桥II课程设计

1桥梁工程（II）课程设计姓名：学号：年级：班级：专业：2015年6月2等截面空腹式石拱桥设计与计算一、设计资料1、设计标准设计荷载：公路——II级汽车荷载2、主拱跨径及桥宽净跨径：ml600净矢高：mf120净矢跨比：5100lf桥面净宽：净7＋2×0.25m安全护栏，B=7.5m3、材料及依据主（腹）拱顶填土高度：mhc45.0M12.5砂浆砌筑MU50粗料石容重为31kN25mM10砂浆砌筑MU40块石容重为32kN24m拱上横墙、拱上侧墙容重33kN24m拱顶填料、桥面铺装层换算容重34kN24m安全护栏：1.0kN/m拱圈材料抗压强度设计值：MPa094.5cdf拱圈材料抗剪强度设计值：MPa0815.0vdf拱圈材料弹性模量：MPa7300mE二、主拱圈计算1、主拱圈几何尺寸31）、截面特性按经验公式取拱圈厚度：d=1.6m主拱圈横桥向取1m单位宽度计算，横截面面积26.1mA惯性矩：333413.0121mdI截面抵抗矩：224267.061mdW截面回转半径：mdr4619.0122）、计算跨径和计算矢高假定拱轴系数：m=2.814，根据拱轴系数m与fy41关系得21.041fy，查《拱桥》上册，表（III）—20（8）得70097.0sin71319.0cosmdLL1216.6170097.06.160sin。计算跨径：m2294.12)71319.01(8.012)cos1(20dff计算矢高：mlLa5852.671216.6110575.111拱轴线长度：3）、拱轴截面投影mdx12155.170097.06.1sinmdy14110.171319.06.1cos4）、计算主拱圈坐标4将拱圈沿跨径24等分，每等分长Δ=61.1216/24=2.5467m以拱顶截面形心为坐标原点，拱轴线各截面纵坐标表1注：（1）本表截面半拱分为12段，与《拱桥（上册）》附录图(Ⅲ)-1对照，本表截面号的2倍为《拱桥（上册）》附录图(Ⅲ)-1的截面号。第2栏数据取自《拱桥（上册）》表(Ⅲ)-1，第四栏数据取自表(Ⅲ)-20主拱圈截面坐标表截面号fy11y(m)coscos22dd(m)21dy(m)21dy(m)x(m)拱脚01.00000012.229400.713191.1217211.1076813.3511230.560410.8100489.906400.764311.046708.8597110.9531028.013720.6472897.915960.811000.986446.929528.9023925.467030.5084716.218300.852380.938555.279757.1568422.920340.3908204.779490.888000.900903.878595.6804020.373650.2919883.570840.917820.871632.699214.4424717.8269L/460.2100002.568170.942120.849151.719033.4173215.280270.1432181.751470.961370.832150.919322.5836212.733580.0903081.104410.976140.819550.284861.9239710.186890.0502130.614070.986960.81057-0.196491.424647.6401100.0221330.270670.994300.80459-0.533911.075265.0934110.0055060.067340.998600.80112-0.733790.868462.5467拱顶12001.000000.80000-0.800000.80000052、拱上构造尺寸1）、腹拱圈腹拱净跨径：ml0.4，净矢高：mf0.1腹拱厚度：md35.0，腹拱墩宽：mb5.7，净矢跨比41lf，查表有8.0sin1，600001.0cos1所以，腹拱圈拱脚截面的投影:水平投影：m28.08.035.0sindx1竖向投影：m21.0600001.035.0cosdy12）、腹拱墩墩厚mb9.0表2腹拱墩高度计算表墩号x(m)1y(m)coscos112dh(m)1#横墙26.67168.857450.78892-0.214047.29342#横墙21.77165.569320.86845-0.121184.09813#横墙16.87163.196720.92694-0.063051.78374#拱座12.28161.636650.96399-0.029880.2568空、实腹段分界线12.14161.601080.96480-0.029190.2219注：表中的1y由表1的有关数据内插计算得到63、确定拱轴系数m1）、主拱圈荷载MKNBlAMMMKNlAMMKNlBAppkjkk121.1465475.74251216.616.152303.04009.353435.74251216.616.112614.0B4873.101375.71216.61256.155288.0221j221414/1112~0脚2）、拱上空腹段的恒载腹拱圈外弧半径：mdll56.48.035.020.4sin20外腹拱内弧半径：ml50.2625001.0R0腹拱上部：利用CAD求面域，得荷载如下：腹拱圈重：kN606.3125.7247367.1B21SPa腹拱侧墙护拱重：kN809.625198.025.7248.021582.42BSPbkN8.929.41cP安全护栏重：拱座部分侧墙护拱重：kN449.544198.025.7248.026176.3B3SPd7腹拱下部：kN235.18245.728.021.05.02568.0b214#kN959.288245.79.07837.1bb3#kN892.663245.79.00981.4b2#kN531.11815.7249.02934.7#12114232221xyhPhPbhPbbhP拱座：横墙：横墙：横墙：kN663.451235.1828.9449.544606.312kN174.1237959.2888.9809.625606.312kN107.1612892.6638.9809.625606.312kN746.2129531.11818.9809.625606.31216151413PPPP集中力：3）、拱上实腹段的恒载拱顶填料及面重kN573.846211416.12198.025.7248.0245.01416.1217P悬链线曲边三角形部分重量：8kN471.936198.025.7248.022224.6218SBPmxlxlKshKKchKKshKxl1290.975188.0)(/)1()2(重心位置各块恒载对拱脚及1/4拱跨截面的弯矩表3分块号恒重（kN）1/4截面拱脚截面力臂（m)弯矩(kN）力臂（m)弯矩(kN)120P10137.87335343.009146547.12113P2129.7463.88928283.00814P1612.1078.789214169.13115P1237.17413.689216935.92216P451.6632.99881354.44718.27928256.03817P846.5739.20967796.59924.490020732.57318P936.4716.15145760.60821.431820070.259总计17351.60750254.662234994.053验算拱轴系数：由上表可得到213.0053.234994662.502544jLMM9该值与假定拱轴系数m=2.814相应的21.041fy接近,故取m=2.814作为拱轴系数三、拱轴弹性中心及弹性压缩系数1、弹性中心mfys0777.42294.12333431.03III值—）表（2、弹性压缩系数015665.0013101.01015870.01013101.02294.122133.018594.9)(11III015870.02294.122133.01272.11)(9III2133.06.13413.012222122frfrmAIr值—）表（值—）表（四、主拱圈截面内力计算1、不计弹性压缩的恒载推力kN067.25622294.125.7053.234994fMHjg2、计入弹性压缩的恒载内力1）、拱顶截面kN932.2521015665.01067.2562111ggHH计入弹性压缩水平推力10kN932.25211/932.2521cosNgHg轴向力：mkN658.163067.2562015665.00777.41111gssgHyyHyyM弹性压缩弯矩2）、拱脚截面kN932.2521015665.01067.2562111ggHH计入弹性压缩水平推力kN130.353671319.0/932.2521cosNgHg轴向力：mkN986.326067.2562015665.00777.42249.121111gssgHyyHyyM弹性压缩弯矩3、汽车荷载冲击力效应拱顶填料厚度平均为mm5.045.0,必须计算汽车冲击力。汽车荷载冲击系数按下式计算：当Hzf5.1时，05.0当HzfHz145.1时，0157.01767.0Inf当Hzf14时，45.011式中f结构基频结构基频f的计算公式：eemEIlWf212式中：4221186733445.16504.5105fffW,f为拱桥矢跨比,226.02.018672.033445.162.0504.51054221Wl—结构的计算跨径，ml1216.610E—结构材料的弹性模量，29/103.77300mNMPaEeI—结构跨中截面的惯性矩，3413.0126.13eIem—结构跨中处单位长度的质量，mkgmkgme/082.4/8.9/256.1故05.04、汽车荷载效应计算拱圈宽度为7.5m，承载双车道公路II级汽车荷载，计入汽车冲击力，每米拱宽承载均布荷载：2×10.5×0.75/7.5×（1+μ）=2.1×1.05=2.205kN/m，承载集中荷载：2×360×0.75/7.5×（1+μ）=72×1.05=75.6kN1）、拱顶截面12表4拱顶截面弯矩及其相应的轴向力影响线面积影响线正弯矩负弯矩均布荷载考虑弹性压缩弯矩影响线面积27.0849-17.0355相应轴向力影响线面积21.127918.0407集中荷载不考虑弹性压缩弯矩影响线坐标3.3036-0.7005相应水平推力影响线坐标1.11460.5446a）拱顶截面正弯矩均布荷载作用下考虑弹性压缩的弯矩：MkN722.590849.27205