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第部分 上部结构I、设计资料一、设计标准及材料标准跨径:16m 计算跨径:15.56m桥面净宽: 9+20.5m 设计荷载:汽20,挂100材料:预应力钢筋:15.24(75.0)钢铰线,后张法施工。非预应力钢筋:钢筋和级螺纹钢筋混凝土:空心板为R40号,空心板铰逢为R30号;桥面铺装为R30号沥青砼;栏杆、人行道采用R30号砼;二、构造与尺寸 50 900/2 2% 图1-1 桥梁横断面 (尺寸单位:cm) 图1-2 面构造及尺寸 (尺单位:cm)三、设计依据与参考书结构设计原理叶见曙主编,人民交通出版社桥梁计算示例集(梁桥)易建国主编,人民交通出版社桥梁工程(1985)姚玲森主编,人民交通出版社公路桥涵标准图公路桥涵标准图编制组,人民交通出版社公路桥涵设计规范(合订本)(JTJ021-85)人民交通出版社公路砖石及混凝土桥涵设计规范(JTJ022-85)II、上部结构的设计过程一、毛截面面积计算(详见图1-2)Ah=9990306331.52(3377127)=4688.28cm2(一)毛截面重心位置 全截面静距:对称部分抵消,除去下部3cm后1/2板高静距S=257/2(2/3714.514)+38(2114.58/2)28/2(14.5218/3)993(43.53/2)=3667.513365=17032.5cm3铰面积:A铰=2(1/2751/22838)=99cm2毛面积的重心及位置为:dh=17032.5/4688.28=3.63cm (向下)则重心距下边缘的距离为:141814.53.63=42.87cm距上边缘距离为:9042.87=47.13cm铰重心对除去下部3cm后1/2板高的距离:d铰=3667.5/99=37.05cm O y OI I 图1-3 (二)毛截面对重心的惯距每个挖空半圆(图1-3)面积:A=1/2R2=1/23.14182=508.68cm2重心:y=4R/(3)=418/(33.14)=7.64cm半圆对自身惯距:I=II-IAy2=3.14184/8508.687.642=41203.0829691.45=11511.63cm4由此可得:Ih=99903/1299903.632236293/1236293.632411511.632508.68(7.6429/23.63)2(7.6429/23.63)22(1/128331/362831573/36)99(37.053.63)2 =4723333.21cm4二、内力计算(一)、永久荷载(恒载)作用下1. 桥面系安全带、栏杆:单侧为6.25kN/m桥面铺装:2(0.06+0.15)/24.523=21.74 kN/mg1= (6.252+21.74)/10=3.43 kN/m2. 铰和接缝:g2=(99+190)10-424=0.45 kN/m3. 行车道板:g3=4688.2810-425=11.72 kN/m恒载总重力:g=g1+g2+g3=3.43+0.45+11.72=15.6kN/m恒载内力计算见表1-1。 表1-1荷载g(kN/m)L(m)M(kN*m)Q(kN)跨中1/8gL21/4点3/32gL2Q支1/2gLQ1/4点1/4gL单块板重全部恒载11.7215.6015.5615.56354.7472.12266.02354.0991.18121.3745.5960.68(二)、基本可变荷载(活载)作用下1. 荷载横向分布系数跨中和四分点的横向分布系数按铰接板法计算。支点按杠杆法计算荷载横向分布系数;支点到四分点间按直线内插求得。(1)跨中和四分点的荷载横向分布系数:刚度系数r=2EI/(4GIT)(b/l)2=5.8I/ IT (b/l)2式中 I=Ih=4723333.21cm4; b=100cm ; L=24.34100cmIT板截面的抵抗扭刚度。图1-2所示截住面简化成图1-4。(略去中间肋板)IT=4b2h2/b(1/t1+1/t2)+2h/t3=4892(9011/27)2/89(1/111/14)2(9011/27)/10=6354404.131cm4r=5.8Ib2/ITl2=5.84723333.211002/6354404.13124342=0.0073 11 10 10 9014 99图1-4 尺寸单位:cm 按r查桥梁工程(1985)附录I之附表的各板的横向分布影响线竖坐标值,见表1-2。说明:1、表中值为小数点后三位有效数字。2、表中I,J分别为板号与荷载作用的板号。3、竖标值应该绘在板的中轴线处 表1-2荷载位置 板号 riji1i2i3i4i5i6i7i8i9i1010.001001001001001001001001001001000.011811581311100930800700630580560.007315914212310709508507807306906820.001001001001001001001001001001000.011581541371140970830730650600580.007314213912711009808808007407106930.001001001001001001001001001001000.011311371371231040900780700650430.007312312712711710309308407807405840.001001001001001001001001001001000.011101141231271161000870780730700.007310711011712011210009108408007850.001001001001001001001001001001000.010930971041161231141000900830800.0073095098103112117110100093088085根据所求得数值作影响线:(如图1-5)根据各板影响线,在其上加载求得各种荷载作用下的横向分布系数如下:汽车荷载作用下:m3=1/2i汽挂车荷载作用下:m2=1/4i挂板号1:三行汽车m3汽=1/2(0.1510.1180.1000.0820.0750.069)=0.298 二行汽车:m2汽=1/2(0.1440.1110.0950.079)=0.215挂100m2挂=1/4(0.1420.1250.1100.099)=0.119板号2:三行汽车:m3汽=1/2(0.1410.1150.1000.0850.0760.070)=0.294二行汽车:m2汽=1/2(0.1390.1150.0980.082)=0.217挂100m2挂=1/4(0.1390.1280.1130.102)=0.121板号3:三行汽车:m3汽=1/2(0.1250.1240.1090.0890.0800.066)=0.297二行汽车:m2汽=1/2(0.1270.1200.1030.086)=0.218挂100m2挂=1/4(0.1270.1270.1190.107)=0.120板号4:三行汽车:m3汽=1/2(0.1090.1180.1150.0960.0860.079)=0.302二行汽车:m2汽=1/2(0.1100.1190.1120.093)=0.217挂100m2挂=1/4(0.1110.1170.1200.113)=0.115板号5:三行汽车:m3汽=1/2(0.0970.1060.1150.1060.0950.087)=0.303二行汽车:m2汽=1/2(0.0980.1090.1170.102)=0.213挂100m2挂=1/4(0.1050.1130.1170.111)=0.112支点、支点到四分点的荷载横向分布系数按杠杆法计算(图1-6)支点荷载横向分布系数求得如下:m3汽= m2汽=1/21.00=0.500m2挂=1/4(1.00+0.10+0.10)=0.300支点到四分点的荷载横向分布系数按直线内插进行。横向分布系数汇总于表1-3。 表1-3荷载跨中到四分点支点三行汽-20m3汽=0.3030.500二行汽-20m2汽=0.2180.500挂-100M2挂=0.1210.3002、活载内力计算弯矩汽-20产生的弯矩M汽车=(1+)miPiyi式中:(1+)为冲击系数,(1+)=1+0.3(45-24.34)/40=1.155为折减系数三列车取0.8,两列车取1.0作荷载横向分布系数沿桥跨方向的变化图形和跨中及1/4点的弯矩影响线(见图1-7)跨中弯矩的计算:M3汽=1.1550.8(604.0851206.0851205.385)0.303=453.47kN.mM2汽=1.1551.0(604.0851206.0851205.385)0.218=408.28 kN.mM挂=1.0250(3.4854.0856.0855.485)0.121=578.99 kN.m1/4点弯矩的计算:M3汽=1.1550.8(601.5640.4331204.5640.303+1204.2140.303+701.7140.3031300.7140.433)=403.18 kN.mM2汽=1.1551.0(601.5640.4031204.5640.218+1204.2140.218+701.7140.2181300.7140.403)=382.32 kN.mM挂=1.0(3.6640.1564.5640.1213.5640.1213.2640.121)250=487.50 kN.m(2)、剪力计算跨中剪力近似按同一个跨中荷载横向分布系数计算见图1-8Q3汽车=(1+)miPiyi=1.1550.8(1200.51200.443600.278)0.303=36.35kNQ2汽车=(1+)miPiyi=1.1551.0(1200.51200.443600.278)0.218=32.69kNQ挂=1.0(2500.50.1212500.4510.1212500.2860.1212500.1410.130) =42.03 kN支点剪力:剪力影响线及横向分布系数见图1-9Q支汽=(1+)miPiyi=1.1551.0(0.51201.00.4551200.9430.325600.7780.3731300.162) =155.36kNQ支挂=1.0(0.32501.00.2652500.9510.1472500.7860.1212500.737) =189.18kN1/4点剪力:Q汽=(1+)miPiyi=1.1551.0(0.3031200.750.3031200.6930.303600.528) =71.69kNQ挂=1.0(0.1212500.750.1212500.7010.1212500.5360.1212500.487) =74.84kN(3)内力组合内力组合按“公预规第4.1.2”条规定进行,恒载产生的效应与活载产生的效应同号时:则 荷载组合 S=1.2SG+1.4SQ荷载组合 S=1.2SG+1.1SQ式中:SG恒载重力产生效应序 号荷载类型弯 矩 (kN.m)剪 力 (kN)跨中1/4处支点跨中1/4L点1恒载472.12354.09121.37060.682汽-20453.47403.18155.3636.3571.693挂-100578.99487.50189.1842.0374.8441.2恒载566.544424.908145.644072.81651.4汽-20634.858564.452217.50450.89100.36661.1挂-100636.889536.25208.09846.23382.3247S=4+51201.402989.36363.14850.89173.1828S=4+61203.433961.158353.74246.233155.149(2)/(1)+(2) 49535610054S提高(%)3000010(3)/(1)+(3)55586110055S提高(%)2233211提高后S1237.44989.36363.1550.89173.1812提高后S1227.50980.38364.35547.62158.24控制设计内力1237.44989.36364.3550.89173.18表中提高系数详见结构设计原理荷载效应组合三、预应力钢筋的设计(一)、预应力钢筋截面积的估算根据桥预规定,预应力梁应满足使用阶段应力要求和承载力极限状态的强度条件。故按承载力极限状态来估算,这时预应力钢筋达到抗拉设计强度,砼达到抗压设计强度。后张法预应力砼空心板可以近似地简化。按下列公式来估算预应力钢筋面积:Ay=cMj/hRyNy=cMj/h(取设计经验值为0.76)则Ny=1.251237.44/0.760.9=2261.40kN选用直径为15.24(75.0)钢铰线,且采用后张法施工。n=Ny/Ry.ay=2261.40103/1860140=8.68 束按施工和使用阶段估算,钢束数也为9束左右,选定钢束数n=9束 Ay=91.40=12.6cm2(二)、预应力钢筋布置后张法预应力钢筋的布置按“公 预规”的要求,取预应力钢束净距保护层为3.5cm,钢束截面重心到板下边缘距离为ag=3.5+1.52=4.26cm, 9束钢束在板横截面中呈不均匀分布,详见 图1-11,预应力钢束沿板跨方向呈直线变化,即保持ag=4.26cm不变。四、净截面和换算截面的几何特性计算(一)换算截面积A0=Ah+(n-1)Ay=4688.28+(5.91-1)12.6=4750.15cm4式中n钢筋弹性模量与砼弹性模量之比n=Ey/Eh=1.95105/3.3104=5.91(二)换算截面的重心位置钢筋换算截面对毛截面重心净距Sg=(5.91-1)12.6(42.87-4.26)=2388.65cm3换算截面对毛截面重心的距偏离:dh0=Sg/A0=2388.65/4750.15=0.50cm换算截面重心到截面下缘距离:y0=42.87-0.50=42.37cm换算截面重心到截面上缘距离:y0=47.13-0.50=46.63cm钢筋重心到换算截面重心距离:ey=42.37-4.26=38.11cm(三)换算截面惯距I0=Ih+Ahdh02+(n-1)Ayey2=4723333.21+4688.280.502+(5.91-1)12.638.112=4814357.732cm4(四)截面抗弯模量W0下=I0/y0上=4814357.732/46.63=103245.93cm3W0上=I0/y0下=4814357.732/42.37=113626.57cm3预加应力阶段净截面几何特性计算:假设砼达到R30时张拉Ah=4688.28 cm2 重心距板顶距离y=47.13cm对板顶边的面积矩S1= Ahy=4688.2847.13= 220959cm3自身惯性矩I1=4723333.21cm4预留管道面积A0=-1652/4=-314cm2 重心距板顶距离y=90-4.26=85.74cm对板顶边的面积矩S0= A0y=-31485.74= -26922.36cm3混凝土净截面对板顶边的面积矩Si=220959-26922.36=194037 cm3混凝土净截面Aj=Ah- A0=4688.28-314=4374.28cm2yjs=Si/Aj=194037/4374.28=44.36cm净截面惯性矩Ij= Ii+Ix= Ii+Ai(ys-yi)2=4723333.21+4688.28(44.36-47.13)2-314(44.36-85.74)2=4221642.33cm4Ws=Ij/ ys=4221642.33/44.36=95167.77cm3Wx=Ij/ yx=4221642.33/45.64=92498.74cm3Wy=Ij/ ey=4221642.33/37.82=111624.60cm3五、截面强度验算以跨中正截面强度验算为例顶板平均宽:bi=A/ hi=(9389)/2*7+(89+93.2)/2*3/11=82.8cm (详见图1-2)顶板厚为:hi=11cm由RYAY=186022.4=41664Rabihi=2382.811=20948.4RYAY Rabihi故说明部分腹板砼参加工作。由RYAY=Rabx+Ra(bi-b)hi(近似矩形)x=RYAYRa(bi-b)hi/ Rab=186022.423(82.87210)11/23(7210)=44.362196.89kN.m 符合要求式中c表示砼安全系数,按“公预规”取用1.25六、预应力损失计算 按公路桥规规定采用k=0.75Ryb=0.751860=1395Mpa(一)预应力钢束与管道之间摩擦引起的预应力损失按“公预规”规定计算s1=k1-e-(+kx)=0.75Ryb 1-e-(0.550.07+0。001512。93)= 78.47Mpa(二)锚具变形、钢铰线回缩引起的应力损失s2=L/LEy=1.22.0105/2394=100.25Mpa式中L表示钢筋回缩值取用6*2=12mmL表示预应力钢筋有效长度Ey=2.0105Mpa(三)分批张拉时砼弹性压缩引起的应力损失s4=(m-1)/2mnyh1h1=Ny/Aj+Nyey2/IjNy=(ks1s2)Ay=(139578.48100.25)12.6=15325kNh1=15325103/4374.28102+15325 10337.822/4221642.33104=35.55 Mpas4=(m-1)/2mnyh1=(16-1)/(216)5.7615.46=95.99Mpah1表示全部筋束的合力Ny在其作用点处所产生的混凝土正应力Ny表示筋束的预加力的合力Aj、Ij混凝土梁的净截面面积和净截面惯性矩(四)钢筋松驰引起的预应力损失s5=0.022k=0.0221395=30.96 Mpa(五)砼收缩徐变损失按“公预规”附录九计算s6=0.9nyh(t,)+Ey(t,)/(1+15A)s6表示全部受力钢筋截面重心点处的预应力损失值h表示后张法构件放松钢筋时,在计算截面上全部受力钢筋重力处由预加力(扣除相应阶段应力损失),产生的砼法向应力表示配筋率=(Ag+Ay)/AA=1+eA2/r2eA表示全部预应力筋与非预应力筋换算截面重心点到构件截面重心轴的距离取eA=ey(t,)表示加载龄期为时砼的徐变系数终值,相对湿度为75%,=28天查得=2.2(t,)表示自龄期为时开始计算的收缩徐变终值取用0.23。代入计算得:=(Ag+Ay)/A=22.4/4798.26=0.47%r2=I/A=4723333.21/4798.26 r=31.37A=1+eA2/r2=1+(37.82/31.37)2=2.45s6=0.9(5.7614.062.22.01050.23103)/(1150.47%2.45)=172.04Mpa(六)永存预应力第一批应力损失(预加应力阶段):s=s1+s2+s4=78.47+100.25+95.99=274.71Mpa第二批应力损失(使用荷载作用阶段):s=s5+s6=30.96 +172.04=203Mpas=s+s=274.71+203=477.71Mpa永存预应力y=1395-477.71=917.29Mpa七、跨中截面应力验算(一)施工阶段正应力验算1、跨中截面正应力 施工阶段构件在预期应力和自重作用下截面上下缘砼正应力验算应力限值:混凝土标号R为40号,张拉时R=0.8R为32号,由附表1-2内插得:Rba=22.4Mpa ; Rbl=2.20Mpa ha=0.70 Rba=0.722.4=15.68 Mpa hl=0.70 Rbl=0.72.2=1.54 MpaNy=(Ay + AyW.cos)(k-s) +(,k-,s) A,y =(1395-274.71)1260=1411.57kNhs= Ny/Aj-Nyeyj/Wjs+Mg1/Wjs=1411.57103/4374.281021411.57103378.2/95167.77103472.12106/95167.77103=2.58Mpa0运输、安装阶段正应力计算Ny=(k-s)Ay=(1395-477.71)12.6=11557.85kNMg1=472.121.2=566.54kN.mhs= Ny/Aj-Nyey/Wjs+Mg1/Wjs=1411.57103/4374.28102-1411.57103378.2/95167.77103+566.54106/95167.77103=3.57 Mpa 02、使用阶段正应力验算Ny=k-s-s(Ay+Aywcos)+( k-s-s)Ay =917.291260=1155.79kN对荷载组合:hs=Ny/Aj+( Mg1 Nyeyj)/Wjs +(Mg2+Mp)/Wos=1155.79103/(4374.28102)+(472.121061155.79103378.2)/(95167.77103)+(472.12+453.47)102/(116073.26103) =3.02Mpa0对荷载组合:Mg2+Mp=1051.11kM.mhs=Ny/Aj+( Mg1 Nyeyj)/Wjs +(Mg2+Mp)/Wos=1155.79103/(4374.28102)+(472.121061155.79103378.2)/(95167.77103)+ 1051.11102/(116073.26103) =3.01Mpa0(二)预应力钢筋最大应力荷载组合:ymax=y+ny(Mg2+ Mp )y0y/I0=(1395-477.7)6.33925.59106378.2/4884362.675104=962.66Mpa0.65Rby=1209Mpa荷载组合:ymax=y+ny(Mg2+ Mp )y0y/I0=(1395412.36)6.331051.11106378.2/4884362.675104=968.81Mpa0.70Rby=1302Mpa八、支点截面主应力验算:换算截面重心处的主应力净距:S0,=9942.1742.17/2+(6.33-1)2.838.55-2508.68(7.3-3.63-0.7+7.64)-236(7.3-3.63-0.7+7.64)2/2=73759.51cm4S0=9942.542.5/2+(5.75-1)2.838.88-2508.68(7.3-3.63-0.7+7.64)-236(7.3-3.63-0.7+7.64)2/2=80052.905cm4b=210+7=27cm对荷载组合:=Qg1s0,/bI0,+(Qg2+Qq)s0/bI0=91.1873759.51/274749000.51+(30.19+155.36)80052.91/274747534.51=0.17Mpa对荷载组合:=Qg1s0,/bI0,+(Qg2+Qq)s0/bI0=0.19Mpa换算截面重心处砼的应力:h=y1 Ay/ A0,-y1Ay/ A0=21582.1216.8102/4778.82+16.8168.9106/4748534.51103=5.1Mpa对荷载组合:主拉应力:z1=h /2-(h2 /4+2)1/2=5.09/2-(5.092/4+0.172) 1/2=-0.006Mpa0.9R1b=0.92.6=2.34Mpaza=h /2+(h2 /4+2)1/2=5.09/2+(5.092/4+0.172) 1/2= 5.10Mpa 0.6Rab对荷载组合:z1=h /2-(h2 /4+2)1/2=5.09/2-(5.092/4+0.192) 1/2=-0.007Mpa0.9R1b=0.92.6=2.34Mpaza=h /2+(h2 /4+2)1/2=5.09/2+(5.092/4+0.192) 1/2= 4.1Mpa za= 4.24Mpa九、预应力阶段支点截面上缘拉应力验算:后张法预应力梁中,梁端一区段长度内为集中区。考虑到应力集中长度的不确切必放松预应力钢筋时的冲击及支点可能不在设计位置等原因,验算支点附近上缘拉应力时偏安全考虑,不计板的自重对上缘拉应力的卸载作用且预应力采用最大值(即放松预应力力钢筋时的应力)。ymax,=k-s1=1395-174.625=1220.375Mpa则上缘拉应力:hs=ymax,Ay/A0,-ymax,Ayey,/Wos,=1220.37516.8/4778.82-1220.37516.838.85/99289.55=-3.67Mpa在砼强度达到设计强度80%以上放松预应力筋,这时强度相当于30号砼强度即R1b,=2.1Mpa。按“公期规”第5.3.4条规定拉应力的限值为:h10.70R1b,=0.72.1=1.47Mpa张拉区不配非预应力钢筋时:h1=1.15R1b,= 1.152.1=2.4Mpa可见h1s1b,现拟定支座附近公有两根预应力钢筋作用于截面上,而其他8根在支座附近使用套管,使它与砼不粘结,则使支点截面附近。则:Ay=2140=2802预应力Ny=ymax,Ay=1220.3752.8=3417.05KN砼的应力为:hs=Ny/ A0,-Nyey,/ Wos,=3417.05/4778.82-3417.0538.55/99289.55=-0.61Mpah1= 0.72.1=1.47Mpahx=Ny/ A0,-Nyey,/ Wox,=3417.05/4778.82-3417.0538.55/112616.06=-0.46Mpah1套管长度:2号钢筋端部套管长度为:2.00m;3号钢筋端部套管长度为:1.50m;4号钢筋端部套管长度为:1.00m;5号钢筋端部套管长度为:0.50m。十、钢筋配筋图(详见图纸):第部分 钻孔灌注桩、双柱式桥墩的计算一、 设计资料1设计标准及上部结构 设计荷载:汽-20,挂-100; 桥面净宽:9+20.5m 标准跨径:16m 计算跨径:15.56m 梁长15.96m; 上部构造:钢筋混凝土空心板梁。2 水文地质条件(本设计为假设条件) 冲刷深度:最大冲刷线为河床线下2.0m处; 地质条件:亚粘土; 按无横桥向的水平力(漂流物、冲击力、水压力等)计算。3 材料: 钢筋:盖梁主筋用级钢筋,其它均用级钢筋; 混凝土:盖梁用C25,墩柱、系梁及钻孔桩用C20。4 计算方法:容许应力法。5 桥墩尺寸:考虑原有标准图,选用如图2-1所示结构尺寸。6设计依据:结构设计原理叶见曙主编,人民交通出版社桥梁计算示例集(梁桥)易建国主编,人民交通出版社桥梁工程(1985)姚玲森主编,人民交通出版社公路桥涵标准图公路桥涵标准图编制组,人民交通出版社公路桥涵设计规范(合订本)(JTJ021-85)人民交通出版社公路砖石及混凝土桥涵设计规范(JTJ022-85)二、盖梁计算(一)荷载计算:1、上部构造恒载见表21及图21表21 自重一孔上部结构自重每一支座恒载反力(KN)单片11.7212285.61142.8全部15.63042.01521.02、盖梁的自重及内力计算:(如图22及表22) 盖梁自重及产生的弯矩、剪力计算表22编号自 重(K N)弯 矩(KNM)剪 力Q左Q右11q1=1/2(0.8+1.2)11.425=35M1=-0.81.21.4251.2/2-1/20.41.21.4251.2/3= -23.52-35-3522q1=1.21.21.425=50.4M2=-0.81.21.4251.2/2-1/20.41.21.425(1.21/3+0.51.2)-1.21.21.4250.6= -58.8-50.414033q1=1.20.61.425=25.2M3=190.40.6-(50.4+25.2)1.8/2-0.81.21.425 2.4-1/20.41.21.425(1.2/3+1.8)=-52.9279.879.844q1=1.21.91.425=79.8M4=190.42.5-(50.4+25.2+79.8)3.7/2-0.81.21.425 4.3-1/20.41.2251.4(1.2/3+3.7)=9.5900q1+q2+q3+q4+q5 =190.4KN3、活载计算:(1)荷载横向分布系数,荷载的对称和对称布置一律采用杠杆法计算。 汽201) 双列车对称布置如图2-3 3,=9=35/801/2=0.2194=8=45/801/2=0.2815,=7=55/801/2=0.3446,=6=25/801/2=0.156其他=02)双列车非对称布置如图2-4。1=-10/801/21/2=-0.03152=2,=90/801/21/2=0.28153=-0.0631/2=-0.03153,=10/801/2=0.0634=70/801/2=0.4385,=1/21=0.57=1/21=0.5其他=03)挂100对称布置如图2-54,=8=25/801/4=0.0785 =7,=55/801/4=0.1725,=7=35/801/4=0.1096 =6,=45/801/4=0.141其他=04)挂100非对称布置如图2-62,=40/801/4=0.1253=40/801/4=0.1253,=50/801/4=0.1564=30/801/4=0.0944,=60/801/4=0.18755=20/801/4=0.06255,=70/801/4=0.2196=10/801/4=0.03125其他=05)三列车布置情况对称与非对称情况相同如图2-71=11=-10/801/21/2=-0.03152=10,=90/801/21/2=0.28153,=9=10/801/2=0.0634=8,=70/801/2=0.4385,=7=0.5其他=0(2)按顺桥方向活载移动情况,求得支座活载反力的最大值 汽20考虑到支点外布置荷载,并以车轮顺桥向着地宽度边缘为限(0.2m),布载长度L为:L=15.56+0.25-0.10=15.71m1) 单孔荷载(图28)单列车:取三种情况中最大值B2=120(1.010+0.920)+600.663=271.38KNB2,=601.010+120(0.753+0.663)+700.02=231.92KNB2,=1301.010+700.753+120(0.11+0.02)=199.61KN取用B2=271.38KN 当为二列车时则:2B2=2271.38=542.76KN当为三列车时:3B2=3271.38=814.14KN2)双孔荷载(图29)单列车时:B1=600.663+1200.920=150.18KNB2=1201.010+700.367+1300.02=149.49KNB1+B2=150.18+149.49=299.67KN三列车时:3(B1+B2)=3299.67=899.01KN 挂100:布载长度L=15.71m1)单孔布载(图210) 图210B2=250(1.010+0.933+0.676+0.599)=809.5KN2)双孔荷载时(按两种方式布载,取最大值)(图211)图211B1=2500.933=233.25KNB2=250(1.010+0.7528+0.6757)=609.63KNB1,= B2,=250(0.8043+0.8814)=421.43KN两种布载方式(B1 + B2)之和基本相等,(B1 + B2)=842.85KN表23荷载横向分布情况汽-20荷载(KN)挂-100荷载(KN)荷载布置横向分布系数i单 孔双 孔单 孔双 孔BR1BR1BR1BR1汽-20双列对称3,=9=0.219542.76118.86599.34131.264=8,=0.281152.52168.415,=7=0.344186.71206.176,=6=0.15684.6793.50其他i=000汽-20双列非对称1=3=-0.0315542.76-17.1599.34-18.882=2,=0.2815152.79168.713,=0.06334.1937.764=0.438237.73262.515,=0.5271.38299.677=0.5271.38299.67其他i=000汽-20三列布置1=11=-0.0315814.14-25.65899.01-28.322=10,=0.2815229.18253.072=10,=0.2815229.18253.073,=9=0.06351.2956.644=8,=0.438356.59393.775,=7=0.5407.07449.50其他i=000挂-100非对称布置2,=3=0.125809.5101.19842.85105.363,=0.156126.28131.484=0.09476.0979.234,=0.1875151.78158.035=0.062550.5952.685,=0.219177.28184.586=0.0312525.326.34其他=000挂-100对称布置4,=8=0.078809.563.14842.8565.745 =7,=0.172139.234144.975,=7=0.10988.2491.876 =6,=0.141114.14118.84其他i=000(3)活栽横向分布后各梁支点反力(计算的一般公式Ri = BI )见表23(4)各梁恒载、活载反力组合:计算见表24(设计计算书第52页),表中均取用各梁的最大值。其中冲击系数为:1+=1+0.3(45-31.12/45)=1.093影响长度按双孔计,即为215.56=31.12m,且表中汽车荷载项已计入冲击系数值。4、双柱反力Gi计算如图211,所引起的各梁反力见表25,由表25可知,偏载左边的立柱反力最大(即G1G2),并由荷载组合9时(汽20双列非对称组合)控制设计,此时G1=2228.20KN,G2=2053.71KN。(二)内力计算1、恒载加活载作用下各截面的内力(1)弯矩计算(图211)截面位置见图示,为求得最大弯矩值支点负弯矩取用非对称布置数值。按(图211)给出截面位置,各弯矩值计算式为:M-=-R10.9-R20.1M-=-R11.5-R20.7-R20.5M-=-R10.2-R21.2-R2,1.0+G10.5-R30.2M-=-R14.9-R24.1-R2,3.9-R3,2.9-R42.1-R4,1.9-R51.1-R5,0.9-R60.1+G13.4双柱反力Gi计算表25荷载组合情 况计 算 式反力Gi(KN)组合7汽20双列对称布置1/5.0(186.136.9+186.136.1+186.135.9+186.135.1+288.274.9+186.134.1+311.163.9+242.833.1+242.832.3+311.162.1+186.
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