L40m空腹式懸鏈線無鉸拱石拱橋計(jì)算

1、L=40m空腹式懸鏈線無鉸拱石拱橋計(jì)算(由85改為04規(guī)范)1設(shè)計(jì)資料某等截面空腹式懸鏈線無鉸拱石拱橋上部結(jié)構(gòu)為等跨40m的石砌板拱，下部結(jié)構(gòu)為重力式墩和U型橋臺(tái)，均置于非巖石土上。(1)設(shè)計(jì)標(biāo)準(zhǔn)l)設(shè)計(jì)荷載公路-I級(jí)汽車荷載，人群荷載3kN/m2。2)跨徑及橋?qū)拑艨鐝絃0=40m，凈矢高f0=8m，凈矢跨比f0/L0=1/5。橋面凈寬為凈7+2×(0.25+0.75m人行道)，B0=9m。(2)材料及其數(shù)據(jù)l)拱上建筑拱頂填料厚度hd=0.5m，包括橋面系的計(jì)算厚度為0.736m，換算平均重力密度=20kN/m3。護(hù)拱為漿砌片石，重力密度=23kN/m3。腹孔結(jié)構(gòu)材料重力密度=24

2、kN/m3。主拱拱腔填料為砂、礫石夾石灰爐渣黃土，包括兩側(cè)側(cè)墻的平均重力密度=19kN/m3。2)主拱圈M10砂漿砌MU60塊石，重力密度=24kN/m3。拱圈材料抗壓強(qiáng)度設(shè)計(jì)值=4.22MPa。拱圈材料抗剪強(qiáng)度設(shè)計(jì)值=0.073MPa。彈性模量Em=7300MPa。拱圈設(shè)計(jì)溫度差為±15。(3)設(shè)計(jì)依據(jù)1)公路橋涵通用設(shè)計(jì)規(guī)范(JTG D60-2004)，簡稱橋規(guī)D60；2)公路圬工橋涵設(shè)計(jì)規(guī)范)(JTG D61-2005)，簡稱橋規(guī)D61；3)公路橋涵設(shè)計(jì)手冊(cè)拱橋上冊(cè)(石紹甫)、下冊(cè)(顧安邦)，簡稱拱橋。2主拱圈計(jì)算(1)確定拱軸系數(shù)拱軸系數(shù)m值的確定，一般采用“五點(diǎn)重合法”，先

3、假定一個(gè)m值，定出拱軸線，擬定上部結(jié)構(gòu)各種幾何尺寸，計(jì)算出半拱恒載對(duì)拱腳截面形心的彎矩和自拱頂至1/4跨的恒載對(duì)1/4跨截面形心的彎矩。其比值。求得值后，可由肌中反求m值，若求出的m值與假定的艦值不符，則應(yīng)以求得的肌值作為假定值，重復(fù)上述計(jì)算，直至兩者接近為止。l)擬定上部結(jié)構(gòu)尺寸主拱圈幾何尺寸a. 截面特性截面高度 =91.4343cm主拱圈橫橋向取1m單位寬度計(jì)算，橫截面面積 A=0.9m2；慣性矩 0.06075m4；截面抵抗矩 =0.135m3；截面回轉(zhuǎn)半徑 =0.2598m。b. 計(jì)算跨徑和計(jì)算矢高假定m=2.814，相應(yīng)的=0.21。查拱橋表()-20(8)得 =0.70097，=

4、0.71319計(jì)算跨徑=40+0.9×0.70097=40.63087m計(jì)算矢高=8+0.9/2×(1-0.71319)=8.1291m。c. 拱腳截面的投影水平投影=0.63087m；豎向投影=0.6419m。d. 計(jì)算主拱圈坐標(biāo)(圖3.4-63)圖3.4-63將拱圈沿跨徑24等分，每等分長l=l/24=1.69295m；以拱頂截面形心為坐標(biāo)原點(diǎn)，拱軸線上各截面的縱坐標(biāo)yl=表()-1值×f，相應(yīng)拱背及拱腹縱坐標(biāo)：其數(shù)值見表3.4-9。 主拱圈截面坐標(biāo)表 表3.4-9 截面號(hào)y1d/2y1- d/2y1+ d/2x1234567801.000008.129064

5、0.713190.630977.498098.7600320.3154410.8100486.584930.764310.588775.996167.1737018.6224820.6472895.261850.811000.554874.706985.8167216.9295330.5084714.133390.852380.527933.605464.6613215.2365840.3908203.177000.888000.506762.670243.68376135436250.2919882.373590.917820.490291.883302.8638811.8506760.21

6、00001.707100.942120.477651.229452.1847510.1577270.1432181.164230.961370.468080.696151.632318.4647780.0903080.734120.976140.461000.273121.195126.7718190.0502130.408180.986960.45595-0.047770.864135.07886100.0221330.179920.994330.45257-0.272650.632493.38591110.0055060.044760.998600.45063-0.405870.14539

7、1.6929512001.000000.45-0.450000.45000注：1)第2欄由拱橋附錄()表()-1查得第4欄由拱橋附錄()表()-20(8)查得；2)本例中出現(xiàn)的表()-值或表()-()均為拱橋下冊(cè)相應(yīng)表格的數(shù)值。上構(gòu)造尺寸a.拱圈腹拱圈為M10砂漿砌MU30粗料石等截面圓弧拱，截面高度d'=0.3m，凈跨徑l=3m，凈矢高f'=0.6m，凈矢跨比f'/l'=1/5，查拱橋上冊(cè)表3-1得 =0.689655=0.724138水平投影=0.2069m豎向投影=0.2172mb.腹拱墩腹拱墩采用M7.5砂漿砌MU30塊石的橫墻，厚0.8m，在橫墻中間留

8、出上部為半徑R=0.5m的半圓和下部高為R寬為2R的矩形組成的檢查孔。腹拱的拱頂拱背和主洪圈的拱頂拱背在同一水平線上，從主拱圈拱背至腹拱起拱線之間橫墻中線的高度，其計(jì)算過程及其數(shù)值見表3.4-10。腹拱墩高度計(jì)算表 表3.4-10 項(xiàng)目Xh1號(hào)橫梁17.230870.848171.437285.482450.742300.802964.47202號(hào)橫墻13.430870.661221.120313.118940.512030.890102.16343號(hào)拱座中心9.927420.488660.828071.626260.346140.944990.7001空、實(shí)腹段分界線9.823970.483

9、570.819451.590680.341760.946270.6651注： 橫墻高度也可根據(jù)表3.4-9的有關(guān)數(shù)值內(nèi)插計(jì)算得到。2)恒載計(jì)算恒載分主拱圈、拱上空腹段、拱上實(shí)腹段三部分進(jìn)行計(jì)算，不考慮腹拱推力和彎矩對(duì)主拱圈的影響，其計(jì)算圖式見圖3.4-64。主拱圈恒載圖3.4-64拱上空腹段的恒載a.腹孔上部(圖3.4-65)圖3.4-65腹拱圈外弧跨徑l'外=l'+2d'sin=3.4138m腹拱內(nèi)弧半徑R0=0.725001l'=2.1750m腹拱圈重Pa=1.53205R0+(d'/2)d'=25.4786kN腹拱側(cè)墻護(hù)拱重Pb=0.118

10、89(R0+d')2=16.7503kN(以上三個(gè)系數(shù)依次分別查拱橋上冊(cè)表3-1、表l-10、表1-9)填料及路面重PC=l'外hd=50.2511kN(hd=0.736m)兩腹拱之間起拱線以上部分的重力(圖3.4-66)：圖3.4-66Pd=(0.8-x')y+(f+d'-y)+ hd(0.8-2x)069)×0.2172×24+(0.6+0.3-0.2172)×23+0.736×20×(0.8-2×0.2069)=14.8416kN一個(gè)腹拱重力p=25.4786+16.7503+50.2511+14

11、.8416=107.3216kNb.腹孔下部1號(hào)橫墻 P=4.4720-(0.5×l.0+×0.52/2)/9×0.8×24=83.9580kN2號(hào)橫墻 P=2.1634-(0.5×l.0+×0.52/2)/9×0.8×24=39.6329kN3號(hào)拱座 P=(0.7001+1/2×0.2172)×(9.92742-9.82397)×2×24=4.0157kNc.集中力P13=107.3216+83.9580=191.2796kNP14=107.3216+39.6329=146

12、.9545kNP15=(107.3216-14.8416)/2+4.0157=50.2557kN拱上實(shí)腹段的恒載(圖3.4-67)圖3.4-67a.拱頂填料及橋面重=9.82397×0.736×20=144.6088kNb.懸鏈線曲邊二角形部分=9.824×1.56513/(2.814-1)×1.6946×(sh1.6946-1.6946)×l9=88.9350kN式中：=1.59068-0.9/(2×0.94627)+0.9/2=1.56513m重心位置=0.76149=7.4809m各塊恒載對(duì)拱腳及拱跨1/4截面的力矩見

13、表3.4-11。半拱恒載對(duì)拱腳和1/4拱跨截面的彎矩 表3.4-11 分塊號(hào)恒重(kN)1/4拱跨截面拱 腳 截 面力 臂(m)力 矩(kN.m)力 臂(m)力 矩(kN.m)P0-12485.2223/1124.49844662.6477P13191.2796/l/2-17.23087=3.0846590.0211P14146.9545/l/2-13.43087=6.88461011.7230P1550.2557l/4-9.9274=0.230311.5739l/2-9.9274=10.3880522.0562P16144.6088l/4-1/2×9.82397=5.2457758

14、.5744l/2-l/2×9.82397=15.40352227.4817P1788.9350l/4-7.4809=2.6768238.0612l/2-7.4809=12.83451141.4363合 計(jì)1107.25592132.707910155.36603)驗(yàn)算拱軸系數(shù)由表3.4-11得=2132.7079/10155.3660=0.21022該比值與假定拱軸系數(shù)m=2.814相應(yīng)的y1/4/f=0.21十分接近，故可確定2.814為設(shè)計(jì)拱軸系數(shù)。(2)拱圈彈性中心及彈性壓縮系數(shù)l)彈性中心ys=表()-3值×f=0.333431×8.1291=2.7105

15、m2)彈性壓縮系數(shù)r2w=I/A=d2/12=0.0675m2r2w /f2=0.0675/8.12912=0.0010214541=表()-9值×r2w /f2=11.1272×0.001021454=0.011366=表()-11值×r2w /f2=9.18594×0.001021454=0.009383l/(l+)=0.01126(3)主拱圈截面內(nèi)力計(jì)算大跨徑拱橋應(yīng)驗(yàn)算拱頂、3/8拱跨、1/4拱跨和拱腳四個(gè)截面，必要時(shí)應(yīng)驗(yàn)算1/8拱跨截面。為節(jié)省篇幅，本例只驗(yàn)算拱頂、1/4拱跨和拱腳三個(gè)截面的內(nèi)力。其余截面，除不計(jì)彈性壓縮的內(nèi)力必須在影響線上直接布

16、載求得以外，其步驟和1/4拱跨相同。l)恒載內(nèi)力計(jì)算計(jì)算拱圈內(nèi)力時(shí)，為了利用現(xiàn)有的表格，一般采用所確定的拱軸線進(jìn)行計(jì)算。但是在確定拱軸系數(shù)時(shí)，計(jì)算得的恒載壓力線與確定的拱軸線很難在“'五點(diǎn)”完全重合，本例中二者相差0.21001-0.21=0.00001。當(dāng)這個(gè)偏差較大時(shí)，要用“假載法”計(jì)入其影響。本例不計(jì)偏離的影響。不計(jì)彈性壓縮的恒載推力H'g=Mj/f=10155.3660/8.1291=1249.2608kN計(jì)入彈性壓縮的恒載內(nèi)力見表3.4-12。計(jì)入彈性壓縮的恒載內(nèi)力 表3.4-12 項(xiàng) 目拱 頂1/4截面拱 腳y=ys-y12.71051.0034-5.4186cos

17、10.942120.71319Hg=1-1/(1+)H'g (kN)1235.19411235.19411235.1941Ng= H'g/ cos-1/(1+)H'g cos (kN)1235.19411312.75781741.6199Mg=1/(1+)H'g y (kN.m)38.127714.1145-76.22172)公路-I級(jí)汽車荷載和人群荷載的內(nèi)力計(jì)算單位拱寬汽車等代荷載Kl=c/9K20式中：c=2為車道數(shù)； 為車道折減系數(shù)，雙車道不折減即=1。單位拱寬人群等代荷載K2=2b/9×g人=2×0.75/9×3=0.5kN

18、式中：b=0.75m，為人行道寬度；g人=3kN，為人群荷載。等代荷載表說明：表列車輛等代荷載是根據(jù)m=2.814，f/l=1/6的等截面懸鏈線無鉸拱內(nèi)力影響線編制的，如計(jì)算的m和f/l與表不同時(shí)，可以用式K=/bKb+(1+/b)Kc進(jìn)行換算。本例只有矢跨比不同且相差不大，故不作換算而直接用表列等代荷載數(shù)值。單位拱寬的荷載計(jì)算見表3.4-13。單位拱寬的計(jì)算荷載 表3.4-13 截 面項(xiàng) 目汽車20級(jí)等代荷載人群荷載合 計(jì)K202/9K20拱 頂Mmax39.79628.84360.59.3436相應(yīng)H124.35935.41380.55.9138Mmin28.08466.24100.56.

19、7410相應(yīng)H122.02244.89370.55.39371/4跨截面Mmax37.18368.26300.58.7630相應(yīng)H124.27195.39380.55.8938Mmin21.48644.77460.55.2746相應(yīng)H120.42434.53870.55.0387拱 腳Mmax20.51174.55820.55.0582相應(yīng)H118.23884.05310.54.5531相應(yīng)V5.60091.24460.5Mmin28.93416.42980.56.9298相應(yīng)H113.49812.99960.53.4996相應(yīng)V13.81073.06900.5注：汽車20級(jí)等代荷載由拱橋上冊(cè)

20、第一章表1-5直線內(nèi)插算得，例如拱頂?shù)腗max=(40.63087-40)/(45-40)×(37.0-40.2)+40.2=39.7962kN.m不計(jì)彈性壓縮的汽車20級(jí)及人群內(nèi)力見表3.4-14。不計(jì)彈性壓縮的汽車及人群荷載內(nèi)力 表3.4-14 截 面項(xiàng) 目計(jì)算荷載影 響 線 面 積力或彎矩(kN或kN.m)表()-14(67)值乘 數(shù)面 積拱 頂Mmax9.34360.00725l211.9688111.8316相應(yīng)H15.91380.06913l2/f14.039083.0239Mmin6.7410-0.00456l2-7.5280-50.7460相應(yīng)H15.39370.05

21、903l2/f11.987964.65911/4跨截面Mmax8.76300.00882l214.5607127.5954相應(yīng)H15.89380.04035l2/f8.194348.2957Mmin5.2746-0.01047l2-17.2846-91.1693相應(yīng)H15.03870.08781l2/f17.832689.8529拱 腳Mmax5.05820.01994l232.9183166.5074相應(yīng)H14.55310.09242l2/f18.768885.4561相應(yīng)V汽車1.24460.5l20.315425.2846人群0.50.170676.93453.4673Mmin6.929

22、8-0.01409l2-23.2607-161.1922相應(yīng)H13.49960.03575l2/f7.260225.4076相應(yīng)V汽車3.06900.5l20.315462.3481人群0.50.3293313.38106.6905注：在求拱腳相應(yīng)反力V時(shí)，以汽車20級(jí)等代荷載乘以全部反力影響線面積。人群荷載反力則只乘以相應(yīng)的影響線面積。計(jì)入彈性壓縮的汽車和人群荷載內(nèi)力見表3.4-15。計(jì)入彈性壓縮的汽車和人群荷載內(nèi)力(kN或kN.m) 表3.4-15 項(xiàng) 目拱 頂1/4截面拱 腳MmaxMminMmaxMminMmaxMmin軸 向 力cos10.942120.71319sin00.3352

23、70.70097與M相應(yīng)的H183.023964.659148.295789.852985.456125.4076與M相應(yīng)的V28.751969.0386N=H1cos+V sin83.023964.659151.262895.373181.100766.5144H=1/(1+)H10.93490.72810.54381.01170.96220.2861N=H cos0.93490.72810.51230.95310.68620.2040NP=N-N82.089063.931050.750594.420080.414566.3104彎 矩M111.8316-50.7460127.5954-91

24、.1693166.5074-161.1922y=ys-y12.71051.0034-5.4186M=H.y2.53411.97350.57571.0151-5.2138-1.5503MP=M+M114.3657-48.7725128.1411-90.1542161.2936-162.7425注：除拱腳截面外，其余截面的軸向力用N=H1/cos作近似計(jì)算。3)溫度內(nèi)力計(jì)算拱圈合攏溫度15拱圈砌體線膨脹系數(shù)=0.000008變化溫差t=±15溫度變化在彈性中心產(chǎn)生的水平力Ht=EIt/表()-5值f2=±(8×10-6×5.2×l06×0

25、.06075)×15/(0.099373×8.12912)=5.7727kN拱圈溫度變化內(nèi)力見表3.4-16拱 圈 溫 度 內(nèi) 力 表3.4-16 項(xiàng) 目溫 度 上 升拱 頂1/4截面拱 腳y=ys-y12.71051.0034-5.4186cos10.942120.71319Nt= Ht cos (kN)5.77275.43864.1170Mt=-Ht y (kN.m)-15.6469-5.792331.2799注：1.溫度下降時(shí)的內(nèi)力與溫度上升的內(nèi)力符號(hào)相反；2.當(dāng)砂漿為小石子混凝土?xí)r，應(yīng)酌情計(jì)入徐變的影響。(4)主拱圈正截面強(qiáng)度驗(yàn)算根據(jù)橋規(guī)022規(guī)定，構(gòu)件按極限狀態(tài)設(shè)

26、計(jì)的原則是：荷載效應(yīng)不利組合的設(shè)計(jì)值小于或等于結(jié)構(gòu)抗力效應(yīng)的設(shè)計(jì)值，即l)正截面受壓強(qiáng)度驗(yàn)算荷載組合根據(jù)橋規(guī)021和橋規(guī)022的規(guī)定，本例可得如下兩種荷載組合：荷載效應(yīng)不利組合的設(shè)計(jì)值見表3.4-17主拱圈荷載效應(yīng)不利組合的設(shè)計(jì)值 表3.4-17 序號(hào)荷載效應(yīng)系數(shù)拱 頂1/4截面拱 腳MNMNMN恒 載1.2(0.9)38.12771235.194114.11451312.7578-76.22171741.6199汽車+人群Mmax1.4114.365782.0890128.141150.7505161.293680.4145汽車+人群Mmin1.4-48.772563.9310-90.154

27、294.4200-162.742566.3104溫度上升1.4-15.64695.7727-5.79235.438631.27994.1170溫度下降1.415.6469-5.77275.7923-5.4386-31.2799-4.1170荷載組合MjNjMjNjMjNj組合I +1205.81731595.6065196.31721644.7116157.28331678.3981組合I +1-34.00251200.0148-113.52621312.4337-319.20982180.5916組合II +1147.12931282.9506150.56641321.8605160.860

28、11347.3295組合II +1-44.7265966.4773-97.30831056.0382-220.33441749.0843組合II +1182.17841270.0198163.54111309.678090.79321338.1074組合II +1-9.6774953.5464-84.33361043.8557-290.40131739.8622注：荷載安全系數(shù)的取值，對(duì)于結(jié)構(gòu)自重，當(dāng)其彎矩與車輛荷載的彎矩同號(hào)取1.2，異號(hào)時(shí)則取0.9，軸向力的荷載安全系數(shù)取值與其相應(yīng)的彎矩相同，對(duì)于其它荷載都取1.4。拱圈截面抗力根據(jù)橋規(guī)022第條規(guī)定，拱圈抗力效應(yīng)的設(shè)計(jì)值為=×0

29、.9×6.45×l03/1.92=3023.4375(kN)相應(yīng)的容許偏心距e0分別為e00.5y (組合I )e00.6y (組合II)具體計(jì)算見表3.4-18主拱圈抗力效應(yīng)的設(shè)計(jì)值 表3.4-18 截面編號(hào)拱頂截面0.12900.80222425.40160.5y=0.225-0.02830.98832988.06330.11470.83692530.31480.6y=0.27-0.04630.96922930.31560.14340.76642317.1625-0.01010.99863019.20471/4截面0.11940.82562496.15000.5y=0.

30、225-0.08650.90022721.69840.11390.82882536.05940.6y=0.27-0.09210.88842686.02190.12490.81222455.6359-0.08040.91262759.1891拱腳截面0.09370.88492675.43980.5y=0.225-0.14640.75892294.48670.11940.82562496.15000.6y=0.27-0.12600.80952447.47270.06790.93612830.2398-0.16690.70762139.3844經(jīng)驗(yàn)算表明：主拱圈截面的荷載效應(yīng)不利組合的設(shè)計(jì)值均小于其

31、抗力效應(yīng)的設(shè)計(jì)值，即Nj<RN。而且軸向力的偏心距都在容許范圍之內(nèi)。2)正截面受剪強(qiáng)度驗(yàn)算一般是拱腳截面處的剪力最大，根據(jù)橋規(guī)022第條規(guī)定，正截面直接受剪的強(qiáng)度，按下式計(jì)算=128.5714+(=2.31)由于拱橋手冊(cè)中沒有Q、N的等代荷載可查，一般可按下式計(jì)算內(nèi)力計(jì)算恒載=1233.9016×0.70097-1105.7933×0.71319=76.2873kN=1739.7975kN汽車20級(jí)+人群荷載=(2/9×17.5612+0.5)×(18.7688+7.2602)×(1-0.01126)=113.3021kN(KH為汽車20

32、級(jí)于懸鏈線拱腳Hmax的等代荷載值與人群荷載K2=0.5之和，為推力影響線面積，采用拱頂Mmax和Mmin兩相應(yīng)的推力影響線面積之和)。=0.5×40.63087×(2/9×12.7098+0.5)=67.5366kN(KV為汽車20級(jí)于懸鏈線拱腳處，與Hmax相應(yīng)的豎向力等代荷載)Qp=113.3021×0.70097-67.5366×0.71319=31.2550kNNp=113.3(121×0.71319+67.5366×0.70097=128.1471kN荷載組合組合IQj=1.2×76.2873+1.4×31.2550=135.3018kNNj=1.2×1739.7975+1.4×128.1471=2267.1629kN抗剪強(qiáng)度驗(yàn)算組合I=128.5714+0.7×2267.1629=1715.5854kN>Qj=135.3018kN(5)主拱圈穩(wěn)定性驗(yàn)算拱上建筑未合擾就脫架的主拱圈，由橋規(guī)022第條及第條規(guī)定應(yīng)接下式驗(yàn)算其縱向穩(wěn)定性式中：=1.92其中：為對(duì)應(yīng)與砂漿(5#)強(qiáng)度有關(guān)的系數(shù)，=0.002其中值的計(jì)算如下：拱軸線長度：S=1/×l=1.10575×4