2014 橋梁工程課程設計 .頁腳11級橋梁工程課程設計專業：交通工程專業：交通工程班級：交通學號：02姓名：指導教師：羅韌南京工業大學交通學院二0一四年六月目錄HYPERLINK1．課程設計任務書 3HYPERLINK1.1設計題目 3HYPERLINK1.2設計資料 3HYPERLINK1.2.1設計標準 3HYPERLINK1.2.2材料數據與結構布置要求 3HYPERLINK1.2.3設計計算依據 4HYPERLINK1.3設計內容 4HYPERLINK1.4設計成果 5HYPERLINK2．空腹式等截面懸鏈線箱形無鉸拱橋設計計算書 5HYPERLINK2.1主拱圈截面幾何要素的計算 5HYPERLINK2.1.1主拱圈橫截面設計 5HYPERLINK2.1.2箱形拱圈截面幾何性質 6HYPERLINK2.2確定拱軸系數 6HYPERLINK2.2.1上部結構構造布置 7HYPERLINK2.2.2主拱圈 7HYPERLINK2.2.3拱上腹孔布置 9HYPERLINK2.3結構恒載計算 9HYPERLINK2.3.1主拱圈 9HYPERLINK2.3.2橫隔板 10HYPERLINK2.3.3拱上空腹段恒載 12HYPERLINK2.3.4拱上實腹段 14HYPERLINK2.3.5腹拱推力 14HYPERLINK2.3.6驗算拱軸系數 15HYPERLINK2.3.7拱圈彈性中心及彈性壓縮系數 16HYPERLINK2.4主拱圈截面內力驗算 16HYPERLINK2.4.1結構自重內力計算 16HYPERLINK2.4.2活載內力計算 26HYPERLINK2.5溫度變化、混凝土收縮、徐變的內力計算 28HYPERLINK2.6主拱圈正截面強度驗算 29HYPERLINK2.7拱上結構強度與穩定性驗算 32HYPERLINK2.7.1立柱強度與穩定性驗算 32HYPERLINK2.7.2橫墻強度驗算 33HYPERLINK3.課程設計小結 33HYPERLINK參考文獻 331．課程設計任務書1.1設計題目空腹式等截面懸鏈線箱形無鉸拱橋設計1.2設計資料1.2.1設計標準設計荷載：公路—I級，人群荷載3.5kN/m2橋面凈空凈－8+2×(0.75m+0.25m)人行道+安全帶凈跨徑L0＝80m凈高f0＝16m凈跨比f0/L0＝1/51.2.2材料數據與結構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

主拱圈實腹段填料容重γ1＝22kN/m3人行道板及欄桿重52.0kN/m(雙側)；混凝土材料：強度等級為C30(C40)，主要強度指標為：強度標準值fck=20.1(26.8)MPa，ftk=2.01(2.65)MPa強度設計值fcd=13.8(18.4)MPa，ftd=1.39(1.65)MPa彈性模量Ec=3.0(3.25)×104MPa普通鋼筋1)縱向抗拉普通鋼筋采用HRB400鋼筋，其強度指標為抗拉強度標準值fsk=400MPa抗拉強度設計值fsd=330MPa彈性模量Es=2.0×l05MPa相對界限受壓區高度xb=0.53，xpu=0.19852)箍筋及構造鋼筋采用HRB335鋼筋，其強度指標為抗拉強度標準值fsk=335MPa抗拉強度設計值fsd=280MPa彈性模量Es=2.0×105MPa本橋采用支架現澆施工方法。主拱圈為單箱六室截面的鋼筋混凝土拱圈，由C30(C40)混凝土現場澆筑而成。拱上建筑可采用簡支板形式或圓弧拱形式，凈跨為5～7m左右，拱腳至拱頂布置4～6跨左右(主拱圈的具體幾何參照指導書實例修改自定)。1.2.3設計計算依據交通部部頒標準《公路橋涵設計通用規范》(JTGD60－2004)交通人民出版社交通部部頒標準《公路鋼筋混凝土及預應力混凝土橋涵設計規范》(JTGD62－2004)交通人民出版社交通部部頒標準《公路圬工橋涵設計規范》(JTGD61-2005)交通人民出版社《公路設計手冊-拱橋(上)》人民交通出版社，2000.71.3設計內容確定主拱圈截面構造尺寸，計算拱圈截面的幾何、物理力學特征值；確定主拱圈拱軸系數m及拱上建筑的構造布置和幾何構造尺寸；結構恒載計算；主拱結構內力計算(恒載、活載)；溫度變化、混凝土收縮徐變引起的內力；主拱結構的強度和穩定驗算；拱上立柱(墻)的內力、強度及穩定性驗算；手工繪制2張相關施工圖。1.4設計成果空腹式等截面懸鏈線無鉸拱設計計算書空腹式等截面懸鏈線無鉸拱設計縱斷面施工圖空腹式等截面懸鏈線無鉸拱設計橫斷面施工圖懸鏈線箱形無鉸拱橋縱斷面參考圖1-4-1懸鏈線箱形無鉸拱橋橫斷面參考圖1-4-22．空腹式等截面懸鏈線箱形無鉸拱橋設計計算書2.1主拱圈截面幾何要素的計算2.1.1主拱圈橫截面設計拱圈截面高度按經驗公式估算D=l0/100+Δ=80/100+0.6=1.4m拱圈由六個各為1.5m寬的拱箱組成，全寬B0=9.0m構造圖如圖2-1-1所示：圖2-1-1拱圈橫斷面構造圖2.1.2箱形拱圈截面幾何性質截面積：繞箱底邊緣的靜面矩：主拱圈截面重心軸：主拱圈截面繞重心軸的慣性矩：拱圈截面繞重心軸的回轉半徑：2.2確定拱軸系數2.2.1上部結構構造布置上部結構構造布置如圖2-2-1所示：圖2-2-1上部結構構造布置（尺寸單位：mm）2.2.2主拱圈假定m=2.514，相應的，，查《拱橋》(上冊)表(III)-20(7)得：sinφj=0.69198，cosφj=0.72191，φj=43.7876?主拱圈的計算跨徑和計算矢高：腳拱截面水平投影腳拱截面豎向投影計算跨徑半跨徑計算矢高將拱軸沿跨徑24等分，每等分長Δl=，每等分點拱軸線的縱坐標y1=[表(III)-1值]×f，相應的拱背曲面坐標:，拱腹曲面坐標:。具體位置見圖2-3-1圖2-3-1拱軸坐標具體位置表2-2-1主拱圈截面坐標表截面號xy1/fy1cosφy上/cosφy下/cosφy1-y上/cosφy1+y下/cosφ040.485116.1930.721910.9793464560.95995345715.21365354177981250.90364914.632788260.746230.9474290770.92866810513.6853591815.56145636237.111250.81401813.181393470.769690.9185516250.90036248412.2628418514.08175596335.4243750.73072411.832613730.792180.8924739330.87480118210.940139812.70741491433.73750.65340810.580635740.81360.8689773840.8517699129.7116583611.43240566532.0506250.5817389.4200834340.833870.8478539820.8310647948.57222945210.25114823630.363750.5154058.3459531650.852910.828926850.8125124577.5170263159.158465622728.6768750.4541257.3536461250.870680.8120090040.7959296186.5416371218.149575743826.990.3976356.4389035550.887180.7969070540.7811267165.6419965017.220030271925.3031250.3456915.5977743630.902380.7834836760.7679691484.8142906876.3657435111023.616250.2980714.8266637030.91630.771581360.7563025214.0550823435.5829662241121.9293750.254574.122252010.928970.7610579460.7459874923.3611940644.8682395021220.24250.2153.4814950.940420.7517917530.7369047872.7297032474.2183997871318.5556250.1791922.9016560560.95070.7436625640.7289365732.1579934923.6305926291416.868750.1469922.3802414560.959850.7365734230.7219878111.6436680333.1022292671515.1818750.1182621.9150165660.967920.7304322670.7159682621.1845842992.6309848281613.4950.0928771.5039572610.974980.725143080.7107838110.7788141812.2147410721711.8081250.070731.145330890.981070.7206417480.7063716150.4246891421.8517025051810.121250.0517240.8375667320.986240.7168640490.7026687220.1207026831.540235454198.4343750.0357790.5793693470.990530.7137593010.699625453-0.134389951.2789948206.74750.0228250.3696052250.993680.7114966590.697407616-0.341891431.067012841215.0606250.0128070.2073837510.996640.7093835290.69533633-0.501999780.902720081223.373750.0056820.0920086260.998510.7080550020.694034111-0.616046380.786042737231.6868750.0014190.0229778670.999630.7072616870.693256505-0.684283820.7162343722400010.7070.693-0.7070.6932.2.3拱上腹孔布置由，查《拱橋》(上冊)表3-2，得sinφ0=0.43219，cosφ0=0.90178，腹拱拱腳的水平投影和豎向投影x'=d'×sinφ0=0.5×0.43219=0.216095m；y'=d'×cosφ0=0.5×0.90178=0.45089m從主拱兩端起拱線起向外延伸后向跨中對稱布置3對圓弧小拱，腹拱圈厚d'=0.5m，凈跨徑l'0=8m，凈矢高f'0=0.8m。腹拱拱頂的拱背和主拱拱頂的拱背在同一標高。腹拱墩墩中線的橫坐標lx，以及各墩中線自主拱拱背到腹拱起拱線的高度，分別計算如表2-2-2：表2-2-2腹拱墩高計算表項目lxξkξy1tanφcosφh1號立墻31.1160.7691.2098.8160.6341.1847.3862號立墻22.6160.5590.8794.4020.4141.0823.0443號腹拱座14.1160.3490.5481.6490.241.0280.329空、實腹段分界線13.6660.3380.5311.5440.2311.0260.225注:,,,,2.3結構恒載計算恒載計算，按主拱圈、橫隔板、拱上空腹段、拱上實腹段以及腹拱推力共五個部分進行。2.3.1主拱圈P0~12=[表（Ⅲ）—19（7）值]Ar2l=0.51408×6.12×25×80.97=6368.6338kN·mM1/4=[表（Ⅲ）—19（7）值]Ar22/4=0.12530×6.12×25×80.972/4=31421.7804kN·mMj=[表（Ⅲ）—19（7）值]Ar2l2/4=0.50610×6.12×25×80.972/4=126915.9063kN·m2.3.2橫隔板橫隔板的設置受箱肋接頭位置的控制，必須先確定接頭位置后再按箱肋軸線等弧長布置橫隔板。①箱肋有關幾何要素a.箱肋截面積A'=2×0.2×1.4+1.1×0.1+2×0.1×0.1/2=0.79m2b.箱肋截面靜矩J'=2×0.2×1.4×1.4/2+1.1×0.2×0.2/2+2×0.1×0.1×(0.1/3+0.2)/2=0.4163m3c.截面重心距箱底的距離y'下=J'/A'=0.527md.箱肋計算跨徑l'=l0+2y'下sinφj=80+2×0.527×0.69198=80.7293me.箱肋軸線弧長S'=2×0.52764l'=85.1920m②確定箱肋接頭、設置橫隔板確定接頭位置箱肋分三段吊裝合攏，接頭宜選在箱肋自重作用下彎矩值最小的反彎點附近，即ξ=0.35~0.37之間，此處相應的弧長為圖：圖2-3-2箱肋分段計算示圖式中值，根據ξ值從《拱橋(例集)》的附表1-1內插算得。b.布置橫隔板橫隔板沿箱肋中軸線均勻設置，取板間間距Δl'=2.56m，中段箱肋設11道橫隔板，端橫隔板到接頭中線的距離為0.3m，座落在寬為0.6m的鋼筋混凝土排架式腹拱墩支承的寬為0.7m的鋼筋混凝土蓋梁上。則中段箱肋弧長之半為：SII/2=(2.56×10+2×0.3)/2=13.1m，則接頭位置剛好在ξ=0.37處。端段箱肋弧長SI=(S'-SII)/2=(85.1920-26.2)/2=29.496m端段箱肋設12道橫隔板，則端橫隔板距起拱面的長度為：ΔS=SI-2.56×11-0.3=1.036m③橫隔板與接頭加強部分的重力橫隔板厚均為0.06m。靠拱腳的一塊為實心板，其余均為空心板。接頭處兩相鄰橫隔板之間以及拱腳截面至第一塊橫隔板之間的箱底板和兩側板均加厚0.10m。加強后的斷面尺寸圖2-3-3圖2-3-3橫隔板a.橫隔板重力空心板P=[(1.1×1.02-0.68×0.62+4×0.12/2)×0.06+4×0.12×1.02/2]×25×7=11.1342kN實心板P=(1.1×1.02×0.06+4×0.12×1.02/2)×7×25=15.351kNb.中接頭加強部分P=[2×0.1×0.54×1.02+0.1×0.54×(1.1-2×0.1)-4×0.12×1.02/2]×7×25=24.213kNc.拱腳加強段P=[0.1×2×1.02×0.6775+0.1×0.6775×(1.1-2×0.1)-2×0.12×1.1/2]×7×25=32.9324kNd.各集中力作用線的橫坐標各集中力作用線的橫坐標lx，可以根據值從《拱橋(例集)》書后附表1查得ξ值，再由l=l'×ξ/2求得。lx的值和各集中力分別對l/4和拱腳截面的力臂見表2-3-1.表2-3-SEQ表\*ARABIC1橫隔板的橫坐標與力臂計算表集中力編號Sx2Sx/l肋ξlx=l肋ξ/2力臂l/4-lxl/2-lx1號2.560.06340.07272.934817.247637.42992號5.120.12680.14535.86614.316334.49863號7.680.19030.21788.789611.392731.5754號10.240.25370.289911.70278.479628.66195號12.80.31710.361714.59915.583225.76566號15.360.38050.378415.27594.906425.08887號17.920.4440.449618.14712.035322.217663.96118號20.480.50740.520120.99219.37269號23.040.57080.589823.806216.558410號25.60.63420.658626.582413.782211號28.160.69760.726229.313811.050912號30.720.76110.792731.99898.365813號33.280.82450.857734.62255.742214號35.840.88790.921337.18883.1759283.285415號38.40.95130.983139.68310.68160號000020.182340.3647中接頭14.080.34880.370114.93785.244525.4269拱腳加強段41.7024791.03310.991640.02390.34082.3.3拱上空腹段恒載①腹孔上部(見圖2-3-4)腹拱圈外弧跨徑l外=l'+2d'sinφ0=8+2×0.5×0.43219=8.43219m腹拱圈內弧半徑R0=l'/(2sinφ0)=8/(2×0.43219)=9.2552m腹拱圈重力Pa=2φ0Rd'γ3B0=2×25?36'24"×π/180×(9.2552+0.5/2)×0.5×23×9=879.3505kN腹拱上面的護拱重Pb=(2sinφ0-sinφ0cosφ0-φ0)R2γ2B0=(2×0.43219-0.43219×0.90178-25?36'24"×π/180?)×(9.2552+0.5/2)2×22×9=495.8681kN填料及橋面系重力Pc=l外hdγ1B0=8.43219×0.5×22×9=834.7868kN圖2-3-4腹孔上部構造Pd={(0.6-x')y'γ4+[(f'0+d'-y')γ2+hdγ1](0.6-2x')}B0={(0.6-0.216095)×0.45089×23+[(0.8+0.5-0.45089)×22+0.5×22]×(0.6-2×0.216095)}×9=80.6576kN一個腹拱總重力：P=ΣPi=879.3505+495.8681+834.7868+80.6576=2290.663kN②腹孔下部1號腹拱墩:P=[7.3861-(0.5×1+3.14×0.52/2）/9]×0.6×25=109.304kN2號腹拱墩:P=[3.0438-(0.5×1+3.14×0.52/2）/9]×0.6×25=44.1695kN3號腹拱墩:P=(0.3294+0.45089/2)×(14.1162-13.6662)×2×25=12.4840125kN圖2-3-5腹孔墩以上部分③腹孔集中力P13=2290.663+109.304=2399.967kNP14=2290.663+44.1695=2334.8325kNP15=（2290.663-80.6576）/2+12.4840125=1117.4867kN2.3.4拱上實腹段圖2-3-6曲邊三角形塊拱頂填料及橋面系重P16=l×hdγ1B0=13.6662×0.5×22×9=1352.9538kN懸鏈線曲邊三角形，見圖2-3-6P17=lf1(shkξ-kξ)γ2B0/[2(m-1)k]=80.97×15.92065/[2×(2.514-1)×1.572999]×(sh0.53098512-0.53098512)×22×9=1356.0686kN式中f1=f+y上(1-1/cosφj)=16.193+0.707×(1-1/0.72191)=15.92065m其重心距原點(拱頂)的水平距離ηlx=[(shkξ-kξ/2)-(chkξ-1)/kξ]lx/(shkξ-kξ)=0.7509lx=10.2625m2.3.5腹拱推力圖2-3-7腹拱拱腳受力圖靠近主拱拱頂一側的腹拱，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g1=γ1hd=22×0.5=11kN/m2g2=γ2{(R+d'/2)-[(R+d'/2)2-l2/4]?}=22×{(9.2552+0.5/2)-[(9.25525+0.5/2)2-8.5972/4]?}=22.6046kN/m2g3=γ3d'=23×0.5=11.5kN/m2由f0/l'0=1/10和b=I/AR2=0.0003查《拱橋》(上冊)表(I)-4得C1=0.6103，C2=0.08473，C3=0.6170F=(0.6103×11+0.08473×22.6046+0.6170×11.5)×9.2552×9=1309.7662kN腹拱拱腳推力作用線的縱坐標見圖2-3-8所示，其距x軸的偏心距為：e=d'+f0-y'/2-y上=0.895345m腹拱推力對各截面重心產生的力矩Mi=Fx(yi-e)2.3.6驗算拱軸系數恒載對l/4截面和拱腳截面的力矩見表2-3-2表2-3-2半拱恒載對拱腳和1/4截面產生的彎矩表集中力編號恒重l/4拱腳截面力臂力矩kN·m力臂力矩kN·mp1195.410118.37253590.172062p2171.443124.68254231.644316p3200.82688.47961702.93093328.66255756.198155p0-126368.63389976.186331745.53761p132399.96718.372544093.39371p142334.832524.682557629.50318p151117.48678.47969475.84022128.662532029.96254p161352.953813.792618660.7505833.876445833.20411p171356.068611.1340215098.4949131.7054642994.77875F1309.76627.637610003.4703324.882732590.51942合計16807.388664917.67328300494.9139假定的拱軸系數m=2.514，y1/4/f=0.215由表2-3-2可知：，小于半級。因此,可選定m=2.514為設計的拱軸系數。2.3.7拱圈彈性中心及彈性壓縮系數彈性中心ys=[表(III)-3值]×f=0.316474×16.193=5.12466m2彈性壓縮系數γ2w=I/A=1.551/6.12=0.25343γ2w/f2==0.25343/16.1932=0.000966511=[表(III)-9值]×γ2w/f2=11.6060×0.00096651=0.0112173=[表(III)-11值]×γ2w/f2=10.9881×0.00096651=0.01062011/(1+)=0.0110992.4主拱圈截面內力驗算2.4.1結構自重內力計算在確定m系數時，其實計算值很難與選定的拱軸系數在“五點”重合，對于大跨徑拱橋必須用“假載法”計入“五點”存在的偏離的影響。當用“假載法”計入“五點的偏離之后，相應三鉸拱的恒載壓力線在“五點”以外與選定的拱軸線有偏離。對于大跨徑無鉸拱橋，這種偏離的影響很大，不可忽視。下面分別計算這兩種偏離的影響:1.用假載法計算確定m系數時在“五點”存在的偏差確定拱軸系數時，恒載壓力線在l/4截面與拱腳截面的縱坐標之比值是0.21603，并不等于為使用手冊數表進行計算所選用的m'=2.514的拱軸線上相應兩點的比值0.215，兩者之間相差0.00103。這個偏差的影響可比擬為虛設的均布荷載作用在選定的拱軸線上，先單獨求出，然后算出所選定的“拱軸線”恒載產生的內力，將兩者相加后為“五點”的恒載壓力線內力。(1)假載內力a.求假載由式得：b.假載內力假載qx產生的內力可以將其直接布置在內力影響線上求得。不考慮彈性壓縮的假載內力見表2-4-1表2-4-1不考慮彈性壓縮的假載內力表項目影響線面積ω乘數ω力或力矩(qxω)[表(III)-14(51)值]拱頂截面M10.00675-0.004540.00221l26556.140914.48907139157.2339538H10.067770.060390.12816l2/f404.87551.88878563.0918517l/4截面M10.00858-0.01006-0.00148l26556.1409-9.703088532-105.2969464H10.039490.088660.12815l2/f404.87551.88473125563.0479151拱腳截面M10.02046-0.015090.00537l26556.140935.20647663382.0571638H10.091910.036240.12815l2/f404.87551.88473125563.0479151V10.166670.333380.50005l80.9740.4890485439.3831054c.計入彈性壓縮的假載內力計入彈性壓縮的假載內力計算見表2-4-2表2-4-2項目拱頂截面l/4截面拱腳截面cosφ10.940420.72191sinφ00.340010.69198H1563.0918517563.0479151563.0479151V100439.3831054m1H1/(1+m)6.2497564626.249268816.24926881N=[1-m1/(1+m)]×H1cosφ+V1sinφ556.841857523.624359706.0026601M1157.2339538-105.2969464382.0571638y=ys-y15.124661.07641-11.06834M=M1+m1H1y/(1+m)189.2630514-98.56991458312.8854956(2)“拱軸線恒載”內力a.推力Hg=(ΣMj+qxl2/8)/f=(300494.9139+10.8519×80.972/8)/16.193=19106.29513kNb.考慮彈性壓縮的內力表2-4-2考慮彈性壓縮的內力表項目拱頂截面l/4截面拱腳截面cosφ10.940420.72191H'g=Hg-F19106.2951317796.5289317796.52893[1-μ1/(1+μ)]H'g18693.447817411.9829317411.98293N'=H'g/cosφ18693.447818515.1133824119.32641ΔN=μ1H'gcosφ/(1+μ)207.4864848205.5070756267.7106067N=N'-ΔN18485.9613218309.6063123851.6158y=ys-y15.124661.07641-11.06834ΔV=μ1H'gy/(1+μ)1086.780763212.624562-2186.342514(3)考慮確定m系數偏差影響的恒載內力考慮m系數偏差影響的恒載內力等于“拱軸線m的恒載”內力減去“假載”的內力，計算結果見表2-4-3表SEQ表格\*ARABIC1-4-3空腹無鉸拱的實際恒載內力計算表截面拱頂截面l/4截面拱腳截面項目恒載內力附加內力合計恒載內力附加內力合計恒載內力附加內力合計水平力Hg18549.45-228.0318321.4217239.69-228.0317011.6517241.27-228.0317013.24軸力Ng17929.12-228.0317701.0917785.98-214.4517571.5323145.61-164.6222980.99彎矩Mg897.52-931.3-33.78311.195551.995863.19-2499.23-10838.54-13337.772.“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”以外的偏離影響可以用一般力學原理進行計算，參見圖13。圖2-4-1拱軸壓力線示意圖(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構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，然后才能求得Mp。下面按主拱圈、拱上實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生的力矩Ml(圖2-4-1)圖2-4-2主拱圈自重計算圖在這里，對于所要求的每一等分點而言，積分上限ξ為常數，并不計等式前面的負號，則上式為：式中：可根據ξ值從《拱橋(例集)》附表1-1查得；可根據ξ值從《拱橋(例集)》附表1-2查得=0.759953k=1.573主拱圈對各截面的力矩M1的值見表2-4-4。表SEQ表\*ARABIC2-4-4主拱圈自重對各截面產生的彎矩值表截面號ξS1S2ξ×S1-S2M1(kN?m)0123452400000230.04170.04170.001700220.08330.08360.00520.0018442.3324210.1250.12570.01050.00521307.1511200.16670.16820.01760.01042617.7979190.20830.21120.02650.01754386.7514180.250.25480.03740.02636595.3138170.29170.29910.05030.03699265.4053160.33330.34420.06540.049312368.5607150.3750.39040.08270.063715974.2012140.41670.43760.10240.079920048.7309130.45830.48610.12460.098224620.7404120.50.53610.14960.118529703.9895110.54170.58760.17750.140835309.4847100.58330.6410.20860.165341451.497390.6250.69630.24320.19248145.164180.66670.75380.28160.22155410.28170.70830.81370.3240.252363280.835160.750.87630.37090.286371802.404450.79170.94170.42270.322880960.333740.83331.01030.47980.362190800.416630.8751.08230.54280.4042101365.334520.91671.1580.61220.4493112681.714410.95831.23770.68860.4975124756.2319011.32180.77270.5491137699.119b.拱上實腹段恒載對各截面產生的彎矩M2計算拱上實腹段的恒載時，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確計算，否則只能是近似的。(a)矩形板塊從拱頂到每個截面的矩形板塊的重力：P1=γ1B0h’dl·ξ1/2對實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、實腹段的分界點，取為：γ1l2B0h’d/4=80.972×9×0.5/4=7376.6585kN·m(b)懸鏈線曲邊三角形塊從拱頂到任意截面的重力Pi=l·f1γ2B0(shkξi-kξi)/[2(m-1)k]=5087.1402×(shkξi-kξi)每一塊Pi的重心的橫坐標：ηi=[(shkξi-kξi/2)-(chkξi-1)/kξi]/(shkξi-kξi)在實腹段里，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2-4-5。表2-4-5拱上實腹段恒載對各截面產生的力矩計算表區間截面號ξ懸鏈線曲邊三角形矩形塊M2=MΔ+M恒kξpηlξ(1-η)/2MΔξ2/2M恒012345678910實腹段24000000000230.04170.06560.23930.750.4220.1010.0009141.08141.1811220.08330.1311.9090.75010.84291.60910.0035562.9677564.5768210.1250.19666.45770.75021.26438.16470.00781267.69131275.8561200.16670.262215.33940.75031.685325.85120.01392254.5752280.4262190.20830.327729.98520.75042.104563.10360.02173520.2383583.3416180.250.393351.9620.75062.5238131.1420.03135070.76525201.9073170.29170.458882.7730.75092.942243.52140.04256903.45267146.9739分界點0.2910.457782.17440.7509l(ξ-0.2536)/2(ξ1-0.1455)×0.1455空腹段160.333382.17440.75093.3617276.24290.05554579.78174856.0245150.37582.17440.75093.7823310.80430.07035152.76965463.5739140.416782.17440.75094.2028345.36570.08685725.75766071.1234130.458382.17440.75094.6224379.84430.1056297.37156677.2158120.582.17440.75095.043414.40570.1256870.35957284.7652110.541782.17440.75095.4636448.96720.14677443.34757892.3147100.583382.17440.75095.8832483.44570.17018014.96148498.407190.62582.17440.75096.3038518.00710.19538587.94949105.956680.666782.17440.75096.7243552.56860.22229160.93749713.50670.708382.17440.75097.1439587.04710.25089732.551310319.59860.7582.17440.75097.5645621.60860.281310305.53910927.14850.791782.17440.75097.9851656.170.313410878.52711534.69740.833382.17440.75098.4047690.64860.347211450.14112140.7930.87582.17440.75098.8253725.210.382812023.12912748.33920.916782.17440.75099.2458759.77140.420212596.11713355.88910.958382.17440.75099.6654794.250.459213167.73113961.9810182.17440.750910.086828.81140.513740.71914569.531(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的橫坐標lx。在前面已經求出，各豎向集中力到截面的力臂a=l·ξi/2-lx(取a>0)，產生的力矩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截面產生的力矩M"3=H'g(y1-e)。具體計算見下表。表2-4-6各集中力對各截面的力矩計算表截面豎向力p1p2p3腹拱水平力合計M3P=11.134211.134211.13421309.7662lx=10.215.821.40.2483ξMMM240.04170230.08330220.1250210.16670200.20830190.250180.2917128.7244128.7244170.291128.4089128.4089160.3333147.4764147.4764150.375166.2734166.273140.416774.2662185.0704259.3367130.458393.0182203.8224296.8406120.5111.8152222.6194334.4346110.5417130.6122241.4165372.0287100.5833149.3642260.1684409.532690.625168.1612278.9654447.126680.6667186.9582124.6067297.7625609.327470.7083205.7102143.3587316.5144665.583360.75224.5072162.1557335.3114721.974450.7917243.3043180.9527354.1085778.365540.8333262.0562199.7047372.8604834.621330.875280.8532218.5017391.6575891.012420.9167299.6503237.2987174.9472410.45451122.350710.9583318.4022256.0507193.6992429.20641197.358501337.1992274.8477212.4962448.00351272.5466(d.)計算偏離彎矩Mp上部結構恒載對拱圈各截面重心的彎矩：Mi=M1+M2+M3壓力線的縱坐標：yi=Mi/Hg式中，Hg為不計彈性壓縮的恒載水平推力：Hg=∑Mj/f=300494.9139/16.193=18557.0876kN各截面上“恒載壓力線”偏離拱軸線的值：Δy=y1-yi偏離彎矩具體數值見表2-4-7。表2-4-7偏離彎矩計算表截面號主拱圈拱上實腹段集中力合計“恒載壓力線”拱軸線偏心偏離彎矩M1M2M3Mi=M1+M2+M3y2=M2/Hgy1Δy=yl-y2Mp=HgΔy1234567892400000000230141.18110141.18110.00540.0230.0176327.043622442.3324564.576801006.90920.07270.0920.0193358.251211307.15111275.856102583.00720.15740.20740.05927.8566202617.79792280.426204898.22410.35950.36960.0101187.6686194386.75143583.341607970.0930.49530.57940.0841559.6035186595.31385201.9073128.724411925.94560.72620.83760.11142066.3641179265.40537146.9739128.408916540.78810.91971.14530.22564186.25171612368.56074856.0245147.476417372.06161.39151.5040.11252087.51971515974.20125463.5739166.273421604.04851.79211.9150.12292280.09331420048.73096071.1234259.336726379.1912.16932.38020.21093913.98051324620.74046677.2158296.840631594.79682.57242.90170.32926109.34941229703.98957284.7652334.434637323.18933.15923.48150.32235980.58871135309.48477892.3147372.028743573.82813.72314.12230.39917406.43341041451.49738498.4071409.532650359.4374.39924.82670.42747931.6137948145.16419105.9566447.126657698.24745.26475.59780.33316181.0838855410.2819713.506609.327465733.11446.10566.43890.33336184.5414763280.835110319.5984665.583374266.01687.03537.35360.31845908.278671802.404410927.1479721.974483451.52678.09858.3460.24744591.3254580960.333711534.6973778.365593273.39659.29579.42010.12432307.5732490800.416612140.7898834.6213103775.827710.513410.58060.06731248.29543101365.334512748.3392891.0124115004.686111.917411.8326-0.0848-1573.19182112681.714413355.88861122.3507127159.953713.326513.1814-0.1452-2693.64331124756.231913961.98111197.3585139915.571514.863614.6328-0.2308-4282.81920137699.11914569.53051272.5466153541.196116.527916.193-0.3349-6214.6835(2)偏離彎矩Mp在彈性中心產生的贅余力贅余力各項的計算見表2-4-8。表2-4-8偏離彎矩Mp在彈性中心產生的贅余力計算表截面Δycosφ1/cosφΔy/cosφys-y1(ys-y1)Δy/cosφ12345672401105.12470230.01760.99961.00040.01765.10170.0898220.01930.99851.00150.01935.03270.0973210.050.99661.00340.05024.91730.2467200.01010.9941.00610.01024.75510.0483190.0840.99051.00960.08484.54530.3855180.11140.98621.0140.1134.28710.4842170.22560.98111.01930.233.97940.9151160.11250.9751.02560.11543.62070.4178150.12290.96791.03310.1273.20970.4075140.21090.95991.04180.21972.74450.603130.32920.95071.05190.34632.2230.7697120.32230.94041.06340.34271.64320.5631110.39910.9291.07650.42961.00240.4306100.42740.91631.09130.46640.2980.13990.33310.90241.10820.3691-0.4731-0.174780.33330.88721.12720.3757-1.3142-0.493770.31840.87071.14850.3657-2.2289-0.815160.24740.85291.17250.2901-3.2213-0.934450.12430.83391.19920.1491-4.2954-0.640340.06730.81361.22910.0827-5.4559-0.45133-0.08480.79221.2623-0.107-6.70790.71812-0.14520.76971.2992-0.1886-8.05671.51991-0.23080.74621.3401-0.3093-9.50812.94090-0.33490.72191.3852-0.4639-11.06835.1347Σ27.70933.135612.4017由以上數據可得ΔX1=-(3.135553602×18557.0876)/27.7093=-2099.898682kN·mΔX2=-（2×12.4017×1.059×18557.0876）/((0.0106201+1)×16.1932×80.97×0.099621)=-228.0338898kN(3)“恒載壓力線”偏離拱軸線的附加內力“恒載壓力線”偏離拱軸線在拱圈任意截面中產生的附加內力為:ΔM=ΔX1-ΔX2(ys-y1)+Mp；ΔN=ΔX2cosφ；ΔQ=ΔX2sinφ拱頂、l/4截面、拱腳三個截面的附加內力見下表:表2-4-9壓力線”偏離拱軸線的附加內力計算表項目拱頂截面l/4截面拱腳截面cosφ10.940420.72191sinφ00.340010.69198y=ys-y15.124661.07641-11.06834ΔN=ΔX2cosφ-228.03389-214.447631-164.619945ΔQ=ΔX2sinφ0-77.5338029-157.794891Mp07406.4334-6214.6835ΔX1-2099.89868-2099.89868-2099.89868ΔM=ΔX1-ΔX2y+Mp-931.3025285551.992677-10838.5388(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力這三個力的合力作用點的偏心距為ei=Mg/Ng，則空腹式無鉸拱橋恒載壓力線的縱坐標y=y1-ei/cosφ空腹式無鉸拱恒載壓力線的縱坐標值見表2-4-10。表2-4-10空腹式無鉸拱的恒載壓力線計算表截面y1ys-yΔyMg/HgcosφNg/Hge1=Mg/Ngy=y1-e1/cosφ0123456782405.124700.006710.97660.0069-0.0069230.0235.10170.01760.00620.99960.9770.00630.0167220.0925.03270.01930.00450.99850.97810.00460.0873210.20744.91730.050.00180.99660.98010.00190.2055200.36964.75510.0101-0.00190.9940.9828-0.0020.3716190.57944.54530.084-0.00690.99050.9864-0.0070.5864180.83764.28710.1114-0.01290.98620.9909-0.0130.8508171.14533.97940.2256-0.02010.98110.9964-0.02021.1659161.5043.62070.11250.37060.9751.00280.36961.1249151.9153.20970.1229-0.03810.96791.0105-0.03771.9539142.38022.74450.2109-0.0490.95991.0194-0.0482.4303132.90172.2230.3292-0.06120.95071.0296-0.05942.9642123.48151.64320.3223-0.07470.94041.0414-0.07183.5578114.12231.00240.3991-0.08970.9291.0547-0.08514.2139104.82670.2980.4274-0.10620.91631.0699-0.09934.93595.5978-0.47310.3331-0.12420.90241.0871-0.11435.724486.4389-1.31420.3333-0.14390.88721.1064-0.13016.585577.3536-2.22890.3184-0.16530.87071.1281-0.14657.521968.346-3.22130.2474-0.18850.85291.1525-0.16368.537859.4201-4.29540.1243-0.21360.83391.1797-0.18119.6373410.5806-5.45590.0673-0.24080.81361.2101-0.19910.8251311.8326-6.7079-0.0848-0.270.79221.2438-0.217112.1067213.1814-8.0567-0.1452-0.30160.76971.2812-0.235413.4872114.6328-9.5081-0.2308-0.33550.74621.3227-0.253714.9728016.193-11.0683-0.3349-0.3720.72191.3683-0.271916.56963.空腹無鉸拱的實際恒載內力空腹式無鉸拱的實際恒載內力等于計人拱軸系數m的偏差影響的內力與“壓力線”及拱軸線偏離的附加內力之和，其結果見表2-4-11。表格SEQ表格\*ARABIC2-4-11空腹無鉸拱的實際恒載內力計算表截面拱頂截面l/4截面拱腳截面項目恒載內力附加內力合計恒載內力附加內力合計恒載內力附加內力合計水平力Hg18549-2281832117240-2281701217241-22817013軸力Ng17929-2281770117786-2141757223146-16522981彎矩Mg898-931-3431155525863-2499-10839-133382.4.2活載內力計算1.公路-I級和人群荷載內力車道荷載的均布荷載標準值采用10.5KN/m，計算剪力時，所加集中力荷載P采用360KN人群荷載K2=2·b·g人=2×0.75×3.5=5.25kN不計彈性壓縮的公路-I級及人群荷載內力見表2-4-11。表2-4-12不計彈性壓縮的公路-I級及人群荷載內力計算表截面項目公路-I級人群荷載合計影響線面積力或力矩車道荷載集中荷載（Ⅲ）-14（51）值乘數面積拱頂截面Mmax36.753605.254020.0069l26556.140945.368518238.135相應H136.753605.254020.0678l2/f404.87527.466711041.622Mmin36.753605.25402-0.0046l26556.1409-30.4205-12229.04相應H136.753605.254020.0601l2/f404.87524.32499778.6058l/4截面Mmax36.753605.254020.0088l26556.140957.497423113.937相應H136.753605.254020.0401l2/f404.87516.22336521.7832Mmin36.753605.25402-0.0102l26556.1409-67.0693-26961.87相應H136.753605.254020.0879l2/f404.87535.572314300.072拱腳截面Mmax36.753605.254020.0198l26556.1409130.008352263.326相應H136.753605.254020.0917l2/f404.87537.114914920.186相應V汽車36.75360396.750.5l80.9740.48516062.424人群3605.25365.250.331616.1935.36961961.246Mmin36.753605.25402-0.0146l26556.1409-95.8508-38532.01相應H136.753605.254020.0363l2/f404.87514.67675900.041相應V汽車36.75360396.750.5l80.9740.48516062.424人群5.255.250.331616.1935.369628.1904計彈性壓縮的公路-I級及人群荷載內力見表2-4-13:。表2-4-13考慮彈性壓縮的汽車和人群荷載內力計算表項目拱頂截面l/4截面拱腳截面MmaxMminMmaxMminMmaxMmincosφ10.94040.7219sinφ00.340.692與M相應的H111041.62159778.60586521.783214300.071714920.18635900.041與M相應的V18023.669816090.6142N=H1cosφ+Vsinφ11041.62159778.605868.7981150.851112592.840911182.161ΔH=μ1H1/(1+μ)122.5556108.536972.388158.7225165.605565.4871ΔN=ΔHcosφ122.5556108.536968.0752149.2659119.552247.2758Np=N-ΔN10919.06599670.06890.7231.585212473.288711134.8853M18238.135-12229.038523113.937-26961.867252263.3262-38532.0135y=ys-y15.12471.0764-11.0683ΔM=ΔHy628.0559556.214677.9192170.8505-1832.9775-724.8329Mp=M+ΔM18866.1909-11672.823923191.8562-26791.016750430.3487-39256.84642.5溫度變化、混凝土收縮、徐變的內力計算溫度變化為其它可變荷載，混凝土收縮、徐變為永久荷載，似乎要分項計算，但考慮到習慣和可能，還是將三者一起計算。拱圈合攏溫度7℃月平均最低氣溫2℃月平均最高氣溫30℃拱圈材料彈性模量E=3.25×104MPa拱圈材料線脹縮系數a=0.000010=1×10-5混凝土收縮作用按下降10℃溫度的影響計入。混凝土徐變作用的影響：當計算溫度內力時以β=0.7；當計算混凝土收縮內力時以β=0.45的系數計入。因此，計算降低溫度時Δt=0.7×(2-7)+0.45×(-10)=-8℃計算升高溫度時Δt=0.7×(30-7)+0.45×(-10)=11.6℃溫度變化、混凝土徐變和收縮在彈性中心產生的水平力Ht=α·EI·Δt/{[(表(III)-5值]×(1+μ)f2}=1×10-5×3×107×1.551Δt/(0.088588×1.0106201×16.1932)=19.8205Δt溫度變化、混凝土徐變和收縮的內力見表2-5-1。表2-5-1溫度變化、混凝土收縮、徐變內力計算表項目溫度上升溫度下降拱頂截面l/4截面拱腳截面拱頂截面l/4截面拱腳截面Δt11.6-8Ht229.9178-158.564cosφ10.94040.721910.94040.7219y=ys-y15.12471.0764-11.06835.12471.0764-11.0683Nt=Htcosφ229.9178216.2147165.9777-158.564-149.1136-114.4674M=-Hty-1178.2597-247.48352544.7992812.5929170.6783-1755.03392.6主拱圈正截面強度驗算根據橋規(JTJD60-2004)的規定，構件按極限狀態設計的原則是：荷載效應不利組合的設計值小于或等于結構抗力效應的設計值。即或式中：承載能力極限狀態下作用幾本基本組合的效應組合設計值；結構重要性系數，對于公路-Ⅰ級標準采用1.1的安全系數；第i個永久作用效應的分項系數，按照JTGD60-2004的表4.1.6采用；第i個永久作用效應的標準值和設計值；汽車荷載效應分項系數，取用1.4；汽車荷載效應的標準值和設計值；在作用效應組合中除去汽車荷載效應和風荷載以外的其他第i個可變作用效應的分項系數，取用1.4在作用效應組合中除去汽車荷載效應外的其他第j個可變作用效應的標準值和設計值；在作用效應組合中，除汽車荷載效應外的其他可變作用效應的組合系數，當永久作用與汽車荷載和人群荷載組合時，人群荷載的組合系