各种梁的弯矩剪力计算(大全)表

1、表1简单载荷下基本梁的剪力图与弯矩图表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1水平直线斜直线或集中力1突变F转折或/或/集中力偶Mef无变化突变/Meq均布载荷III斜直线、抛物线厂或零点极值yTV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）固定端尸=w=0，0=0简支端jrw=0M二0自由端注：力边界条件即剪力图、弯矩图在该约束处的特征资料常用截面几何与力学特征表表2-5戡血边缘至上轴的距吗歳由边缘至主轴的距离VI卡6A十载面边缘全卞轴的距离-H：|6AI旳心（不一山）ByB8截面简图y资料序号对上轴的惯性範A-

2、f+m-k）截面枳截闻边绿全上轴的距离吉肿+272-（R-b）h：.A-liH-Ui-bVtA-HH-8bh主轴的跑离主轴的距离yih%1lJU1b.15.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。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。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：1=Jy2dAA2.W称为截面抵抗矩（mm3）,它表示截面抵抗弯曲变形能力的大小，基本计算公式如下：W二3.截面边绦至主轴的距离i称截面回转半径（mm）,其基本计算公式如下：i珂Tbh(62jh2上列各式中，A为截面面积（mm2）,y为截面边缘

3、到主轴（形心轴）的距离（mm）,丨为对主轴（形心轴）资料资料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序次图类荷载图*21剪力iiniiiH反力荷载剪力3弯矩55力挠度m反力荷载剪力弯矩7HF剪力荷載迎川也irrrr项目反力剪力反力剪丿j弯矩挠度弯矩挠度反力弯矩剪力计算式叽-心-号二_R_48jRa7FiRe二宁-FrsvB-JKjlmoptib时*在工二（A+姑）处*二用K宀2肿讪g-g虽V3vA=nAivB=-RBM帕厂甩卯3=嗇7竹广-如A=B_辛FMnux松唤=1W384EJ必3S4/序次圏示顶目ir算式7荷載剪力荷戟弯矩剪力厘力Ha-心=

4、QHrnw7川II剪力弩矩挠度反力剪力弯走挠度反力荷栽弯矩剪力挠度反力荷载主上口丄/丄凸剪力弯建弯矩Va-Ka；Va-Ru爲d心/A时）（CH段）剪力挠度序狀项口序氏荷載荷救反力妙弯矩挠度反力剪力VrRiVB-RnfrmmR片=J?日=qbVARxiVE=-二翳S呻曲P伍式中；r=arba弯矩剪力图类荷載弯矩剪力fnrtTbv*wrn彗矩挽度(2)悬臂梁的反力、剪力、弯矩和挠度表2-7项丨1反力剪力rrTrrmnTTnjI反力荷戦剪力弯矩弯矩挠度剪力nminnno挠度Mk=-Fk；NTg三胚e-FlHp-F2113EIMK=-F(JU)；Mrrj=jMfc=-Ffr3-4序次屈类图示项目计算式

5、3荷载,.nFH11反力nF剪力V-b-Re弯矩丄I；打1hrnTirnnMe-n21巩剪力屮11111挠度3n2+4n+1“24.EI用4荷载a_.ILllllltlTTJT04-1反力剪力%Rb弯矩11infTTlTT3弯矩Mg-MB-剪力-WLLUj挠度wira=WA=aE/5荷裁I.LI占反力R=qu.剪力F-J?B厂才FI弯矩-rrrrrTTTUni曹矩M*=Mb=-竽(2-a)剪力wnnnn挠度叫f计舶（4知划6荷戟ArnrrnlaLb.t反力Kfl-qb*剪力-PH专矩弯矩Mr=-字剪力挠度S=翥A-于）图类图示顼目计算式1荷載疔予扌反力况R_斟剪力仆-Rb弯矩TTrrTTHl弯

6、矩Mb=qcb剪力挠度叫-磊门21-4衣+砂巧端简支另一端固定梁的反力、剪力、弯矩和挠度表2-8项冃反力荷載剪力弯矩剪力挠度当工-0,44兀时，址3-0”0旳炭粤荷載反力剪力Va=Ra；Vb=-J?b弯币弯拒剪力挠度璋矩剪力MJjjllllJUlimr呼inIill反力CB駁：=尺已(Hihf芒)-3F巾U+F(m)A=ft2-3!)1尺L号(2+3亍-3%)剪力J=Ra；Ve-Kb弯矩肚轲尸RmMr-1_JJ挠度CD段：叫=777：RA3fJ：Er-3F(I22ai2ax)xpjtlfF序决图类图示项口计n式反力尺人占卡“；尺万=-|皿荷载TrmrL/-JtaQil31剪力FSVb=陷r弯緬

7、弯矩当二一铲时,皿严空i1LLJ5AC段：rnr叫-24；L4Ra几一/)-4(3R亠J)+肿*1BC段；7L1；I剪力撓度wx*.(4-Ra(32jc-t3)-qa(aJ+12&Zx)+6iij?2-4t3=aU；suLi.禹茁AuR*(3t2-i；2-3空i*C4ZA+a_!4反力活w剖-沪勻荷载川屉1Mill【：6卜a一th剪力沪鬆;VB-/?HT弯矩d弯矩T.r-口+爭h冏映-/?a+制6ITrtrAC段：叫g&fI.尺A(3/z-：Ll)-rfijr1BCtvui.in圜力挠度tC：-24/4J；a(i2-TT)4fl63.rm:r.a)艸上一口吋：叫&；fLKa(3厂-/)qb序次

8、图类图示项甘计M盍7荷载rnfmkL反力1空(.121-4丹厨h弟EL-酬1一纵码力A=J?AiVB=-Kb弯矩当|+牛时t融十尺叭十謝剪力挠度皿段；叫一24EJ-届衣口：丁-工-)-7*1(12fr2+蓟-T1CD段:題严24.ARa咯-申-讪|(12b2Uj?)x+Q(丈-0L)：两端固定梁的反力、剪力、弯矩和挠度表2-9严弋町莎t.Ttr，Er?9气十严亦-严迓-卜严珂严-普-也嚼W亠-口辻严十昨-9)U=aA=VA皿#TnWrrb驚f:，叫；:阿1籍亠巩冉HTTirnTTrz纟W一呵叫严V糅八叫二臥年固侶林-ha!M-va兀_n阳_已_廿目竝LLUJdYnTTrTTr,严7iiMiii

9、umiHiiiiiiiii籌星华廡車品霸舉第国爼闿资料资料序伙图类图示项目th算式6荷载才_IlWl一B屮曰扌b葦a扌*n.挠度wc=D=f（2+t）.-r*0.5/时，ttn.n-詈吉7荷載fL4-反力K号（2+3亍hR沪書剪力*人二-R;Fr二JSn弯砸dflrrrnuyj弯矩血-Fd；AfD-y剪力1llLHillIliPTr挠度叭箸b+斗亍）当工三口+十时.witAi=-荷载1c岭反力盼普3目亍+哼b吩普-厝）Jr-剪力bAi=-QiJiVa3_Rfi；vb-Rb弯矩uinppA弯矩ML怡阪八曾（为剪力挠度咱黠卜“曙T）9荷栽24_40.096-0.U6.3,0.4377.箕30.06

10、30.0630+&12-o.jyi3r尸zrJAIBtcF140.1560.156-0.1S80.312-0,6SB0.68&-0.3120.9110.9114|F令4bABC4$“I+0.203-0.0940.406-0,5940加0.0941,497-n,5865rFif卜-Lt0.222D.222-0.667-1.3331,333-D.6671.4661.4666T会合0,278-(JJ670,833-1.1670.1670,1672+508-1.042注:1.在均布荷载作用下：M二表中系数xq|2；v二表中系数xql;w=表中系数。100EI2在集中荷载作用下：M二表中系数xFl；V二

11、表中系数xF；w=表中系数X亘。100EI2）三跨等跨梁的内力和挠度系数表2-12荷载图鹭内Jft大弯頫支麼弯矩剪力跨度中点挠度Mlm2Me*畑%-10.0800.025-0.100-0.10C0.400-0.6000.500-fl.5000.600-0.4000.677O.OJ2o.6n序荷载图跨内最丸弯矩支座彎矩剪力跨度中点挽度w,MiMrMevAVbk心VcfiVdW5Wy2-rjm.fta!.1O1-0.0500-4500.550000*5507.4500.990-0.6250.903T_丿htWij一.075-0,050-0.050-O.OSfl-0.0500,500-0.5000.

12、0500.050-0.3130.677-0.313fb4qnTTTTTFITJriTnf*?0.073D.054-0.117-0.0330.383-0*6170JS3-0+4I70.0330.0330,5730.365-0,2085fitiItit&、444dCD0.094-0.0670.0170.433-0.5670.0830.083-0J)170.&85-0.3130.1045rrr/(M)倉伽勺Cw844】*.1&+175),100-0,150-0.1500.350-0.6500.500-0.5000.650-0.35C1.1460.2081.1467、Fr).213一-0.0750.0

13、750.425-0.575000,575-0.4251+615-0.9371.615B?8?8DA75-0.075-0.075-0,075_0.0750.500-0.5000.0750,075-0.4691,146-0,4699|F广2厂飞D0.1623.1370+175-0+0500.325-0.6750.625-03750,0500,0500.9900.67?-0.312序荷载fl跨内盘大支座彎矩力跨度屮点挠度M;MeMeVaN沁Jr/ivDW11iJ310ArAL2DC一CL1DD0.D250.400-0,600.1250.125-0,025-0,0251.458-0.4&90.1561

14、1A|FFf厲A24出).D67-0.267-0.2670.7SS-1.2671.000-1.OOC1.267-0.7331.8甜10.21612AFF?s7.133-1.134001,134-0.8662.7161.6672E613AAAB-U.133U-133-0.133-0.133】,000-14000J330333-0.8331.883-0.83314F|LA|FqrCDn.zsyK17C-0.3L1-0,0890.689-13H1.222-0t770.0890.0891.6051.049-0.55(AV；对*?8_-0.1740.0440.822-1,17；0.2220.222-0.

15、0412.438-0.83：0+278注I在均布荷载作用下：匸表中系数g表中系数心；w=表中系数X册2在集中荷载作用下M表中系数汨2表中系数心w=表中系数数100EI3）四跨等跨连续梁内力和挠度系数表2-13荷裁團弯篦剪h谿就中点挠度toMz中McsvAW咄：畑%VcrrWJl0.077().036-U.1U7-0.07103M3-0.6070.5360应404M0.632Q.186半启i7C匸管!罩TrrfD.1&90.116-O.lhl-0.101(M鹑-0.6610.554-0,4460.461.070,409A7严(tD.2380.111-().2B-0.191().714-1.2S6

16、1,095-0.9050,9051.7640.573:i:4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荷朝倚图胯度中点挠度-0.606-0.474J.046-0-LU5-Q.0791).3150.5260.500-O.65H-0.46(.1710.112).132-0.158-U.118DM1.09?0.5400.500弯矩剪Ji035(5Lfi031.24CD.LOOL122-0.2810.2110.719-1.2811.07E1.7950.479.918注：同三跨等跨连续梁nMjy：%(叭J1VVc1.0-U.125L)0,0703(k07)30.3750-Q.SZ50

17、Q.W50-0,37500-0957-0.13880.065310,HH93J).3613-0.63870.6761-0.42390,09701.27”15500.05P50.LIDS0.3450-0.65500.7292-0.47080.09821.3O.173S0.05320*13330.32-0-67370.7836-0.51640+09931.4-0,19500.04650.15720.3050-0.69500.8393-n.56070.10031.3-0.21R80.93%0.18250.2S13Ck7t870.8958-G.6042ij.ltin1.60+2450O.(B250.2

18、09242烦-0.745D0.9S310.64690.10211.7-().27330-02560.2374(1.2263-0.7737roiw-Q.6SW0.10291.8-0.30500.0190O,2t69(1.-orSOSOL0694-0.73060-171.9-0.53880.0130().29780.16B-0.83871,12143-0.77170.10442,0-0.S750(Ln(J7K0+330t0.12M)-O.87SO1.1875-0,8125比呃2.25-0.47660.0003UM0.02340,97661.3368-0.9132u.g2.5-0.5938).512

19、6-0.W3S-1.09381,4875-1.01250.1073资料注：1.M二表中系数xql2i;v二表中系数xqli;2.（M）、（V）表示它为相应跨内的最大内力11maxmax2）三不等跨梁内力系数表2-i61皿盯-0.35400.1111-0,08310.0680-卜)4910.41690.416-0,58040.20000.2500-0.09470.460S0.45020.08900.00.6-5.08W0,7-0.0819(S.H0.08590.9-o.oyis1”0-(I-KHIOKI-1).】帕1.2-0.12181.3-(L1355k4-0.1510U5-0.1631.6-

20、0.1874-0.08040.07150.06640.06090.0S5OU.04R90.加820.0882-0.0350-0.021)60.08740.414IH.0095(L4O820.02500.4WU0*0761().04130.05820.07580.09400.11300.1327(1.1)4260.15310.42000.41810.590()0.3782(1.36450.34900.3317().31270.2918-0.58D0-U.5S19-0.59180.60U0-D.filOD-0.62LS0.6355-0.6510-(I.66B3fl.7(1820.4SD30.482

21、50.0964-0.11670.MW0.65OUG.15220.7D0U0.B50U0.16760.1848-0.2037-0.2244-0.6U21*0.6167-D.6267-(1.6676-0.6848-U.7037-0.72440.S1T60.5833-0.2308-0.2S52th03620J7420.2692-0.73080.90(X)-0.2468().0300(KDL060.1961I.218KCL27B8(i.3437(k24480.21880.1462-0.0625-0.7552-0.7812-C.8538-n.93750.95001.00001.1250-1).2710-

22、0.7710-0.299-0.86911.C3I2-0.45210.952TUO9820,09980,1013资料资料4双向板在均布荷载作用下的内力及变形系数表（表2-17表2-22符号说明如下：Eh312(1-u2)刚度式中E弹性模量；h板厚；v泊松比；3、3分别为板中心点的挠度和最大挠度；maxM为平行于l方向板中心点的弯矩；XXM为平行于l方向板中心点的弯矩；yyM0固定边中点沿l方向的弯矩；XXM0固定边中点沿l方向的弯矩。yy正负号的规定：弯矩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2-17YpJ1I;JJJJJI；zTIT11fI111V111I挠度匚衣

23、出系数$弓A弯矩-农中系数巾广式中耽比和如中之较小者3wM,0.5()0.010130.09651)-0174o.&o0J)D6O30.05610.03340.55(J.0094(!(L0B920.02KJ0.R50,(K15470.05060.0348O.600.008670.D82D0+02420.9fJ0,004960.0456山03580.650.007射6O.DSCO.D27110.5O.OD449(L04100.036*0.700,00727(LO6830.02961.000.00406U.Q368(J.05680.750.00663f+06200.03171三边简支，一边固定表2

24、-18挠度-表屮系數技甞令矩-表中祭敎理式屮2耽匚和山中之较小斤人亿MX应MzM?W-Afy翊0.500.005040.05830.0(160-0.1212U.950.00324(1.0324(L0(280(.1咖0.550.004920,05630.00810.900.D036H0.03280.0322-0.09260.600.004720.05390.0104-0.tL5Sn.350.004170.03290.0370-0.09700.650.QQ44S0.05130.0126-A.U241D.SO0.004730.03260.0424-0.10140.700.00422D.O4S30.0

25、H8-0.1087U.750,005560.03190.04B5-0,10H0.750.UU399卜加0,0168-0.1048r.m0.UU6O50.030S0.0553-DJ0960.800.W376.042B0.01S70.10070.650.DD6SCIQ.Q2910.0627-011330.850.00352Q.OW0.0204-0.09650.600.007620.02680.0?07-U.1H6().900.00329(!.O37200219-00922f-550.0(&48U-023M0.0792-D.11930,951.00LOO0.00306).002850.03450.0

26、3190.0232D.0243(J.0880-O.OB391.50(J.009350,02050.)8801.-0.1215两边简支，两边固定表2-19资料资料_-I-L-二匚匚一一-二_二一-=!=挠度丧出系数V習K弯距=表中系数凭4厂式中J耽仃切*中之较少若W呦2*叽Aly0.500.C02610.04160JI017-0.08430.950.002230.0296ci,(n黔0.07460.550.002591).04100.0028-0.084110.9(10.002600.03060,0224-U.C)770.600.002550.04020.0042-0.1JKA4B.850.00

27、303003140.0266-41用刊0-65(J.002SO0.03920.0057-1).08260.80000354(L03190.0316r1).09040.700*002430.()3790.(1072-0.08140.750.004130.03210.0374-0.09590.75).002360,0366U.U08S-0.07990,700.004820,031S0.0441-U.10130.800+00228(1.03510.(1103-0.07821U.650.005600.0308D.0518-0.1066C.850.002200.03S50,0118-*Q.07fi311

28、,600.006470.02920.06040.11140.90D.00Z1L0.0319D.0133-0.0743(1.550.0(17430-02670.0698-0.11561).951.D01.W0.002010.001920.C3020.02B5042石0.0158-0.D721-0.069814刃Q.008440.02340.0798-C.1191边简支，三边固定表2-20挠度二战中XjK暉矩=農中奈数成屮I取4和-屮之较小苦资料资料X.矶1max陆Mr0.500.002580.04080.002B-0.0836-0.0569(J.550+W2550.05980.0042-0.08

29、27-0.05700.600+002490.D3M0.005SJ-0.0814-0.05710.650.002400.03680.0076-0.07%0.05720.700,002290,03500*003-0.0774-0.D5720.75().00219(1.0331O.ni(K-0.Q75Q-O.OS720,8()0.0020E(1.0310D.01124-0.0722-0.0570U,50.001960.02890.0138-0.0693-0.0567D.90.05.5(1U,9S0.001820.0229Q.0194-0.0629-0.05990.900-002060.02280.0

30、223-0.065fi-0.06530.850.002330.02250.0255-0.0683-0,0711O.tf0.002620.0219o.o2y()-0.0707-0.07720.75G-00294fl.r)20M0.0329-(L0729-0.08370.700.003270.01.94min兀-0.074R-0.Q9O30.650,003650.U1750.0412-0.0762-0.09700.6(10.004030.01,53D.D454-0.U773-.1。站0.550.004370.01270.04%-0,10930.500,004630,00990.US34-0.078

31、J-0.1146四边固定表2-21挠度二表中系舉八弓K.弯炜h凰中系弍屮2耽匚和5中之较小斤w叽My讹0*002530.04000.(H)J-0,0829-0.05701).550+002晰0.03850.00560,0814-0+05711).00+00236(J.03670.0076-0,0793-D.05710.650.002240.0095-0.0765-D,O5710.7D).002110.03210.0113-0.735-0.05690.7O.OD1Q70.02960.0130-omi-0.0565血帥0.0Q1820,02710.0144-0,0654-0.05590.S50.0

32、016S0.0216).0136-0,0626-0.0551D.900.0DL530.02210.Q165-0.0588-0.05410.950.001400.O19Sfl.ni72-0.0550-O.OJ2S1.(JO0.001270.01760.D176-0.0513-0*0513两边简支，两边固定表2-22MgM；J何05flD.00471(1.0559().0079-0.1H9-0.0786L)550-004540.0529().0104-0.1140-0.07850fil)0.004290.04960.0129-0.1055-0.07820650.003990.UJ610.01511

33、-0.1045-0.0777(J700,003680.0426U.(H72-0+0992-0.07700750.003400.03900.0189-0.0938-(1.07600800.003130,03560.0204-o.om-0.0748085),002腑0,03220.0215-0.0829ogon002610.02910.0224-0.0776-0.07160950.002370.02610.0230-0.0726-0.069S100J.UD215C.02S40.0234-0.0677-O.OS775拱的内力计算表（表2-23）各种荷载作用下双铰抛物线拱计算公式表2-23资料简图公式

34、资料简图公式扣讣一气荃*厂4专*M尸将卅资料希图公式资料希图公式辄:一除64-61Ki茹厂甲Caa资料资料Mc=丼支座情况：无拉杆;带拉杆,R为可功恢支座：独拉A为可勃校支座Z-专咏Ha-0.T20K-2Lr3H沪昉Mc=/丄二丄/ZZZI2V4/支座情况：无拉杆；蒂拉杆”H为可动檢支座；带拉坏，A为可动诙支座，禺一訝5-t)a+16a1-】2+yasIqfHa-层亠斬Me-竽-linfZ=t2(5-lQff-1Q1卅亠号討q/K也二-讥时。瓯-乎-苛方二a25-lOcj*L6trJ-L6w*+晋”-乡g/KHa=IHb=fl/|Me=-1jj#L-Z/R扎-一Rb-等H=遗跖支座情祝：(1)无拉杆中带拉杆乙吕为可动校支座.(3带拉秆乙4为可幼较支座:lJH厂急如円人二誥甘Mu二哈Z-2qfKtHs-0,H晋，血急崔帖)f、rKH“常If101K-1吧卢E_2立讨心JA-0,Hji-,-Vfc-252X(2)2-J?B=-哈支座悄况：(1)兀拉杆；(2J带拉杆艮B为可动較支座；3带f2+T-Z.A为可动較支座。(1)He-:.Ha-；,Mc-0Z-:K,Hb-0.Ha-P,Afc-12KPfpK二1)Z-yK,HiHh-PiMc-Pf门(3Ra=-J?p=一卒fS圏公式血三于口(1-a-2a2+4(r3-yff