橋梁工程課程設(shè)計-拱橋結(jié)構(gòu)設(shè)計計算說明書

南京工業(yè)大學(xué)課程設(shè)計用紙第32頁拱橋結(jié)構(gòu)設(shè)計計算說明書一．課程設(shè)計的目的1.培養(yǎng)學(xué)生綜合運(yùn)用所學(xué)橋梁工程理論知識，解決鋼筋混凝土拱橋結(jié)構(gòu)的設(shè)計和計算問題，掌握鋼筋混凝土拱橋結(jié)構(gòu)分析和計算的理論與方法。2.強(qiáng)調(diào)規(guī)范在橋梁結(jié)構(gòu)設(shè)計中的重要性，培養(yǎng)學(xué)生運(yùn)用專業(yè)理論知識和專業(yè)規(guī)范進(jìn)行橋梁結(jié)構(gòu)設(shè)計的能力。3.進(jìn)一步提高學(xué)生繪制橋梁工程施工圖、使用計算機(jī)的能力。二．課程設(shè)計的內(nèi)容1.確定主拱圈截面構(gòu)造尺寸，計算拱圈截面的幾何、物理力學(xué)特征值；2.確定主拱圈拱軸系數(shù)m及拱上建筑的構(gòu)造布置和幾何構(gòu)造尺寸；3.結(jié)構(gòu)恒載計算；4.主拱結(jié)構(gòu)內(nèi)力計算(永久作用、可變作用)；5.溫度變化、混凝土收縮徐變引起的內(nèi)力；6.主拱結(jié)構(gòu)的強(qiáng)度和穩(wěn)定計算；7.拱上立柱(墻)的內(nèi)力、強(qiáng)度及穩(wěn)定性計算；8.繪制1～2張相關(guān)施工圖。三．課程設(shè)計的時間時間：兩周；安排在理論課結(jié)束之后。四．課程設(shè)計的方法1．獨(dú)力思考，繼承與創(chuàng)新設(shè)計時要認(rèn)真查閱和閱讀參考資料，繼承前人的設(shè)計成果和經(jīng)驗(yàn)，根據(jù)課程設(shè)計的具體要求，大膽改進(jìn)和創(chuàng)新。2．結(jié)合和參考本指導(dǎo)的算例，進(jìn)行拱橋結(jié)構(gòu)的設(shè)計計算，掌握拱橋的計算理論和設(shè)計內(nèi)容與方法。五．課程設(shè)計的步驟1．設(shè)計準(zhǔn)備：了解設(shè)計任務(wù)書，明確設(shè)計要求、設(shè)計內(nèi)容、設(shè)計步驟；通過查閱教科書和相關(guān)設(shè)計資料，了解設(shè)計的理論和方法；準(zhǔn)備好設(shè)計所需資料、工具書、工具軟件；擬好設(shè)計計劃。2．設(shè)計實(shí)施：根據(jù)課程設(shè)計任務(wù)書的要求，參考設(shè)計指導(dǎo)書和教科書，確定設(shè)計的主要內(nèi)容、計算順序；根據(jù)相關(guān)計算理論，計算和填寫相關(guān)圖表的內(nèi)容。使用圖表給出計算結(jié)果和結(jié)構(gòu)的相關(guān)驗(yàn)算結(jié)果。3．匯總設(shè)計成果：課程設(shè)計計算書，課程設(shè)計要求繪制的工程圖紙。六．拱橋課程設(shè)計計算空腹式等截面懸鏈線無鉸拱設(shè)計一．設(shè)計題目空腹式等截面懸鏈線無鉸拱設(shè)計二．設(shè)計資料1．設(shè)計標(biāo)準(zhǔn)設(shè)計荷載：汽車荷載公路－I級，人群荷載3.5kN/m2橋面凈空凈－7+2×(1.25m+0.25m)人行道+安全帶凈跨徑L0＝80ｍ凈高f0＝13.3m凈跨比f0/L0＝1/62．材料數(shù)據(jù)與結(jié)構(gòu)布置要求拱頂填料平均厚度(包括路面，以下稱路面)hd＝0.5m，材料容重γ1＝22.0kN/m3主拱圈材料容重(包括橫隔板、施工超重)γ2＝25.0kN/m3拱上立柱（墻）材料容重γ2＝25kN/m3腹孔拱圈材料容重γ3＝23kＮ/m3

腹孔拱上填料容重γ4＝22kN/m3主拱圈實(shí)腹段填料容重γ1＝22kN/m3本橋采用支架現(xiàn)澆施工方法。主拱圈為單箱六室截面，由現(xiàn)澆30號混凝土澆筑而成。拱上建筑采用圓弧腹拱形式，腹拱凈跨為5m，拱腳至拱頂布置6跨(主拱圈的具體幾何尺寸參照指導(dǎo)書實(shí)例修改自定)。3．設(shè)計計算依據(jù)交通部部頒標(biāo)準(zhǔn)《公路橋涵設(shè)計通用規(guī)范》(JTGD60－2004)交通人民出版社交通部部頒標(biāo)準(zhǔn)《公路鋼筋混凝土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范》(JTGD62－2004)交通人民出版社交通部部頒標(biāo)準(zhǔn)《公路圬工橋涵設(shè)計規(guī)范》(JTGD61-2005)交通人民出版社《公路設(shè)計手冊-拱橋(上)》人民交通出版社，2000.7二.主拱圈截面幾何要素的計算(一)主拱圈橫截面設(shè)計拱圈截面高度按經(jīng)驗(yàn)公式估算H=l0/100+Δ=80/100+0.7=1.5m(Δ=0.6～0.8)拱圈由六個各為1.5m寬的拱箱組成，全寬B0=9.0m?！b…訂……線……………...拱圈橫斷面的構(gòu)造如圖1所示。(二)箱形拱圈截面幾何性質(zhì)截面積：A=(1.5×1.5-1.05×1.14)×6=6.318m2繞箱底邊緣的靜面矩：S=m3主拱圈截面重心軸：y下=S/A=0.778my上=1.5-0.778=0.722m主拱圈截面繞重心軸的慣性矩：Ix=拱圈截面繞重心軸的回轉(zhuǎn)半徑：三、確定拱軸系數(shù)(一)上部結(jié)構(gòu)構(gòu)造布置上部結(jié)構(gòu)的構(gòu)造布置如圖2所示。圖2上部結(jié)構(gòu)構(gòu)造（尺寸單位：mm）1.主拱圈假定m=2.514，相應(yīng)的，，查《拱橋》(上冊)表(III)-20(7)得：sinφj=0.62411，cosφj=0.78133，φj=38?46'40"主拱圈的計算跨徑和計算矢高：l=l0+2y下sinφj=80.9711mf=f0+y下(1-cosφj)=13.470m拱腳截面的水平投影和豎向投影x=Hsinφj=0.9362my=Hcosφj=1.1720m將拱軸沿跨徑24等分，每等分長Δl=l/24=3.3738m，每等分點(diǎn)拱軸線的縱坐標(biāo)y1=[表(III)-1值]×f，相應(yīng)的拱背曲面坐標(biāo)y'1=y12y上/cosφ，拱腹曲面坐標(biāo)y"1=y1+y下/cosφ?！b…訂……線……………...具體數(shù)值見表1。主拱圈幾何性質(zhì)表表1截面號xy1/fy1cosφy上/cosφy下/cosφy1-y上/cosφ040.48561.00000013.47000.781330.92410.99571254614.4657137.11180.81401810.96480.822620.87770.945810.08711.9106233.7380.6534088.801410.859190.84030.90557.96119.7069330.36420.5154056.94250.890810.81050.87346.1327.8159426.99040.3976355.35610.917520.78690.84794.56926.204523.61660.2980714.01500.939620.76840.82803.24664.843620.24280.2150002.89610.957480.75410.81252.1423.7086716.8690.1469921.9800.971600.74310.80071.23692.7807813.49520.0928771.25110.982430.73490.79190.51622.043910.12140.0517240.69670.990380.72900.7856-0.03231.4823106.74760.0228250.30750.995810.72500.7813-0.4181.0888113.37380.0056820.07650.998970.72270.7788-0.6460.8553120.00000.0000000.00001.000000.72200.7780-0.7220.77802.拱上腹孔布置從主拱兩端起拱線起向外延伸后向跨中對稱布置五對圓弧小拱，腹拱圈厚d'=0.4m，凈跨徑l'0=5m，凈矢高f'0=0.625m，座落在寬為0.5m的鋼筋混凝土排架式腹拱墩支承的寬為0.6m的鋼筋混凝土蓋梁上。腹拱拱頂?shù)墓氨澈椭鞴肮绊數(shù)墓氨吃谕粯?biāo)高。腹拱墩墩中線的橫坐標(biāo)lx，以及各墩中線自主拱拱背到腹拱起拱線的高度h=y1+y上×(1-1/cosφ)-(d'+f'0)，分別計算如表21.573腹拱墩高計算表表2項(xiàng)目lxξ=2lx/lkξy1=f(chkξ-1)/(m-1)tgφ=2kfshkξ/l(m-1)1/cosφ=(tg2φ+1)?h1號立柱35.600.87931.38319.95600.64581.19048.79352號立樁30.000.74101.16566.75990.50061.11835.60283號立柱24.400.60270.94804.30640.37901.06943.23134號立柱18.800.46440.73052.48160.27561.03731.42975號立柱13.200.32600.51281.19570.18511.01700.1584空、實(shí)腹段分界線12.750.31490.49531.11380.17831.01580.0774由f'0/l'0=1/8，查《拱橋》(上冊)表3-2得sinφ0=0.513918，cosφ0=0.85784，φ0=30?55'35"腹拱拱腳的水平投影和豎向投影x'=d'×sinφ0=0.4×0.513918=0.2056m；y'=d'×cosφ0=0.4×0.85784=0.3431m(二)上部結(jié)構(gòu)恒載計算三、結(jié)構(gòu)恒載計算（一）各部分恒載重力1、腹拱各部分重力1）腹拱數(shù)據(jù)由圓弧拱算得:sinφ0=0.513918，cosφ0=0.85784腹拱內(nèi)弧半徑R=5.3125m，拱軸線長度s=5.7394m一個腹拱圈上填料面積A=2.52一孔腹拱重力2、橫墻頂填料、路面重力1號、2號、3號、4號、5號橫墻3、橫墻墩帽重力1號、2號、3號、4號、5號橫墻4、橫墻重力1號橫墻2號橫墻3號橫墻……裝…訂……線……………...4號橫墻5、橫墻壓力6、拱頂實(shí)腹段路面重力7、拱頂實(shí)腹段填料重力作力點(diǎn)距離拱頂（二）驗(yàn)算壓力線同拱軸線的重合度以拱腳為固定端，拱頂為懸臂端，計算半跨拱各部分重力對L/4和拱腳的力矩。主拱圈重力對L/4和拱腳的垂直截面剪力和彎矩，查附錄表（Ⅲ）-19計算，得其余各力對L/4和拱腳彎矩列入表2表2重力名稱重力(kN）拱腳L/4力臂彎矩力臂彎矩P7682.7329.3520038.1310.34787064.75P61228.9232.3539755.5614.837518234.1P5585.6426.415460.908.18754794.93P41572.48520.932864.942.45683863.28P31889.65515.429100.69P22332.4059.923090.81P12924.8854.412869.5合計173180.533957.78拱腳彎矩173180.5+133707.37=306887.87KN.mL/4處彎矩32576.387+33957.78=66534.17KN.m根據(jù)判別條件，得（與選用的拱軸系數(shù)相符）按無矩法計算，不計彈性壓縮恒載水平推力腹拱推力靠近主拱拱頂一側(cè)的腹拱，一般多做成兩平鉸拱，在較大的恒載作用下和考慮到周圍的填料等構(gòu)造的作用，可以折中地按無鉸圓弧拱計算其推力，而不計彎矩的影響。腹拱拱腳的水平推力F=(C1g1+C2g2+C3g3)RB0式中g(shù)1=γ1hd=22×0.5=11kN/m2g2=γ2{(R+d'/2)-[(R+d'/2)2-l2/4]?}=23×{(5.3125+0.40/2)-[(5.3125+0.40/2)2-5.31252/4]?}=15.690kN/m2g3=γ3d'=23×0.40=9.20kN/m2由f0/l'0=1/8和b=I/AR2=0.000203查《拱橋》(上冊)表(I)-4得C1=0.78893，C2=0.109，C3=0.8023F=(0.78893×11+0.109×15.690+0.8023×9.20)×5.3125×9.0=849.609kN四.拱圈彈性中心及彈性壓縮系數(shù)1.彈性中心ys=[表(III)-3值]×f=0.329011×13.470=4.43177817m2彈性壓縮系數(shù)γ2w/f2=(0.543/13.470)2=0.001621=[表(III)-9值]×γ2w/f2=11.2581×0.00162=0.0182=[表(III)-11值]×γ2w/f2=9.795×0.00162=0.01591/(1+)=0.0179五.主拱圈截面內(nèi)力驗(yàn)算(一)結(jié)構(gòu)自重內(nèi)力計算(1)假載內(nèi)力a.求假載由式(∑M?+qxl2/32)/(∑Mj+qxl2/8)=0.2415得：qx=(∑M?-0.215×∑Mj)/(0.215/8-1/32)l2=31.5927kN/mb.假載內(nèi)力假載qx產(chǎn)生的內(nèi)力可以將其直接布置在內(nèi)力影響線上求得。不考慮彈性壓縮的假載內(nèi)力見表5?！b…訂……線……………...不計彈性壓縮的假載內(nèi)力表5項(xiàng)目影響線面積ω乘數(shù)ω力或力矩(qxω)[表(III)-14(51)值]拱頂截面M10.00703-0.004700.00164l26556.302810.7523339.694H10.067890.059900.12703l2/f486.733761.83031953.38l／4截面M10.00887-0.010310.00797l26556.302852.25371650.84H10.040400.087390.12779l2/f486.733762.19971965.06拱腳截面M10.01950-0.014370.00513l26556.302833.63381062.58H10.091550.036250.12775l2/f486.733762.13471963.00V10.168450.331550.5l80.971140.48561279.05c.計入彈性壓縮的假載內(nèi)力計入彈性壓縮的假載內(nèi)力計算見表6。計入彈性壓縮的假載內(nèi)力表6項(xiàng)目拱頂截面l/4截面拱腳截面cosφ10.945620.78133sinφ00.325270.62412H11953.381965.061963.00V11279.051H1/(1+)34.96635.17435.138N=[1-1/(1+)]×H1cosφ+V1sinφ1918.4141824.9382304.577M1339.6941650.841062.58y=ys-y14.4321.526-9.038M=M1+1H1y/(1+)494.6631704.515745.003注：l/4截面的軸力以N?=[1-m1/(1+m)]H1/cosφ?作近似計算。(2)“拱軸線恒載”內(nèi)力a.推力Hg=(∑Mj+qxl2/8)/f=(440591.24+31.5927×80.97112/8)/13.470=34631.233kNb.考慮彈性壓縮的內(nèi)力考慮彈性壓縮的“拱軸線恒載”內(nèi)力見表7?？紤]彈性壓縮的拱軸線恒載內(nèi)力表7項(xiàng)目拱頂截面l/4截面拱腳截面cosφ10.945620.78133H'g=Hg-F33781.62433034.66533034.665[1-1/(1+)]H'g33176.93332443.34532443.345N'=H'g/cosφ33176.93334309.07241523.230ΔN=1H'gcosφ/(1+)604.691559.164462.014N=N'-ΔN32572.24233749.90841061.216y=ys-y14.4321.526-9.038ΔV=1H'gy/(1+)2679.991902.355-5344.355(3)考慮確定m系數(shù)偏差影響的恒載內(nèi)力考慮m系數(shù)偏差影響的恒載內(nèi)力等于“拱軸線m的恒載”內(nèi)力減去“假載”的內(nèi)力，計算結(jié)果見表8。考慮“五點(diǎn)”偏差的恒載內(nèi)力表8截面拱頂截面l/4截面拱腳截面項(xiàng)目拱軸線恒載假載qx合計拱軸線恒載假載qx合計拱軸線恒載假載qx合計水平力33781.6241918.41431863.2133034.6651918.41431116.24233034.6651918.41431116.242軸力32572.2421918.41430653.8333749.9081824.93833749.9741061.2162304.57738756.639彎矩2679.991494.6632185.328902.3551704.515-802.16-5344.355745.003-6089.3582.“恒載壓力線”偏離拱軸線的影響“恒載壓力線”(指空腹式無鉸拱橋不考慮拱軸線的偏離和恒載彈性壓縮影響的恒載壓力線，也就是人們所說的“三鉸拱恒載壓力線”)與拱軸線在“五點(diǎn)”以外的偏離影響可以用一般力學(xué)原理進(jìn)行計算，參見圖13。(1)“恒載壓力線”偏離拱軸線的偏離彎矩Mp計算恒載偏離彎矩Mp，首先要計算出橋跨結(jié)構(gòu)沿跨徑各等分段的分塊恒載對各截面的力矩，再算各截面壓力線的縱坐標(biāo)，然后才能求得Mp。下面按主拱圈、拱上實(shí)腹段和各集中力三部分計算各分塊恒載對各截面的力矩。a.主拱圈自重對各截面產(chǎn)生的力矩Ml(圖14)在這里，對于所要求的每一等分點(diǎn)而言，積分上限ξ為常數(shù)，并不計等式前面的負(fù)號，則上式為：式中：可根據(jù)ξ值從《拱橋(例集)》附表1-1查得；可根據(jù)ξ值從《拱橋(例集)》附表1-2查得……裝…訂……線……………...主拱圈對各截面的力矩M1的值見表9。主拱圈自重對各截面產(chǎn)生的彎矩表9截面號ξS1S2ξ×S1-S2M1(kN·m)0123451200000110.08330.074230.003320.0029750.7887100.16670.163450.014840.01243210.268890.25000.250890.030350.03248388.121880.33330.329280.053220.056514627.43570.41670.418520.087220.087222575.43960.50000.514700.126910.130433759.60150.58330.584630.169870.171144296.53240.66670.688480.234300.224758173.17830.75000.789420.290360.301778107.91220.83330.872280.363600.363394055.69910.91670.965790.443930.4414114275.215011.080270.547890.5324137834.446b.拱上實(shí)腹段恒載對各截面產(chǎn)生的彎矩M2計算拱上實(shí)腹段的恒載時，必須將拱頂填料及面層的矩形板塊和其下面的懸鏈線曲邊三角形塊分開才能準(zhǔn)確計算，否則只能是近似的。(a)矩形板塊從拱頂?shù)矫總€截面的矩形板塊的重力：P1=γ1B0h’dl·ξ1/2對實(shí)腹段里每個截面的力矩：Mi=Pi(l·ξ/2)/2=(l2/4)γ1B0h’dξ2i/2對空腹段里每個截面的力矩：Mi=Pk[l·ξi/2-(l/2)ξk/2]=(l2/4)γ1B0h’dξk(ξi-ξk/2)(i<k)式中k表示空、實(shí)腹段的分界點(diǎn)，取為：l2B0h’d/4=248754.3749kN·m各截面的力矩見表10。(b)懸鏈線曲邊三角形塊從拱頂?shù)饺我饨孛娴闹亓?參見表11)Pi=l·f1γ2B0(shkξi-kξi)/[2(m-1)k]每一塊Pi的重心的橫坐標(biāo)：ηi=[(shkξi-kξi/2)-(chkξi-1)/kξi]/(shkξi-kξi)在實(shí)腹段里，截面重心到任意截面的力臂為l·(1-ηi)·ξi/2，在空腹段里，整塊曲邊三角形面積的重心到每個截面的力臂為l·(ξi-ηkξk)/2。每個截面的力矩見表10。c.各集中力對各截面的力矩M3拱上空腹段的腹孔和橫隔板等各集中力及其相應(yīng)的橫坐標(biāo)lx。在前面已經(jīng)求出，各豎向集中力到截面的力臂a=l·ξi/2-lx(取a>0)，產(chǎn)生的力矩M'3=Pa；腹拱水平推力H'g作用在第7與第8截面之間，對0~7截面產(chǎn)生的力矩M"3=H'g(y1-e)。具體計算見表11。d.計算偏離彎矩Mp上部結(jié)構(gòu)恒載對拱圈各截面重心的彎矩：Mi=M1+M2+M3壓力線的縱坐標(biāo)：yi=Mi/Hg式中，Hg為不計彈性壓縮的恒載水平推力：Hg=∑Mj/f=33976.8645kN拱上實(shí)腹段恒載對各截面產(chǎn)生的力矩表10區(qū)間截面ξ懸鏈線曲邊三角形矩形塊M2=MΔ+M恒號kξPηlξ(1-η)/2MΔξ2/2M恒012345678910實(shí)腹段12000000000110.08330.131024.85380.75000.843320.95920.0035876.4876897.4468100.16670.2622198.83040.75021.6845334.9290.01393168.49873503.427790.25000.3933695.90640.75042.52631758.0680.031257373.91099131.9789分界點(diǎn)0.32650.51361366.76650.7508(ξ1-0.263)/2(ξ1-0.1751)ξx空腹段80.33331366.76650.75082.84613889.95480.055513419.107617309.062470.41671366.76650.75086.22268504.84120.082720053.075428557.916660.50001366.76650.75089.595113120.9580.109928654.143241775.101250.58331366.76650.750814.048419200.8830.137233297.207952498.092740.66671366.76650.750816.344022338.4320.164440775.181963113.613930.75001366.76650.750819.716526947.8520.191648965.246675913.098620.83331366.76650.750823.088931557.1350.218851929.311283486.446210.91671366.76650.750826.465436172.0220.246060507.285296679.307201.00031366.76650.750829.850040797.9800.273369111.6284109909.6084各截面上“恒載壓力線”偏離拱軸線的值：Δy=y1-yi偏離彎矩具體數(shù)值見表12。(2)偏離彎矩Mp在彈性中心產(chǎn)生的贅余力贅余力各項(xiàng)的計算見表13。由表13得ΔX1=-400.9854kN·mΔX2=547.3724kN(3)“恒載壓力線”偏離拱軸線的附加內(nèi)力“恒載壓力線”偏離拱軸線在拱圈任意截面中產(chǎn)生的附加內(nèi)力為ΔM=ΔX1-ΔX2(ys-y1)+Mp；ΔN=ΔX2cosφ；ΔQ=6ΔX2sinφ拱頂、l/4截面、拱腳三個截面的附加內(nèi)力見表14?！b…訂……線……………...(4)空腹式無鉸拱的恒載壓力線空腹式無鉸拱橋在恒載作用下考慮壓力線與拱軸線的偏離以及恒載彈性壓縮的影響之后，拱中任意截面存在三個內(nèi)力Mg=[m1Hg/(1+m)-ΔX2](ys-y1)+ΔX1+Mp；Ng=Hg/cosφ-[m1Hg/(1+m)-ΔX2]cosφQg=7[m1Hg/(1+m)-ΔX2]sinφ這三個力的合力作用點(diǎn)的偏心距為：ei=Mg/Ng拱上各集中力對各截面產(chǎn)生的力矩表11截面豎向力P0P1P2P3P18(柱）P4P17(柱）P5P=57.876758.544659.344360.2985854.632763.18611457.552864.6013lx=051015.515.520.520.525.5ξaMMMMMMMM120000110.08333.378195.50754.9873100.16676.7476390.5288156.376890.250010.1214585.7932401.765985.455480.333313.4952781.0576574.3819337.692012.3454176.882770.416716.869976.3221823.5987598.9285223.48513523.831460.500020.24281171.58651009.4387829.1650509.57596735.7801154.51074003.462850.583323.61661366.85091287.38641001.4015776.66679603.7288412.15209456.181442.166540.666726.99041562.11531539.43331138.6380983.757411231.6775698.793415325.9001300176430.750030.36421757.37971799.65561343.87451010.848213874.6262933.434820098.6187578.186320.833333.7381931.00981987.23451651.11101347.939018754.57491028.076128745.3373785.196110.916737.11182147.90852234.18191876.34751655.029820643.52371321.717535489.0560998.206001.000040.48562341.17292547.77862098.58401852.120522098.47241654.358941984.77461256.2159截面豎向力P6P15(柱)P7P14(柱)P8P13(柱)腹拱水平力合計P=72.34761746.810180.56431934.492783.72671987.8843F915.2315lx=30.530.535.535.540.5040.50e0.0426ξMMMMMMMM31200110.0833200.4948100.1667546.905690.25001073.014580.33331.621287.13681882.359670.41672.761987.91856146.165860.50003.452978.253114413.519750.58334.894021.606823946.534240.66676.225820.057735482.08430.7500200.8734567.01968.347098.459346164.516320.8333498.659910118.950563.85731092.403410.769234.722068004.349810.9167791.537917863.8815392.70198123.589112.4310987.932493537.681301.0000965.415923987.8124732.546514524.7748246.27115008.296013.4712458.7980121312.9907所以，空腹式無鉸拱橋恒載壓力線的縱坐標(biāo)：y=y1-ei/cosφ空腹式無鉸拱恒載壓力線的縱坐標(biāo)值見表15。3.空腹無鉸拱的實(shí)際恒載內(nèi)力空腹式無鉸拱的實(shí)際恒載內(nèi)力等于計人拱軸系數(shù)m的偏差影響的內(nèi)力與“壓力線”及拱軸線偏離的附加內(nèi)力之和，其結(jié)果見表16。(二)活載內(nèi)力計算1.汽車-A級和人群荷載內(nèi)力車道荷載的均布荷載標(biāo)準(zhǔn)值qM采用10.0KN/m，計算剪力時，均布荷載標(biāo)準(zhǔn)值qQ采用15.0KN/m，所加集中力荷載P采用300KN人群荷載K2=2·b·g人=2×1.25×3.5=8.75kN偏離彎矩Mp表12截面號主拱圈拱上實(shí)腹段集中力合計“恒載壓力線”拱軸線偏心偏離彎矩M1M2M3Mi=M1+M2+M3y1=Mi/Hgy1Δy=yl-yiMp=HgΔy123456789120000000011750.7887897.4468200.49481848.73030.0533830.07650.023117800.5702103210.26883503.4277546.90567260.60210.2096540.30750.0978463388.527698388.12189131.97891073.014518593.11520.653720.69670。042981488.4504814627.43517309.06241882.359633818.51191.203341.25210.048761688.6189722575.43928557.91666146.165857279.52141.90431.9800.07572621.5843633759.60141775.101214413.519789948.22192.2.85232.89610.04381516.8480544296.53252448.092723946.5342120741.1589 3.9854.0150.03001038.93699458173.17863113.613935482.084156768.87595.18825.35610.16795814.5840378107.91275913.098646164.5163200485.52686.58946.94250.353112228.2884294055.69983486.446268004.3498245546.4958.743278.801410.058142013.45991114275.21596679.307293537.1813304492.203510.8736310.96480.091173157.32950137834.446109909.6084121312.9907369057.045113.0450713.4700.4249314715.8498………………………..……………...冗余力ΔX1、ΔX2計算表表13截面Δycosφ1/cosφΔy/cosφys-y1(ys-y1)Δy/cosφy1123456781201.00000104.43200110.0231170.998971.013170.0231414.35550.1007910.0765100.0978460.995811.004210.0982574.12450.405260.307590。042980.990381.009710.043397 3.7353 0.1621010.696780.048760.982431.017880.0496323.18090.157871.251170.07570.971601.029230.0779132.4520.1910431.9860.04380.957471.044400.0457461.53590.070262.896150.03000.939621.064260.0319280.4170.0133144.01540.16790.917521.089890.18299-0.9241-0.169105.356130.35310.89081.122570.39639-2.5105-0.9951376.942520.058140.859191.163890.067668-4.36941-0.295678.8014110091170.822621.216530.110829-6.5328-0.7240210.964800.424930.781331.279870.54385-9.038-4.9153213.47∑14.05561.65091-5.99627“壓力線”偏離拱軸線的附加內(nèi)力表14項(xiàng)目拱頂截面l/4截面拱腳截面cosφ10.957470.78133sinφ00.28853 0.62412 y=ys-y14.4321.5359-9.038ΔN=ΔX2cosφ547.3724524.0927427.6785ΔQ=ΔX2sinφ0157.3336341.6261Mp01516.848014715.8498ΔX1-400.9854-400.9854-400.9854ΔM=ΔX1-ΔX2y+Mp-2485.31382750162恒載內(nèi)力匯總表8恒載內(nèi)力匯總表項(xiàng)目截面拱腳L/4拱腳M（kNm）N(kN)M（kNm）N(kN)M（kNm）N(kN)無矩內(nèi)力032912.24028425.58026867.33彈性壓縮內(nèi)力-20119.2-2519.12-76.2063-3777.823271.751-2546.19壓力線偏離內(nèi)力19262.016-290.82275.15333-360.4-2485.313-375.91合計-857.2630102.3198.94724287.36786.43823945.23不計彈性壓縮的汽車-A級及人群荷載內(nèi)力見表17。計人彈性壓縮的汽車-A級及人群荷載內(nèi)力見表18。五、溫度變化、混凝土收縮徐變引起的內(nèi)力（一）溫度變化和混凝土收縮內(nèi)力1、月平均最高氣溫37℃；月平均最低氣溫3℃；拱圈合攏溫度15℃規(guī)范規(guī)定，考慮混凝土徐變影響，溫度變化內(nèi)力應(yīng)乘以折減系數(shù)0.7。溫度升高值=（37℃-15℃）0.7=15.4℃；溫降值=（3℃-15℃）0.7=-8.4℃主拱圈分5段預(yù)制，然后吊裝合攏成拱，因此混凝土收縮內(nèi)力按溫降8℃考慮。規(guī)范規(guī)定，考慮混凝土徐變影響，拱圈混凝土的收縮內(nèi)力應(yīng)乘以折減系數(shù)0.45.=-8℃0.45=-3.6℃內(nèi)力計算單位溫變引起彈性中心的贅余力拱圈采用30號混凝土，彈性模量查附表（Ⅲ）-5，……裝…訂……線……………...(2）內(nèi)力計算表溫度和混凝土收縮內(nèi)力表9項(xiàng)目拱腳L/4拱頂單位溫變（△t=1℃）0.781330.957471.000004.4321.5359-9.03825.32825.32825.328N（kN）19.79024.25125.328M(kN.m)87.70937.247-228.914溫升（△t1=15.4℃）N（kN）304.759373.462390.0512M(kN.m)1728.707599.080-3525.283溫降（△t2=-8.4℃）N（kN）-166.232-203.707-212.7552M(kN.m)-942.931-326.7711922.881混凝土收縮（△t3=-3.6℃）N（kN）-71.239-87.303-91.181M(kN.m)-404.113-140.045824.092（六）主拱結(jié)構(gòu)的強(qiáng)度和穩(wěn)定計算根據(jù)橋規(guī)(JTJ022-85)的規(guī)定，構(gòu)件按極限狀態(tài)設(shè)計的原則是：荷載效應(yīng)不利組合的設(shè)計值小于或等于結(jié)構(gòu)抗力效應(yīng)的設(shè)計值。即Sd(γs0ψΣγslQ)≤Rd(Rj/γm，αk)計入荷載安全系數(shù)的荷載組合表10荷載類型項(xiàng)目拱腳L/4拱頂M(kN.m)N(kN)M(kN.m)N(kN)M(kN.m)N(kN)永久荷載結(jié)構(gòu)自重基本效應(yīng)-857.2630102.3198.94724287.36786.43823945.23荷載安全系數(shù)1.2-1028.71236122.76238.73642914.032943.752628734.276荷載安全系數(shù)0.9-771.53427091.8179.052321858.624707.794221550.707混凝土收縮基本效應(yīng)-404.113-71.239-140.04-87.303824.092-91.181荷載安全系數(shù)1.4-565.7582-99.7346-196.056-122.22421153.7288-127.6534可變荷載汽車和人群Mmax時基本效應(yīng)4447.741059.632883.02439.8352006981.85荷載安全系數(shù)1.46226.8361483.4824036.228615.7692808.41374.59Mmin時基本效應(yīng)-3813.3398.593-2355.11091.97-1083.7890.46荷載安全系數(shù)1.4-5338.62558.0302-3297.141528.758-1517.181246.644其他可變荷載溫度變化溫升基本效應(yīng)1728.707304.759599.080373.462-3525.283390.0512荷載安全系數(shù)1.42420.1898426.6626838.712522.8048-4935.3962406.0717溫降基本系數(shù)-942.931-166.232-326.771-203.7071922.881-212.7552荷載安全系數(shù)1.4-1320.1034-232.7248-457.4794-285.18982692.0334-297.85728荷載組合計算表表11項(xiàng)目拱腳L/4拱頂M（kN.m）N(kN)M（kN.m）N(kN)M（kN.m）N(kN)荷載組合Ⅰ1Mmax時5014.009441789.844156.086232367.1224098.8230345.52Mmin時-8204.92138006.27-2838.1830901.359-244.0829457.95荷載組合Ⅱ1Mmax+溫升7826.96539883.463976.60230093.443198.3529174.742Mmax+溫降198.7383866.9174710.4329864.8055023.6928242.423Mmin+溫升-500.64632379.95-3671.46631203.172-1126.530024.284Mmin+溫降-9236.737223.47-2333.30832133.794600.33230261.27注：荷載安全系數(shù)的取值：結(jié)構(gòu)自重彎矩與汽車荷載彎矩同號時恒載系數(shù)取1.2，異號時取0.9，其余荷載系數(shù)取值見表中。(一)正截面受壓強(qiáng)度驗(yàn)算1.荷載組合根據(jù)橋規(guī)(JTJ021-89、JTJ022-85))的規(guī)定，本設(shè)計得如下兩種組合：SI=γs0ψΣγslS=1.03×1×[+1.4(+))SII=γs0ψΣγslS=1.03×0.8×[SI/1.03+1.4St]……裝…訂……線……………...每種荷載組合的設(shè)計值見表23。2.拱圈截面抗力主拱圈為30號鋼筋混凝土，抗壓極限強(qiáng)度Rja=21MPa，安全系數(shù)γm=1.54，根據(jù)橋規(guī)(用022-85)第3.0.2條規(guī)定，拱圈截面抗力效應(yīng)的設(shè)計值RN=ARja/γm=×6.318×21×103/1.54=84508.28kN具體數(shù)值計算見表12。拱圈抗力效應(yīng)設(shè)計值表12截面編號e0=Mj/Nja=[1-(e0/y)3]/[1+(e0/rw)2]RN=aARja/γm拱腳截面10.14738460.9388457879340.22-0.2375370.858547472554.430.1747340.884362074735.940.055326220.972464182142.15-0.01435760.995859484085.76-0.2446670.7884557566630.9L/4截面10.1166610.938764979333.42-0.0787230.974204582328.330.10690380.9548478980692.640.12306690.9046474776450.25-0.09382030.9388822793