南京工業(yè)大學交通工程橋梁工程課程設計教程

1、橋梁工程課程設計（交通工程專業(yè)用）專 業(yè)： 交通工程班級學號:交通1204班姓 名：孫善雷指導教師：羅韌學 期：2015-2016第二學期南京工業(yè)大學交通工程學院二O 一五年七月橋梁工程課程設計拱橋結構設計計算說明書一. 課程設計的目的1培養(yǎng)學生綜合運用所學橋梁工程理論知識，解決鋼筋混凝土拱橋結構的設計和計算問題，掌握鋼筋混凝土拱橋結構分析和計算的理論與方法。2. 強調規(guī)范在橋梁結構設計中的重要性，培養(yǎng)學生運用專業(yè)理論知識和專業(yè)規(guī)范進行 橋梁結構設計的能力。.3進一步提高學生繪制橋梁工程施工圖、使用計算機的能力。二. 課程設計的內容1. 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

2、值;2. 確定主拱圈拱軸系數(shù) m及拱上建筑的構造布置和幾何構造尺寸;3. 結構恒載計算；4. 主拱結構內力計算（永久作用、可變作用）；5. 溫度變化、混凝土收縮徐變引起的內力；6. 主拱結構的強度和穩(wěn)定計算；7. 拱上立柱（墻）的內力、強度及穩(wěn)定性計算；8. 繪制12張相關施工圖。三. 課程設計的時間時間：兩周；安排在理論課結束之后。四. 課程設計的方法1. 獨力思考，繼承與創(chuàng)新線設計時要認真查閱和閱讀參考資料，繼承前人的設計成果和經(jīng)驗，根據(jù)課程設計的具體要求，大膽改進和創(chuàng)新。2. 結合和參考本指導的算例，進行拱橋結構的設計計算，掌握拱橋的計算理論和設計 內容與方法。五. 課程設計的步驟1.

3、設計準備：了解設計任務書，明確設計要求、設計內容、設計步驟；通過查閱教科 書和相關設計資料，了解設計的理論和方法；準備好設計所需資料、工具書、工具軟件；擬 好設計計劃。2. 設計實施：根據(jù)課程設計任務書的要求，參考設計指導書和教科書，確定設計的主 要內容、計算順序；根據(jù)相關計算理論，計算和填寫相關圖表的內容。使用圖表給出計算結 果和結構的相關驗算結果。3. 匯總設計成果：課程設計計算書，課程設計要求繪制的工程圖紙。六. 拱橋課程設計計算空腹式等截面懸鏈線無鉸拱設計一設計題目空腹式等截面懸鏈線無鉸拱設計二設計資料 1設計標準設計荷載：汽車荷載公路一 I級，人群荷載3.5kN/m2橋面凈空 凈8+

4、2 2) 25.64 m2繞箱底邊緣的靜面矩：s= (1.5 *2 0.6-1.1 0.782 0.6) 6= 3.38m3主拱圈截面重心軸： y下=S/A=0.6my上=1.5-0.6=0.6m主拱圈截面繞重心軸的慣性矩：6 (1.5 1.23/12 1.5 1.2 (0.6 -1.2/2)2 -1.1 0.7823/12 1.1 0.782 02) 1.033m4拱圈截面繞重心軸的回轉半徑：r ( Ix/A)1/2(1.033/5.64)2 =0.428m三、確定拱軸系數(shù)(一)上部結構構造布置上部結構的構造布置如圖所示。5：pn11D丄JLLl(尺寸單位：cm)IQ2Q0號&15 1521

5、5圖2上部結構構造（尺寸單位：mm）1主拱圈假定m=2.514，相應的f =0.215，f/l =1/5，查拱橋（上冊）表（山）-20得：sin 爐0.69198 , cos 護0.72191 ,沏=43.7876?主拱圈的計算跨徑和計算矢高：l=l+2y 下 sin j=50+2*0.6*0.69198=50.83mf =f+y 下（1-cos j） =10.167m拱腳截面的水平投影和豎向投影x=Hsin也=0.83 my=Hcos巾=0.866 m將拱軸沿跨徑24等分，每等分長 Al=l/24=2.118 m,每等分點拱軸線的縱坐標y1=表（III）-1值沫，相應的拱背曲面坐標y1=y1

6、_y 上/cos，拱腹曲面坐標 y1=y1+y 下/cos。截面 號xyfy1cos y 上/cos y 下 /cos yy 上/cos yl-y下 / cos025.41501.000010.16700.721910.83110.83119.335910.9981124.35600.90379.18790.746230.80400.80408.38389.9919223.29700.81408.27610.769690.77950.77957.49669.05573廠22.23800.73077.42900.792180.75740.75746.67168.1864421.17900.653

7、46.64320.813600.73750.73755.90577.3807520.12000.58175.91410.833870.71950.71955.19466.6337619.06100.51545.24010.852910.70350.70354.53665.9436718.00200.45414.61680.870680.68910.68913.92775.30608 :16.94300.39764.04280.887180.67630.67633.36654.7191915.88400.34573.51470.902380.66490.66492.84984.17961014.

8、82500.29813.03050.916300.65480.65482.37573.68531113.76600.25462.58850.928970.64590.64591.94263.234412 :12.70700.21502.18590.940420.63800.63801.54792.82391311.64800.17921.82190.950700.63110.63111.19082.45301410.58900.14701.49450.959850.62510.62510.86942.1196159.53000.11831.20280.967920.61990.61990.58

9、291.8226168.47100.09290.94430.974980.61540.61540.32891.559717 17.41200.07070.71880.981070.61160.61160.10721.3304186.35300.05170.52590.986240.60840.6084-0.08251.1342195.29400.03580.36400.990530.60570.6057-0.24180.9697204.23500.02280.23210.993980.60360.6036-0.37160.8357213.17600.01280.13010.996640.602

10、00.6020-0.47190.732222 :2.11700.00570.05780.998510.60090.6009-0.54310.6587231.05800.00140.01440.999630.60020.6002-0.58580.6147240.00000.00000.00001.000000.60000.6000-0.60000.60002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 3對圓弧小拱，腹拱圈厚 d=0.4m，凈跨徑lo=5m，凈矢高fo=O.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?/p>

11、頂?shù)墓氨吃谕粯烁?。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 h=yi+y上X(1-1/cos B)d+fo)，分別計算如表 2k = ln(m . m2 -1) =1.573腹拱墩咼計算表表2項目lxE =2/1kEy1 =f (ch k E1)/(m-1)tg 0 =kfshk E(/-1)1/cos 0 =2 ?(tg 0 +1)h1號立柱21.40000.84201.32456.80340.72621.31385.59012號立柱15.80000.62170.97793.47510.47441.21422.32153號立柱10.20000.40130.6313

12、1.38320.28021.13140.2794空、實腹 段分界 線9.75000.38360.60351.26030.26631.12530.1601由f0/l0=1/8，查拱橋(上冊)表3-2得sin 滬0.470588 , cos 0=0.882353 ,腹拱拱腳的水平投影和豎向投影x=d x si0=0.4 )0.470588=0.1882 m ; y=d x cos=CH 0882353=0.3534 m三、結構恒載計算1主拱圈恒載P012=表(川)一19 ( 7)值Ar 21=0.55235*5.64*25* 50.83=3958.711 KN MM1/4=表(川)一19 (7)值

13、Ar212/4= 0.12619*5.64*25* 50.83 2/4=1149207596 KN MM=表(川)一19 (7)值Ar212/4=0.52328 *5.64*25* 50.83 2/4=476570.7415 KN M橫隔板橫隔板位置lx橫隔板重 力力臂 l /4- lx力矩(kN m)力臂 1 /2- 1 x力矩(kN m)121.4121.523674.015487.9175215.8109.35969.6151051.493310.2124.113842.5075311.215515.2151888.3922拱上空腹段恒載腹拱圈外弧跨徑I =1 2d in 機=5+2*0

14、.4*0.470588=5.376腹拱內弧半徑Ro=1.O625l5.3125腹拱圈重Pa=0.979914*23*0.45.3125+0.2=46.0902腹拱側墻護拱重Pb=1.9255*22=42.361填料及路面重Pc=l外 hdri =5.376*22*0.5=59.136兩腹拱之間起拱線以上部分重力Pd=(0.6-0.1882)*0.3534*23+(0.625+0.4-0.3534)*22+0.5*22(0.6-2*0.1882)=9.1105孔上部構造圖9拱腳構造一個腹拱重力：P=(46.0902+42.361+59.136+9.1105)*9=156.698 *9=1410.

15、2793 KN腹孔下部1 號橫墻 P=5.5901- (0.5*1+3.14*0.5 2/2 ) /9*0.6*25=82.36372 號橫墻 P=2.3215- (0.5*1+3.14*0.5 2/2 ) /9*0.6*25=32.68023 號橫墻 P=(0.2794+ 0.3534/2)*( 10.2-9.75)*2*25=10.26225集中力P13=1410.2793+82.3637=1492.643Pi4=1410.2793+ 32.6802=1442.95952Pi5= (1410.2793-9.1105) /2+10.26225=674.4047腹拱推力拱上實腹段的荷載靠近主拱

16、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=(C 式中 g 1= Y1g1+Cg2+C?g3)RB01hd=22x 0. 5=14.9314kN/m2g2= y 2(R+d/2)-(R+d/2)2-1 2/4 ?=25x (5.3125+0.4/2)-(? 2=17.4944kN/mg 3= y 3d=23腹拱拱腳受力圖得2 25.3125+0.4/2)-5.376 /4x 0. 4=9.2kN/m2由 fo/1 0=1/8 和 b=l/AR 2=0.000157 查拱橋(上

17、冊)表(1)-4C 1=0.84256 , G=0.11671 , G=0.85714F=(0.84256x 14. 9314+0.11671 x 17.4944+0.85714 x 9.2)X5.3125*9=1076.1669 kN腹拱拱腳推力作用線的縱坐標見圖12所示，其距x軸的偏心距為：e=d+ f0-y/2-y上=0.4+0.625- 0.3534/2-0.6=0.2483m腹拱推力對各截面重心產(chǎn)生的力矩M i=Fx( yi-e)拱頂填料及橋面重P16=9.75*0.5*22*9=965.25懸鏈線曲邊三角形部分f1=【y1-d/ (2cos(f)】 +d/2=【1.2603-1.2

18、/(2*1.1253)】+0.6=1.3271P17=9.75*1.3271/(2.514-1)*1.573/(sh1.573-1.573)*22*9=1465.9569重心位置=【(shk-k/2) - (chk-1) /k 】/(shk-k)=0.759953l x=7.40954 m分塊號恒重l / 4 截面拱腳截面力臂力矩(kN m)力臂力矩(kN m)p1121.523674.015487.91754P2109.359609.6151051.49255P3124.113842.5075311.2154515.2151888.39208P0-123958.7112445.2681013

19、9.945P131492.6434.0155992.961645P141442.959529.61513874.05578P15674.40472.50751691.06978515.21510261.06751P16965.257.83257560.32062520.5419826.235P171465.95695.297967766.58101818.0054626395.22832f1076.16691.93762085.1809859.918710674.17663合計11431.0891321859.63587100591.472063驗算拱軸系數(shù)刀 Mi/4/ 刀 Mj=21859

20、.63587 /100591.47206 =0.21731與假定的m=2.514, y/f =0.215，十分接近，顧可確定2.514為設計的拱軸系數(shù)(二)拱圈彈性中心及彈性壓縮系數(shù)21 彈性中心 ys=表(III) -3 值沫=0.336314 W.167=3.4193m 彈性壓縮系數(shù)Yw=I/A=d 2/12=0.122 2 2Yw/f =0.12/10.167 =0.001161221=表(III) -9 值X Y/f =11.089 0.00116=0.012862 2上表(III) -11 值X Yw/f =9.167 X00116=0.01063 1/(1+)=0.01272主拱圈

21、截面內力計算(一)結構自重內力計算(1)假載內力a. 求假載2 2由式(刀M?-qxl/32)/(刀Mj -qxl / 8)=0.215 得：2qx=-( EM?-0.215 xEMj)/(0.215/8-1/32) l = 20.5658882 kN/mb. 假載內力假載qx產(chǎn)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F表項目影響線面積3乘數(shù)3力或力矩 9x3)表(III)-14(51)值拱頂 截面M10.00703-0.00470.00233l22583.68896.0200123.8065H10.067890.05990.12779l2/f254.125003

22、2.4746667.8697l / 4截面M10.00887-0.01031-0.001442l2583.6889-3.7205-76.5156H10.04040.087390.12779l2/f254.1250032.4746667.8697拱腳 截面M10.0195-0.014370.00513l22583.688913.2543272.5869H10.091550.036250.12780l2/f254.1250032.4772667.9220V10.168450.331550.5l50.8325.4150522.6820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下表項目拱頂截面

23、l/4截面拱腳截面cos $10.940420.72191sin $00.340010.69198H1667.8697667.8697667.9220V100522.6820hH1/(1+H8.49538.49538.4960N=1- 口/(1+ H H1COS $+V 1Sin $659.3744620.0889837.7317M1123.8065-76.5156272.5869y=ys-y13.41931.2334-6.7477M=M 1 + MH1y心+ H152.8545-66.0376215.2587(2) “拱軸線恒載”內力a推力2 2Hg=(刀 Mj+qxl /8)/f=(100

24、591.47206 +20.5658882 50.83 /8)/10.167=10547.20706 kNb.考慮彈性壓縮的內力項目拱頂截面l /4截面拱腳截面cos$1.00000.94040.7219HFHg-F9906.77171632.58591632.58591- P/(1 +a )H g9780.75751611.81941611.8194N=Hg/ COs $9906.77171736.01782261.4812 N=yHgCOS $ /(1+ a)126.014119.529214.9915N=N- N9780.75751716.48862246.4897y=ys-y 13.4

25、1931.2334-6.7477 V=1Hgy/(1+ a)430.880125.6133-140.1261(3)考慮確定m系數(shù)偏差影響的恒載內力考慮m系數(shù)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，計算結果見下表考慮“五點”偏差的恒載內力面 面拱頂截面l/4截面拱腳截面項拱軸線恒 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10547.2071667.86979879.33749471.0402667.86978803.17059471.0402667.92208803.1182軸力10413.0466659.37449753.67229957.7

26、809620.08899337.692013032.4499837.731712194.7181彎 矩458.7349152.8545305.8804148.5891-66.0376214.6267-812.9064215.2587-1028.16512“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。（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

27、 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(chǎn)生的力矩Mi|2 - ,M 1 =從丫5 玄 0 ( 2)H1l2sh2k：1dq.2 - , -2sh2k id 1A 5；12sh2k 1d 1-.0 1在這里，對于所要求的每一等分點而言，積分上限E為常數(shù)，并不計等式前面的負號,則上式為：2 二 八. 2MA 5 4 0 d2sh2k id i - -I2sh2k id J =A 5 4 禺-S2式中：S = .o .1 2sh2k 1d 1可根據(jù)E值從拱橋（例集）附表1-1查得；U s2 =。

28、2sh2k 1d 可根據(jù)E值從拱橋（例集）附表1-2查得2= 5.64*25*50.83 /4 =91075.032kN m=0.759953k=1.573主拱圈對各截面的力矩M1的值見下表主拱圈自重對各截面產(chǎn)生的彎矩截面號ESiS2E x S1-S2Mi (kN m)0123452400000230.04170.04170.00170.00000.0000220.08330.08360.00520.0017158.31272i0.12500.12570.01050.0052475.5288200.16670.16820.01760.0105952.6394i90.20830.21120.02

29、650.01751591.0451i80.25000.25480.03740.02632392.5695i70.29170.29910.05030.03693359.4758i60.33330.34420.06540.04934494.4871i50.37500.39040.08270.06375800.8102i40.41670.43760.10240.08007282.1624i30.45830.48610.12460.09828942.8015i20.50000.53610.14960.118410787.5590ii0.54170.58760.17750.140812821.8757i

30、O0.58330.64100.20860.165315051.840590.62500.69630.24320.192017484.231480.66670.75380.28160.221020126.559570.70830.81370.32400.252422987.115360.75000.87630.37090.286326075.017750.79170.94170.42270.322829400.266240.83331.01030.47980.362132973.795230.87501.08230.54280.404136807.531520.91671.15800.61220

31、.449240914.456010.95831.23770.68860.497545308.667601.00001.32180.77270.549150005.4518b.拱上實腹段恒載對各截面產(chǎn)生的彎矩M 2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?shù)矫總€截面的矩形板塊的重力：Pi = Y iBOh dl E i/2對實腹段里每個截面的力矩：2 2M=R(| E /2)/2=( l /4) y iBoh dE i/2 對空腹段里每個截面的力矩：M=RI E i /2-( l /2) E k/

32、2=(12/4) y iBOh dE k( E i - E k/2) (i 035222.035E222.ccS:Q.腑totii0,75020t 79373.2106J4毀 5804 KZ 7911曲0.1S70.2c229.C02E0.7503l.7710.15740.3135BS1 1430E遲罷I130.10830.3377IB. 791S0.7504L 32130.021713S7.7234：.5 和：ISQ駆0.3333眾54和:口1.5844-0- C3111瀕屈182陽帆1 J灑；0.45 開:L 53110.750SL8457?5.7U2Q.M252713.337328155

33、42分顯占0.25100.457751.47400,7509JUr 叮185)/2(L-0.: Wd1455d r 止13333= 1.474：C.75C92.9185:兒滋l-0.02731話化6M3；S97.8：7150.3750:L474C0.75093.9774204.735：0.03342133.3107234C.0459f Ji0.4：；51.474：0.5.0354299.24410.03952522. MSI* * *ft“九130,4533二二二 0l75H.09543；二 75291-04552rl： c=r：3224.41231 iCOC51.47400.7509i. 1

34、54336i2t：&o. m32祁,3卻：5957kl0.5417:L.4?4：0.75095.2133422.770cO.O57fi巫MM4：E.7；?：10 0, 5833注族flL 7509SL 212247：.2?0)，產(chǎn)生的力矩 M3=Pa;腹拱水平推力 Hg作用在第7 與第8截面之間，對07截面產(chǎn)生的力矩 M 3=H g(yi- e)。具體計算見下表。截面豎向力P1P2P3腹拱水平力合計M3P=798.518541552.319121614.166671076.1669l x =10.215.821.40.2483EMMM240.00000.0000230.04170.000022

35、0.08330.0000210.12500.0000200.16670.0000190.20830.0000180.2500298.7202298.7202170.2917506.3440506.3440160.3333748.9911748.9911150.37501027.15411027.1541140.4167311.089511341.08441652.1739130.45831156.687381693.48462850.1720120.50002002.285242085.18644087.4716110.54172847.883102518.46545366.3485100.5

36、8333693.480962994.09856687.579490.62504539.078833515.22598054.304780.66675384.676691774.818194083.466911242.961870.70836230.274553418.659464701.272414350.206560.75007075.872415062.500735372.034317510.407450.79177921.470276706.342006097.393720725.205940.83338767.068148350.183276881.978823999.230230.8

37、7509612.666009994.024537727.660627334.351120.916710458.2638611637.86580 3062.208698639.275233797.613610.958311303.8617213281.70707 4771.543939620.455238977.568001.000012149.4595914925.54834 6480.8791810674.176644230.0637d.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=M什M 2+M 3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=刀

38、 Mj/f=100591.47206/10.167=9893.918763 kN各截面上“恒載壓力線”偏離拱軸線的值： y=y-yi偏離彎矩具體數(shù)值見下表截面號主燉拱上實腹段集中力合計“恒養(yǎng)壓力銭”拱軸鑽偏右偏宙彎矩壯HLMt%y=y：yi12345&TB9240O.OCMO0.300000.00000.0000o.oaoo0.0000230.000055.54850.000055.54850.X560.01440.0J3637.291422156.3127222.66050,0000380.99220.03650.05760.0193190.51362i475.5288502-7911cTo

39、oooOT8.319Q0.0989043010.0313309.2510P 20962.6394396 30040.0D001350.93970J8710.23210.0450445.0606191591.04511412 55370.00003003.90890.30360.35400.050459T. 5759IE2392.5M52049 690928.72024741.1606D.4TB20.52590.04S7461 6127IT3359.47582815 6542506.34405661.47400.&7530.71060 0435430 3431IB4494.40711697.B6

40、2774E.M117141.34090.72130.94430.222S2201.32155SD0.81022340 04591027.15419166,QI020.92661 20280.2T&12731.9609L 147282.16242782.22921652.17391171B.5655L18421.49050.31023069.5762 13G942.30153224.41252E5D.172015017.38S9L51T81.62190.30413006. 6059I?10787.5590365&. 59574037.471618541.5263l.87402. 13590.31

41、193085.54021112621.61574108.77%5368.348522297,00312.25362.5885D.333313.5886ID15051.64054550,S6226687,5W426290,39222.65723.03050.37333693.0185917484.23144993.14558054,304730531.63173.08593.51470.42384242.7502P 82D12S. 55965435 3288112.961836804.85013.719904280322313.8399T22987,11535677 512014350.205543214.83384 367861680.24902463.7537P 66075.01776319 695317510.40T449905.12055.04405 24010.19&11940 2272529400 25626