等截面懸鏈線圬工拱橋課程設(shè)計(jì)實(shí)例全解

1、- -等截面懸鏈線圬工拱橋計(jì)算1設(shè)計(jì)資料一.設(shè)計(jì)資料1.設(shè)計(jì)標(biāo)準(zhǔn)1.1設(shè)計(jì)荷載公路I級(jí)，人群荷載3kN/m?。1.2跨徑及橋?qū)拑艨鐝絣0=51.4m，凈失高f0=10.28m,凈失跨比f(wàn)=1/5。l橋面凈寬為凈7+2X1.5m,B=7m。02.材料及其數(shù)據(jù)2.1拱上建筑拱頂填料厚度，h=0.5m，包括橋面系的計(jì)算厚度為0.736m，平均重力密度d=20kN/m3。12.1拱上建筑拱頂填料厚度，h=0.5m，包括橋面系的計(jì)算厚度為0.736m，平均重力密度d=20kN/m3。1拱上護(hù)拱為漿砌片石，重力密度y=23kN/m3。2腹孔結(jié)構(gòu)材料重力密度y=24kN/m3。3主拱拱腔填料為砂、礫石夾石灰

2、爐渣黃土，包括兩側(cè)側(cè)墻的平均重力密度=21kN/m342.2主拱圈M10砂漿砌MU40塊石，重力密度y二24kN/m3。3軸心抗壓強(qiáng)度設(shè)計(jì)值f=3.44x103kN/m2x1.2=4.12x103kN/m2。cd抗剪強(qiáng)度設(shè)計(jì)值f二0.073MPa。vd彈性模量E二0.073MPa。m拱圈設(shè)計(jì)溫差為土15C3主拱圈計(jì)算3.1確定拱軸系數(shù)工Mj和自拱軸系數(shù)m值的確定，一般采用“五點(diǎn)重合法”先假定一個(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)拱橋截面形心的彎矩Smy1L-_工M44拱頂至4跨的恒載對(duì)4跨截面形心的彎矩：。其比值厶Mj=f。求得f值1f2(丄-2-1中反求m值，若求出

3、的m值與假定的m值不符，則2乙后，可由m=4應(yīng)以求得的m值作為假定值，重復(fù)上述計(jì)算，直至兩者接近為止。3.1.1擬定上部結(jié)構(gòu)尺寸(1)主拱圈幾何尺寸截面特性截面高度d=mK3_=4.8x1.4x35140二115.97cm,取d=1.2m主拱圈橫橋向取1m單位寬度計(jì)算，橫面面積A=0.9m慣性矩i=-2d3=0.144JL厶截面抵抗矩W=d2=0.24截面回轉(zhuǎn)半徑丫=0.3464wJ122）計(jì)算跨徑和計(jì)算失高假定m=2.814,相應(yīng)的f=0.21。查“拱橋”表（III）-20（8）得sin*=0.70097,cosq=0.71319計(jì)算跨徑l=l+d-sin0二51.4+1.2x0.70097

4、=52.241211c計(jì)算失高f=f+-（1COS申）=10.28+i0.71319）=10.452102j23）拱腳截面的投影水平投影x=dsin*=0.8411j豎向投影x=dcos申=0.8558j4）計(jì)算主拱圈坐標(biāo)（圖1-1）將拱圈沿跨徑24等分，每等分長(zhǎng)Al二24二21417m。以拱頂截面的形心為坐標(biāo)原點(diǎn)，拱軸線上個(gè)截面的縱坐標(biāo)d=表（III）1值Xf,相應(yīng)拱背坐標(biāo)y=yd，相應(yīng)拱腹坐標(biāo)y=x12cosq1j+-。其數(shù)值見(jiàn)表1-1。2cos*j主拱圈截面坐標(biāo)表表1-1截面號(hào)y/fy1cos申dddy+12cos*x2cos申y12cos*1234567801.000010.45210

5、.713100.841409.6107011.2935025.9706410.810048.46670.764310.78507.681689.2517223.806482220.647286.76550.811000.73986.025677.5553321.642293030.508475.31460.852330.70394.610656.0544319.4779185840.390824.08490.888000.67563.409224.7605817.313708650.919889.61470.917820.65378.9609810.2684215.14952460.21000

6、2.19490.942120.63681.558042.8317612.985306270.143211.49690.961370.62410.872792.1210110.821181080.090300.94390.976140.61460.329231.558578.656888790.050210.52480.986960.6079-0.065131.132733.828843310.022130.23130.994330.6034-0.371120.834724.3284403210.005500.05750.998600.6008-0.543340.658342.164221641

7、001.000000.6000-0.600000.60000020注：第2欄由拱橋附錄（III）表查得第4欄由拱橋附錄（III）表（III）-20（3）查得出現(xiàn)的表（III）-A值或表（III）-A（A）值均為拱橋下冊(cè)相應(yīng)表格的數(shù)值。312上構(gòu)造尺寸1）腹拱圈腹拱圈為M10號(hào)沙漿砌M30粗料石等截面圓弧拱，截面高度d=3m，靜失高廣二6m，凈失跨比廣/1=1/5。查拱橋上冊(cè)表3-1得sin甲=0.689655,cos甲=0.72413800水平投影x=dsin申=0.2069m豎向投影y=dcos申=0.2172m2）腹拱墩腹拱墩采用M7.5沙漿M30塊石的橫墻，厚0.8m。在橫墻中間留出上部

8、為半徑- -foR=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拱圈的拱頂拱背在同一水平線上。從主拱圈拱背至腹拱起拱軸線之間h-y+(1_)_(d+f)橫墻中線的高度1C0Si，其計(jì)算過(guò)程及其數(shù)值見(jiàn)表1-2腹拱墩高度計(jì)算表表1-2項(xiàng)目xEk乜fy=(chk1m1)2fk-(m1)!gosq=,1tg29+h11*橫墻23.14120.870081.468647.357560.774350.784266.204232*橫墻19.34120.722631.221554.821680.574160.855433.84121肚座15.84120.587750.993533.

9、061520.433320.907482.13687空實(shí)腹段分界線15.74120.583840.976543.004450.419510.914432.05467注：橫墻高度也可根據(jù)表1-1的有關(guān)數(shù)值內(nèi)插計(jì)算得到。3.2恒載計(jì)算恒載分主拱圈、拱上實(shí)腹三部分進(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(jiàn)圖1-2。- -Pl單位呂on3.2.1主拱圈恒載p二表(III)19(8)值A(chǔ)y1=0.55288x1.2x52.5412x24二836.6105kNTOC o 1-5 h z0-125M=表(III)19(8)值A(chǔ)J2=0.12614x1.2x52.54122x24/4=2507

10、.1787kNm1/44M=表(III)19(8)值=0.52303x1.2x52.54122x24/4=10395.8276kNmj43.2.2拱上空腹段的恒載1）腹孔上部（圖1-3）圖1-3腹拱圈外弧跨徑1=l+2dsin申二3+0.6x0.689655二3.14138m0腹拱內(nèi)弧半徑R=0.7250011=2.1750m0d腹拱圈重P=0.52202(R+)dY=0.52202x(2.1750+0.15)x0.3x24=8.7386kNa022d腹拱側(cè)墻護(hù)拱重P=0.11889(R+)2dY=0.11889x(2.1750+0.15)2x23=14.7815kNb022(以上三個(gè)系數(shù)依次

11、分別查拱橋上冊(cè)表3-1、表1-10、表1-9)填料及路面重P=hy=50.2511kN外d1兩腹拱之間起拱線以上部分勺重量ri圖1-4P=(0.8-x)yY=(f+d-y)Y+hY(0.8-2x)d32d1=(0.8-0.2069)x0.2172x24+(0.6+0.3-0.2172)x23+0.736x20 x(0.8-2x0.2069)=14.8416kN一個(gè)腹拱重P仝p=8.7386+16.7503+50.2511+14.8416=90.5816kN腹拱下部1#橫墻P=6.30432-(0.5+兀x0血/2)/8x0.8x24=118.48577kN2#橫墻P=3.83131-(0.5+

12、兀xO.62/2)/8x0.8x24=71.0039kN3#拱座P=(2.10775+0.5x0.2172)x0.2069x24=11.0055kN集中力P=90.5816+118.466=209.0476kN13P=90.5816+70.9847=161.5663kN14P=(90.5816-14.8416)/2+11.0055=48.8755kN153.2.3拱上實(shí)腹段的恒載（圖1-5）1）拱頂填料及面重15.16363P二lh丫二15.16363x0.736x20二231.3970kN16xd1懸鏈線曲邊三角形部分：重量P=l1f1(shK-Kg)y17(m1)K004=94.6523k

13、N11式中：f=fy(1)=10.45210.6x(1)=10.2108m1icos00.71319ja疋仇L單匚（泅:化J）（.碼=0.753971=11.4329x重心位置h3疋你_32）各塊恒載對(duì)拱腳及拱跨1/4截面的力矩見(jiàn)表1-3半拱橫載對(duì)拱腳和1/4拱跨截面的彎矩表1-3塊號(hào)恒重(kN)l/4截面拱腳截面力臂（m）力矩(kNm)力臂（m）力矩(kNm)P827.05622450.239910159.7351012P13199.95201/2-22.57058=3.4679.8368P152.47011/2-18.77058=7.21097.7847P1547.89061/2-15.2

14、6708=10.7035512.5970P16231.39701/4-1/2=5.40351250.34791/2-1/=18.3887714255.1051p17302.98021/4-11.4329=1.5524470.34341/2-11.4329=14.53774404.6292合計(jì)1761.74614170.431221109.68793.3驗(yàn)算拱軸系數(shù)由表1-3得YM/YM=1670.6835=0.19769l4J8450.8916該比值與假定拱軸系數(shù)y./f=0.21十分接近，故可確定2.814為設(shè)計(jì)拱軸系數(shù)m=2.814相應(yīng)的144拱軸彈性中心及彈性壓縮系數(shù)4.1彈性中心y=表

15、（III）-3值-f=0.333431x10.4521=3.4851m4.2彈性壓縮系數(shù)ta=0.12m2wA12012ta/；=0.001098434w/f210.45212卩=11.1272x0.001098434=0.0122221卩=9.18594x0.001098434=0.01009=0.01211+卩5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載求得以外，其步驟和1/4拱跨者相同。51恒載內(nèi)力計(jì)算計(jì)算拱圈內(nèi)力

16、時(shí)，為利用現(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0.21-0.19769=0.01231。當(dāng)這個(gè)偏差較大時(shí)，要用“假載法”計(jì)入其影響計(jì)入彈性壓縮的恒載內(nèi)力表1-4項(xiàng)目拱頂1/4截面拱腳y=y廣y13.44831.2802-6.9635cos申10.941950.71501H=1Hg(1+卩丿g2009.10252009.10252009.1025Hp,N=一1-Hcos9gcos91+pg2009.10252136.71012835.8692M=-Hyg1+pg86.510132.1038-172

17、.8996(1)不計(jì)彈性壓縮的恒載推力HZM21110.9687910.4521二2019.7825KN計(jì)入彈性壓縮的恒載內(nèi)力見(jiàn)表1-45.2活載內(nèi)力計(jì)算(1)公路一級(jí)和人群荷載的內(nèi)力單位拱寬汽車(chē)等代荷載式中,K1c=2為車(chē)道數(shù)；也K9二級(jí)二級(jí)E=1為車(chē)道折減系數(shù)，雙車(chē)道不折減。2X0.759x3=0.5KN單位拱橋人群等代荷載K-2bq29q人式中，b=0.75m為人行道寬度；Q人=3KN為人群荷載。不計(jì)彈性荷載的公路一級(jí)及人群內(nèi)力見(jiàn)表1-5不計(jì)彈性荷載的公路一級(jí)及人群內(nèi)力表1-5截項(xiàng)目計(jì)算何載影響線面積縱力與彎面22q人表中乘面積標(biāo)矩8pk8qk值數(shù)值拱902.620.5620.00712

18、19.5592.8074315.012M25max5575頂相應(yīng)902.620.5620.069/2z17.9811.1669162.3365513/f7H1902.620.562-0.00-12.30-0.5952-92.781M12min55456249相應(yīng)902.620.5620.0591215.3540.545798.78195503/fH11/4M902.620.5620.0081223.7953.0697352.120截max558235面相應(yīng)902.620.5620.04012710.4950.691595.68915535/fH1902.620.562-0.01-28.24-1

19、.1437-192.96M12min550476897相應(yīng)902.620.5620.08712,22.8401.1669177.8245581/21H1拱Mmax902.620.5620.019153.7951.9260344.814腳559481相應(yīng)H1902.6250.56250.0924212/0391.1669181.6463相應(yīng)V902.6250.56250.17067l8.86480.500073.2566Mmin902.6250.5625-0.01409l2-38.0132-3.0713-397.2566相應(yīng)H1902.6250.56250.0357512/*29890.3230

20、58.7102相應(yīng)V902.6250.56250.32933l17.10580.9376138.9087注：在求拱腳相應(yīng)反力V時(shí)，以公路II級(jí)等代荷載乘以全部反力影響線面積。人群反力則只乘以相應(yīng)的影響線面積。計(jì)如彈性壓縮的公路I級(jí)和人群荷載內(nèi)力見(jiàn)表1-6計(jì)如彈性壓縮的公路I級(jí)和人群內(nèi)力表1-6目項(xiàng)拱頂l/4截面拱腳MmaxMminMmaxMminMmaxMminCOSP10.942120.71319sin申00.335270.70097軸與M相應(yīng)的H162.3398.05495.689177.824181.6458.71026781163與M相應(yīng)的V73.256138.908向67N=Hcos

21、p+V162.336798.054890.1506167.5316180.8990139.24241力sinpAH=-H1.99511.20511.17602.18552.23240.72151+p1AN=AHcosp1.99511.20511.10792.05901.59210.5146N=NAN160.3496.84989.042165.472179.30138.727p16776698M315.01-92.78352.12-192.96344.81-397.58彎251905974141矩y=yys13.45841.2803-6.9137AMAN-y6.89994.16771.41842

22、.6361-11.0073-3.5578MMAMp321.9124-88.6142353.5389-190.3336333.8067-401.1419注：初拱腳截面外，其余截面的軸向力用=H/cos申作近似計(jì)算。5.3溫度內(nèi)力計(jì)算拱圈合攏溫度15C拱圈砌體線膨脹系數(shù)二0.000008變化溫差A(yù)t=15C溫度變化在彈性中心產(chǎn)生的水平力:aElAtt表（III）5值f28xlO-6x5.2x106x0.1440.099373x10.45212x158.27697KN拱圈溫度變化內(nèi)力見(jiàn)表1-7溫度內(nèi)力表1-7項(xiàng)目溫度上升拱頂l/4截面拱腳cosp10.942120.71310y=yys13.4584

23、1.2803-6.9137J丄NHcosp-8.4051-7.9186-5.9944MHytt29.068210.7610-58.1103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。6主拱圈正截面強(qiáng)度驗(yàn)算根據(jù)橋規(guī)規(guī)定，構(gòu)件按極限狀態(tài)設(shè)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rsR(f,a)0dd式中Y結(jié)構(gòu)重要性系數(shù)，本題為二級(jí)設(shè)計(jì)安全等級(jí)為1.0；0S作用效應(yīng)組合設(shè)計(jì)值，按公路橋涵設(shè)計(jì)通用規(guī)范(JTGD602004)的規(guī)定計(jì)算；R(構(gòu)件承載力設(shè)計(jì)值函數(shù)；f材料強(qiáng)度設(shè)計(jì)值；da幾何參數(shù)設(shè)計(jì)值，可采用集合參數(shù)標(biāo)準(zhǔn)

24、值ak，即設(shè)計(jì)文件規(guī)定d值。6.1正截面受壓強(qiáng)度驗(yàn)算611荷載組合荷載效應(yīng)不利組合的設(shè)計(jì)值見(jiàn)表1-8主拱圈荷載效應(yīng)不利組合的設(shè)計(jì)值表1-8編號(hào)荷載效應(yīng)系數(shù)拱頂1/4截面拱腳MNMNMN1恒載1.286.50522009.003432.02332136.7090-172.93312835.87122公路I級(jí)Mmax315.0125162.3367352.120595.6891344.8141181.64633公路I級(jí)Mmin1.4-92.781998.0548-192.9697177.8241-397.584158.71024溫度上升-29.06828.4051-10.76107.918658.

25、11035.99445溫度下降29.0682-8.405110.7610-7.9186-58.1103-5.9944荷載組合MlN1M1N1M1N16恒+汽Mmax+溫升412.60442117.1845416.50862164.7473266.66422930.67587組合恒+汽Mmin+溫升0.8-44.12532045.1887-193.99252256.7385-564.82182792.98738恒+汽Mmax+溫降459.11352103.7363433.72622152.0775173.68782921.08479恒+汽Mmin+溫降2.38382031.7406-176.77

26、492244.0687-657.79822783.3962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(chē)輛荷載的彎矩同號(hào)時(shí)取1.2，軸向力的荷載安全系數(shù)與其相應(yīng)的彎矩相同，對(duì)于其它荷載都取1.4。6.1.2拱圈截面抗力根據(jù)橋規(guī)第4.0.5條規(guī)定，拱圈抗力效應(yīng)的設(shè)計(jì)值為YSR(f,a)0dd相應(yīng)的容許偏心距e分別為0e0.6S0具體計(jì)算見(jiàn)表1-9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)值均小于其抗力效應(yīng)的設(shè)計(jì)值卩N5Af而且軸向力的偏心距都在容許范圍之內(nèi)。jcd。主拱圈抗力效應(yīng)的設(shè)計(jì)值表1-9截面編號(hào)Me二一j0Nj9-A-fcde0拱頂60.19490.1730855.31200.6S=0.277-0.02160.24531212.763280.21820.1546764.342490.00120.27341351.68961/4截面60.19240.1859919.08960.6S=0.277-0.08600.1926952.214480.20150.1688834.54729-0.07880.20321004.6208拱腳60.09100.1698839.49120.6S=0.277-0.20220.1685833.064080.05950.22561115.3