南京工業(yè)大學(xué)橋梁工程課程設(shè)計報告書

..11級橋梁工程課程設(shè)計專業(yè)：交通工程專業(yè)：交通工程班級：交通學(xué)號：02姓名：指導(dǎo)教師：羅韌XX工業(yè)大學(xué)交通學(xué)院二0一四年六月目錄HYPERLINK1．課程設(shè)計任務(wù)書3HYPERLINK1.1設(shè)計題目3HYPERLINK1.2設(shè)計資料3HYPERLINK設(shè)計標(biāo)準(zhǔn)3HYPERLINK材料數(shù)據(jù)與結(jié)構(gòu)布置要求3HYPERLINK設(shè)計計算依據(jù)4HYPERLINK1.3設(shè)計內(nèi)容4HYPERLINK1.4設(shè)計成果5HYPERLINK2．空腹式等截面懸鏈線箱形無鉸拱橋設(shè)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(shè)計5HYPERLINK2.1.2箱形拱圈截面幾何性質(zhì)6HYPERLINK2.2確定拱軸系數(shù)6HYPERLINK上部結(jié)構(gòu)構(gòu)造布置7HYPERLINK2.2.2主拱圈7HYPERLINK拱上腹孔布置9HYPERLINK2.3結(jié)構(gòu)恒載計算9HYPERLINK2.3.1主拱圈9HYPERLINK橫隔板10HYPERLINK拱上空腹段恒載12HYPERLINK2.3.4拱上實(shí)腹段14HYPERLINK2.3.5腹拱推力14HYPERLINK驗(yàn)算拱軸系數(shù)15HYPERLINK拱圈彈性中心及彈性壓縮系數(shù)16HYPERLINK2.4主拱圈截面內(nèi)力驗(yàn)算16HYPERLINK2.4.1結(jié)構(gòu)自重內(nèi)力計算16HYPERLINK活載內(nèi)力計算26HYPERLINK2.5溫度變化、混凝土收縮、徐變的內(nèi)力計算28HYPERLINK2.6主拱圈正截面強(qiáng)度驗(yàn)算29HYPERLINK2.7拱上結(jié)構(gòu)強(qiáng)度與穩(wěn)定性驗(yàn)算32HYPERLINK立柱強(qiáng)度與穩(wěn)定性驗(yàn)算32HYPERLINK橫墻強(qiáng)度驗(yàn)算33HYPERLINK3.課程設(shè)計小結(jié)33HYPERLINK參考文獻(xiàn)331．課程設(shè)計任務(wù)書1.1設(shè)計題目空腹式等截面懸鏈線箱形無鉸拱橋設(shè)計1.2設(shè)計資料設(shè)計標(biāo)準(zhǔn)設(shè)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＝1/5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人行道板及欄桿重52.0kN/m<雙側(cè)>；混凝土材料：強(qiáng)度等級為C30<C40>,主要強(qiáng)度指標(biāo)為：強(qiáng)度標(biāo)準(zhǔn)值fck=20.1<26.8>MPa,ftk=2.01<2.65>MPa強(qiáng)度設(shè)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(qiáng)度指標(biāo)為抗拉強(qiáng)度標(biāo)準(zhǔn)值fsk=400MPa抗拉強(qiáng)度設(shè)計值fsd=330MPa彈性模量Es=2.0×l05MPa相對界限受壓區(qū)高度b=0.53,pu=0.19852>箍筋及構(gòu)造鋼筋采用HRB335鋼筋,其強(qiáng)度指標(biāo)為抗拉強(qiáng)度標(biāo)準(zhǔn)值fsk=335MPa抗拉強(qiáng)度設(shè)計值fsd=280MPa彈性模量Es=2.0×105MPa本橋采用支架現(xiàn)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(xiàn)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(dǎo)書實(shí)例修改自定>。1.2.3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,2000.71.3設(shè)計內(nèi)容確定主拱圈截面構(gòu)造尺寸,計算拱圈截面的幾何、物理力學(xué)特征值；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；結(jié)構(gòu)恒載計算；主拱結(jié)構(gòu)內(nèi)力計算<恒載、活載>；溫度變化、混凝土收縮徐變引起的內(nèi)力；主拱結(jié)構(gòu)的強(qiáng)度和穩(wěn)定驗(yàn)算；拱上立柱<墻>的內(nèi)力、強(qiáng)度及穩(wěn)定性驗(yàn)算；手工繪制2張相關(guān)施工圖。1.4設(shè)計成果空腹式等截面懸鏈線無鉸拱設(shè)計計算書空腹式等截面懸鏈線無鉸拱設(shè)計縱斷面施工圖空腹式等截面懸鏈線無鉸拱設(shè)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(shè)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(shè)計拱圈截面高度按經(jīng)驗(yàn)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(gòu)造圖如圖2-1-1所示：圖2-1-1拱圈橫斷面構(gòu)造圖2.1.2箱形拱圈截面幾何性質(zhì)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(zhuǎn)半徑：2.2確定拱軸系數(shù)2.2.1上部結(jié)構(gòu)構(gòu)造布置上部結(jié)構(gòu)構(gòu)造布置如圖2-2-1所示：圖2-2-1上部結(jié)構(gòu)構(gòu)造布置〔尺寸單位：mm2.2.2主拱圈假定m=2.514,相應(yīng)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(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):,拱腹曲面坐標(biāo):。具體位置見圖2-3-1圖2-3-1拱軸坐標(biāo)具體位置表2-2-1主拱圈截面坐標(biāo)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?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,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(shí)腹段分界線13.6660.3380.5311.5440.2311.0260.225注:,,,,2.3結(jié)構(gòu)恒載計算恒載計算,按主拱圈、橫隔板、拱上空腹段、拱上實(shí)腹段以及腹拱推力共五個部分進(jìn)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·m橫隔板橫隔板的設(shè)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(guān)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(shè)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(diǎn)附近,即ξ=0.35~0.37之間,此處相應(yīng)的弧長為圖：圖2-3-2箱肋分段計算示圖式中值,根據(jù)ξ值從《拱橋<例集>》的附表1-1內(nèi)插算得。b.布置橫隔板橫隔板沿箱肋中軸線均勻設(shè)置,取板間間距Δl'=2.56m,中段箱肋設(shè)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(shè)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(qiáng)部分的重力橫隔板厚均為0.06m?？抗澳_的一塊為實(shí)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(cè)板均加厚0.10m。加強(qiáng)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(shí)心板P=<1.1×1.02×0.06+4×0.12×1.02/2>×7×25=15.351kNb.中接頭加強(qiáng)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(qiáng)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(biāo)各集中力作用線的橫坐標(biāo)lx,可以根據(jù)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(biāo)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(qiáng)段41.7024791.03310.991640.02390.3408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(nèi)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(hù)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(gòu)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(shí)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(diǎn)<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(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]?}=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(biāo)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(chǎn)生的力矩Mi=Fx<yi-e>2.3.6驗(yàn)算拱軸系數(shù)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(chǎn)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(shù)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(shè)計的拱軸系數(shù)。拱圈彈性中心及彈性壓縮系數(shù)彈性中心ys=[表<III>-3值]×f=0.316474×16.193=5.12466m2彈性壓縮系數(shù)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(nèi)力驗(yàn)算2.4.1結(jié)構(gòu)自重內(nèi)力計算在確定m系數(shù)時,其實(shí)計算值很難與選定的拱軸系數(shù)在"五點(diǎn)"重合,對于大跨徑拱橋必須用"假載法"計入"五點(diǎn)"存在的偏離的影響。當(dāng)用"假載法"計入"五點(diǎn)的偏離之后,相應(yīng)三鉸拱的恒載壓力線在"五點(diǎn)"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(shù)時在"五點(diǎn)"存在的偏差確定拱軸系數(shù)時,恒載壓力線在l/4截面與拱腳截面的縱坐標(biāo)之比值是0.21603,并不等于為使用手冊數(shù)表進(jìn)行計算所選用的m'=2.514的拱軸線上相應(yīng)兩點(diǎn)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(shè)的均布荷載作用在選定的拱軸線上,先單獨(dú)求出,然后算出所選定的"拱軸線"恒載產(chǎn)生的內(nèi)力,將兩者相加后為"五點(diǎn)"的恒載壓力線內(nèi)力。<1>假載內(nèi)力a.求假載由式得：b.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2-4-1表2-4-1不考慮彈性壓縮的假載內(nèi)力表項目影響線面積ω乘數(shù)ω力或力矩<qxω>[表<III>-14<51>值]拱頂截面M10.00675-0.004540.00221l26556.140914.48907139157.2339538H10.067770.060390.12816l2/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(nèi)力計入彈性壓縮的假載內(nèi)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(nèi)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(nèi)力表2-4-2考慮彈性壓縮的內(nèi)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(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2-4-3表SEQ表格\*ARABIC1-4-3空腹無鉸拱的實(shí)際恒載內(nèi)力計算表截面拱頂截面l/4截面拱腳截面項目恒載內(nèi)力附加內(nèi)力合計恒載內(nèi)力附加內(nèi)力合計恒載內(nèi)力附加內(nèi)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(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。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(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(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=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(chǎn)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(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：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?shù)饺我饨孛娴闹亓i=l·f1γ2B0<shkξi-kξi>/[2<m-1>k]=5087.1402×<shkξi-kξi>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2-4-5。表2-4-5拱上實(shí)腹段恒載對各截面產(chǎn)生的力矩計算表區(qū)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(shí)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(diǎn)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(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(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=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(shù)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(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+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(chǎn)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(chǎn)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(shù)據(jù)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(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=ΔX2sinφ拱頂、l/4截面、拱腳三個截面的附加內(nèi)力見下表:表2-4-9壓力線"偏離拱軸線的附加內(nèi)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(nèi)力這三個力的合力作用點(diǎn)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(biāo)y=y1-ei/cosφ空腹式無鉸拱恒載壓力線的縱坐標(biāo)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(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2-4-11。表格SEQ表格\*ARABIC2-4-11空腹無鉸拱的實(shí)際恒載內(nèi)力計算表截面拱頂截面l/4截面拱腳截面項目恒載內(nèi)力附加內(nèi)力合計恒載內(nèi)力附加內(nèi)力合計恒載內(nèi)力附加內(nèi)力合計水平力Hg18549-2281832117240-2281701217241-22817013軸力Ng17929-2281770117786-2141757223146-16522981彎矩Mg898-931-3431155525863-2499-10839-13338活載內(nèi)力計算1.公路-I級和人群荷載內(nèi)力車道荷載的均布荷載標(biāo)準(zhǔn)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(nèi)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(nèi)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(shù)面積拱頂截面Mmax36.753605.254020.0069l26556.140945.368518238.135相應(yīng)H136.753605.254020.0678l2/f404.87527.466711041.622Mmin36.753605.25402-0.0046l26556.1409-30.4205-12229.04相應(yīng)H136.753605.254020.0601l2/f404.87524.32499778.6058l/4截面Mmax36.753605.254020.0088l26556.140957.497423113.937相應(yīng)H136.753605.254020.0401l2/f404.87516.22336521.7832Mmin36.753605.25402-0.0102l26556.1409-67.0693-26961.87相應(yīng)H136.753605.254020.0879l2/f404.87535.572314300.072拱腳截面Mmax36.753605.254020.0198l26556.1409130.008352263.326相應(yīng)H136.753605.254020.0917l2/f404.87537.114914920.186相應(yīng)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(yīng)H136.753605.254020.0363l2/f404.87514.67675900.041相應(yīng)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(nèi)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(nèi)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(yīng)的H111041.62159778.60586521.783214300.071714920.18635900.041與M相應(yīng)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(nèi)力計算溫度變化為其它可變荷載,混凝土收縮、徐變?yōu)橛谰煤奢d,似乎要分項計算,但考慮到習(xí)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(shù)a=0.000010=1×10-5混凝土收縮作用按下降10℃溫度的影響計入?；炷列熳冏饔玫挠绊懀寒?dāng)計算溫度內(nèi)力時以β=0.7；當(dāng)計算混凝土收縮內(nèi)力時以β=0.45的系數(shù)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(chǎn)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(nèi)力見表2-5-1。表2-5-1溫度變化、混凝土收縮、徐變內(nèi)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(qiáng)度驗(yàn)算根據(jù)橋規(guī)<JTJD60-2004>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。即或式中：承載能力極限狀態(tài)下作用幾本基本組合的效應(yīng)組合設(shè)計值；結(jié)構(gòu)重要性系數(shù),對于公路-Ⅰ級標(biāo)準(zhǔn)采用1.1的安全系數(shù)；第i個永久作用效應(yīng)的分項系數(shù),按照J(rèn)TGD60-2004的表4.1.6采用；第i個永久作用效應(yīng)的標(biāo)準(zhǔn)值和設(shè)計值；汽車荷載效應(yīng)分項系數(shù),取用1.4；汽車荷載效應(yīng)的標(biāo)準(zhǔn)值和設(shè)計值；在作用效應(yīng)組合中除去汽車荷載效應(yīng)和風(fēng)