1、截面积:绕箱底边缘的静面矩:主拱圈截面重心轴: 主拱圈截面绕重心轴的惯性矩:拱圈截面绕重心轴的回转半径:2.2确定拱轴系数 2.2.1上部结构构造布置上部结构构造布置如图2-2-1所示:图2-2-1 上部结构构造布置 (尺寸单位:mm)2.2.2 主拱圈假定m=2.514,相应的,查拱桥(上册)表(III)-20(7)得: sinj =0.69198,cosj=0.72191,j=43.7876 主拱圈的计算跨径和计算矢高:脚拱截面水平投影 脚拱截面竖向投影 计算跨径 半跨径 计算矢高 将拱轴沿跨径24等分,每等分长l=,每等分点拱轴线的纵坐标 y1=表(III)-1值f,相应的拱背曲面坐标:
2、, 拱腹曲面坐标:。具体位置见图2-3-1图2-3-1 拱轴坐标具体位置表 2-2-1主拱圈截面坐标表截面号 x y1/f y1 cos y上/cos y下/cos y1-y上/cos y1+y下/cos 40.485116.1930.721910.9793464560.95995345715.2136535417.1529534638.7981250.90364914.632788260.746230.9474290770.92866810513.6853591815.56145636237.111250.81401813.181393470.769690.9185516250.900362
3、48412.2628418514.08175596335.4243750.73072411.832613730.792180.8924739330.87480118210.940139812.70741491433.73750.65340810.580635740.81360.8689773840.8517699129.7116583611.43240566532.0506250.5817389.4200834340.833870.8478539820.8310647948.57222945210.25114823630.363750.5154058.3459531650.852910.828
4、926850.8125124577.5170263159.158465622728.6768750.4541257.3536461250.870680.8120090040.7959296186.5416371218.149575743826.990.3976356.4389035550.887180.7969070540.7811267165.6419965017.220030271925.3031250.3456915.5977743630.902380.7834836760.7679691484.8142906876.3657435111023.616250.2980714.826663
5、7030.91630.771581360.7563025214.0550823435.5829662241121.9293750.254574.122252010.928970.7610579460.7459874923.3611940644.8682395021220.24250.2153.4814950.940420.7517917530.7369047872.7297032474.2183997871318.5556250.1791922.9016560560.95070.7436625640.7289365732.1579934923.6305926291416.868750.1469
6、922.3802414560.959850.7365734230.7219878111.6436680333.1022292671515.1818750.1182621.9150165660.967920.7304322670.7159682621.1845842992.6309848281613.4950.0928771.5039572610.974980.725143080.7107838110.7788141812.2147410721711.8081250.070731.145330890.981070.7206417480.7063716150.4246891421.85170250
7、51810.121250.0517240.8375667320.986240.7168640490.7026687220.1207026831.540235454198.4343750.0357790.5793693470.990530.7137593010.699625453-0.134389951.2789948206.74750.0228250.3696052250.993680.7114966590.697407616-0.341891431.067012841215.0606250.0128070.2073837510.996640.7093835290.69533633-0.501
8、999780.902720081223.373750.0056820.0920086260.998510.7080550020.694034111-0.616046380.786042737231.6868750.0014190.0229778670.999630.7072616870.693256505-0.684283820.716234372240.7070.693-0.7072.2.3拱上腹孔布置 由,查拱桥(上册)表3-2 ,得 sin0=0.43219,cos0=0.90178, 腹拱拱脚的水平投影和竖向投影 x= dsin0=0.50.43219=0.216095 m; y=dc
9、os0=0.50.90178=0.45089 m从主拱两端起拱线起向外延伸后向跨中对称布置3对圆弧小拱,腹拱圈厚d=0.5m,净跨径l0=8m,净矢高f0=0.8m。腹拱拱顶的拱背和主拱拱顶的拱背在同一标高。腹拱墩墩中线的横坐标lx,以及各墩中线自主拱拱背到腹拱起拱线的高度 ,分别计算如表2-2-2:表 2-2-2腹拱墩高计算表 项目 lxk y1tancosh 1 号立墙 31.1160.7691.2098.8160.6341.1847.3862 号立墙 22.6160.5590.8794.4020.4141.0823.0443 号腹拱座 14.1160.3490.5481.6490.241
10、.0280.329空、实腹段分界线 13.6660.3380.5311.5440.2311.0260.225注:, 2.3结构恒载计算恒载计算,按主拱圈、横隔板、拱上空腹段、拱上 实腹段以及腹拱推力共五个部分进行。2.3.1 主拱圈P012=表()19(7)值 Ar2l=0.514086.122580.97=6368.6338kNm M1/4=表()19(7)值 Ar22/4=0.1253080.972/4=31421.7804 kNMj=表()19(7)值 Ar2l2/4=0.5061080.972/4=126915.9063kN2.3.2横隔板 横隔板的设置受箱肋接头位置的控制,必须先确定
11、接头位置后再按箱肋轴线等弧长布置横隔板。箱肋有关几何要素 a.箱肋截面积 A=20.21.4+1.10.1+20.10.1/2=0.79m2 b.箱肋截面静矩 J1.41.4/2+1.10.2/2+20.1 (0.1/3+0.2)/2=0.4163 m3 c.截面重心距箱底的距离 y下=J/A=0.527m d.箱肋计算跨径 l=l0+2 y下sinj=80+20.5270.69198=80.7293m e.箱肋轴线弧长 S0.52764l=85.1920m 确定箱肋接头、设置横隔板 a.确定接头位置箱肋分三段吊装合拢,接头宜选在箱肋自重作用下弯矩值最小的反弯点附近,即=0.350.37 之间
12、,此处相应的弧长为图:图2-3-2 箱肋分段计算示图式中值,根据值从拱桥(例集)的附表1-1内插算得。b.布置横隔板 横隔板沿箱肋中轴线均匀设置,取板间间距l=2.56m,中段箱肋设11 道横隔板,端横隔板到接头中线的距离为0.3m,座落在宽为 0.6m 的钢筋混凝土排架式腹拱墩支承的宽为 0.7m 的钢筋混凝土盖梁上。则中段箱肋弧长之半为:SII/2=(2.5610+20.3)/2=13.1m,则接头位置刚好在=0.37 处。端段箱肋弧长 SI=(S-SII)/2=( 85.1920-26.2)/2=29.496m 端段箱肋设12道横隔板,则端横隔板距起拱面的长度为: S=SI -2.561
13、1-0.3=1.036m横隔板与接头加强部分的重力 横隔板厚均为0.06m。靠拱脚的一块为实心板,其余均为空心板。接头处两相邻横隔板之间以及拱脚截面至第一块横隔板之间的箱底板和两侧板均加厚0.10m。加强后的断面尺寸图2-3-3图2-3-3 横隔板a.横隔板重力 空心板 P=(1.11.02-0.680.62+40.12/2)0.06 +40.121.02/27=11.1342kN 实心板 P=(1.11.021.02/2)725=15.351kN b.中接头加强部分 P=20.541.02+0.1(1.1-20.1) -425=24.213kN c.拱脚加强段 P=0.120.6775+0.
14、10.67750.1)-21.1/225=32.9324kN d.各集中力作用线的横坐标 各集中力作用线的横坐标lx,可以根据值从拱桥(例集)书后附表1 查得 值,再由l=l/2 求得。lx 的值和各集中力分别对l/4和拱脚截面的力臂见表2-3-1.表 2-3-1横隔板的横坐标与力臂计算表集中力编号 Sx 2Sx/l 肋 lx=l 肋/2 力臂 l/4-lx l/2-lx 1 号 2.560.06340.07272.934817.247637.42992 号 5.120.12680.14535.86614.316334.49863 号 7.680.19030.21788.789611.3927
15、31.5754 号 10.240.25370.289911.70278.479628.66195 号 12.80.31710.361714.59915.583225.76566 号 15.360.38050.378415.27594.906425.08887 号 17.920.4440.449618.14712.035322.217663.96118 号 20.480.50740.520120.99219.37269 号 23.040.57080.589823.806216.558410 号 25.60.63420.658626.582413.782211 号 28.160.69760.726
16、229.313811.050912 号 30.720.76110.792731.99898.365813 号 33.280.82450.857734.62255.742214 号 35.840.88790.921337.18883.1759283.285415 号 38.40.95130.983139.68310.68160号 20.182340.3647中接头 14.080.34880.370114.93785.244525.4269拱脚加强段 41.7024791.03310.991640.02390.34082.3.3拱上空腹段恒载 腹孔上部(见图2-3-4) 腹拱圈外弧跨径 l外=l+
17、2dsin0 =8+20.50.43219=8.43219m 腹拱圈内弧半径 R0= l/(2sin0)=8/(20.43219)=9.2552m 腹拱圈重力 Pa=20Rd3B0=2253624/180(9.2552+0.5/2)239 =879.3505kN 腹拱上面的护拱重Pb=(2sin0-sin0cos0-0)R22B0=(20.43219-0.432190.90178-2536/180)(9.2552+0.5/2)2229=495.8681kN 填料及桥面系重力 Pc=l外hd1B0=8.432199=834.7868kN 图2-3-4 腹孔上部构造 Pd=(0.6-x)y4+(f
18、0+d-y)2+hd1(0.6-2x)B0=(0.6-0.216095)0.4508923+(0.8+0.5-0.45089)22+0.522(0.6-20.216095)9=80.6576kN 一个腹拱总重力: P=Pi=879.3505+495.8681+834.7868+80.6576=2290.663kN 腹孔下部 1号腹拱墩: P=7.3861-(0.51+3.140.5/2)/90.625=109.304 kN 2号腹拱墩: P=3.0438-(0.525=44.1695 kN 3号腹拱墩: P=(0.3294+0.45089/2)( 14.1162-13.6662)25=12.4
19、840125 kN 图2-3-5 腹孔墩以上部分腹孔集中力 P13=2290.663+109.304=2399.967 kN P14=2290.663+44.1695=2334.8325 kN P15=(2290.663-80.6576)/2+12.4840125=1117.4867 kN2.3.4 拱上实腹段图2-3-6 曲边三角形块拱顶填料及桥面系重 P16=lhd1B0=13.66629=1352.9538kN 悬链线曲边三角形 ,见图2-3-6 P17=lf1(shk-k)2B0/2(m-1)k=80.9715.92065/2(2.514-1)1.572999 (sh0.5309851
20、2-0.53098512)9=1356.0686kN 式中 f1=f+y上(1-1/cosj)=16.193+0.707(1-1/0.72191)=15.92065m 其重心距原点(拱顶)的水平距离 lx=(shk-k/2)-(chk-1)/ k lx/(shk-k)=0.7509lx=10.2625m 2.3.5 腹拱推力 图2-3-7腹拱拱脚受力图靠近主拱拱顶一侧的腹拱,一般多做成两平铰拱,在较大的恒载作用下和考虑到周围的填料等构造的作用,可以折中地按无铰圆弧拱计算其推力,而不计弯矩的影响。腹拱拱脚的水平推力 F=(C1g1+C2g2+C3g3)RB0 式中 g1=1hd=220.5=11
21、kN/m2 g2=2(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/m2 g3=3d=230.5=11.5kN/m2 由f0/l0=1/10和b=I/AR2=0.0003查拱桥(上册)表(I)-4得 C1=0.6103,C2=0.08473,C3=0.6170 F=(0.610311+0.0847322.6046+0.617011.5) 9.25529=1309.7662kN 腹拱拱脚推力作用线的纵坐标见图2-3-8所示,其距x轴的偏心距为: e=d+ f0-y/2-y上=0.895345m 腹拱推力对各截面重心产生的力矩 Mi=Fx(yi-e) 2.3.6验算拱轴系数 恒载对l/4截面和拱脚截面的力矩见表2-3-2表2-3-2半拱恒载对拱脚和1/4截面产生的弯矩表 集中力编号恒重l/4拱脚截面力臂力矩kNmp1195.410118.37253590.172062p2171.443124.68254231.644316p3200.82681702.93093328.66255756.198155p0-126368.63389976.1863
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