拱涵計(jì)算書(shū)-6.0m-1m

1、拱圈計(jì)算書(shū)一.設(shè)計(jì)資料 1.計(jì)算荷載: 公路-I級(jí) 2.凈 跨 徑: L0 = 6m, 凈矢高: f0 =3m 凈矢跨比:f0/L0 =0.50 ,填土高: H =2m 3.拱圈用C30砼Raj=21Mpa, RWlj =3.2Mpa,Rjj = 4.7Mpa 涵臺(tái)用C25砼Raj=17.5Mpa, RWlj =2.8Mpa,Rjj = 4.2Mpa 基礎(chǔ)用C25砼Raj=17.5Mpa, RWlj =2.8Mpa,Rjj = 4.2Mpa 4.地基及拱上填料: 土的容重: 1 =18KN/m3, 內(nèi)摩擦角 =30度 拱背填料: 3 =19KN/m3, 砼的容重2 =25KN/m3 基底置于中

2、等密實(shí)的粗砂土,地基容許承載力 =400Kpa 5.結(jié)構(gòu)尺寸: 如圖示二.拱圈(等截面)尺寸擬定 1.拱圈厚度 石拱 t = m*k*L01/3 砼拱 t = 1.37*(R0+L0/2)1/2 + 6 磚拱 t = 1.37*(R0+L0/2)1/2 + 8 查涵洞手冊(cè)附表3-14（P620頁(yè)）得參數(shù) 0，sin0 ,cos0 R0 = L0/(2*sin0) 2.計(jì)算跨徑 L = L0 + t*sin0 計(jì)算半徑 R = L/(2*sin0) 計(jì)算矢高 f = R*(1-cos0) 拱圈尺寸擬定項(xiàng) 目L0(m)0（度） sin0R0(m)t(m)L(m)R(m)f(m)拱圈尺寸 6901.

3、00003.000.506.503.253.25三.荷載效應(yīng)計(jì)算及組合(一).恒載計(jì)算 1.恒載豎直壓力 拱頂填土壓力: q1 = 1* H 拱腳與拱頂填土壓力差 q2 = 2* f+t/2-t/(2*cos0) 拱圈自重力 q3 = qz = 3*t恒載豎直壓力項(xiàng) 目1(KN/m3)H(m)2(KN/m3)f (m)t (m)cos03(KN/m3) qi(KN/m2)拱頂填土182-36.0拱腳頂差-193.250.000.00-62拱圈自重-0.50-2512.5 .恒載水平壓力拱頂處： q4 = eq = 1*H*tan2(45-/2)恒載水平壓力項(xiàng) 目1(KN/m3)H(m)(度)4

4、(KN/m2)恒載水平力1823012.0(二).活載計(jì)算 1.汽車(chē)荷載豎直壓力 汽 = G/(a*b) a = a1 + 2*H*tan b = b1 + 2*H*tan汽車(chē)荷載豎直壓力項(xiàng) 目a1(m)H(m)(度)a(m)b1(m)b(m)G(KN)汽(KN/m2)汽載水平力0.32307.810.13.9156018.34 2.汽車(chē)荷載水平壓力 ep汽 = p汽*tan2(45-/2)汽車(chē)荷載水平壓力項(xiàng) 目汽(KN/m2)(度)e汽(KN/m2)備 注汽載水平力18.34306.11(三).內(nèi)力計(jì)算 1.彈性中心 查涵洞手冊(cè)附表3-14（P620頁(yè)）,得Ks ys = Ks*R Ic =

5、 b*t3/12 EI = 0.8*Ec*Ic彈性中心項(xiàng) 目KsR(m)ys(m)b(m)t(m)Ic(m4)Ec(Kpa)EI(KNm2)彈性中心0.363383.251.1810.500.01043.00E+072.50E+05 2.常變位 查涵洞手冊(cè)附表3-15（P621頁(yè)）,得k0,k1,k2,k3 11 = (k0*R)/EI 22 = R/EI*(k2*R2+k1*t2/12) 33 = (k3*R3)/EI常變位 項(xiàng) 目k0k1k2k3R(m)11(*EI)22(*EI)33(*EI)常變位 3.1415927 1.57079633 0.29755678 1.57079633.2

6、510.2110.3253.92 3.載變位 查涵洞手冊(cè)附表3-15（P621頁(yè)）各種形式的載變位項(xiàng) 目全跨均布載 倒圓形荷載拱圈重力雙側(cè)水平力 單側(cè)水平力 半跨均布載乘 數(shù)備 注i =123441-R (m)3.253.253.253.253.253.25-qi(KN/m2)36.061.712.512.012.036.0-ai-0.785398 -0.0548177 -0.8584088 -0.356195 -0.356195 -0.785398-載變位1pa1*R3(*q1) a2*R3(*q2) a3*R3(*q3) a4*R3(*q4)a4*R3/2(*q4)a1*R3/2(*q1)

7、qi/EI公 式ai*R3*qi-26.96-1.88-29.47-12.23-6.11-13.48-數(shù) 值bi-0.166667 -0.0166459 -0.1902846 -0.13089-0.13089 -0.166667-載變位2pb1*R4(*q1) b2*R4(*q2) b3*R4(*q3) b4*R4(*q4)b4*R4/2(*q4)b1*R4/2(*q1)qi/EI公 式bi*R4*qi-18.59-1.86-21.23-14.60-7.30-9.30-數(shù) 值ci0.000.000.000.00-0.16670.3333-載變位3pc1*R4(*q1) c2*R4(*q2) c

8、3*R4(*q3) c4*R4(*q4) c5*R4(*q4)c6*R4(*q1)qi/EI公 式ci*R4*qi0.000.000.000.00-18.5937.19-數(shù) 值 4.彈性中心處的贅余力 M0 = - 1p / 11 H0 = - 2p / 22 V0 = - 3p / 33彈性中心處的贅余力項(xiàng) 目全跨均布載 倒圓形荷載拱圈重力雙側(cè)水平力單側(cè)水平力半跨均布載左半拱右半拱左半拱右半拱1p-26.96-1.88-29.47-12.23-6.11-6.11-13.48-13.481110.2110.2110.2110.2110.2110.2110.2110.212p-18.59-1.8

9、6-21.23-14.60-7.30-7.30-9.30-9.302210.3210.3210.3210.3210.3210.3210.3210.323p0.000.000.000.00-18.59-18.5937.1937.193353.9253.9253.9253.9253.9253.9253.9253.92M0(KNm)2.640.182.891.200.600.601.321.32H0(KN)1.800.182.061.410.710.710.900.90V0(KN)0.000.000.000.000.340.34-0.69-0.69 5.外荷載在基本結(jié)構(gòu)上產(chǎn)生的內(nèi)力外荷載在基本結(jié)構(gòu)上

10、產(chǎn)生的內(nèi)力項(xiàng) 目全跨均布載 倒圓形荷載拱圈重力雙側(cè)水平力單側(cè)水平力半跨均布載左半拱右半拱左半拱右半拱i =12344411R (m)3.253.253.253.253.253.253.253.25qi(KN/m2)36.0061.7512.5012.0012.0012.0036.0036.00(-i)-0.5000-0.0479-0.5708-0.5000-0.50000.0000-0.50000.0000Mp(KNm)1*R2(*q1)2*R2(*q2)3*R2(*q3) 4*R2(*q4) 4*R2(*q4) 4*R2(*q4) 1*R2(*q1) 1*R2(*q1)(-i*R2*qi)-

11、5.28-0.51-6.03-5.28-5.280.00-5.280.00(-i)0.00000.00000.0000-1.0000-1.00000.00000.00000.0000Hp(KN)1*R(*q1) 2*R(*q2) 3*R(*q3) 4*R(*q4)4*R(*q4)4*R(*q4) 1*R(*q) 1*R(*q1)(-i*R*qi)0.000.000.00-3.25-3.250.000.000.00i1.00000.21461.57080.00000.00000.00001.00000.0000Pp(KN)1*R(*q1) 2*R(*q2) 3*R(*q3) 4*R(*q4)4*

12、R(*q4)4*R(*q4)1*R(*q1) 1*R(*q1)i*R*qi3.250.705.110.000.000.003.250.00 6.恒載作用下的內(nèi)力計(jì)算 拱頂截面 Md = M0 - H0 * ys Hd = H0 Vd = V0 拱腳截面 Mj = M0 + H0 * (f - ys) + Mp Hj = H0 + Hp Vj = V0 + Vp恒載作用下的內(nèi)力計(jì)算項(xiàng) 目全跨均布載 倒圓形荷載拱圈重力雙側(cè)水平力單側(cè)水平力半跨均布載拱頂填土拱背填土拱圈自重水平土壓力左半拱右半拱左半拱右半拱i =12344411ys (m)1.181.181.181.181.181.181.181.

13、18f (m)3.253.253.253.253.253.253.253.25qi(KN/m2)36.0061.7512.5012.000.000.000.000.00M0i(KNm)95.0611.3836.0814.370.000.000.000.00H0i（KN）64.8611.1125.7116.980.000.000.000.00V0i (KN)0.000.000.000.000.000.000.000.00Mp(KNm)-190.13-31.26-75.36-63.370.000.000.000.00Hp (KN)0.000.000.00-39.000.000.000.000.00

14、Vp (KN)117.0043.0763.810.000.000.000.000.00拱頂M(KNm)18.47-1.745.71-5.680.000.000.000.00拱頂H (KN)64.8611.1125.7116.980.000.000.000.00拱頂V (KN)0.000.000.000.000.000.000.000.00拱腳M(KNm)39.133.1113.91-13.870.000.000.000.00拱腳H (KN)64.8611.1125.71-22.020.000.000.000.00拱腳V (KN) 117.0043.0763.810.000.000.000.00

15、0.00 6.汽車(chē)荷載作用下的內(nèi)力計(jì)算 1).全跨均布荷載，雙側(cè)水平力作用時(shí) 拱頂截面 Md = M0 - H0 * ys Hd = H0 Vd = V0 拱腳截面 Mj = M0 + H0 * (f - ys) + Mp Hj = H0 + Hp Vj = V0 + Vp 2).半跨均布荷載，單側(cè)水平力作用時(shí) 拱頂截面 Md = M0 - H0 * ys Hd = H0 Vd = V0 左拱腳截面 Mj = M0 + H0 * (f - ys) + Mp - V0*L/2 Hj = H0 + Hp Vj = V0 + Vp 右拱腳截面 Mj = M0 + H0 * (f - ys) + Mp

16、 + V0*L/2 Hj = H0 + Hp Vj = -V0 + Vp汽車(chē)荷載作用下的內(nèi)力計(jì)算項(xiàng) 目全跨均布載 倒圓形荷載拱圈重力雙側(cè)水平力 左側(cè)水平力(汽車(chē)荷載) 左半跨均布載(汽車(chē)荷載)汽車(chē)荷載 汽車(chē)土壓力左半拱 右半拱左半拱右半拱i =12344411ys (m)1.181.181.181.181.181.181.181.18f (m)3.253.253.253.253.253.253.253.25L (m)6.506.506.506.506.506.506.506.50qi(KN/m2)18.340.000.006.116.116.1118.3418.34M0i(KNm)48.440

17、.000.007.323.663.6624.2224.22H0i（KN）33.050.000.008.654.334.3316.5216.52V0i (KN)0.000.000.000.002.112.11-12.65-12.65Mp(KNm)-96.870.000.00-32.29-32.290.00-96.870.00Hp (KN)0.000.000.00-19.87-19.870.000.000.00Vp (KN)59.610.000.000.000.000.0059.610.00拱頂M(KNm)9.410.000.00-2.89-1.45-1.454.704.70拱頂H (KN)33.

18、050.000.008.654.334.3316.5216.52拱頂V (KN)0.000.000.000.002.112.11-12.65-12.65拱腳M(KNm)19.940.000.00-7.07-26.5319.462.6517.29拱腳H (KN)33.050.000.00-11.22-15.554.3316.5216.52拱腳V (KN)59.610.000.000.002.11-2.1146.9612.65(四).內(nèi)力組合 1.恒載內(nèi)力合計(jì)恒 載 內(nèi) 力 合 計(jì)荷 載 項(xiàng) 目拱 頂 截 面拱 腳 截 面(左右側(cè))M（KN）H（KN）V（KN）M（KN）H（KN）V（KN）拱 頂

19、 填 土18.4764.860.0039.1364.86117.00拱 背 填 土-1.7411.110.003.1111.1143.07拱 圈 自 重5.7125.710.0013.9125.7163.81恒 載 內(nèi) 力 合 計(jì)22.44101.680.0056.15101.68223.88水 平 土 壓 力-5.6816.980.00-13.87-22.020.00 2.汽車(chē)荷載內(nèi)力合計(jì)汽 車(chē) 荷 載 內(nèi) 力 合 計(jì)荷 載 項(xiàng) 目拱 頂 截 面拱 腳 截 面M（KN）H（KN）V（KN）M（KN）H（KN）V（KN）汽車(chē)荷載拱頂作用(全跨） 9.4133.050.0019.9433.055

20、9.61汽車(chē)荷載拱頂作用(半跨） 4.7016.52-12.652.6516.5246.96汽車(chē)荷載水平土壓力(雙側(cè))-2.898.650.00-7.07-11.220.00汽車(chē)荷載水平土壓力(單側(cè))-1.454.332.11-26.53-15.552.11汽 車(chē) 荷 載 內(nèi) 力 合 計(jì)荷 載 項(xiàng) 目左 側(cè) 拱 腳 截 面右 側(cè) 拱 腳 截 面M（KN）H（KN）V（KN）M（KN）H（KN）V（KN）汽車(chē)荷載拱頂作用(全跨） 19.9433.0559.6119.9433.0559.61汽車(chē)荷載拱頂作用(半跨） 2.6516.5246.9617.2916.5212.65汽車(chē)荷載水平土壓力(雙側(cè)

21、)-7.07-11.220.00-7.07-11.220.00汽車(chē)荷載水平土壓力(單側(cè))-26.53-15.552.1119.464.33-2.11 3.拱圈荷載內(nèi)力組合 組合I: Sd = 1.1*1.2*(1)+1.4*(2)項(xiàng) 目 Sd = 1.1*1.2*(1)+1.4*(2)+1.4*(3)+0.8*1.4*(5) Sd = 1.1*1.2*(1)+1.4*(2)+1.4*(4)+0.8*1.4*(6) 組合II: Sd = 1.0*(1)+1.0*(2) - 長(zhǎng)期效應(yīng) Sd = 1.0*(1)+1.0*(2) - 短期效應(yīng) Sd = 1.0*(1)+1.0*(2)+0.7*(3)+

22、1.0*(5) - 長(zhǎng)期效應(yīng) Sd = 1.0*(1)+1.0*(2)+0.4*(3)+1.0*(5) - 短期效應(yīng) Sd = 1.0*(1)+1.0*(2)+0.7*(4)+1.0*(6) - 長(zhǎng)期效應(yīng) Sd = 1.0*(1)+1.0*(2)+0.4*(4)+1.0*(6) - 短期效應(yīng) 組合II: Sd = 1.0*(1)+1.0*(2) Sd = 1.0*(1)+1.0*(2)+1.0*(3)+1.0*(5) Sd = 1.0*(1)+1.0*(2)+1.0*(4)+1.0*(6)拱 圈 荷 載 內(nèi) 力 組 合序 號(hào)荷 載 項(xiàng) 目拱 頂 截 面拱 腳 截 面M（KN）H（KN）V（KN

23、）M（KN）H（KN）V（KN）1恒 載 自 重22.44101.680.0056.15101.68223.882恒 載 土 壓 力-5.6816.980.00-13.87-22.020.003汽 車(chē) 荷 載(全跨)9.4133.050.0019.9433.0559.614汽 車(chē) 荷 載(半跨)4.7016.52-12.652.6516.5246.965汽 車(chē) 土 壓(雙側(cè))-2.898.650.00-7.07-11.220.006汽 車(chē) 土 壓(單側(cè))-1.454.332.11-26.53-15.552.11組合I1 + 2 20.87160.370.0052.75100.31295.521

24、 + 2 + 3 + 531.79221.920.0074.74137.37387.331 + 2 + 4 + 626.33191.14-16.8824.13106.60370.44組合II1 + 2 16.76118.660.0042.2779.66223.881 + 2 16.76118.660.0042.2779.66223.881 + 2 + 3 + 520.45150.440.0049.1691.57265.611 + 2 + 3 + 517.62140.530.0043.1881.66247.731 + 2 + 4 + 618.60134.55-6.7517.5975.68258.

25、861 + 2 + 4 + 617.19129.59-2.9516.8070.72244.78組合III1 + 2 16.76118.660.0042.2779.66223.881 + 2 + 3 + 523.27160.360.0055.14101.49283.491 + 2 + 4 + 620.01139.51-10.5418.3980.64272.95拱 圈 荷 載 內(nèi) 力 組 合序 號(hào)荷 載 項(xiàng) 目左 側(cè) 拱 腳 截 面右 側(cè) 拱 腳 截 面M（KN）H（KN）V（KN）M（KN）H（KN）V（KN）1恒 載 自 重56.15101.68223.8856.15101.68223.882

26、恒 載 土 壓 力-13.87-22.020.00-13.87-22.020.003汽 車(chē) 荷 載(全跨)19.9433.0559.6119.9433.0559.614汽 車(chē) 荷 載(半跨)2.6516.5246.9617.2916.5212.655汽 車(chē) 土 壓(雙側(cè))-7.07-11.220.00-7.07-11.220.006汽 車(chē) 土 壓(單側(cè))-26.53-15.552.1119.464.33-2.11組合I1 + 2 52.75100.31295.5252.75100.31295.521 + 2 + 3 + 574.74137.37387.3374.74137.37387.331

27、+ 2 + 4 + 624.13106.60370.44103.35131.08312.41組合II1 + 2 42.2779.66223.8842.2779.66223.881 + 2 42.2779.66223.8842.2779.66223.881 + 2 + 3 + 549.1691.57265.6149.1691.57265.611 + 2 + 3 + 543.1881.66247.7343.1881.66247.731 + 2 + 4 + 617.5975.68258.8673.8495.55230.631 + 2 + 4 + 616.8070.72244.7868.6590.59

28、226.83組合III1 + 2 42.2779.66223.8842.2779.66223.881 + 2 + 3 + 555.14101.49283.4955.14101.49283.491 + 2 + 4 + 618.3980.64272.9579.03100.51234.42四.拱圈截面強(qiáng)度驗(yàn)算(一).按素砼構(gòu)件計(jì)算(當(dāng)填土較低時(shí)) 1.抗抗壓壓強(qiáng)強(qiáng)度度驗(yàn)驗(yàn)算算 計(jì)算強(qiáng)度時(shí), Nj Nu1 = *A*Raj/m (KN) 計(jì)算穩(wěn)定時(shí), Nj Nu2 = *A*Raj/m (KN) 拱圈計(jì)算長(zhǎng)度 l0 = S = 2*R*0 式中 Nj - 計(jì)算縱向力; A - 構(gòu)件的截面面積, A =

29、 b*h; Raj - 材料的抗壓極限強(qiáng)度; m - 材料安全系數(shù),m = 2.31 ; - 受壓構(gòu)件縱向彎曲系數(shù); = 1/1+a*b*(b-3)*1+1.33*(e0/h)2, a = 0.002 , b = l0/h - 縱向力的偏心影響系數(shù), = 1-(e0/y)m / 1+(e0/rw)2 y - 截面或換算截面重心至偏心方向截面邊緣的距離, y = h/2 (m); rw - 在彎曲平面內(nèi)截面(或換算截面)的回轉(zhuǎn)半徑; rw = (I/A)1/2 = 31/2*h/6 縱向力的偏心影響系數(shù)的計(jì)算截 面Md(KNm)Nd(KN)e0(m)y=t/2(m)mm l0(m)拱頂I20.8

30、70.00-0.258.00-2.3110.2131.790.00-0.258.00-2.3110.2126.33-16.88-0.258.00-2.3110.21拱腳I52.75295.520.180.258.000.372.3110.2174.74387.330.190.258.000.312.3110.21103.35312.410.330.258.00-1.342.3110.21左側(cè)拱腳I52.75295.520.180.258.000.372.3110.2174.74387.330.190.258.000.312.3110.2124.13370.440.070.258.000.832

31、.3110.21右側(cè)拱腳I52.75295.520.180.258.000.372.3110.2174.74387.330.190.258.000.312.3110.21103.35312.410.330.258.00-1.342.3110.21抗壓強(qiáng)度驗(yàn)算截 面b(m)h=t(m)A (m2)Raj(Kpa)Nu1(KN)Nu2(KN)拱頂I-10.500.5021000-10.500.5021000-10.500.5021000-拱腳I0.54580.36910.500.50210001675.96914.810.53980.31410.500.50210001425.35769.460.

32、4704-1.34410.500.5021000-6107.99-2873.39左側(cè)拱腳I0.54580.36910.500.50210001675.96914.810.53980.31410.500.50210001425.35769.460.57890.83110.500.50210003776.072185.83右側(cè)拱腳I0.54580.36910.500.50210001675.96914.810.53980.31410.500.50210001425.35769.460.4704-1.34410.500.5021000-6107.99-2873.39 2.正正截截面面受受彎彎強(qiáng)強(qiáng)度度

33、驗(yàn)驗(yàn)算算 Mj Mu = W*Rwlj/m 式中 Mj - 計(jì)算彎矩; m - 材料安全系數(shù), m = 2.31 ; W - 截面受拉邊緣的彈性抵抗矩, W = bh2/6 ; Rwlj - 受拉邊邊層的彎曲抗拉極限強(qiáng)度;正截面受彎強(qiáng)度驗(yàn)算截 面b(m)h=t(m)W(m3)Rwlj(Kpa)m Mu (KNm)Md(KNm)備注拱頂I1.000.500.041732002.3157.720.9可以1.000.500.041732002.3157.731.8可以1.000.500.041732002.3157.726.3可以拱腳I1.000.500.041732002.3157.752.7可以

34、1.000.500.041732002.3157.774.7不可以1.000.500.041732002.3157.7103.4不可以左側(cè)拱腳I1.000.500.041732002.3157.752.7可以1.000.500.041732002.3157.774.7不可以1.000.500.041732002.3157.724.1可以右側(cè)拱腳I1.000.500.041732002.3157.752.7可以1.000.500.041732002.3157.774.7不可以1.000.500.041732002.3157.7103.4不可以 3.應(yīng)應(yīng)力力強(qiáng)強(qiáng)度度驗(yàn)驗(yàn)算算 max = N/A +

35、 M/W min = N/A - M/W 式中 N - 軸力; M - 彎矩; A - 拱圈截面面積, A = b*h ; W - 拱圈截面的截面抵抗矩, W = bh2/6 ;應(yīng)力強(qiáng)度驗(yàn)算截 面N(KN)A (m2)M(KNm)W (m3)max(Kpa) min(Kpa) a (Kpa)l (Kpa)拱頂I0.000.5020.870.0417501-500.819090.91-1385.280.000.5031.790.0417763-762.979090.91-1385.28-16.880.5026.330.0417598-665.669090.91-1385.28拱腳I295.520

36、.5052.750.04171857-674.869090.91-1385.28387.330.5074.740.04172568-1019.119090.91-1385.28312.410.50103.350.04173105-1855.649090.91-1385.28左側(cè)拱腳I295.520.5052.750.04171857-674.869090.91-1385.28387.330.5074.740.04172568-1019.119090.91-1385.28370.440.5024.130.04171320161.689090.91-1385.28右側(cè)拱腳I295.520.5052

37、.750.04171857-674.869090.91-1385.28387.330.5074.740.04172568-1019.119090.91-1385.28312.410.50103.350.04173105-1855.649090.91-1385.28 4.拱拱圈圈偏偏心心距距驗(yàn)驗(yàn)算算 = W/A , y = h/2 e0 = M/N Md 符合規(guī)定截面抗彎承載力計(jì)算截 面fcd(Kpa)b(m)x(m)h0(m)Mu1(KNm)Md(KNm)強(qiáng)度合理拱頂I138001.000.030.45169.7420.87是138001.000.030.45169.7431.79是13800

38、1.000.030.45169.7426.33是拱腳I138001.000.030.45169.7452.75是138001.000.030.45169.7474.74是138001.000.030.45169.74103.35是左側(cè)拱腳I138001.000.030.45169.7452.75是138001.000.030.45169.7474.74是138001.000.030.45169.7424.13是右側(cè)拱腳I138001.000.030.45169.7452.75是138001.000.030.45169.7474.74是138001.000.030.45169.74103.35是

39、 2.斜截面抗剪計(jì)算 1).構(gòu)件尺寸驗(yàn)算 (規(guī)范第5.2.9條) P29頁(yè) 0*Vd 0.51x10-3*fcu,k1/2*b*h0 = Qu1 式中: h0 - 用于抗剪配筋設(shè)計(jì)的最大剪力截面的有效高度(mm); b - 用于抗剪配筋設(shè)計(jì)的最大剪力截面的梁腹寬度(mm); fcu,k - 砼強(qiáng)度標(biāo)準(zhǔn)值(MPa);構(gòu)件尺寸驗(yàn)算截 面fcu,k(Mpa)b(mm)h0(mm)Qu1(KN)0*Vd (KN)尺寸合理拱頂I20.101000.00445.001017.490.00是20.101000.00445.001017.490.00是20.101000.00445.001017.49(16.

40、88)是拱腳I20.101000.00445.001017.49100.31是20.101000.00445.001017.49137.37是20.101000.00445.001017.49106.60是左側(cè)拱腳I20.101000.00445.001017.49100.31是20.101000.00445.001017.49137.37是20.101000.00445.001017.49106.60是右側(cè)拱腳I20.101000.00445.001017.49100.31是20.101000.00445.001017.49137.37是20.101000.00445.001017.4913

41、1.08是 2).按構(gòu)造配置箍筋條件 (規(guī)范第5.2.9條) P30頁(yè) 0*Vd 0.50 x10-3*ftd*b*h0 = Qu2 式中: h0 - 用于抗剪配筋設(shè)計(jì)的最大剪力截面的有效高度(mm); b - 用于抗剪配筋設(shè)計(jì)的最大剪力截面的梁腹寬度(mm); ftd - 砼抗拉強(qiáng)度標(biāo)準(zhǔn)值(MPa);按構(gòu)造配置箍筋截 面ftd(Mpa)b(mm)h0(mm)Qu2(KN)0*Vd (KN)構(gòu)造配筋拱頂I1.391000.00445.00309.280.00是1.391000.00445.00309.280.00是1.391000.00445.00309.28(16.88)是拱腳I1.3910

42、00.00445.00309.28100.31是1.391000.00445.00309.28137.37是1.391000.00445.00309.28106.60是左側(cè)拱腳I1.391000.00445.00309.28100.31是1.391000.00445.00309.28137.37是1.391000.00445.00309.28106.60是右側(cè)拱腳I1.391000.00445.00309.28100.31是1.391000.00445.00309.28137.37是1.391000.00445.00309.28131.08是 3).斜截面抗剪計(jì)算 (規(guī)范第5.2.7條) P2

43、8頁(yè) 0*Vd Vcs + Vsb + Vpb 箍筋間距的計(jì)算 Sv = 12*22*0.2x10-6*(2+0.6*P)*fcu,k1/2*Asv*fsv*b*h02/(*0*Vd)2 式中:Vd-斜截面受壓端上由作用(或荷載)效應(yīng)所產(chǎn)生的最大剪力 組合設(shè)計(jì)值(KN); -用于抗剪配筋設(shè)計(jì)時(shí)的最大剪力設(shè)計(jì)值分配于砼和箍筋 共同承擔(dān)的分配系數(shù),取=1.0(0.6); Asv-配置在同一截面內(nèi)箍筋總截面面積(mm2) P-斜截面內(nèi)縱向受拉鋼筋的配筋百分率,當(dāng)P2.5時(shí),p=2.5; P = 100*=100*As /(b*h0)=100* 1-異號(hào)彎矩影響系數(shù),1 = 1.0 ; 2-預(yù)應(yīng)力提高

44、系數(shù), 2 = 1.0 ; fsv-箍筋抗拉強(qiáng)度 箍筋的選取 截 面直徑(mm)Ag(cm2)根數(shù)nAsv(cm2)箍筋距Sk(cm)b(cm)svsvmin拱頂I12.001.13144.5225.00100.000.00180.001212.001.13144.5225.00100.000.00180.001212.001.13144.5225.00100.000.00180.0012拱腳I12.001.13144.5225.00100.000.00180.001212.001.13144.5225.00100.000.00180.001212.001.13144.5225.00100.0

45、00.00180.0012左側(cè)拱腳I12.001.13144.5225.00100.000.00180.001212.001.13144.5225.00100.000.00180.001212.001.13144.5225.00100.000.00180.0012右側(cè)拱腳I12.001.13144.5225.00100.000.00180.001212.001.13144.5225.00100.000.00180.001212.001.13144.5225.00100.000.00180.0012 箍筋間距的計(jì)算 截 面fcu,k(Mpa)Asv(mm2)As(cm2)P=100*fsv(Mp

46、a)h0(mm)Vd(KN)Sv(mm)拱頂I20.10452.3914.070.32280.00445.000.00#DIV/0!20.10452.3914.070.32280.00445.000.00#DIV/0!20.10452.3914.070.32280.00445.00(16.88)172769拱腳I20.10452.3914.070.32280.00445.00100.31489520.10452.3914.070.32280.00445.00137.37261020.10452.3914.070.32280.00445.00106.604334左側(cè)拱腳I20.10452.391

47、4.070.32280.00445.00100.31489520.10452.3914.070.32280.00445.00137.37261020.10452.3914.070.32280.00445.00106.604334右側(cè)拱腳I20.10452.3914.070.32280.00445.00100.31489520.10452.3914.070.32280.00445.00137.37261020.10452.3914.070.32280.00445.00131.082866 3.斜截面抗彎計(jì)算 0*Md fsd*As*Zs+fsv*Asv*Zsv = Mu2 0*Vd fsv*As

48、v = Qu2 式中: Md-斜截面受壓端正截面彎矩組合設(shè)計(jì)值; Vd-斜截面受壓端正截面相應(yīng)于最大彎矩組合設(shè)計(jì)值 的剪力組合設(shè)計(jì)值; ZS-縱向普通受拉鋼筋合力點(diǎn)至受壓區(qū)中心點(diǎn)O的距離; Zsv-與斜截面相交的同一平面內(nèi)箍筋合力點(diǎn)至斜截面 受壓端的水平距離; 抗彎主筋選用HRB335鋼筋, fsd = 280.00Mpa As = n*Ag Zs = h0 - x/2 箍筋選用HRB235鋼筋, fsv = 195.00Mpa Asv = n*Agv 廣義剪跨比 m = Md/(Vd*h0) Zsv = C/2 = 0.6*m*h0/2 梁的剪跨比m計(jì)算截 面x (m)h0(m)Zs(m)M

49、d(KNm)Vd(KN)mh0(m)Zsv(m)拱頂I0.030.450.4320.870.00#DIV/0!0.45#DIV/0!0.030.450.4331.790.00#DIV/0!0.45#DIV/0!0.030.450.4326.33(16.88)(1.56)0.45-0.2082拱腳I0.030.450.4352.75100.310.530.450.07020.030.450.4374.74137.370.540.450.07260.030.450.43103.35106.600.970.450.1294左側(cè)拱腳I0.030.450.4352.75100.310.530.450.0

50、7020.030.450.4374.74137.370.540.450.07260.030.450.4324.13106.600.230.450.0302右側(cè)拱腳I0.030.450.4352.75100.310.530.450.07020.030.450.4374.74137.370.540.450.07260.030.450.43103.35131.080.790.450.1053 斜截面抗彎計(jì)算 截 面fsd(Mpa)As(mm2)Zs(m)fsv(Mpa)Asv(mm2)Zsv(m)Mu2(KNm)Qu2(KN)拱頂I280.001407.430.431953619.1#DIV/0!#

51、DIV/0!705.73280.001407.430.431953619.1#DIV/0!#DIV/0!705.73280.001407.430.431953619.1(0.21)22.82705.73拱腳I280.001407.430.431953619.10.07219.28705.73280.001407.430.431953619.10.07221.00705.73280.001407.430.431953619.10.13261.08705.73左側(cè)拱腳I280.001407.430.431953619.10.07219.28705.73280.001407.430.43195361

52、9.10.07221.00705.73280.001407.430.431953619.10.03191.07705.73右側(cè)拱腳I280.001407.430.431953619.10.07219.28705.73280.001407.430.431953619.10.07221.00705.73280.001407.430.431953619.10.11244.02705.73 所以 Mu2 = fsd*As*Zs+fsv*Asv*Zsv 0*Mud 符合規(guī)定 Qu2 = fsv*Asv 0*Vd 符合規(guī)定 4.偏心受壓構(gòu)件強(qiáng)度計(jì)算 (規(guī)范第5.3.5條) P35頁(yè) 大小偏心受壓構(gòu)件的判定

53、: a.當(dāng)b時(shí)為大偏心受壓構(gòu)件,s = fsd ,p = fpd , = x/h0 b.當(dāng)b時(shí)為小偏心受壓構(gòu)件,(規(guī)范第5.3.4條) P34頁(yè) 1.構(gòu)造要求 拱圈采用對(duì)稱(chēng)配筋,縱向鋼筋配筋率= As /(a*b) 拱圈配筋構(gòu)造要求截 面Md(KNm)Nd(KN)e0(m)a(cm)b(cm)As(cm2)配筋率min拱頂I20.870.00-100.0044.5014.070.00630.00531.790.00-100.0044.5014.070.00630.00526.33-16.88-100.0044.5014.070.00630.005拱腳I52.75295.520.18100.00

54、44.5014.070.00630.00574.74387.330.19100.0044.5014.070.00630.005103.35312.410.33100.0044.5014.070.00630.005左側(cè)拱腳I52.75295.520.18100.0044.5014.070.00630.00574.74387.330.19100.0044.5014.070.00630.00524.13370.440.07100.0044.5014.070.00630.005右側(cè)拱腳I52.75295.520.18100.0044.5014.070.00630.00574.74387.330.191

55、00.0044.5014.070.00630.005103.35312.410.33100.0044.5014.070.00630.005 2.偏心距增大系數(shù) 拱圈計(jì)算長(zhǎng)度 l0 = S = 2*R*0 1 = 0.2+2.7*e0/h0 1.0 ,取1 = 1.0 2 = 1.15 0.01*l0/h 1.0 所以 = 1+1/(1400*e0/h0)*(l0/h)2*1*2偏心距增大系數(shù)截 面l0(m)h(m)h0(m)12e0(m)*e0(m)拱頂I10.210.450.45-0.92-10.210.450.45-0.92-10.210.450.45-0.92-拱腳I10.210.450

56、.451.000.921.860.180.3310.210.450.451.000.921.800.190.3510.210.450.451.000.921.470.330.48左側(cè)拱腳I10.210.450.451.000.921.860.180.3310.210.450.451.000.921.800.190.3510.210.450.450.600.922.410.070.16右側(cè)拱腳I10.210.450.451.000.921.860.180.3310.210.450.451.000.921.800.190.3510.210.450.451.000.921.470.330.48 3.

57、按大偏心受壓構(gòu)件計(jì)算 0*Nd fcd*b*x + fsd*As -s*As = fcd*b*x x = 0*Nd/(fcd*b) = x/h0 b,為大偏心受壓構(gòu)件 e = *e0 + h/2 - a 0*Nd*e fcd*b*x*(h0-x/2) + fsd*As*(h0-as) = Mue 式中: e - 軸向力作用點(diǎn)至截面受拉邊或受壓較小邊縱向鋼筋A(yù)s的距離; e0 - 軸向力對(duì)截面重心軸的偏心距, e0 = Md/Nd; Md - 相應(yīng)于軸向力的彎矩組合設(shè)計(jì)值; h0 - 截面受壓較大邊邊緣至受拉邊或受壓較小邊縱向鋼筋合力點(diǎn)的距離, h0 = h - a - 偏心受壓構(gòu)件軸向力偏心矩

58、增大系數(shù).(見(jiàn)第5.3.10條)按大偏心受壓構(gòu)件計(jì)算截 面0*Nd(KN)fcd(Kpa)b(m)x(m)h0(m)b備 注拱頂I0.0013800.001.000.000.45-0.56-0.0013800.001.000.000.45-0.56-16.8813800.001.000.000.45-0.56-拱腳I295.5213800.001.000.020.450.050.56大偏心387.3313800.001.000.030.450.060.56大偏心312.4113800.001.000.020.450.050.56大偏心左側(cè)拱腳I295.5213800.001.000.020.4

59、50.050.56大偏心387.3313800.001.000.030.450.060.56大偏心370.4413800.001.000.030.450.060.56大偏心右側(cè)拱腳I295.5213800.001.000.020.450.050.56大偏心387.3313800.001.000.030.450.060.56大偏心312.4113800.001.000.020.450.050.56大偏心大偏心受壓構(gòu)件強(qiáng)度計(jì)算截 面*e0(m)h(m)a(m)e(m)0*Nd*eAs(cm2)fsd(Kpa)Mue(KNm)拱頂I-0.450.06-14.07280000153.69-0.450.

60、06-14.07280000153.69-0.450.06-14.07280000146.17拱腳I0.330.450.060.50147.7714.07280000282.040.350.450.060.51199.2814.07280000320.620.480.450.060.65203.8014.07280000289.18左側(cè)拱腳I0.330.450.060.50147.7714.07280000282.040.350.450.060.51199.2814.07280000320.620.160.450.060.32120.1514.07280000313.57右側(cè)拱腳I0.330.