1、静定结构与超静定结构静力计算公式

1、静定结构与超静定结构静力常用计算公式、短柱、长柱压应力极限荷载计算公式1、短柱压应力计算公式荷载作用点一般截面轴方向荷载偏心荷载偏心荷载AFA长短柱分界点如何界定？2、长柱方程式及极限荷载计算公式支座形式两端钱支3 =1一端自由他端固定3 =2F<T =AFcr =bhFye:一(1 -2 )Aijmy = f (ye)W AixF MY x:二一 二A Iy. Mx xIxF 6e “J"F6 ex 6ey(1 -)bh h b方程式极限荷载一M式n=1d2y 2TV =a 'y dxy = A cos ax + Bsin ax2 F 一 a = , M = F yE

2、I2 2EIl2打2了日d2y 22 a y dxy = A cos ax + Bsin ax22(2n-1)n E2EI4l2 22 EI4l2图示F2 Fa = , M = F y EI两端固定3 =0.54尸P2- -d yM a-4+a(y-A)=0dxFM Ay = A cosax + Bsin ax +F2 F 一一a =,M =F ,y+MA EIAA 2 4nl2 EI/24冗l2 EI一端钱支他 端固定3 =0.75d2y2Q2- + a *y =(l -x)dx2EI-.Q -、y = A cosax + Bsin ax +(l -x)a -,Q-水平荷载EI1.7778J

3、12 EI l2注：压杆稳定临界承载水平计算公式:二 2EI二、单跨梁的反力、剪力、弯矩、挠度计算公式1、简支梁的反力、剪力、弯矩、挠度计算公式M图LLLLL7yj 江c1 口 口【iThrr>7V图“ 1111【rm*LLII 口 口 11反 力Ra = Rb = 5cFb LRb=E LRa -Rb -qL2Ra- Rb-生4男 力Va=RaVb=-RbVa=RaVb=-RbVa=RaVb=-RbVa=RaVb=-Rb弯 矩M 工ivi max -4.FabM =IVI maxlM _qL2M max 8M _qL2M max12挠 度FL3m max 一 48EI假设a> b

4、时,Fb 叵 +2ab)3门3一9E|l3(在 x = J|(a+2b)处)qL4m max 一8EIqL4m max 一120EI注：1、弯矩符号以梁截面下翼缘手拉为正+,反之为负一.2、剪力符号以绕梁截面顺时针方向为正+,反之为负一2、悬臂梁的反力、剪力、弯矩、挠度计算公式柚鼓 形式E3 1aR卜L1r1M图rrrrrrrrnTnnrrnTIV图III 口川川川LlllllilU反力Rb=FRb=-F剪力：V b=-RbVb=-Rb弯矩M b=-FLMB=-Fb挠度FL38 A - 3EIFb20A =-b-(3L -b)A 6EIRB=qLRB=qaVb=-RbVb=-Rb.1 . 2M

5、b =qL 2Mb(2L a)2FL40 A - 8EI0A =-q24EI434M(3L4 -4b3L +b4)3、外伸梁的反力、剪力、弯矩、挠度计算公式何裁f 1f_,形式t A At_La juLr tMl图M 0<njV图i t i n 11t i i r i i i1 111 LI 1qc U 匾3 rLC砰a ,Lr1-rvdlTtK-rTrffriYk,rrrrT_"LLLL反力Ra=F(1 +：)Fa LRa =F(2+3a) 2L-3FaRb =-2LRa=?(1 +1)2 Rb=9(T)_qLa 6a2Ra =-L (3+8_ +_)A8L Uq qL,L

6、6a2、Rb q-(5-一) 8L剪力Va 左=-F Vb= - RbVa 左=-FVa 右=-RbVa 左=-qa VA右=RA-qa Vb= - RbVa左=-qaVa 左=生(5_) 8(L2 )弯矩M max二-FaMA=-FaMB=Fa/22nqaM A =-22 ma=£ 222Mb=W (i-2) 8L挠度0max _(L +a)3EIFa能一 12EI(3L 十四FaL2°max -27EIqa0c =24EI323x(-L3 +4La2 +3a3)qa0c =-48EI3 .2 .3m(-L +6La +6a )4、一端固定、一端简支梁de反力、剪力、弯矩

7、、挠度计算公式柚鼓 形式产i7J<7A TJ|：1r t i 11 + H iR T B t41LJM图oNV图11111riTTTTrII反力Fb2bRa=2Lt(3T)Fa a2Rb = (3-) 2LLRa=Rb1=-qL 2c 3 , R十LTl剪力Va=Ra Vb=-Rbvx 2(1卓Va=Ra Vb=-Rb弯矩Mmax =笃(3-b) 2LLMa=MM中=qL2B=- 7224 qL2.9. 2M max =-qL128挠度8 max_qL4_一 384EI0max = 0.00542 qL三、等截面等跨连续梁的弯矩、剪力、挠度计算系数及公式1、二等跨连续梁的弯矩、剪力、挠度

8、计算系数及公式荷载图示静载活载最大活载最小 静载活载最大活载最小活载最小弯矩系数Km剪力系数KV挠度系数KcoM中MB支VAVb左、Vb右3 1中0.070 1-0.125F 0.375-0.6250.5210.6250.096 1-0.1250.437-0.6250.1920.625-0.032-0.3910.156-0.1880.312-0.6880.9110.6880.203 1-0.1880.406-0.6881.4970.688-0.047-0.5860.222-0.3330.667-1.3331.4661.3330.278 10.3330.833-1.3332.5081.333-0

9、.084-1.042注：1、均布荷载作用下:2qL4M = KMqL , v = KvqL , K = kiooei ；3集中荷载作用下：M = Km FL , V = Kv F , 0 = K®工 ；100 EI2、支座反力等于该支座左右截面剪力的绝对值之和；3、求跨中负弯矩及反挠度时,可查用上表“活载最小 一项的系数,但也要与静 载引起的弯矩或挠度相组合.4、求跨中最大正弯矩及最大挠度时,该跨应满布活荷载,相邻跨为空载；求支座 最大负弯矩及最大剪力时,该支座相邻两跨应满布荷载,即查用上表中“荷载最大一 项的系数,并与静载引起的弯矩剪力或挠度相组合.2、三等跨连续梁的弯矩、剪力、挠

10、度计算系数及公式荷载图示弯矩系数Km剪力系数KV挠度系数KcoM中M中MB支VAVb左、Vb右3 1中2中静载0.0800.025-0.100-0.400-0.6000.6770.052Q0.101-0.0250.075-0.050-0.1770.0170.4500.500-0.6170.5830.990-0.3130.677-0.6251*升！1%升巨L L ._L_1_L_1牯截取大活载最小F1I静载0.1750.100-0.1500.350-0.6501.1460.208在期旦一P0.2130.175-0.1750.4250.5001.6151.146扇型L L 1_策rL _J_ L沽

11、软取人-0.6750.625活载最小-0.038-0.0750.025-0.469-0.937注：1、2、3条同上述二等跨连续梁;4、求某跨的跨中最大正弯矩及最大挠度时,该跨应满布活荷载,其余每隔一跨满 布活荷载；求某支座的最大负弯矩及最大剪力时,该支座相邻两跨应满布活荷载,其余 每隔一跨满布活荷载,即查上表中“活载最大 一项的系数,并与静载引起的弯矩(剪 力或挠度)相组合.3、四等跨连续梁的的弯矩、剪力、挠度计算系数及公式荷载图示弯矩系数Km剪力系数Kv挠度系数KoM中M2中MB支MC支VAVb左、Vb右V：左、M右1中2中静 载0.0770.036-0.107-0.0710.393-0.6

12、07-0.4640.6320.186见0.5360.464图 沿载取人0.1000.081-0.121-0.1070.446-0.620-0.5710.9670.660a0.6030.571活载最小0.0230.0450.0130.018-0.307-0.588静 载0.1690.116-0.161-0.1070.339-0.661-0.4461.0790.409见0.2100.183-0.181-0.1610.4200.5540.4461.5811,121图 沿载取人-0.681-0.607b0.6540.607活载最小0.040-0.0670.0200.020-0.460-0.711p i

13、f p If曲夏 光致纪I L L,L | L | L |图a图b注：事项同三跨连续梁四、不等跨连续梁在均布荷载作用下的弯矩、剪力计算系数及公式1、二跨不等跨连续梁的弯矩、剪力计算系数及公式荷载简图计算公式q弯矩=表中系数x qL12 (KN m) 剪力丫=表中系数x qL1 (KN)L LIL2=nU静载时活载取不利仰直时nM1M2M B最大VaV b左最大V b右最大VaM 1最大M 2最大V a最大V c最大1.00.0700.070-0.1250.375-0.6250.625-0.3750.0960.0960.433-0.4381.10.0650.090-0.1390.361-0.63

14、90.676-0.4240.0970.1140.440-0.4761.20.0600.111-0.1550.345-0.6550.729-0.4710.0980.1340.443-0.5181.30.0530.133-0.1750.326-0.6740.784-0.5160.0990.1560.446-0.5581.40.0470.157-0.1950.305-0.6950.839-0.5610.1000.1790.448-0.5981.50.0400.183-0.2190.281-0.7190.896-0.6040.1010.2030.450-0.6381.60.0330.209-0.245

15、0.255-0.7450.953-0.6470.1020.2290.452-0.6771.70.0260.237-0.2740.226-0.7741.011-0.6890.1030.2560.454-0.7161.80.0190.267-0.3050.195-0.8051.069-0.7310.1040.2850.455-0.7551.90.0130.298-0.3390.161-0.8391.128-0.7720.1040.3160.457-0.7942.00.0080.330-0.3750.125-0.8751.188-0.8130.1050.3470.458-0.8332.250.003

16、0.417-0.4770.023-0.9761.337-0.9130.1070.4330.462-0.9302.50.513-0.594-0.094-1.0941.488-1.0130.1080.5270.464-1.0272、三跨不等跨连续梁的弯矩、剪力计算系数及公式荷载简图jaU i蝇？ Ki5Hi 与2身1 4r1t1静载时nMiM2Mb支VaV b左0.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.02.252.50.0870.0880.0880.0870.0860.0830.0800.0760.0720.0660.0610.0550.

17、0490.0430.0360.0300.0240.0110.002-0.063-0.049-0.035-0.021-0.0060.0100.0250.0410.0580.0760.0940.1130.1330.1530.1740.1960.2190.2790.344-0.083-0.080-0.080-0.082-0.086-0.092-0.100-0.110-0.122-0.136-0.151-0.163-0.187-0.203-0.231-0.255-0.281-0.354-0.4330.4170.4200.4200.4130.4140.4080.4000.3900.3780.3650.3

18、490.3320.3130.2920.2690.2450.2190.1460.063-0.583-0.580-0.580-0.582-0.586-0.592-0.600-0.610-0.622-0.363-0.651-0.663-0.687-0.708-0.731-0.755-0.781-0.854-0.938计算公式弯矩=表中系数x qL12 (KN m) 剪力丫=表中系数X qL1 (KN)活载取不利仰直时V b右M1最大m2最大mb最大V a最大V b左最大V b右最大0.2000.2500.3000.3500.4000.4500.5000.5500.6000.6500.7000.750

19、0.8000.8500.9000.9501.0001.1251.2500.0890.0920.0940.0960.0980.1000.1010.1030.1040.1050.1060.1070.1070.1080.1090.1090.1100.1110.1120.0150.0220.0310.0400.0510.0630.0750.0890.1030.1180.1340.1510.1690.1880.2030.2290.2500.3070.370-0.096-0.095-0.095-0.098-0.102-0.108-0.117-0.127-0.139-0.152-0.168-0.185-0.

20、204-0.224-0.247-0.271-0.297-.0369-0.4520.4220.4290.4340.4390.4430.4470.4500.4530.4550.4580.4600.4620.4630.4650.4660.4680.4690.4710.474-0.596-0.595-0.595-0.593-0.602-0.608-0.617-0.627-0.639-0.652-0.668-0.635-0.704-0.724-0.747-0.771-0.797-0.869-0.9520.4610.4500.4600.4830.5120.5460.5830.6230.6650.7080.7530.7980.8430.8900.9370.9851.0311.1511.272五、双向板在均布荷载作用下的弯矩、挠度计算系数及公式四边固定板的弯矩、挠度计算系数及公式简图| Lx/L