等截面懸鏈線圬工拱橋計(jì)VIP

1、黑龍江東方學(xué)院課程設(shè)計(jì)黑龍江東方學(xué)院建筑工程學(xué)部課程設(shè)計(jì)等截面懸鏈線壇工拱橋?qū)I(yè)：道路與橋梁課程：橋梁工程學(xué)號(hào)：044175104學(xué)生姓名：指導(dǎo)教師：余詩(shī)泉教授完成期限：2007-6-252007-7-0215等截面懸鏈線后工拱橋計(jì)算一.設(shè)計(jì)資料（一）設(shè)計(jì)標(biāo)準(zhǔn)1 .設(shè)計(jì)荷載公路二級(jí)，人群荷載3kN/nf。2 .跨徑及橋?qū)拑艨鐝絠o=40m凈失高f8m,凈失跨比f(wàn)01。105橋面凈寬為凈7+2X（0.25+0.75m人行道），B9m。（二）材料及其數(shù)據(jù)1.拱上建筑拱頂填料厚度，hd0.5m,包括橋面系的計(jì)算厚度為0.736m,平均重力密度3產(chǎn)20kN/m。拱上護(hù)拱為漿砌片石，重力密度223kN/

2、m3。腹孔結(jié)構(gòu)材料重力密度324kN/m3。主拱拱腔填料為砂、礫石夾石灰爐渣黃土，包括兩側(cè)側(cè)墻的平均重力密度4=kN/m32 .主拱圈M10砂漿砌MU40塊石，重力密度324kN/m3。軸心抗壓強(qiáng)度設(shè)計(jì)值fcd=3.44103kN/m21.24.12103kN/m2?？辜魪?qiáng)度設(shè)計(jì)值均0.073MPa0彈性模量Em0.073MPa0拱圈設(shè)計(jì)溫差為15C3 .橋墩地基土為中等密實(shí)的軟石夾沙、碎石，具容許承載力0=500kN/nf?；A(chǔ)與地基間的滑動(dòng)摩擦系數(shù)取0.5。（三）設(shè)計(jì)依據(jù)1 .交通部部標(biāo)準(zhǔn)公路橋涵設(shè)計(jì)通用規(guī)范，（JTGD60-2004）2004年。簡(jiǎn)稱橋規(guī)1;2 .交通部部標(biāo)準(zhǔn)公路土虧工橋

3、涵設(shè)計(jì)規(guī)范（JTGD61-2005）2005年，人民交通出版社，簡(jiǎn)稱橋規(guī)2；3 .交通部部標(biāo)準(zhǔn)公路橋涵地基與基礎(chǔ)設(shè)計(jì)規(guī)范，人民交通出版社，簡(jiǎn)稱橋規(guī)3；4 .公路設(shè)計(jì)手冊(cè)-拱橋上下冊(cè)，人民交通出版社，1978。簡(jiǎn)稱拱橋。二、主拱圈計(jì)算（一）確定拱軸系數(shù)拱軸系數(shù)m值的確定，一般采用“五點(diǎn)重合法”，先假定一個(gè)m值，定出拱軸線，擬定上部結(jié)構(gòu)各種幾何尺寸，計(jì)算出半拱包載對(duì)拱橋截面形心的彎矩i 。其比值4j和自拱頂至1跨的恒載對(duì),跨截面形心的彎矩44iyiyi二。求得值后，可由m=1（f2）21中反求m值，若求出的jff2yi4m值與假定的m值不符，則應(yīng)以求得的m值作為假定值，重復(fù)上述計(jì)算，直至.兩者接近

4、為止。1 .擬定上部結(jié)構(gòu)尺寸（1）主拱圈幾何尺寸1）截面特性截面高度d=mK-J；4.81.2V400091.4343cm,取d=0.9m主拱圈橫橋向取1m單位寬度計(jì)算，橫面面積A=0.9m2;慣性矩|二1d30.06075m4;12截面抵抗矩W=1d20.135m3;6截面回轉(zhuǎn)半徑Wd120.2598m。2）計(jì)算跨徑和計(jì)算失高y：假定m=2.814，相應(yīng)的;=0.21。查“拱橋”表（III）-20（8）得sinj=0.70097,cosj=0.71319計(jì)算跨徑ii0dsin400.90.7009740.63087m；計(jì)算失高ffdff o23）拱腳截面的投影(1cos j )0.9(10.

5、71319 )8.1291 m。水平投影xd sin0.63087 m豎向投影ydcosj0.6419m4）計(jì)算主拱圈坐標(biāo)（圖1-1）將拱圈沿跨徑24等分，每等分長(zhǎng)-l-1.69295m°以拱頂截面24y x y1-d,相應(yīng)拱腹坐標(biāo)2 cos jVi的形心為坐標(biāo)原點(diǎn)，拱軸線上個(gè)截面的縱坐標(biāo)y1表（III）1值f,相應(yīng)拱背坐標(biāo)y1一do其數(shù)值見(jiàn)表11。表1-12cosj主拱圈截面坐標(biāo)表截面號(hào)y1/fy1cosd2cosdy102cosdy102cosx1234567801.00008.12906450.713100.830977.498098.7600320.3154410.81004

6、86.584930.764310.588775.996167.1737018.6224820.6472894.261850.811000.554874.706985.8167216.9295830.5084714.133390.8523380.527933.605464.6613215.2365840.3908203.177000.888000.506762.670243.6837613.5436250.919882.373590.917820.490291.883302.8638811.8506760.2100001.707100.942120.477651.229452.1847510.1

7、577270.1432181.64230.961370.468080.696151.632318.4647780.0903080.734120.976140.461000.273121.195126.7718190.0502130.408180.986960.45595-0.047770.364135.07886100.0221330.179920.994330.45257-0.272850.632493.33594110.0055060.044760.998600.45063-0.405870.495391.6929512001.000000.45000-0.450000.450000注：第

8、2欄由拱橋附錄(III)表(III)-1查得第4欄由拱橋附錄(III)表(III)-20(3)查得出現(xiàn)的表(III)-值或表(III)-()值均為拱橋下冊(cè)相應(yīng)表格的數(shù)值。(2)拱上構(gòu)造尺寸1)腹拱圈腹拱圈為M10號(hào)沙漿砌M30粗料石等截面圓弧拱，截面高度d'0.3m,靜失高f'0.6m,凈失跨比f(wàn)'/l'1/5。查拱橋上冊(cè)表3-1得sin00.689655,cos00.724138水平投影xdsin0.2069m豎向投影y'd'cos0.2172m2)腹拱墩腹拱墩采用M7.5沙漿M30塊石的橫墻，厚0.8m。在橫墻中間留出上部為半徑R=0.5m的

9、半圓和下部高為R寬為2R的矩形組成的檢查孔。腹拱的拱頂拱背和主拱圈的拱頂拱背在同一水平線上。從主拱圈拱背至腹拱起拱軸線之間橫墻中線的高度hy1d(1)(d'f'),其計(jì)算過(guò)程及2cos1其數(shù)值見(jiàn)表1-2腹拱墩高度計(jì)算表表1-2項(xiàng)目xkfy1(chk)m12fktgshk(m1)!1cos-v'tg21*1橫墻17.230870.848171.437285.482450.742300.802960.47202*橫墻13.430870.661121.120313.118940.512030.890102.00553*拱座9.927420.488660.828071.6262

10、60.34140.944990.6681空、實(shí)腹段分界線9.823970.483570.819451.590680.341760.946270.6339注：橫墻高度也可根據(jù)表1-1的有關(guān)數(shù)值內(nèi)插計(jì)算得到2 .恒載計(jì)算恒載分主拱圈、拱上實(shí)腹三部分進(jìn)行計(jì)算。不考慮腹拱推力和彎矩對(duì)主拱圈的影響。其計(jì)算圖式見(jiàn)圖1-2。1)圖1-3(1)主拱圈恒載p012表(HI)19(8)值A(chǔ)510.552880.940.6308724485.2223kNAJ2oM1/4表(HI)19(8)值0.126140.940.63087224/41124.4984kN?m4AJ29Mj表(HI)19(8)值0.523030.

11、940.63087224/44662.6477kN?mj4(2)拱上空腹段的恒載腹孔上部(圖1-3)腹拱圈外弧跨徑1'1'2d'sin03.4138m腹拱內(nèi)弧半徑R0 0.725001l2.1750mdo，腹拱圈重Pa0.52202(Rod)2d3254786kN腹拱側(cè)墻護(hù)拱重Pb0.11889(Rod)2216.7503kN(以上三個(gè)系數(shù)依次分別查拱橋上冊(cè)表3-1、表1-10、表1-9)填料及路面重Pl外hd150.2511kN兩腹拱之間起成戔以上部分的重量（圖1-4）!''''''Pd(0.8x)y3(fdy)2兒i(

12、0.82x)(0.80.20690.217224(0.60.30.2172)230.73620(0.820.2069)14.8416kNd一個(gè)腹拱重Pp25.478616750350.251114.8416107.3216kNa2)腹拱下部1#橫墻P4.4720(0.50.52/2)/90.82483.9580kN2#橫墻P2.0955(0.50.52/2)/90.82438.3292kN3#拱座P(0.668110.2172)0.2069243.8568kN23)集中力P310732168395801912796kNP4107.32163832921456508kNP5(107.321614

13、.8416)/23.856850.0968kN(3)拱上實(shí)腹段的恒載(圖1-5)1)拱頂填料及面重&lxhd19.823970.73620144.6088kN懸鏈線曲邊三角形部分llfl，一，、重重P17(shK0K0)4(m1)K94.6523kN1式中：f1f yi( 1) 8.1291cos j0.450.713191)7.9481 m重心位置K 0(shK 0 -) (chK 0 1)/K 02(shK 0K 0)0.75277 lx 7.3952 m（3）各塊包載對(duì)拱腳及拱跨1/4截面的力矩見(jiàn)表1-3分塊號(hào)恒重(kN)l/4 截 面拱腳截面力臂（m）力矩(kN m)力臂（m）

14、力矩（kN mmP0-12485.22231124.49844662.6477P13191.2796P l/2-17.23087=3.0846590.0211P14145.6508l/2-13.43087=6.88461002.7475P1550.0968l/4-9.9274=0.230311.5373l/2-9.92742=10.3880520.4056P16144.6088l/4-1/29.82397=5.2457758.5744l/2-l/2 X 9.82397=15.40352227.4817目794.6523l/4-7.3952=2.725261.4770l/2-7.3952=12.

15、92031222.9361合計(jì)1111.51062156.087110226.2397半拱橫載對(duì)拱腳和1/4拱跨截面的彎矩表1-33 .驗(yàn)算拱軸系數(shù)2156 .087110226 .2397由表1-3得 M l4 / M j0.21034該 比 值 與 假 定 拱 軸 系 數(shù) m=2.814 相 應(yīng) 得 y1Jf 0.21十分接近，故可確定2.814為設(shè)計(jì)拱軸系數(shù) （二）拱軸彈性中心及彈性壓縮系數(shù)1、彈性中心 y 表(III) 3值f 0.333431 3.1291 2.7105m2 .彈性壓縮系數(shù)d- 0.0675 m2 12aw0.06758.129120.001021451111.127

16、2 0.0010214540.0113669.18594 0.0010214540.009383-0.01126 1（三）主拱圈截面內(nèi)力計(jì)算大跨徑拱橋應(yīng)驗(yàn)算拱頂、3/8拱跨、1/4拱跨和拱腳四個(gè)截面， 必要時(shí)應(yīng)驗(yàn)算1/8拱跨截面。為節(jié)省篇幅，本例只驗(yàn)算拱頂，1/4拱跨和拱腳三個(gè)截面的內(nèi)力。其余截面，除不計(jì)彈性壓縮的內(nèi)力必須在影響線上直接布載求得以外，其步驟和1/4拱跨者相同。1.恒載內(nèi)力計(jì)算計(jì)算拱圈內(nèi)力時(shí)，為利用現(xiàn)有的表格，一般采用所確定的拱軸線進(jìn)行計(jì)算。但是在確定拱軸系數(shù)時(shí)，計(jì)算得的恒載壓力線與確定的拱軸線很難在“五點(diǎn)”完全重合，本例中二者相差0.21084-0.21=0.00084。當(dāng)這個(gè)

17、偏差較大時(shí)，要用“假載法”計(jì)入其影響計(jì)入彈性壓縮的恒載內(nèi)力表1-4項(xiàng)目拱頂1/4截面拱腳yyy12.71051.0034-5.4186cos10.942120.71319Hg1Hg11243.31451243.81451243.8145Hg1'NgHgcosgcos1g1243.81451321.91941753.7746Mg1-Hgygg138.393814.2131-76.7536(1)不計(jì)彈性壓縮的恒載推力M j 10226 .2397f8.12911257 .9793 KN(2)計(jì)入彈性壓縮的恒載內(nèi)力見(jiàn)表2.活載內(nèi)力計(jì)算(1)公路二級(jí)和人群荷載的內(nèi)力1-4單位拱寬汽車等代荷載K

18、1K二級(jí)K 一級(jí) 9式中，c=2為車道數(shù)；e1為車道折減系數(shù)，雙車道不折減。3= 0.5KN單位拱橋人群等代荷載k2b20.75k2q人一99式中，b=0.75m為人行道寬度；Q人=3KN為人群荷載。不計(jì)彈性荷載的公路二級(jí)及人群內(nèi)力見(jiàn)表1-5不計(jì)彈性荷載的公路二級(jí)及人群內(nèi)力表1-5截面項(xiàng)目計(jì)算荷載影響線面積縱標(biāo)值力與彎矩29pk29qkq人表中值乘數(shù)面積拱Mmax53.75391.750.50.00725l211.96882.1960144.9734頂相應(yīng)H153.75391.750.50.06913l2/f14.03901.165194.2164Mmin53.75391.750.5-0.00

19、456l2-7.5280-0.4656-41.9658相應(yīng)H153.75391.750.50.05903l2/f11.98790.544954.26331/4截面Mmax53.75391.750.50.00882l214.56072.4013161.8408相應(yīng)H153.75391.750.50.04035l2/f8.19430.690455.5489Mmin53.75391.750.5-0.01047l2-17.28461.2080-103.7441相應(yīng)H153.75391.750.50.08781l2/f17.83261.037195.8715拱腳Mmax53.75391.750.50.0

20、1994l232.91832.1945192.0291相應(yīng)H153.75391.750.50.09242l2/f18.76880.992395.5698相應(yīng)V53.75391.750.50.17067l6.93450.293531.3799Mmin53.75391.750.5-0.01409l2-23.2607-2.4025-181.4803相應(yīng)H153.75391.750.50.03575l2/f7.26020.322534.2086相應(yīng)V53.75391.750.50.32933l13.38100.937680.5053注：在求拱腳相應(yīng)反力V時(shí)，以公路II級(jí)等代荷載乘以全部反力影響線面積。

21、人群反力則只乘以相應(yīng)的影響線面積。計(jì)如彈性壓縮的公路II級(jí)和人群荷載內(nèi)力見(jiàn)表1-6計(jì)如彈性壓縮的公路II級(jí)和人群內(nèi)力表1-6拱頂l/4截面拱腳項(xiàng)目MmaxMminMmaxMminMmaxMmincos10.942120.71319sin00.335270.70097軸與M相應(yīng)的H94.216454.263355.548995.871595.569834.2086與M相應(yīng)的V31.379980.5053向NH1cos+vsin94.216454.263352.333792.206790.155880.8290力HH111.08950.62730.64211.10821.10470.3955NHc

22、os1.08950.62730.60491.04400.78790.2821NpNN93.162953.636051.728891.162789.367980.5419M144.9734-41.9658161.8408-103.7441192.0291-181.4803彎y=ysYi2.71051.0034-5.4186矢巨MNy2.95311.70020.60701.0475-4.2693-1.5286MpMMp147.9625-40.2656162.4478-102.6966187.7598-183.0089注：初拱腳截面外，其余截面的軸向力用N=H1/cos作近似計(jì)算。3 .溫度內(nèi)力計(jì)算

23、拱圈合攏溫度15C拱圈砌體線膨脹系數(shù)0.000008變化溫差t15C溫度變化在彈性中心產(chǎn)生的水平力:HtEI t表(III)5值f28 10 6 5.2 106 0.0607520.099373 8.12912155.7727KN拱圈溫度變化內(nèi)力見(jiàn)表1-7溫度內(nèi)力表1-7項(xiàng)目溫度上升拱頂l/4截面拱腳cos10.942120.71319y=ysy12.71051.0034-5.4186NtHtcos8.10407.63495.7797MtHty21.9659-7.660931.3179注：1.溫度下降時(shí)的內(nèi)力與溫度上升的內(nèi)力符號(hào)相反；2.當(dāng)砂漿為小石子混凝土?xí)r，應(yīng)酌情計(jì)入徐變的影響。(四)主拱

24、圈正截面強(qiáng)度驗(yàn)算根據(jù)橋規(guī)規(guī)定，構(gòu)件按極限狀態(tài)設(shè)計(jì)的原則是：荷載效應(yīng)不利組合的設(shè)計(jì)值小于或等于結(jié)構(gòu)抗力效應(yīng)的設(shè)計(jì)值，即r°sR(fd,ad)式中0結(jié)構(gòu)重要性系數(shù)，本題為二級(jí)設(shè)計(jì)安全等級(jí)為1.0;S作用效應(yīng)組合設(shè)計(jì)值，按公路橋涵設(shè)計(jì)通用規(guī)范(JTGD602004)的規(guī)定計(jì)算；R()構(gòu)件承載力設(shè)計(jì)值函數(shù)；fd材料強(qiáng)度設(shè)計(jì)值；ad幾何參數(shù)設(shè)計(jì)值，可采用集合參數(shù)標(biāo)準(zhǔn)值ah即設(shè)計(jì)文件規(guī)定值。1 .正截面受壓強(qiáng)度驗(yàn)算(1)荷載組合荷載效應(yīng)不利組合的設(shè)計(jì)值見(jiàn)表1-8主拱圈荷載效應(yīng)不利組合的設(shè)計(jì)值表1-8編號(hào)荷載雙班數(shù)拱頂l/4截面拱腳MNMNMN1恒載1.238.39381234.814514.21

25、301321.9194-70.75361753.77402公路II級(jí)Mmax1.4144.973494.164161.840855.5489192.029195.56983公路II級(jí)Mmin-41.965854.2633-103.744195.8715-181.480334.20864溫度上升-21.96598.1040-7.66097.634931.31795.77975溫度下降121.9659-810407.6609-76349-3.3179-57797荷載組合M1N1M1N1M1N16組合恒+汽Mmax+溫升0.8233.37351639.3014243.15181675.5691223

26、.55792253.18817恒+汽Mmin+溫升-37.89491582.3620-144.16331736.7436-326.88292161.64328恒+汽Mmax+溫降276.42661634.4034258.27511160.6047162.17482241.85989恒+汽Mmin+溫降5.15831588.4782-129.14791721.7792-388.26602150.3149注：荷載安全系數(shù)的取值，對(duì)于結(jié)構(gòu)自重，當(dāng)其彎矩與車輛荷載的彎矩同號(hào)時(shí)取1.2,軸向力的荷載安全系數(shù)與其相應(yīng)的彎矩相同，對(duì)于其它荷載都取1.4。(2)拱圈截面抗力根據(jù)橋規(guī)第4.0.5條規(guī)定，拱圈抗力

27、效應(yīng)的設(shè)計(jì)值為0sR(fda)相應(yīng)的容許偏心距eo分別為eo0.6S具體計(jì)算見(jiàn)表1-9經(jīng)驗(yàn)算表明主拱圈截面的荷載效應(yīng)不利組合的設(shè)計(jì)值均小于其抗力效應(yīng)的設(shè)計(jì)值，即Nj<Ab。而且軸向力的偏心距都在容許范圍之內(nèi)。主拱圈抗力效應(yīng)的設(shè)計(jì)值表1-9截面編號(hào)Mje。NjAfcd0拱頂60.14240.17302448.53190.6S=0.277-0.02390.24532876.543480.16910.15462288.467990.00330.27342976.3806l/4截面60.14510.18592526.34650.6S=0.277-0.08300.19262594.438780.2

28、2250.16882356.19329-0.07500.20322618.1618拱腳60.09920.16982401.11040.6S=0.277-0.15120.16852398.032480.07230.22562689.05249-0.18060.10762075.35272 .正截面受剪強(qiáng)度驗(yàn)算一般是拱腳截面處的剪力最大，根據(jù)橋規(guī)4.0.13條規(guī)定正截面直接受剪的強(qiáng)度，按下式計(jì)算oVdAfvdfL1.4式中Vd剪力設(shè)計(jì)值；A受剪截面面積；fvd砌體或混凝土抗剪強(qiáng)度設(shè)計(jì)值；f摩擦系數(shù)，采用f0.7;Nk與受剪截面垂直的壓力標(biāo)準(zhǔn)值。(1)內(nèi)力計(jì)算恒載QqHqsinjVqcosj1243.81450.700971111.51060.71319ggg79.1584kNNq1753.7746kNg公路II級(jí)+人群荷載Hp 9Pk1 195.5698kN2-qk1 190.5 1VP9 Pk1 280.5053kN29qk1 20.5 2Qp95.56980.7009780.50530.713199.5760kNNp95.56980.7131980.50530.70097124.5912kN(五)主拱圈穩(wěn)定性驗(yàn)算拱上建筑未合攏就脫架的主拱圈，由橋規(guī)第4.0.5條及第4.0.8.1條規(guī)定按下式驗(yàn)算其縱向穩(wěn)定性0刈fcdA式中Nd軸向力設(shè)計(jì)值；A構(gòu)件截面面積；fcd砌體