城-A級,16m跨圬工拱橋計算

1、一、設(shè)計資料（一）設(shè)計標(biāo)準(zhǔn)1.設(shè)計荷載：2.跨徑及橋?qū)拑艨鐝絣0= 15.74凈矢高f0= 3.8橋面凈寬為（二）各部分尺寸及其材料1.主拱圈主拱圈采用等截面板供，其寬度B=,主拱圈厚度D=，主拱圈用塊石筑成，材料容重0= kN/m，抗壓極限強(qiáng)度Rj= MPa，砌體彈性模量=2、腹拱圈 主拱圈上每半跨布置 個圓弧形腹拱，腹拱圈凈跨徑l0=1.93m，腹拱厚度d=0.43m，腹拱座寬b=24m，腹拱圈選用塊石筑成，材料容重0= kN/m，抗壓極限強(qiáng)度Rj= MPa，砌體彈性模量=二、橋跨結(jié)構(gòu)計算（一）拱軸系數(shù)1、上部結(jié)構(gòu)幾何特征（1）主拱圈截面積：A= 18.72靜面距：S= 7.3008中性軸

2、：y下= 0.39y上= 0.39慣性矩：I= 0.949104回轉(zhuǎn)半徑：rw= 0.225166605rw2= 0.0507拱腳投影及傾角函數(shù)：假定m=1.534，f0/l0= 1/4sinj= 0.73439cosj= 0.67873x=d*sinj= 0.5728242y=d*cosj= 0.5294094計算跨徑及矢高：l=l0+2y下sinj= 16.3128242f=f0+y下（1-cosj）= 3.9252953主拱圈截面坐標(biāo)將拱中性軸沿跨徑24等分，每等分長為l/24= 0.679701008曲面的坐標(biāo)y1=y1-y上/cos，腹拱曲面相應(yīng)點的坐標(biāo)y1=y1+y下/cos，具體

3、見下表：截面號xy1/fy1123412000110.6797010080.0063970.025110114101.3594020170.0256330.10061709492.0391030250.0578410.22704300582.7188040330.1032460.40527103973.3985050420.1621620.63653373664.078206050.2350.92244439554.7579070580.3222651.2649852945.4376080670.4245651.66654299936.1173090750.5426092.1299005572

4、6.7970100830.6772192.65828455817.4767110920.829333.25536515108.156412113.9252953（2）拱上結(jié)構(gòu)a、腹拱拱腳的投影由f0/l0= 1/6查拱橋（上冊）表（）-20（3）3-2得：sin0= 0.6cos0= 0.8投影x=dsin0= 0.258y=dcos0= 0.344b、腹拱重力作用線橫坐標(biāo)x1#橫墻 6.292#橫墻 4空實腹段界線 3.8712、上部結(jié)構(gòu)恒重（1）主拱圈拱腳P012= 拱橋（上冊）表（）-19（3）值*A*1*L=4218.807039 KN拱頂P012= 拱橋（上冊）表（）-19（3）值*

5、A*1*L= 0KN拱腳M= 拱橋（上冊）表（）-19（3）值*A*1*L*L/4= 16050.24273KN*m1/4拱M= 拱橋（上冊）表（）-19（3）值*A*1*L*L/4= 3805.502719KN*m拱頂M= 拱橋（上冊）表（）-19（3）值*A*1*L*L/4= 0KN*m（2）拱上空腹段a、腹拱上部腹拱外弧跨徑：l外= l+2dsin0l= 2.446腹拱內(nèi)弧半徑：R0= 拱橋（上冊）表3-2值*l= 1.8534腹拱圈重：Pa= 基表3-25值*（R0+d/2）*d*B0*2=614.7615744通過面積計算腹拱護(hù)拱重：Pb= 基表3-27值*(R0+d/2)2*B0*

6、3=通過面積計算路面及橋面系重：Pc=854.04672腹拱墩以上部分：Pd= 163.296一個腹拱重：P= 1797.368294b、腹拱墩重1#腹拱墩：P= 760.852224面積=2#腹拱墩：P= 31.977216面積=c、腹拱集中恒重1#腹拱恒載：P1= 1829.345512#腹拱恒載：P2= 849.0133632（3）拱上實腹段拱上填料及橋面系P3= 3419.5968面積=m= 1.543k= 0.999931383x=lx/l1= 0.255933611lx=kx= 0.255916049f1=f+y上（1-1/cos）= 3.911986096x0= 3.159410

7、42shx= 0.2587368043、驗算拱軸系數(shù)上部結(jié)構(gòu)的恒載對拱跨l/4截面和拱腳截面的力矩比值等于或接近選定的m系數(shù)相應(yīng)的y1/4/f值的條件。（1）半拱恒載對拱跨l/4截面和拱腳的力矩分塊號恒重l/4截面力臂（m）力矩（KN*m）P0124218.8070393805.502719P11829.34551P2849.01336320.0782060566.39798153P33419.59680.918795633141.91059610316.76271（2）驗算拱軸系數(shù)設(shè)計的拱橋在主拱圈兩截面的恒重力矩的比值0.174990333假定的拱軸系數(shù)m=1.543,相應(yīng)的y1/4/f=

8、0.235（二）拱圈彈性中心及彈性壓縮系數(shù)ys=表（）-3值f=1.6139mrw2/f2=0.003290511u1=拱橋（上冊）表（）-9值rw2/f2=0.035415436u1=拱橋（上冊）表（）-11值rw2/f2=0.027088404u1/(1+u)=0.03448139（三）永久荷載內(nèi)力計算1.不計彈性壓縮的恒載推力Hg=10210.986092.計入彈性壓縮的恒載內(nèi)力項目拱頂3l/8截面l/4截面y100.2270430050.922444395y1.61391.3868569950.691455605cos10.974010.90161Ng9858.89709110140.

9、5127711007.83347Mg568.2364335488.2970893243.4539108(四）可變荷載內(nèi)力計算1.基本可變荷載汽車和掛車荷載，統(tǒng)稱為活載l2=266.1082334截面項目等代荷載K206K20拱頂Mmax102.5444615.2664相應(yīng)H185.4014512.4084Mmin77.7994466.7964相應(yīng)H156.3298337.97903l/8截面Mmax96.0008576.0048相應(yīng)H171.9152431.4912Mmin81.9286491.5714相應(yīng)H171.6806430.0834拱腳Mmax78.0242468.1454相應(yīng)H168

10、.2853409.7117相應(yīng)V62.3818374.2906Mmin80.9872485.9232相應(yīng)H138.3012229.8072相應(yīng)V58.5200351.12002.計入彈性壓縮的汽車-20級內(nèi)力項目拱頂3l/8截面MmaxMminMmax軸力cos10.97401sin00.22652與M相應(yīng)的H12629.511951734.6726022212.165247與M相應(yīng)的VN2629.511951734.6726022271.193568H90.6692281459.8139232176.27853355N90.6692281459.8139232174.29605446Np25

11、38.8427221674.8586782196.897514彎矩M1245.638476-794.50066481541.379856y100.227043005y1.61391.386856995M146.331067396.53369067105.7874178Mp1391.969543-697.96697411647.1672743.計入彈性壓縮的掛車-100內(nèi)力項目拱頂MmaxMmin軸力cos1sin0與M相應(yīng)的H1970.855935433.5215666與M相應(yīng)的VN970.855935433.5215666H33.4764625314.94842639N33.47646253

12、14.94842639Np937.3794725418.5731402彎矩M373.3038007-189.7674367y10y1.6139M54.0276628824.12526535Mp427.3314635-165.64217134.溫度內(nèi)力拱圈合攏溫度15拱圈砌體線膨脹系數(shù)=0.000008變化溫差t=15彈性模量E=4.0*106溫度下降在彈性中心產(chǎn)生的水平力：Ht=20.982876溫度下降在拱圈中產(chǎn)生的內(nèi)力：項目拱圈3l/8截面拱腳cos10.974010.67873y1.61391.386856995-2.3113953Nt20.98287620.4375310514.241

13、70743Mt-33.86426358-29.1002483548.49972097(五）主拱圈強(qiáng)度和穩(wěn)定性驗算1.主拱圈正截面受壓強(qiáng)度驗算（1）荷載效應(yīng)匯總荷載安全系數(shù)及荷載效應(yīng)匯總表荷載效應(yīng)系數(shù)拱頂MN軸力恒載1568.23643359858.897091汽車-20級Mmax1391.9695432538.842722汽車-20級Mmin-697.96697411674.858678掛車-100Mmax427.3314635937.3794725掛車-100Mmin-165.6421713418.5731402溫度下降-33.8642635820.982876恒載1.2681.883720

14、211830.676510.9511.41279028873.007381汽車-20級Mmax1.41948.757363554.379811汽車-20級Mmin-97780215掛車-100Mmax598.26404891312.331262掛車-100Mmin-231.8990399586.0023963溫度下降-47.4099690129.3760264（2）荷載效應(yīng)組合系數(shù)及荷載效應(yīng)最不利組合的設(shè)計值荷載效應(yīng)組合系數(shù)拱頂Mj組合I(恒+汽）Mmax12630.641081(恒+汽）Mmin-465.7409736組合II(恒+汽）Mmax+溫降0.82066.

15、584889(恒+汽）Mmin+溫降-410.5207541組合III(恒+掛）Mmax1160.494959(恒+掛）Mmin359.9877443（3）結(jié)構(gòu)（主拱圈）抗力效應(yīng)的設(shè)計值結(jié)構(gòu)抗力效應(yīng)的設(shè)計值為：RN=19470.12987 kN其中：=1-(e0/y)3.5/（1+e0/rw)2,e0=Mj/Nj計算結(jié)果如下：荷載效應(yīng)組合系數(shù)拱頂RN組合I(恒+汽）Mmax0.598861592 11659.91298(恒+汽）Mmin0.96673832318822.5207組合II(恒+汽）Mmax+溫降0.610054415 11877.83869(恒+汽）Mmin+溫降0.960035

16、533 18692.01652組合III(恒+掛）Mmax0.796550523 15508.94213(恒+掛）Mmin0.974511102 18973.85772（2）與（3）比較得到兩者數(shù)值相接近，若裂縫繼續(xù)發(fā)展，則可能導(dǎo)致橋梁倒塌?。?）主拱圈裸拱強(qiáng)度和穩(wěn)定性計算1.彈性中心的彎矩和推力Ms=表（）-15值A(chǔ)yl2/4=5772.21713Hs=表（）-16值A(chǔ)yl2/4(1+u)f=3967.0757862.截面內(nèi)力裸拱截面內(nèi)力項目拱頂3l/8截面拱腳cos10.974010.67873sin00.226520.73439表（）-19值00.126110.57563N3967.07

17、57864073.3356385790.823049ys-y11.61391.386856995-2.3113953表（）-19值00.031590.53699M-630.2464807-673.7519246-1108.545277e0-0.158869282-0.165405453-0.1914313853.裸拱圈強(qiáng)度驗算項目拱頂3l/8截面拱腳Nj3665.5780263763.7621295350.720498e0-0.158869282-0.165405453-0.1914313850.6388330990.6172401610.5323569890.9346860760.93264

18、83450.923823452RN24194.5222623325.7689119927.6374計算表明4.主拱圈穩(wěn)定性驗算荷載效應(yīng)組合拱頂Nje0組合I(恒+汽）Mmax15385.056320.17098677(恒+汽）Mmin11217.80953-0.041517996組合II(恒+汽）Mmax+溫降12331.545880.167585225(恒+汽）Mmin+溫降8997.748446-0.045624831組合III(恒+掛）Mmax10514.406220.110371897(恒+掛）Mmin9933.3431240.036240341截面寬B= 24厚度D= 0.78查拱橋

19、（上冊）表（）-20（3）得：每等分點拱軸線的縱坐標(biāo)y1=拱橋（上冊）表（）-1值f，相應(yīng)拱背cosy上/cosy下/cosy1y15678910.390.39-0.390.390.997060.3911499810.391149981 -0.36604 0.416260.988330.3946050410.394605041 -0.29399 0.4952220.974010.4004065670.400406567 -0.17336 0.627450.954450.408612290.40861229 -0.00334 0.813883主拱圈用塊石筑成，材料容重0= kN/m，抗壓極限強(qiáng)度

20、Rj= MPa，砌體彈性模量=l0=1.93m，腹拱厚度d=0.43m，腹拱座寬b=24m，腹拱圈選用塊石筑成，材料容重0= kN/m，抗壓極限強(qiáng)度Rj= MPa，砌體彈性模量=曲面的坐標(biāo)y1=y1-y上/cos，腹拱曲面相應(yīng)點的坐標(biāo)y1=y1+y下/cos，具體見下表：0.930130.4192962270.419296227 0.217238 1.055830.901610.4325595320.432559532 0.489885 1.3550040.869510.4485284820.448528482 0.816457 1.7135140.834510.4673401160.4673

21、40116 1.199203 2.1338830.797280.4891631550.489163155 1.640737 2.6190640.75850.5141727090.514172709 2.144112 3.1724570.718790.54257850.54257852.712787 3.7979440.678730.5746025670.574602567 3.350693 4.499898腹拱圈厚度= 0.43主拱圈材料容重= 241.93d= 0.43165.264查拱橋（上冊）表（）-20（3）3-2得：1.3209240.0555165.93688.35shkx= 0.

22、258718664chx= 1.03293chkx= 1.032926拱腳截面力臂（m）力矩（KN*m）16050.242731.86641213414.31259648494164.9970016817087.7309540081.1357上部結(jié)構(gòu)的恒載對拱跨l/4截面和拱腳截面的力矩比值等于或接近選定的m系數(shù)相應(yīng)的y1/4/f值的條件。拱腳3.9252953-2.31139530.6787314805.28-813.8168547l2/f=67.79317556影響線面積力（kN*m或kN)K100【拱橋（上冊）表（）-14（19）值】乘數(shù)面積汽車-20級掛車-1

23、00級184.38840.00634l21.687126 1245.638 373.3038189.18900.06308l2/f4.276394 2629.512 970.8559111.4949-0.00533l2-1.41836 -794.501 -189.767101.35940.06309l2/f4.277071 1734.673 433.5216220.63720.00838l22.229987 1541.38 590.4217131.48660.06302l2/f4.272326 2212.165 674.1043197.1077-0.00789l2-2.09959 -1238.

24、52 -453.805164.25700.06315l2/f4.281139 2209.496 771.0994180.11620.01736l24.619639 2595.195 998.4859150.09620.08788l2/f5.957664 2929.11 1073.068125.08100.16045l2.617393 1175.598 392.8634171.6918-0.01518l2-4.03952 -2355.48 -832.264100.35610.03829l2/f2.595801 715.8404 312.6053122.05060.33955l5.539019 2

25、333.833 811.2488拱腳MminMmaxMmin0.678730.734392209.4959942929.109563715.84042651175.598432333.8326142268.4530892851.4222652199.805706等代荷載3l/8截面0.974010.2265276999770424.6831732274.2064069968.5515741716.753210162194.2466822782.870692183.052496-1238.5203112595.19548-2355.477523.9252953-2.31

26、13953105.6597721-233.4503946 -57.0525706-1132.8605392361.745086-2412.530093l/8截面拱腳MmaxMminMmaxMmin0.974010.678730.226520.73439674.1043317771.09944671073.067607 312.6053392.8634326 811.2488692.0917975791.67508211016.838153 807.947623.2440546426.5885810737.00086309 10.7790722.6399416625.8975438525.113

27、59581 7.316076669.4518559765.7775383991.7245573 800.6315590.4217041-453.8049623 998.4859499 -832.2640.2270430053.92529531.386856995-2.311395332.2361797636.87455963-85.523621 -24.9147622.6578839-416.9304026 912.9623289 -857.1783l/8截面拱腳MNMN0.2270430051.386856995488.297089310140.51277-813.816855 14805.

28、281647.1672742196.8975142361.745086 2782.871-1132.8605392194.246682-2412.53009 2183.052622.6578839669.4518559912.9623289 991.7246-416.9304026765.7775383-857.178249 800.6315-29.1002483520.4375310548.49972097 14.24171585.956507212168.61533-976.580226 17766.34439.46738049126.461497-732.435169 13324.752

29、306.0341843075.6565193306.44312 3896.019-1586.0047543071.945355-3377.54213 3056.273871.7210374937.23259821278.14726 1388.414-583.70256371072.088554-1200.04955 1120.884-40.7403476928.6125434767.89960935 19.938393l/8截面拱腳Nje0MjNje0MjNje015385.056320.170986772891.990691 15244.27 0.18971 2574.008 17220.7

30、7 080953-0.041517996 -1146.53737 12198.41 -0.09399 -4354.12 20822.61 -0.2091112331.545880.1675852252336.482587 12249.74 0.190737 2059.206 13776.62 0.1494718997.748446-0.045624831 -894.339864 9813.045 -0.09114 -3483.3 16658.09 -0.2091110514.406220.1103718971166.142036 10484.68 0.111223 436.5697 11770.530.037099933.3431240.036240341-115.388147 17036.06 -0.00677 -1741.3 15109.78 -0.115243l/8截面拱腳RNRN0.58333783511357.663410