1、靜定結(jié)構(gòu)與超靜定結(jié)構(gòu)靜力計(jì)算公式

1、靜定結(jié)構(gòu)與超靜定結(jié)構(gòu)靜力常用計(jì)算公式、短柱、長(zhǎng)柱壓應(yīng)力極限荷載計(jì)算公式1、短柱壓應(yīng)力計(jì)算公式荷載作用點(diǎn)一般截面軸方向荷載偏心荷載偏心荷載AFA長(zhǎng)短柱分界點(diǎn)如何界定？2、長(zhǎng)柱方程式及極限荷載計(jì)算公式支座形式兩端錢(qián)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方程式極限荷載一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圖示F2 Fa = , M = F y EI兩端固定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一端錢(qián)支他 端固定3 =0.75d2y2Q2- + a *y =(l -x)dx2EI-.Q -、y = A cosax + Bsin ax +(l -x)a -,Q-水平荷載EI1.7778J

3、12 EI l2注：壓桿穩(wěn)定臨界承載水平計(jì)算公式:二 2EI二、單跨梁的反力、剪力、彎矩、撓度計(jì)算公式1、簡(jiǎn)支梁的反力、剪力、彎矩、撓度計(jì)算公式M圖LLLLL7yj 江c1 口 口【iThrr>7V圖“ 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彎 矩M 工ivi max -4.FabM =IVI maxlM _qL2M max 8M _qL2M max12撓 度FL3m max 一 48EI假設(shè)a> b

4、時(shí),Fb 叵 +2ab)3門(mén)3一9E|l3(在 x = J|(a+2b)處)qL4m max 一8EIqL4m max 一120EI注：1、彎矩符號(hào)以梁截面下翼緣手拉為正+,反之為負(fù)一.2、剪力符號(hào)以繞梁截面順時(shí)針?lè)较驗(yàn)檎?,反之為負(fù)一2、懸臂梁的反力、剪力、彎矩、撓度計(jì)算公式柚鼓 形式E3 1aR卜L1r1M圖rrrrrrrrnTnnrrnTIV圖III 口川川川LlllllilU反力Rb=FRb=-F剪力：V b=-RbVb=-Rb彎矩M b=-FLMB=-Fb撓度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、彎矩、撓度計(jì)算公式何裁f 1f_,形式t A At_La juLr tMl圖M 0<njV圖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 )彎矩M max二-FaMA=-FaMB=Fa/22nqaM A =-22 ma=£ 222Mb=W (i-2) 8L撓度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、一端簡(jiǎn)支梁de反力、剪力、彎矩

7、、撓度計(jì)算公式柚鼓 形式產(chǎn)i7J<7A TJ|：1r t i 11 + H iR T B t41LJM圖oNV圖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彎矩Mmax =篤(3-b) 2LLMa=MM中=qL2B=- 7224 qL2.9. 2M max =-qL128撓度8 max_qL4_一 384EI0max = 0.00542 qL三、等截面等跨連續(xù)梁的彎矩、剪力、撓度計(jì)算系數(shù)及公式1、二等跨連續(xù)梁的彎矩、剪力、撓度

8、計(jì)算系數(shù)及公式荷載圖示靜載活載最大活載最小 靜載活載最大活載最小活載最小彎矩系數(shù)Km剪力系數(shù)KV撓度系數(shù)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、均布荷載作用下:2qL4M = KMqL , v = KvqL , K = kiooei ；3集中荷載作用下：M = Km FL , V = Kv F , 0 = K®工 ；100 EI2、支座反力等于該支座左右截面剪力的絕對(duì)值之和；3、求跨中負(fù)彎矩及反撓度時(shí),可查用上表“活載最小 一項(xiàng)的系數(shù),但也要與靜 載引起的彎矩或撓度相組合.4、求跨中最大正彎矩及最大撓度時(shí),該跨應(yīng)滿布活荷載,相鄰跨為空載；求支座 最大負(fù)彎矩及最大剪力時(shí),該支座相鄰兩跨應(yīng)滿布荷載,即查用上表中“荷載最大一 項(xiàng)的系數(shù),并與靜載引起的彎矩剪力或撓度相組合.2、三等跨連續(xù)梁的彎矩、剪力、撓

10、度計(jì)算系數(shù)及公式荷載圖示彎矩系數(shù)Km剪力系數(shù)KV撓度系數(shù)KcoM中M中MB支VAVb左、Vb右3 1中2中靜載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牯截取大活載最小F1I靜載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、軟取人-0.6750.625活載最小-0.038-0.0750.025-0.469-0.937注：1、2、3條同上述二等跨連續(xù)梁;4、求某跨的跨中最大正彎矩及最大撓度時(shí),該跨應(yīng)滿布活荷載,其余每隔一跨滿 布活荷載；求某支座的最大負(fù)彎矩及最大剪力時(shí),該支座相鄰兩跨應(yīng)滿布活荷載,其余 每隔一跨滿布活荷載,即查上表中“活載最大 一項(xiàng)的系數(shù),并與靜載引起的彎矩(剪 力或撓度)相組合.3、四等跨連續(xù)梁的的彎矩、剪力、撓度計(jì)算系數(shù)及公式荷載圖示彎矩系數(shù)Km剪力系數(shù)Kv撓度系數(shù)KoM中M2中MB支MC支VAVb左、Vb右V：左、M右1中2中靜 載0.0770.036-0.107-0.0710.393-0.6

12、07-0.4640.6320.186見(jiàn)0.5360.464圖 沿載取人0.1000.081-0.121-0.1070.446-0.620-0.5710.9670.660a0.6030.571活載最小0.0230.0450.0130.018-0.307-0.588靜 載0.1690.116-0.161-0.1070.339-0.661-0.4461.0790.409見(jiàn)0.2100.183-0.181-0.1610.4200.5540.4461.5811,121圖 沿載取人-0.681-0.607b0.6540.607活載最小0.040-0.0670.0200.020-0.460-0.711p i

13、f p If曲夏 光致紀(jì)I L L,L | L | L |圖a圖b注：事項(xiàng)同三跨連續(xù)梁四、不等跨連續(xù)梁在均布荷載作用下的彎矩、剪力計(jì)算系數(shù)及公式1、二跨不等跨連續(xù)梁的彎矩、剪力計(jì)算系數(shù)及公式荷載簡(jiǎn)圖計(jì)算公式q彎矩=表中系數(shù)x qL12 (KN m) 剪力丫=表中系數(shù)x qL1 (KN)L LIL2=nU靜載時(shí)活載取不利仰直時(shí)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、三跨不等跨連續(xù)梁的彎矩、剪力計(jì)算系數(shù)及公式荷載簡(jiǎn)圖jaU i蠅？ Ki5Hi 與2身1 4r1t1靜載時(shí)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計(jì)算公式彎矩=表中系數(shù)x qL12 (KN m) 剪力丫=表中系數(shù)X qL1 (KN)活載取不利仰直時(shí)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、雙向板在均布荷載作用下的彎矩、撓度計(jì)算系數(shù)及公式四邊固定板的彎矩、撓度計(jì)算系數(shù)及公式簡(jiǎn)圖| Lx/L