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空腹式等截面悬链线无皎拱设计交通1001朱天南、设计资料1. 设计标准设计荷载:汽车荷载公路I级,人群荷载3.5kN/m2桥面净空:净8+2X(0.75m+0.25m)人行道+安全带净跨径:净高:净跨比:f=2. 材料数据与结构布置要求拱顶填料平均厚度(包括路面,以下称路面海=OSm,材料容重yl=22.0kM/m3主拱圈材料容重(包括横隔板、施工超重):”=25,OkN/ni墙上立柱(墙)材料容重:孔孔拱圈材料容重:V3=23,0kN冲腹孔拱上与主拱圈实腹段填料容重:V4=2Z0kN冲H1,人行道板及栏杆重:Vr=52,0kN,jn混凝土材料:强度等级为C30,主要强度指标为:强度标准值以=皿气f=2.01MPa强度设计值3.:皿吼弹性模量E。3.0XloWPa普通钢筋:1)纵向抗拉普通钢筋采用HRB400钢筋,其强度指标为抗拉强度标准值抗拉强度设计值京=弹性模量E.s-=2.0X10MPa相对界限受压区高度=53,街=049852)箍筋及构造钢筋采用HRB335钢筋,其强度指标为抗拉强度标准值赢335MPa来源网络,仅供参考抗拉强度设计值M=280MPH弹性模量本桥采用支架现浇施工方法。主拱圈为单箱六室截面,由现浇30号混凝土浇筑而成。拱上建筑采用圆弧腹拱形式,腹拱净跨为5m,拱脚至拱顶布置6跨(主拱圈的具体几何尺寸参照指导书实例修改自定)。3. 设计计算依据交通部部颁标准公路桥涵设计通用规范(JTGD60-2004)交通人民出版社交通部部颁标准公路钢筋混凝土及预应力混凝土桥涵设计规范(JTGD62-2004)交通人民出版社交通部部颁标准公路坊工桥涵设计规范(JTGD61-2005)交通人民出版社公路设计手册-拱桥(上)人民交通出版社,2000.7二、确定主拱圈截面构造尺寸,计算拱圈截面的几何、物理力学特征值1. 主拱圈截面尺寸拟定拱圈截面高度按以下公式估算:式中:内一一拱圈高度(mm)拱圈净跨径(mm)处对多室箱取600mm故,”=L3m。乂为施工方便,取h=L5m主拱圈横桥向取1m单位宽度计算,横截面积A=1.2m2拱圈由六个各为1.5m宽的拱箱组成,全宽B0=9.0m。箱型截面挖空率可取50%70%。腹板厚度宜取100200mm,顶底板厚度宜取100250mn综上布置拱截面如下图所示:图1主拱圈截面尺寸(尺寸单位:mm)2. 主拱圈截面几何性质截面积:=9X1,5-(LlXinOT4)*6=648m主拱圈重心高度,显然有1绕箱底边缘的静面矩:$=6屈X075=4.86m3主拱圈截面绕重心轴的惯性矩:】=(9xxL1x6)/12=17992m*回转半径:七=,=05269m三、确正主拱圈拱轴系数m及拱上建筑的构造布置和几何构造尺寸1. 确定共轴系数m假定m=2.240,对血/知=1/5,查拱桥(上册)表(III)-20(6)得:sin啊=0.68284,*的=0.73057,叫=43?0356主拱圈的计算跨径和计算欠高:!=儿+2ysin=70+2X0.75X0.68284=71.02mf=+y-U-cos/J=14+0,75X(1-0.73057)=14.20m拱脚截面的水平投影和竖向投影:x=hsm(pj=1,024m*=he。的=1,096m。将拱轴沿跨径5等分,每等分长4I=|/5=14.168m0查表(111)-20(6)并计算将各截面计算参数汇于下表:一即* 心oaIQ1Q6*J57O0顷JU图1拱上建筑结构布置图(单位:mm厚度取600mm。构造布置图如图2。各墩中线自主拱拱背到腹拱起拱线的高度按汇丁表2:对丁拱式腹孔,每半跨内的布置范围一般不超过主拱跨径的1/41/3。本例中,腹拱跨径5m,净欠高九=1m,板拱厚度=300mm,腹拱按等跨处理以利丁施工及腹拱墩的受力。腹拱拱顶的拱背和主拱拱顶的拱背在同一标高。1、2号腹孔墩采用立柱式,宽度600mm,间距2m,3号腹孔墩采空横墙式,h=yi+yx(1-1/ss初-(d+/o)计算,并5m,净欠高截面计算参数表表1截面位置|yi/曰CD晔y/costp拱背yi-y/cos|拱腹yl+步。5研拱顶00010.750-0.7500.750尚417.710.2153.0490.938720.7992.253.848拱脚35.42114.1800.730571.02713.15315.2072.确正拱上建筑的构造布置和几何构造尺寸腹拱墩局计算表表2项目f=2lx/l:tgW=2kfshkf/l(,1/costp=寻gw)+A1号立柱30.500.85871.241710.0290.80511.28388.5162号立柱24.900.70111.01386.4110.60731.17004.9833号横墙19.300.54340.78583.7230.44111.09302.354空、实腹段14.000.39410.56991.9120.30521.04550.578分界线注:其中k=hi(m+-1)=1.446因为fMo=1/5,故sin伽=0.68284,C。时u=0.73057。腹拱卅脚的水平投影和竖向投影:x=dsinWo0,3X0.682840.205my=iJcoso=03X0.73057=0.219m四、结构包载计算包载计算先将桥面系换算为填料厚度,再按主拱圈、拱上空腹段。拱上实腹段及腹拱推力四部分进行。1. 桥面系换算由已知,栏杆及人行道板每延米重度为S2.0kN/m,沥宵表处面层每延米重度:II-(0.5+0.57)X8X22=9416kN/m以上各部分包载由拱圈平均分担,则换算容重为乃=2NOkN,的计算平均填料厚度为:hd=(52+94.16)+9丰22=0.738m2. 主拱圈由表(III)-19(6)查得数据并代入计算为-口=7V直xAy2l=0.55184X6.48X25x7L03=6349.95kNAy2l20.12625x6.48x25x71.032Mi/4=表值X力一=二25797.05kNmAy2l20.55184x6.48x25x71.032叫=表值X=43. 拱上空腹段(1) 腹孔上部构造图及尺寸如图3所示1) 腹拱圈外弧跨径:=+2dsi】华。=5+2X0.205=S.41m2) 腹拱圈内弧半径:上5=;=-=3.661m2sm财02X0.682643) 腹拱圈重力:P*2叩d/科=2x07594x(3,6614-O3p)x03x23x94) =359.44kN腹拱上的护拱重力:Pb=(2sinp0-茹牝cds牝-牝)盼5) =(2X0.68284一0.68284X073057一0.7594)X3.8112X22x9=308.30kN填料及桥面系重力:Pc=外ZidViBu=5,416X0.738X22X9=791,40kN腹拱墩起拱线以上部分结构图如图4所示|Pd=(0.56-jc4+(/o+d-y)+如y11(0.56.x)8。=(0.56-0.219)x0.217x22+|(1.3-0.217)4-().783x22(0.56-0.205)x9=7315kN综上,单个腹拱总重力:P=ZP产35944+308,30+791,40+73.15a=1532J9kN腹拱下部(包括横隔板)结构示意图如图5所示,在计算立柱与横墙重力时折入横隔板,等效为立柱高度。1)梁盖重力:P=(1.3+OS)X0.56X9X22=13958kN7CU02)底梁重力:P=0,4X0*56X9X25=50.4kN3) 1号立柱重力:4) P=4x(8,516-0.8+1.53)X0.62X25=27778kN*12号立柱重力:4too图4腹孔下部构造(单位:mmF=4x(4,9830.8+1.46)X0.62X25=150.59kN5) 3号横墙重力:P=1(2354-0.4+1.30)X9-(2X178+0.6气)X0.6X25=193.43kN(3)腹孔集中力Pli=1532,29+139,58+50,4+27778=2000.05kNP2=1532J9+139.584-50.4+150.59=1872.86kNPi3=1532.29+193.43=1725.72kNPm=(1532.29-73.15)/2=729.57kN4. 拱上实腹段计算图示如图6所示。(1)拱顶填料及桥面系重P临=凿o=14x0.738x22x9(2)悬链线曲边三角形=2045,74kN7102x1393.(2.24-nxl.446(Sh0-57爵7)25x9=1947.25kN式中:fi=f+y(i-.1).=1121+0751-_1).-13.。10.7305刃其重心至拱顶的距离:心)中Mf_*=0/7513。=10.52m5. 腹拱推力靠近主拱拱顶一侧的腹拱多采用两皎拱,在较大的包载作用下和考虑到周围的填料等构造的作用,可以折中地按无皎圆弧拱计算其推力,而不计弯矩的影响。计算图示如图7所示。腹拱水平推力:F=(Ggi+Cgi+。仙)/?8()式中:gi=Yhd=22X0.738=16,24kN5-2O52=23x(4.111)-,4,111)2一=21.36kNgj=yM=23x03=69kN由/u/u=l/5与人=J胆=0.00049。,查拱桥(上册)表(I)-4并线性内插得:C=0.822559,C2=0,109345,C3=0.855734故:|F-(0,822559x16.24+0109345x2136+0B55734x6.9)x3.961x9=760.44kN腹拱拱脚推力作用线距x轴的偏心距:,y0.219e=d+/0-y-y=03+1-一0.75=0.441m腹拱推力对各截面重心产生的力矩按IFe)计算。6. 验收拱轴系数包载对拱脚与1/4截面的力矩见表3,得=0,2176该值与0.22之差小丁半级0.0025,故可确定拱轴系数m=2.240五、拱圈弹性中心与弹性压缩系数1. 弹性中心ys=aj=0339193x142=4.817m式中可查表(|)-3得。弹性压缩系数05269=0.001377Pi=表(11)-9值=1L0S01X0.001377=0.01522jptwp=表Oil)-llffx-=9.14719x0.001377=0.01260=0.01503六、主拱圈结构内力计算1. 结构自重内力计算对拱脚与|】/4截面进行验算,如表3所示:半拱恒载对拱脚与|1/4截面的弯矩计算表表3项目集中力编与重力(kN)4aw拱脚截面力臂(m)弯矩(kNm)力臂(m)弯矩(kNm)主拱圈6349.9525797.05112759.16%|2000.055.0110020.25拱上空腹段Pn1872.8610.6119871.041725.7216.2127973.92729.573.7552739.5421.5115693.05实腹段%|2045.7410.75522001.9328.5158324.051947.257.23514088.3524.9948661.78腹拱推力760.441.93761473.4313.75910462.89266100.30303766.15当确定m系数时,其实算值很难与选定的拱轴系数在“五点”重合,因此必须用“假载法”计入偏离的影响。当计入该部分影响后,相应三皎拱的包载压力线在“五点”以外与选定的拱轴线有偏离。以下分别计算这两种偏离的影响。(1)假载法确定m系数时在“五点”存在的偏差确定拱轴系数时,包载压力线在截面与拱脚截面的纵坐标之比为0.2176,并不等丁所取用的2.240的拱轴线上相应两点的比值0.22,两者之差为0.0024.该偏差的影响可比拟为一层虚设的均布荷载作用丁选定的拱轴线上。按式:I=022V以=38.50kN/lll得虚设均布荷载:02I8327假载队产生的内力可以将其直接布置在内力影响线上求得。不考虑弹性压缩的假载内力见下不计弹性压缩的假载内力计算表项目影响线面积力或力矩表(111)-14(43)值乘数I-J(m)拱顶截面M40.00198卜=5043.849.9868284.62倒0.12742S=355.2045.25961289.901/4截回版4-0.00124=5043.84-6.2544-178.25倒0.12742阳=355.2045.25961289.90版40.00440=5043.8422.1929632.50拱脚截面0.12642肋=355.2044.90441279.780.500001=71.0235.51001012.04计入弹性压缩的假载内力见下表5项目拱顶截面1词截面拱脚截面COS10.938720.7305700.344680.68284Hi1289.901289.901279.78Vi1012.0419.3919.3919.24F=(*)Kicm巾+Visin1270.511353.451611.98Ml284.62-178.25632.50|y=4.8171.768-9.383W=Ml+俨1/1+向的378.01-143.97452.02计入弹性压缩的假载内力计算表表5mLpmHi注:114截面轴力按1/4一-诈力顽赢近似计算拱轴线包载内力推力:V*38.5x71.O22十-g-303766.15+g=j=2310L49kN考虑弹性压缩的拱轴线包载内力汇丁表6考虑弹性压缩的拱轴线恒载内力计算表表6项目拱顶截面l/4截面拱脚截面COSi|10.938720.73057帕-B-F23101.4922341.0522341.05H1,L,n22754.2722005.2622005.261II23101.4923799.4830580.30P1.N-Hgcos347.22315.21245.32N=N-削22754.2723484.2730334.99y=虹乂4.8171.768-9.383U1.?wimJ1672.54593.67-3150.68由、F叫1注:拱顶截面取F=0,拱脚与截面取F=760.44kN考虑确定m系数偏差影响的包载内力考虑m系数偏差影响的包载内力等丁拱轴线m的包载内力减去假载的内力,计算结果见下表7考虑“五点”偏差的恒载内力表7项、拱顶截面1阀截回拱脚截面拱轴线恒载假载Qr合计拱轴线恒载假载qx合计拱轴线恒载假载合计水平力23101.491289.9021811.5923799.481289.9022509.5830580.301279.7829300.52轴力22754.271270.5121483.7623484.271353.4522130.8230334.991611.9828723.01弯矩1672.54378.011294.53593.67-143.97737.64-3150.68452.02-3602.70(2)包载压力线偏离拱轴线的影响1)包载压力线偏离拱轴线的偏离弯矩、a.主拱圈自重对各截面产生的力矩河1计算包载偏离弯矩|苗济首先要计算出桥跨结构沿跨径各等分段的分块包载对各截面的力矩,再算各截面压力线的纵坐标,然后才能求得主拱圈自重对各截面产生的力矩时1:I2、Mj=村上不任xSj-S?)71.O22=648x25x(xSi-S2)=20427554(xS|-S2)式中Si与,分别从拱桥(例集)附表1-1与图7主拱圈自重计算图示1-2查得。将计算结果汇丁表8:主拱圈自重对各截面产生的力矩表8截面号&$1财1(kNm)120.000000.000000.000000.000000.00110.083330.083390.003760.00319651.41100.166670.167040.014220.013622782.3590.250000.251210.031480.031326398.4280.333330.336290.056590.0555111338.4370.416670.422550.088960.0871017793.2060.500000.510310.128900.1262625790.8150.583330.600300.177970.1722035176.8640.666670.692830.235840.2260546176.2830.750000.788460.303300.2880558840.5520.833330.888450.382830.3575473037.0910.916670.993220.474590.4358689036.5501.000001.103670.580130.52354106946.42b.拱上实腹段包载对各截面产生的弯矩峋计算拱上实腹段的包载时,必须将拱顶填料及面层的矩形板块和其下面的悬链线曲边三角形块分开才能准确计算(a) 矩形板块从拱顶到每个截面的矩形板块的重力:Pi=J2对实腹段里每个截面的力矩:Mr=P做4对空腹段里每个截面的力矩:阴=P*-*)式中k表示空、实腹段的分界点,并取:Z1D/irf=209382.42kN(b) 悬链线曲边三角形块从拱顶到任意截面的重力:1、山3州-柘)=6207180(sh/-fcO对每一Pf的重心横坐标:(-1在实腹段里,截面重心到任意截面的力臂为U-,在空腹段里,整块曲边三角形面积的重心到每个截面的力臂为a、b两部分力矩计算结果汇丁表9:区界4悬链线曲边三角形矩形块也表9拱上实腹段恒载对各截面产生的力矩间面号nMa|1/2L22实腹段120.000000.00000.000.00000.000.000.00000.000.00110.083330.120518.110.75010.7413.400.0035726.96740.36100.166670.2410145.240.75021.48214.690.01392908.213122.8990.250000.3615491.930.75052.211089.410.03136543.207632.6180.333330.48201171.960.75102.953454.620.055611632.1215086.74k0.374260.54121663.890.75133.305498.470.070014664.1620162.62空腹段70.416671663.890.75134.818004.230.086618123.2726127.5060.500001663.890.75137.7712927.770.119425002.2637930.0350.583331663.890.751310.7317851.320.152331881.2449732.5540.666671663.890.751313.6922775.450.185138761.0561536.5030.750001663.890.751316.6527698.990.218045640.0373339.0320.833331663.890.751319.6132622.540.250852519.0285141.5510.916671663.890.751322.5737546.670.283759398.8396945.5001.000001663.890.751325.5242470.210.316566277.81108748.02(c) 各集中力对各截面的力矩修拱上空腹段的腹孔各集中力及其相应的横坐标I“在之前的计算中已经求出,各竖向集中力到截面的力臂|口=佐/2-U(取a0),产生的力矩腹拱水平推力%作用在7、8截面之间,对07截面产生的力矩=幻。计算过程与结果见表10:各集中力对各截面的力矩表10截回竖向力PMHpl2腹拱水平推力合计P729.571725.721872.862000.05=760.44曲1419.324.930.5e=0.441LMMMMyf-qMMB120.00000.00110.08330.00100.16670.0090.25000.0080.33330.0070.4167580.621.7001292.741873.3660.50002739.542.6832040.264779.8050.58334898.452440.463.8782948.8310287.7440.66677057.377547.155.3024031.6318636.1530.75009216.2912653.843244.736.9755304.4030419.2620.833311375.2117760.548786.838.9236785.6444708.2210.916713534.1322867.2314328.944101.7711.1748496.8563328.9101.000015693.0527973.9219871.0410020.2513.75910462.8984021.16(d) 计算偏离弯矩“P上部结构包载对拱圈各截面重心的弯矩:压力线的纵坐标:式中,为不计弹性压缩的包载水平推力:%=M町=21391.98kN各截面上“包载压力线”偏离拱轴线的值:表11偏离弯矩:坊=HJy。具体数值见下表11:偏离弯矩计算表截面号主拱圈拱上实腹段集中力合计恒载压力线拱轴线偏心偏离弯矩MlM2垢Mj凹?yMp1200.000.000.000.0000.00000.0011651.41740.360.001391.770.0650.0830.018388.00102782.353122.890.005905.240.2760.3340.0581239.6496398.427632.610.0014031.030.6560.7560.1002142.39811338.4315086.740.0026425.171.2351.3550.1202571.12717793.2026127.501873.3645794.062.1412.1410.0005.98625790.8137930.034779.8068500.633.2023.124-0.078-1672.09535176.8649732.5510287.7495197.154.4504.319-0.131-2809.72446176.2861536.5018636.15126348.935.9065.743-0.164-3501.05358840.5573339.0330419.26162598.847.6017.416-0.184-3946.66273037.0985141.5544708.22202886.869.4849.364-0.120-2565.87189036.5596945.5063328.91249310.9611.65411.615-0.040-851.850106946.42108748.0284021.16299715.6114.01114.2000.1894050.512)偏离弯矩在弹性中心产生的赘余力:b厂?yJ。CD晔?*=_/=_%心1吕Yii2?y(ys-yi)?x_-土.J。esW,L一硕=(1+什表值|!尸赘余力各项计算结果见表12:赘余力参数计算表表12截面CDSl/cus巾ys-yi(ys-巾120.0001.000000.5000.0004.8170.000110.0180.998421.0020.0184.7340.086100.0580.993631.0060.0584.4830.26190.1000.985501.0150.1024.0610.41380.1200.973821.0270.1233.4620.42770.0000.958331.0430.0002.6760.0016-0.0780.938751.065-0.0831.693-0.1415-0.1310.914841.093-0.1440.498-0.0724-0.1640.886441.128-0.185-0.9260.1713-0.1840.853531.172-0.216-2.5990.5622-0.1200.816291.225-0.147-4.5470.6681-0.0400.775131.290-0.051-6.7980.34900.1890.730670.6840.130-9.383-1.216213.251-0.3951.510-0.395?Xi=-%=637.68kN4V9kJL2x2.959x1.1507XZ=/.(1+0.01260)X0.099879X71.02x14.22E=13011kN3)包载压力线偏离拱轴线的附加内力包载压力线偏离拱轴线在拱圈任意截面中产生的附加内力为:|?M=?X1-?X2(ys-Q+Mp|?N=你?Q=?Xzsin中拱顶、4截面、拱脚三个截面的附加内力见表13。项目拱顶截面|i/4aw拱脚截面cos10.938750.73067sin山00.344600.68273yj-yf4.8171.693-9.383?N=?网0$巾130.11122.1495.07?Q=?X2sin巾0.0044.8488.83阳0.00-1672.094050.51637.68637.68637.68|?M=?X1-?XAyJ-wJ+M,10.94-1254.685909.01表134)空腹式无皎拱的包载压力线附加内力计算表空腹式无皎拱桥在包载作用下考虑压力线与拱轴线的偏离以及包载弹性压缩的影响之后,拱中任意截面存在三个内力:叫=(官厂?小f)+?X+MNg=s/cos-(山且/1+-项Jeos巾Qe=+-?知sin4这三个力的合力作用点的偏心距为玷=My/Vg。所以空腹式无皎拱桥包载压力线的纵坐标y=y外。冲。相应包载压力线纵坐标值见下表14:空腹式无皎拱包载压力线表表14截面Y1Aycose=eY=Vi120.0004.8170.0000.0731.0000.9910.074-0.074110.0654.7340.0180.0900.9980.9930.091-0.026100.2764.4830.0580.1280.9940.9980.1280.14790.6564.0610.1000.1660.9851.0060.1650.48881.23513.4620.12010.181P0.9741.0180.178:1.05372.1562.6760.0000.0540.9581.0350.0522.08663.2571.693-0.078-0.033P0.9391.057-0.0313.23654.5440.498-0.131-0.0970.9151.085-0.0894.54846.040-0.926-0.164-0.142P0.8861.120-0.1276.05037.774-2.599-0.184-0.1780.8541.164-0.1537.78029.696-4.547-0.120-0.1310.8161.218-0.1079.616111.906-6.798-0.040-0.0710.7751.283-0.05511.726014.301-9.3830.1890.1350.7311.3620.09913.875表中数据由相关数据代入后按以下内力公式计算:Afs=0,00895yi)+0.02981+?yHp1I临=(0.00895gm)HgCOS+Vsin4*997.08922.36616.291330.291272.231370.72ah=1m)14.9913.869.8721.3020.009.88iN=AHcos4)14.9913.869.2619.9914.617.22Np=N-Ah982.10908.49607.031310.301257.621363.50M2521.76-1269.173189.72-2536.484620.09-4464.32y=yr-yl4.8171.768-9.383AM=iHy72.1966.7817.4537.66-187.63-92.69Mji=M+AM2593.94-1202.393207.16-2498.824432.47-4557.01七、温度变化与混凝土收缩徐变引起的内力计算时将混凝土收缩折算为温度的额外降低。拱圈合拢温度7月平均最低气温2月平均最高气温30拱圈材料弹性模量|E=30。X104MPa拱圈材料线胀缩系数混凝土收缩作用按下降10C温度的影响计。考虑混凝土徐变作用影响时,温度变化影响力P=0.7;混凝土收缩影响力P=0.45。因此:温度降低时温度升高时:在弹性中心产生的水平力:H*=a-El-At1L表(山)-5值Jx(1卜:产1xIO-5x3x107x1,7992=At=26.4740.099879X1.0126X14+22温度变化、混凝土徐变和收缩的内力见下表18:温度变化、混凝土徐变和收缩内力计算表表18项目温度上升温度下降拱顶截面P4截面拱脚截面拱顶截面1/4截面拱脚截面11.6-8叫307.05-211.76cos4)10.938750.7306710.938750.73067y-ys-vi4.8171.768-9.3834.8171.768-9.383此=寺307.05288.24224.35-211.76-198.79-154.73M=-Hy-1479.07-509.622105.101020.05351.46-1451.79八、主拱圈正截面强度与稳定性验算1.荷载组合计算根据桥规(JTGD60-2004)的规定,构件按极限状态设计的原则是:荷载效应不利组合的设计值小丁或等丁结构抗力效应的设计值。即:irlrT=/。(/萨5y(?iSg+驱矿(?卢妣)MLj=2式中:5&承载能力极限状态下作用几本基本组合的效应组合设计值;皿一一结构重要性系数,对丁公路-I级标准采用1.1的安全系数;V一一第个永久作用效应的分项系数,按照JTGD60-2004的表4.1.6采用;S饥第,个永久作用效应的标准值;h1汽车荷载效应分项系数,取用1.4;SqM汽车荷载效应的标准值;,QJ在作用效应组合中除去汽车荷载效应和风荷载以外的其他第,个可变作用效应的分项系数,取用1.4;8在作用效应组合中除去汽车荷载效应外的其他第/个可变作用效应的标准值;R在作用效应组合中,除汽车荷载效应外的其他可变作用效应的组合系数,当永久作用与汽车荷载和人群荷载组合时,人群荷载的组合系数取=0.80,当除汽车荷载外尚有两种其他可变作用参与组合时,片=0.70;以此类推。对丁本例取永久作用为结构自重;可变荷载作用为汽车和人群荷载;其他可变荷载作用为温度变化与混凝土收缩徐变。根据桥规(JTGD60-2004)的规定,承载力极限状态组合设计值为:-片$自重+L45苗督+(L7xL45谖虔+收缩徐变其中当对结构承载不利时,险取1.2;当对结构承载有利时,耻取1.0。组合设计值见下表19:荷载组合结果表表19佝载组日拱顶截面截面拱脚截面(kNm)N(kN)可(kNm)件|(kN)M(kNm)N(kN)组合I1恒+动max5198.0927311.583869.5727553.398973.0336342.352恒+动min-377.8722885.76-4015.3924087.38-4073.5130726.98组合II1恒+动max+温升3748.6027612.493370.1527835.8711036.0336562.222恒+动max+温降6197.7327104.054214.0027358.587550.2836190.723恒+动min+温升-1827.3623186.67-4514.8224369.86-2010.5130946.854恒+动min+温降621.7722678.24-3670.9623892.56-5496.2630575.352.正截面抗压强度与稳定性验算按规范,拱圈应进行整体的“强度一稳定”验算,将拱换算为直杆并按直杆承载力计算公式验算拱的承载力。现先进行构造配筋并按下式校核:险电W。月+人也;)式中:&结构重要性系数,对丁公路-I级标准采用1.1的安全系数;Nd-轴向力设计值;M构件截面面积f*混凝土抗压强度设计值,C30混凝土为Am=13.8MPa&纵向钢筋截面面积hd钢筋抗压强度设计值,采用HRB400钢筋,人d=330MPaW拱圈换算压杆纵向弯曲系数,对混凝土拱圈按桥梁工程表4-3-2取0.66其中构造配筋主筋采用HRB400钢筋,对一侧翼缘取1612,按双层布置。普通箍筋与附加箍筋采用HRB355取08,纵向间距100mm,纵向钢筋截面积心=475。加仃局部构造钢筋配置示意图如右图9所示:图8截面配筋示意图计算结果见下表20:何载组合拱顶截面1/4截面拱脚截面利组合I1恒+动max30042.7430308.7339976.592恒+动min25174.3426496.1233799.68组合II1恒+动max+温升30373.7430619.4640218.442恒+动max+温降29814.4630094.4439809.793恒+动min+温升25505.3426806.8434041.534恒+动min+温降24946.0626281.8233632.89结构抗力效应设计值OWCAM+京启=54048.9kN强度与稳定性验算表表20由表20可知,验算截面均满足“强度一稳定”验算要习的强度与稳定性。即米用构造配筋已保证主拱圈截面九、拱上结构强度与稳定性验算1. 立柱强度与稳定性验算图9立柱配筋示意图取力作用、号立柱采用钢筋混凝土设计,先按构造要求配宵行强度与稳定性校核。纵向钢筋为812的HRB400,箍;08的HRB355钢筋,间距S=100mm。立柱构造配筋示意右图10所示。由丁、号立柱与底梁接触都有相同的截面面积,最大处即号立柱按下式进行校核验算:W0.9甲(/瑚+/Mm)式中符号意义同上。立柱上下固结,故S=0&=0.5,459=4,230m由硕=4,230/0.6=7.049,查表得卯取1.0y0/Vri=1.1x(1532,29+139.58+5.4+27778)=2200.06kN+fAsd)=0.9x1.0x(13.8x0.62+330xnx0.0062x8)=47399.2kN丫洲&=2200.06kN故、号立柱强度与稳定性满足要求。2. 横墙强度验算号横墙采用素混凝土设计,并按下式进行强度验算:缨4*5式中符号意义同上。VoNd=YPn=LIx(1532.29+193.43)=1898.29kN甲fA=1.0x13.8x0.6x9.0=74S20.0kNyQN(i=1898,29kN故号横墙满足强度要求。
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