梁的内力和挠度系数表2-12序次荷载图跨内最大等矩支座弯矩翦力跨度中点梯度M1M2MbMeVA丫3vD的1W21O.OBOO+O25-0,100-0.1000+400-0.6000.500-0.500Q.600-0,4000.6770.0520.677knrirtnnirmnirj注：1.在均布荷载作用下：”=表中系数xql2；丫=表中系数xql；亚=表中系数父ql4100EI2.在集中荷载作用下：”=表中系数XFl;丫=表中系数X

11、F;亚=表中系数父一亡，100EI3）四跨等跨连续梁内力和挠度系数表2-13注：同三跨等跨连续梁。4）五跨等跨连续梁内力和挠度系数表2-14荷载荷图弯矩黄力跨度中点挠度M中Ma中M,中A!联Me支VA旷色卜断%皿加3口.046-0.105-0.0790.3940.6060.526-0,4740,5000.6443.1510,315川口"|"4c%上苫”*由，*Q，0.1710.112hl婴-0.158-0.1180.342-0.6580.540-0.4600.5001.097口.356U.6(B1AC小口FJX此门仁门:0.240口.10。队122-0.281().2110

12、.713-1.2011.071-0.9301.0001.795).479).918q产1,，"%/南F4I（2）不等跨连续梁的内力系数（表2-15、表2-16）1）二不等跨梁的内力系数表2-15XX荷载4-i-，iI_q_女也JnilAB1J'产打AjA<w_u_>>“如(MQMfiAVa炉侬(.Va)F防（忆）VcMab3血)vA（噎）Mbc(M皿)Vc(VJ1.0-y.iisu0.07030,07030.3750-0.62500.6250-0*37r500.09570.43750.0957-0.4375L1-0.13880.06530.08980.361

13、3-0,63870.6761-0.42390.D97D0.44050.1142'0,47fi0L2TL155。U.Q595ILins0.3450-0.6550(L7292-0.47080.09620,44320.1343-0.51821,3-0.17380.05320.13330.3263-0.673707836-0.51640,09930.44570.1558-0.55821.4-0.195。O,G4650.1572U.3O50-0.69500.8393-0.5607UJ0030.44790.17880.59791.5-0.21880.03960.18250.2813.*0,7187

14、08958-0.6G420.10130,45W)0.2032-0.63751.60,24500.0325Q.2Q920.2550-0.74500.95310.64690.1021依45190.2291-0.6769】.7ft.27330.0256k2rM0.2263-0.7737L0L10-0.6弱00.10290,45370.2564-0.71621.8-0.305Q001900.26690.19500.8050L0694-0.73060.10370.45540.2850-0.75541*9-0,3388口,01300.29780.16130.83871.1283-0,7717fl.1044

15、0.45690.3155-0.79442.00.37500.007S0,330L0.1250-0,37501.1875-0.81250.10500,45830.3472-0.83332.25-0.47660.00030.417P0,02340.9766L336g-0.91320.106504615Q.4327-0.93032.5-0.5938负值0.5126-0.09381.09381.48751l4】250.1078(M6430.5272-1.0266注：1.”=表中系数xql21；丫=表中系数xql1；2.（Mmax）、（Vmax）表示它为相应跨内的最大内力。2）三不等跨梁内力系数表2-1

16、6载、irmigUJIII1141X.g_IllIrHl11uL741-*-411!1h1111liiinh=nlCZ!,.bt、含L4-ffAJLUAA1zEA|!1.九lhLh=nhi、数-JJ*“TT上彳LM1s.1M嵋M/VaVbSL喂Mb(Mz)Vb左（嚏）(k)Mab(JW(VaMbc(Mm)（M-O.OS31口.0869一0.06310.4169-0.58310.2000-0.09()2-0.5962O.46OS0,08900.42L90.01500.5=仇网40.08别J-0.0491"41960,58040.2500-0.0947-59470.45020A>9

17、1)30.42860,02230,6-0,08000.0882-0.03500.4200-0,58000.3000-0.0952一0.59520,46030.09430.43420,03080.7-0.08190,0874-0.02060.4181-0*58190.350。-O09R-0.59790.482596,I0.43000.04050.80.08590,0857-0.00590.4141-0.5浮590.4000-0.1021-0.602J0.5116(LI19&J0.4432!0.05090.9-0.09130.08330,00950.4082-0.591N0,4500-0.

18、1083-0.60830.54%0.09980.44680.0625L0-0.10000.08000.02500,40000.600。0.5000-0.1167-0.61670.58330.1013(L4SU00.07501.1-O.UOO0.07610.1)4130.390。-0.61000.5500-0.12670.62670.62330.10250.45280.08851.2-D.121B0.07150.05820,3782-0,62180.6000-0.1385-0.63850.66510.103。r0.45540.10291.3-0.13550.(16640.07580.3645-0

19、.63550.6500-0.1522-0.6522W.70B20.104-70.45760.11S21,4-0.15100.060。0.09400.3490-0.65100.7000-U.1676-0,6671&0.75250.10570.45970.13441.5-O.16S30.05500.11300.3317-0.66830.75典0.1848-0.6S4810.79760,10650.46150,15141.6-038740.04890.13270.3127-Ux6R730.8000-IL2037-0,70370.H4340,1or0,46320.16941,7-0.20820

20、.04260.15310,29180.70820.S50C-0.2244-0.72440.88970.10800.46480.18B31.8-0.2304C0.03626.17420.2692-&.73080.9000-O.246S-0.746B0.9366仇1U870.46620.20801,9-0,25520,03000.19610,2448-0.75520.9500-0.2710-0.77100.08460.10930.46750.22862,0-0,28130.(12390.21880.2188-0*78121.0000-0,2969796!1.03120.1。则0.46880

21、.25002,25-O,S54O0.01060.27股0.14620-35381.1250-0.3691-0.86911.15110.11110,47140.30742.5-0.43750.001903437-0.06250.93751.2500-0.45210.95211,27220.11220.47370.3701注：1.”=表中系数xql2i；丫=表中系数xqli；2.（Mmax）、（Vmax）为荷载在最不利布置时的最大内力。4.双向板在均布荷载作用下的内力及变形系数表(表2-17Y2-22)符号说明如下：刚度K二Eh212(1-2)式中E弹性模量；h板厚；V泊松比；、max分别为板中心

22、点的挠度和最大挠度；Mx为平行于lx方向板中心点的弯矩；My为平行于ly方向板中心点的弯矩；Mx0固定边中点沿lx方向的弯矩；My°固定边中点沿ly方向的弯矩。正负号的规定：弯矩一一使板的受荷面受压者为正；挠度变位方向与荷载方向相同者为正。四边简支表2-17挠度=表中系数弯矩之表中系数式式中1取人和0中之较小者U'%My3MkMy0.500.010130,365(L01740.800,006030.05610.03340.55a.009400.0892口,02100.650,005470.05060.03480.600,008670.08200.02420.900.00496

23、0-04560.03580.650.007960.07500.02710.950,004490.04100.03&40.700,007270.06830.0296LOO0,004060.03680,03680.750.0()6630.06200.0317Uiy筋H叫MX乂方MyM21rmix时工0.500.005040.05830.0060-0.121；0.950J1QJ240.03240.U28。-Q.0S820.550,004920.05630JW81=0.1187。，如0+003680.03281)332-0.09260.600.004720.05390.0104-0.11580

24、.850.001170.0320g03700.09700,650.004480.05130.0126-0.11241|18。0.004730.03260.0424-0/1U140.700.004220,04850.0148-0.10870.750.005360.0319口.0485-0.10560.750.003990.04570.0168-0.104U0.700.006050.03080.0553-0,10960.800.0037610.04280.0187r0.10070.650.006800.02910.0627-0,11330.850.003520.04000.0204-0.096S0

25、.600.007620.0268IL0707-0.11660.90D.003290,03720,0219-0.09220.550.DD8480.02390.0792-D.11930.950.003060.03450.0232-0.08800.500.00935U.02050.1)88。-0.12151.001.000,00285L0.03190,0243-"Q839两边简支，两边固定表2-19饶度=表中系数X*弯矩=表中系数乂修炉式中，取，和G中之较小者ljlvwMm孙泌筋工W同工MyMi0,500.002610.04160+0017-0+Q843必950.002230.02960.

26、0189-Oh07460,550.002590.04100.0028-O.0S4O0.900.00260kO30A0.0224-0.0797U&0.002550,0如20.0042-0.0834(1.850.003030.03140.0266-0500,650,002500.03920,0057-0.08260.800.003540.03190.03160.09040,700,002430.03790.0072-0.08140.751).004130.03210.0374-0,09590,750.002360.03660-0088-0.07990.700.004820,03180.04

27、41-().10130.800.002280.03510.0103-0.07820.6S0.005600.03080.051fi-0.10660.850.002200.033S0.0118-0.07630.600.006470.02奥00604-0.11140,900,002110.03190.0133-0.07730.550.007430.02670.0698-0/11560.950.002010.03020.0146-0,07210.500.008440,02340.0798-0,11911,001.0。0.001920.02850.0158-0.069g一边简支，三边固定表2-20Uma

28、x疑工My0.500,002580.04080,0028-0.0836-0.05690.55。.002550.039S0.0042-0.0827-0,05700.60k002490.03840.0。59-0.0814-0,05710.650.002400.036S0.0076-0.0796-0.05720.700.。2290.03500.。口93-0.0774-0.0572U.750.002190.03310.0109-0.0750-0.05720.800.002D80.03100.0124-0.0722-0.05700.850,001960.02890.0138-0,0693-0.05670

29、.900-001840,026B0.0159-0.0663-0,0563D+950.001720.02470.0160-00631-0.0558LOO1.D00,001600.02270.0168-0.0600-0.0550。朋0.001820.02290.0194-0.0629-U.0599U.9Q0,002060.02280.0223-0.06560.06530,850,002330.02250.0255-0.0683-0,07110,800.002620.02190.0290-0.0707-0,07720.750.002940.02080.0329'0.0729-0.08370.700.003270.01940.0370-0.0748-0.09030.650口03650.01750.0412-0.0762-0.09700,600.004030.01530.0454-0,0773-0.10330.550.004370.01270.0496-0.0780-o.nm0.500.004630.00990.0534-0.0784四边固定表2-21两边简支，两边固定表2-22挠度表中系数父耳ri等矩=表中系数XqN式中L取和八中之按小者M,MyM；0.500.004710.05590,0079-0,11790.07860.550.004540