16米空心板橋設(shè)計(jì)計(jì)算書

第I部分上部結(jié)構(gòu)I、設(shè)計(jì)資料一、設(shè)計(jì)標(biāo)準(zhǔn)及材料標(biāo)準(zhǔn)跨徑：16m計(jì)算跨徑：15.56m橋面凈寬：9+2x0.5m設(shè)計(jì)荷載：汽一20,掛一100材料：預(yù)應(yīng)力鋼筋：①15.24（705.0）鋼鉸線，后張法施工。非預(yù)應(yīng)力鋼筋：1鋼筋和II級螺紋鋼筋混凝土：空心板為R號,空心板鉸逢為R號；橋面鋪裝為4030R號瀝青砼；欄桿、人行道采用R號砼;3030二、構(gòu)造與尺寸圖1-1橋梁橫斷面（尺寸單位：cm）

lH18Id6L廠圖lH18Id6L廠圖1-2面構(gòu)造及尺寸（尺單位：cm）三、設(shè)計(jì)依據(jù)與參考書《結(jié)構(gòu)設(shè)計(jì)原理》葉見曙主編，人民交通出版社《橋梁計(jì)算示例集》（梁橋）易建國主編，人民交通出版社《橋梁工程》（1985）姚玲森主編，人民交通出版社《公路橋涵標(biāo)準(zhǔn)圖》公路橋涵標(biāo)準(zhǔn)圖編制組，人民交通出版社《公路橋涵設(shè)計(jì)規(guī)范（合訂本）》（JTJ021-85）人民交通出版社《公路磚石及混凝土橋涵設(shè)計(jì)規(guī)范》（JTJ022-85）II、上部結(jié)構(gòu)的設(shè)計(jì)過程一、毛截面面積計(jì)算(詳見圖1-2)A=99X9O—30x63—nx31.52—(3x3+7x7+12x7)h=4688.28cm2(一)毛截面重心位置全截面靜距：對稱部分抵消，除去下部3cm后1/2板高靜距S=2[5x7/2(2/3x7+14.5+14)+3x8x(21+14.5+8/2)+2x8/2(14.5+21+8/3)]+99x3x(43.5+3/2)=3667.5+13365=17032.5cm3鉸面積：A=2x(1/2x7x5+1/2x2x8+3x8)=99cm2鉸毛面積的重心及位置為：d=17032.5/4688.28=3.63cm(向下)h則重心距下邊緣的距離為：14+18+14.5—3.63=42.87cm距上邊緣距離為：90—42.87=47.13cm鉸重心對除去下部3cm后1/2板高的距離：d=3667.5/99=37.05cm鉸圖1-3(二)毛截面對重心的慣距圖1-3每個(gè)挖空半圓(圖1-3)面積：A，=1/2xnxR2=1/2x3.14x182=508.68cm2重心：y=4R/(3xn)=4x18/(3x3.14)=7.64cm半圓對自身慣距：I=I~Afy2=3.14x184/8—508.68X7.642I-I=41203.08—29691.45=11511.63cm4由此可得：I=99x903/12+99x90x3.632—2[36X293/12+36X29Xh3.632]—4x11511.63—2x508.68x[(7.64+29/2+3.63)2+(7.64+29/2—3.63)2]—2(1/12x83X3+1/36x2x83+1X5X73/36)—99x(37.05+3.63)2=4723333.21cm4二、內(nèi)力計(jì)算(一)、永久荷載(恒載)作用下1.橋面系安全帶、欄桿：單側(cè)為6.25kN/m橋面鋪裝：2x(0.06+0.15)/2x4.5x23=21.74kN/mg=(6.25x2+21.74)/10=3.43kN/m鉸和接縫：g=(99+1x90)x10-4x24=0.45kN/m2行車道板：g=4688.28x10-4x25=11.72kN/m3恒載總重力：g=g+g+g=3.43+0.45+11.72=15.6kN/m123恒載內(nèi)力計(jì)算見表1-1。表1-L(m)M(kN*m)Q(kN)g(kN/m)跨中1/8gL21/4點(diǎn)3/32gL2Q支1/2gLQ1/4點(diǎn)1/4gL11.7215.56354.7266.0291.1845.5915.6015.56472.12354.09121.3760.68荷載單塊板重全部恒載二）、基本可變荷載（活載）作用下1.荷載橫向分布系數(shù)跨中和四分點(diǎn)的橫向分布系數(shù)按鉸接板法計(jì)算。支點(diǎn)按杠桿法計(jì)算荷載橫向分布系數(shù)；支點(diǎn)到四分點(diǎn)間按直線內(nèi)插求得。(1)跨中和四分點(diǎn)的荷載橫向分布系數(shù)：剛度系數(shù)r=n2EI/(4Gt)?(b/l)2=5.8I/片(b/l)2式中I=I=4723333.21crm；b=100cm；L=24.34x100cmhIT――板截面的抵抗扭剛度。圖1-2所示截住面簡化成圖1-4。(略去中間肋板)I=4b2h2/[b(1/t+1/t)+2h/t]=4x892x(90—11/2—7)2/[89xT123(1/11+1/14)+2(90—11/2—7)/10]=6354404.131cm4r=5.8xIb2/Il2=5.8x4723333.21x1002/6354404.131x24342=0.0073圖1-4尺寸單位：cm按r查《橋梁工程》(1985)附錄I之附表的各板的橫向分布影響線豎坐標(biāo)值，見表1-2。說明：1、表中值為小數(shù)點(diǎn)后三位有效數(shù)字。2、表中I，J分別為板號與荷載作用的板號。

10.001001001001001001001001001001000.011811581311100930800700630580560.007315914212310709508507807306906820.001001001001001001001001001001000.011581541371140970830730650600580.007314213912711009808808007407106930.001001001001001001001001001001000.011311371371231040900780700650430.007312312712711710309308407807405840.001001001001001001001001001001000.011101141231271161000870780730700.007310711011712011210009108408007850.001001001001001001001001001001000.010930971041161231141000900830800.0073095098103112117110100093088085根據(jù)所求得數(shù)值作影響線：（如圖1-5）根據(jù)各板影響線，在其上加載求得各種荷載作用下的橫向分布系數(shù)如下：m=i/2Snm=i/2Snm=i/4Sn掛車荷載作用下板號1：三行汽車m3汽=1/2(0.151+0.118+0.100+0.082+0.075+0.069)=0.298二行汽車：m2汽=1/2(0-144+0-111+0-095+0-079)=0-215掛—100m=1/4(0.142+0.125+0.110+0.099)=0.1192掛板號2：三行汽車：m=1/2(0.141+0.115+0.100+0.085+0.076+0.070)=0.2943汽二行汽車：m=1/2(0.139+0.115+0.098+0.082)=0.2172汽掛—100m=1/4(0.139+0.128+0.113+0.102)=0.1212掛板號3：三行汽車：m=1/2(0.125+0.124+0.109+0.089+0.080+0.066)=0.2973汽二行汽車：m=1/2(0.127+0.120+0.103+0.086)=0.2182汽掛—100m=1/4(0.127+0.127+0.119+0.107)=0.1202掛板號4：三行汽車：m=1/2(0.109+0.118+0.115+0.096+0.086+0.079)=0.3023汽二行汽車：m=1/2(0.110+0.119+0.112+0.093)=0.2172汽掛—100m=1/4(0.111+0.117+0.120+0.113)=0.1152掛板號5：三行汽車：m=1/2(0.097+0.106+0.115+0.106+0.095+0.087)=0.3033汽二行汽車：m=1/2(0.098+0.109+0.117+0.102)=0.2132汽掛—100m=1/4(0.105+0.113+0.117+0.111)=0.1122掛⑵支點(diǎn)、支點(diǎn)到四分點(diǎn)的荷載橫向分布系數(shù)按杠桿法計(jì)算(圖1-6)支點(diǎn)荷載橫向分布系數(shù)求得如下:0909cC0.90909cC0.9■2500.9■250(250“2”2501.0圖1-6:支點(diǎn)荷載分布影響線掛-20汽-20m=m=1/2x1.00=0.5003汽2汽m=1/4(1.00+0.10+0.10)=0.3002掛支點(diǎn)到四分點(diǎn)的荷載橫向分布系數(shù)按直線內(nèi)插進(jìn)行。橫向分布系數(shù)匯總于表1-3。表1-3何載跨中到四分點(diǎn)支點(diǎn)三行汽-20m=0.3033汽0.500二行汽-20m=0.2182汽0.500掛-100M=0.1212掛0.3002、活載內(nèi)力計(jì)算⑴彎矩汽-20產(chǎn)生的彎矩M=(1+p)?g?工m?P?y汽車iii式中：(1+p)為沖擊系數(shù),(1+p)=1+0.3(45-24.34)/40=1.155g為折減系數(shù)三列車取0.8,兩列車取1.0作荷載橫向分布系數(shù)沿橋跨方向的變化圖形和跨中及1/4點(diǎn)的彎矩影響線(見圖1-7)

1.4.0]11.225(2502502504.01.41025(2501.24.02502501.2I4.0605000.65004.b跨中彎矩影響線0.5160「1201207013040.4331點(diǎn)彎矩影響線三行汽-203汽25(2501.24.02502501.2I4.0605000.65004.b跨中彎矩影響線0.5160「1201207013040.4331點(diǎn)彎矩影響線三行汽-203汽圖廠__Q.-403__0.2180.403.-n243030.433二行汽-20的圖0.50.H0.3圖1-7跨中彎矩的計(jì)算：M=1.155X0.8X(60X4.085+120X6.085+120X5.385)X3汽0.303=453.47kN.mM2汽=1.155X1.0X(60X4.085＋120X6.085＋120X5.385)X0.218=408.28kN.mM=1.0X250X(3.485＋4.085＋6.085＋5.485)X0.121掛=578.99kN.m1/4點(diǎn)彎矩的計(jì)算：M=1.155X0.8X(60X1.564X0.433＋120X4.564X0.303+120X3汽4.214X0.303+70X1.714X0.303＋130X0.714X0.433)=403.18kN.mM2汽=1-155X10X(60X1564X0-403+120X4564X0-218+120X4.214X0.218+70X1.714X0.218＋130X0.714X0.403)

=382.32kN.mM=1.0x(3.664x0.156+4.564x0.121+3.564x0.121+3.264x掛0.121)X250=487.50kN.m(2)、剪力計(jì)算跨中剪力近似按同一個(gè)跨中荷載橫向分布系數(shù)計(jì)算見圖1-85025012圖1-8跨中剪力影響線0.5(1+P)?g5025012圖1-8跨中剪力影響線0.5(1+P)?g?工m?P?yiiiQ=3汽車=1.155X0.8X(120X0.5+120X0.443+60X0.278)X0.303=36.35kNQ=(1+p)?g?工m?P?y2汽車iii=1.155X1.0X(120X0.5+120X0.443+60X0.278)X0.218=32.69kNQ=1.0X(250X0.5X0.121+250X0.451X0.121+250X0.286X掛0.121+250X0.141X0.130)=42.03kN支點(diǎn)剪力：剪力影響線及橫向分布系數(shù)見圖1-9

12J40121-T-——"10.265014711r1.414.010.121151120J120*60-__nQMQ￥130■10.4550.3250.373圖1-9支點(diǎn)剪力影響線0.30.52502500.7860.7780.9510.9430.737_一_0.162■-_L——一一—250250Q=(0.7860.7780.9510.9430.737_一_0.162■-_L——一一—250250支汽iii=1.155X1.0x(0.5X120X1.0+0.455x120x0.943+0.325x60X0.778+0.373X130X0.162)=155.36kNQ=1.0X(0.3X250X1.0+0.265X250X0.951+0.147X250X支掛0.786+0.121X250X0.737)=189.18kN1/4點(diǎn)剪力：一一一—0.75———0.6930.536_———-0.5280.4870.5,0.3035—0.5,0.3035—_——_?5m掛圖圖1-100.3|——II-0.3m汽圖0.1210.121Q=(1+p)?g?工m?P?y汽iii=1.155X1.0X(0.303X120X0.75+0.303X120X0.693+0.303X60X0.528)=71.69kNQ=1.0X(0.121X250X0.75+0.121X250X0.701+0.121X250掛

X0.536+0.121X250X0.487)=74.84kN（3）內(nèi)力組合內(nèi)力組合按“公預(yù)規(guī)第4.1.2”條規(guī)定進(jìn)行，恒載產(chǎn)生的效應(yīng)與活載產(chǎn)生的效應(yīng)同號時(shí)：則荷載組合IS=1.2S+1.4SGQ荷載組合IIIS=1.2S+1.1S荷載組合IIIS=1.2S+1.1SGQ式中：S一，恒載重力產(chǎn)生效應(yīng)G序號荷載類型彎矩(kN.m)剪力（kN)跨中1/4處支點(diǎn)跨中1/4L點(diǎn)1恒載472.12354.09121.37060.682汽-20453474031815536363571693掛-1005789948750189184203748441.2X恒載566.544424.908145.644072.816514X汽-20634.858564.452217.50450.89100.366611X掛-100636.889536.25208.09846.23382.3247S=4+51201.402989.36363.14850.89173.1828S中=4+61203.433961.158353.74246.233155.149III(2)/(1)+(2)49535610054S.提高（％）3000010I⑶/⑴+⑶55586110055S帀提高（％）2233211III提高后ST1237.44989.36363.1550.89173.1812I提高后S—1227.50980.38364.35547.62158.241控制設(shè)計(jì)內(nèi)力1237.44989.36364.3550.89173.18表中提高系數(shù)詳見《結(jié)構(gòu)設(shè)計(jì)原理》荷載效應(yīng)組合三、預(yù)應(yīng)力鋼筋的設(shè)計(jì)（一）、預(yù)應(yīng)力鋼筋截面積的估算根據(jù)橋預(yù)規(guī)定,預(yù)應(yīng)力梁應(yīng)滿足使用階段應(yīng)力要求和承載力極限狀態(tài)的強(qiáng)度條件。故按承載力極限狀態(tài)來估算，這時(shí)預(yù)應(yīng)力鋼筋達(dá)到

抗拉設(shè)計(jì)強(qiáng)度，砼達(dá)到抗壓設(shè)計(jì)強(qiáng)度。后張法預(yù)應(yīng)力砼空心板可以近似地簡化。按下列公式來估算預(yù)應(yīng)力鋼筋面積：A=yM/ahRycjyN=yM/ah(a取設(shè)計(jì)經(jīng)驗(yàn)值為0.76)ycj則N=1.25x1237.44/0.76x0.9=2261.40kNy選用直徑為015.24(705.0)鋼鉸線，且采用后張法施工。n=N/R.a=2261.40x103/1860x140=8.68束yyy按施工和使用階段估算，鋼束數(shù)也為9束左右，選定鋼束數(shù)n=9束A=9x1.40=12.6cm2y、預(yù)應(yīng)力鋼筋布置J15X6Al19953一C圖1-11(尺寸單位：cm)后張法預(yù)應(yīng)力鋼筋的布置按“公預(yù)規(guī)”的要求，取預(yù)應(yīng)力鋼束凈距保護(hù)層為3.5cm53一C圖1-11(尺寸單位：cm)a=3.5+1.52=4.26cm,9束鋼束在g板橫截面中呈不均勻分布，詳見圖1-11，預(yù)應(yīng)力鋼束沿板跨方向呈直線變化，即保持a=4.26cm不變。g四、凈截面和換算截面的幾何特性計(jì)算換算截面積A二A+(n-1)A=4688.28+(5.91-1)x12.6=4750.15cm40hy式中n—鋼筋彈性模量與砼彈性模量之比n=E/E=1.95x105/3.3x104=5.91yh換算截面的重心位置鋼筋換算截面對毛截面重心凈距S=(5.91-1)x12.6x(42.87-4.26)=2388.65cm3g換算截面對毛截面重心的距偏離：d=S/A=2388.65/4750.15=0.50cmh0g0換算截面重心到截面下緣距離：y=42.87-0.50=42.37cm0換算截面重心到截面上緣距離：y=47.13-0.50=46.63cm0鋼筋重心到換算截面重心距離：e=42.37-4.26=38.11cmy換算截面慣距I=I+Ad2+(n-1)Ae20hhh0yy=4723333.21+4688.28x0.502+(5.91-1)x12.6x38.112=4814357.732cm4截面抗彎模量W下=I/y上=4814357.732/46.63=103245.93cm3000W上=I/y下=4814357.732/42.37=113626.57cm3000預(yù)加應(yīng)力階段凈截面幾何特性計(jì)算：假設(shè)砼達(dá)到R30時(shí)張拉A=4688.28cm2重心距板頂距離y=47.13cmh對板頂邊的面積矩S=Axy=4688.28x47.13=220959cm31h自身慣性矩I=4723333.21cm4預(yù)留管道面積A=-16Xnx52/4=-314cm20重心距板頂距離y=90-4.26=85.74cm對板頂邊的面積矩S=Axy=-314x85.74=-26922.36cm300混凝土凈截面對板頂邊的面積矩工S=220959-26922.36=194037cm3i混凝土凈截面A=A-A=4688.28-314=4374.28cm2jh0y=ZS/A=194037/4374.28=44.36cmjsij凈截面慣性矩I=I+I=I+A(y-y)2jixiisi=4723333.21+4688.28x(44.36-47.13)2-314x(44.36-85.74)2=4221642.33cm4W=I/y=4221642.33/44.36=95167.77cm3sjsW=I/y=4221642.33/45.64=92498.74cm3xjxW=I/e=4221642.33/37.82=111624.60cm3yjy五、截面強(qiáng)度驗(yàn)算以跨中正截面強(qiáng)度驗(yàn)算為例頂板平均寬：b'=A/h'=[(93+89)/2*7+(89+93.2)/2*3]/11=82.8cmii(詳見圖1-2)頂板厚為：h'=11cmi由RA=1860x22.4=41664YYRb'h'=23x82.8x11=20948.4aiiRA>Rab'h'故說明部分腹板砼參加工作。YYii由RA=Rbx+R(b'-b)h'(近似矩形)Yaaiix=[RA－R(b'-b)h]/RbYaiia二[1860X22.4—23X(82.8—7—2X1O)X11]/23X(7+2X1O)=44.36<0.55h=47.51cm截面抵抗矩為：M=1/y[Rbx(h-x/2)+R(h'-b)(h-h'/2)h']dca0ai0ii=1/1.25[23X(7+2X10)X44.36X(85.74—44.36/2)+23X(82.8—7—2X10)X(85.74—11/2)X11]=2306.96kN.m>2196.89kN.m符合要求式中Y表示砼安全系數(shù)，按“公預(yù)規(guī)”取用1.25c六、預(yù)應(yīng)力損失計(jì)算按《公路橋規(guī)》規(guī)定采用o=0.75Rb=0.75x1860=1395Mpaky(一)預(yù)應(yīng)力鋼束與管道之間摩擦引起的預(yù)應(yīng)力損失按“公預(yù)規(guī)”規(guī)定計(jì)算o=o[1-e-(M0+kx)]=0.75Rbx[1-e-(0.55x0.07+0?0015x12?93)]=78.47Mpas1ky(二)錨具變形、鋼鉸線回縮引起的應(yīng)力損失o二工AL/LE=1.2X2.0x105/2394=100.25Mpas2y式中AL表示鋼筋回縮值取用6*2=12mmL表示預(yù)應(yīng)力鋼筋有效長度E=2.0x105Mpay分批張拉時(shí)砼彈性壓縮引起的應(yīng)力損失o=(m-1)/2m?n?o°s4yh1o°=N/A+Ne2/Ih1yjyyjN=(o―o―o)Ayks1s2y=(1395—78.48—100.25)x12.6=15325kNo°=15325x103/4374.28x102+15325h1x103x37.822/4221642.33x104=35.55Mpao=(m-1)/2mno°=(16-1)/(2x16)x5.76x15.46=95.99Mpas4yh1o°表示全部筋束的合力N在其作用點(diǎn)處所產(chǎn)生的混凝土正應(yīng)力h1yN表示筋束的預(yù)加力的合力yA、I混凝土梁的凈截面面積和凈截面慣性矩jj鋼筋松馳引起的預(yù)應(yīng)力損失o=0.022o=0.022x1395=30.96Mpas5k砼收縮徐變損失按“公預(yù)規(guī)”附錄九計(jì)算o=0.9x[no屮(t,t)+Ee(t,t)]/(1+15pp)s6yh8y00Ao表示全部受力鋼筋截面重心點(diǎn)處的預(yù)應(yīng)力損失值s6o表示后張法構(gòu)件放松鋼筋時(shí)，在計(jì)算截面上全部受力鋼筋重力處由h預(yù)加力(扣除相應(yīng)階段應(yīng)力損失)，產(chǎn)生的砼法向應(yīng)力M表示配筋率p=(A+A)/Agyp=1+e2/r2AAe表示全部預(yù)應(yīng)力筋與非預(yù)應(yīng)力筋換算截面重心點(diǎn)到構(gòu)件截面重心軸A的距離取e=eAye(t,t)表示加載齡期為T時(shí)砼的徐變系數(shù)終值，相對濕度為75%,■oot=28天查得e=2.2￡(t,T)表示自齡期為T時(shí)開始計(jì)算的收縮徐變終值取用0.23。oo代入計(jì)算得：M=(A+A)/A=22.4/4798.26=0.47%gyr2=I/A=4723333.21/4798.26r=31.37p=1+e2/r2=1+(37.82/31.37)2=2.45AAo=0.9x(5.76x14.06x2.2+2.0x105X0.23x10-3)/(1+15Xs60.47%x2.45)=172.04Mpa永存預(yù)應(yīng)力第一批應(yīng)力損失(預(yù)加應(yīng)力階段)：oi=o+o+oss1s2s4=78.47+100.25+95.99=274.71Mpa第二批應(yīng)力損失(使用荷載作用階段)：oii=o+o=30.96+172.04=203Mpass5s6o=oi+oi=274.71+203=477.71Mpasss永存預(yù)應(yīng)力o=1395-477.71=917.29Mpay七、跨中截面應(yīng)力驗(yàn)算(一)施工階段正應(yīng)力驗(yàn)算1、跨中截面正應(yīng)力①施工階段構(gòu)件在預(yù)期應(yīng)力和自重作用下截面上下緣砼正應(yīng)力驗(yàn)算應(yīng)力限值：混凝土標(biāo)號R為40號，張拉時(shí)R'=0.8R為32號，由附表1-2內(nèi)插得：Rb'=22.4Mpa；Rb'=2.20Mpaal[o]=0.70Rb'=0.7x22.4=15.68Mpahaa[o]=0.70Rb'=0.7x2.2=1.54MpahllN=(A+A.cosa)(o-oi)+(o,-o,i)A,yyyWksksy=(1395-274.71)x1260=1411.57kNo=N/A-Ne/W+M/Whsyjyyjjsg1js=1411.57X103/4374.28X102—1411.57x103x378.2/95167.77x103+472.12X106/95167.77x103=2.58Mpa<[o]=15.68Mpahao=N/A+Ne/W-M/Whxyjyyjjxg1jx=1411.57x103/4374.28x102+1411.57x103x378.2/92498.74x103-472.12x106/92498.74x103=3.76Mpa>0②運(yùn)輸、安裝階段正應(yīng)力計(jì)算N=(o-o)A=(1395-477.71)x12.6=11557.85kNyksyM=472.12x1.2=566.54kN.mg1o=N/A-Ne/W+M/Whsyjyyjsg1js=1411.57x103/4374.28x102-1411.57x103X378.2/95167.77X103+566.54x106/95167.77x103=3.57Mpa<[o]hao=N/A+Ne/W-M/Whxyjyyjxg1jx=1411.57x103/4374.28x102+1411.57x103x378.2/92498.74x103-566.54x106/92498.74x103=2.87Mpa>02、使用階段正應(yīng)力驗(yàn)算N=[o-oi-oii](A+A?cosa)+(o'-oi'-oii')A‘yllkssyywkssy=917.29x1260=1155.79kN對荷載組合I：o=N/A+(M—N?e)/W+(M+M)/Whsyijg1yiyjjsg2pos=1155.79x103/(4374.28x102)+(472.12x106—1155.79x103x378.2)/(95167.77X103)+(472.12+453.47)X102/(116073.26X103)=3.02Mpa<[o]=0.5Rb=14Mpahaao=N/A-(M-N?e)/W-(M+M)/Whxylljg1yllyjjxg2pox=1155.79X103/(4374.28X10"-(472.12X106—1155.79X103X/(92498.74X103)-(472.12+453.47)X102/(105630.68X103)=1.54Mpa>0對荷載組合III：M+M=1051.11kM.mg2po=N/A+(M-N?e)/W+(M+M)/Whsylljg1yllyjjsg2pos=1155.79X103/(4374.28X102)+(472.12X106—1155.79X103X/(95167.77X103)+1051.11X102/(116073.26X103)=3.01Mpa<[o]=0.5Rb=14Mpahaao=N/A-(M-N?e)/W-(M+M)/Whxylljg1yllyjjxg2pox=1155.79X103/(4374.28X102)-(472.12X106—1155.79X103X/(92498.74X103)-1051.11X102/(105630.68X103)=2.26Mpa>0(二)預(yù)應(yīng)力鋼筋最大應(yīng)力荷載組合I：o=on+n?(M+M)?y/Iymaxyyg2p0y0=(1395-477.7)＋6.33X925.59X106X378.2/4884362.675X104=962.66MpaV0.65Rb=1209Mpay荷載組合III：o=on+n?(M+M)?y/Iymaxyyg2p0y0=(1395-412.36)＋6.33X1051.11X106X378.2/4884362.675X104=968.81MpaV0.70Rb=1302Mpay八、支點(diǎn)截面主應(yīng)力驗(yàn)算：換算截面重心處的主應(yīng)力凈距：S,=99X42.17X42.17/2+(6.33T)X2.8X38.55-2X508.68X0(7.3-3.63-0.7+7.64)-2X36X(7.3-3.63-0.7+7.64)2/2=73759.51cm4S=99X42.5X42.5/2+(5.75-1)X2.8X38.88-2X508.680X(7.3-3.63-0.7+7.64)-2X36X(7.3-3.63-0.7+7.64)2/2=80052.905cm4b=2X10+7=27cm對荷載組合I：T=Qs,/bI,+(Q+Q)s/bIg100g2q00=91.18X73759.51/27X4749000.51+(30.19+155.36)X80052.91/27X4747534.51=0.17Mpa對荷載組合III：T=Qs,/bI,+(Q+Q)s/bIg100g2q00=0.19Mpa換算截面重心處砼的應(yīng)力：o=0?A/A,-△□?A/Ahy1y0y1y0=21582.12X16.8X102/4778.82+16.8X168.9X106/4748534.51X103=5.1Mpa對荷載組合I:主拉應(yīng)力：o=o/2-(o2/4+T2)1/2z1hh=5.09/2-(5.092/4+0.172)1/2=-0.006Mpa<0.9Rb=0.9X2.6=2.34Mpa1o=o/2+(o2/4+t2)1/2zahh=5.09/2+(5.092/4+0.172)1/2=5.10Mpa<0.6Rba對荷載組合III：o=o/2-(o2/4+t2)1/2z1hh=5.09/2-(5.092/4+0.192)1/2=-0.007Mpa〈0.9Rb=0.9X2.6=2.34Mpa1o=o/2+(o2/4+t2)1/2zahh=5.09/2+(5.092/4+0.192)1/2=4.1Mpa〈[o]=4.24Mpaza九、預(yù)應(yīng)力階段支點(diǎn)截面上緣拉應(yīng)力驗(yàn)算：后張法預(yù)應(yīng)力梁中，梁端一區(qū)段長度內(nèi)為集中區(qū)?？紤]到應(yīng)力集中長度的不確切必放松預(yù)應(yīng)力鋼筋時(shí)的沖擊及支點(diǎn)可能不在設(shè)計(jì)位置等原因，驗(yàn)算支點(diǎn)附近上緣拉應(yīng)力時(shí)偏安全考慮，不計(jì)板的自重對上緣拉應(yīng)力的卸載作用且預(yù)應(yīng)力采用最大值(即放松預(yù)應(yīng)力力鋼筋時(shí)的應(yīng)力)。o，=o-o=1395-174.625=1220.375Mpaymaxks1則上緣拉應(yīng)力：o=o,?A/A,-o,?Ae,/Wos,hsymaxy0ymaxyy=1220.375X16.8/4778.82-1220.375X16.8X38.85/99289.55=-3.67Mpa在砼強(qiáng)度達(dá)到設(shè)計(jì)強(qiáng)度80%以上放松預(yù)應(yīng)力筋,這時(shí)強(qiáng)度相當(dāng)于30號砼強(qiáng)度即Rb,=2.1Mpa。1按“公期規(guī)”第5.3.4條規(guī)定拉應(yīng)力的限值為：OV0.70Rb,=0.7X2.1=1.47MpaTOC\o"1-5"\h\zhl1張拉區(qū)不配非預(yù)應(yīng)力鋼筋時(shí)：O=1.15Rb,二1.15X2.1=2.4Mpahl1可見O〉O,現(xiàn)擬定支座附近公有兩根預(yù)應(yīng)力鋼筋作用于截面hlslb上,而其他8根在支座附近使用套管,使它與砼不粘結(jié),則使支點(diǎn)截面附近。貝Ij：A=2X140=280mm2y預(yù)應(yīng)力N=O,?A=1220.375X2.8=3417.05KNyymaxy砼的應(yīng)力為：O=N/A,-N?e,/Wos,hsy0yy=3417.05/4778.82-3417.05X38.55/99289.55=-0.61MpaV[o]=0.7X2.1=1.47Mpah1O=N/A,-N?e，/Wox,hxy0yy=3417.05/4778.82-3417.05X38.55/112616.06=-0.46MpaV[o]h1套管長度：號鋼筋端部套管長度為：2.00m；3號鋼筋端部套管長度為：1.50m；4號鋼筋端部套管長度為：1.00m；5號鋼筋端部套管長度為：0.50m。十、鋼筋配筋圖（詳見圖紙）：第II部分鉆孔灌注樁、雙柱式橋墩的計(jì)算一、設(shè)計(jì)資料1設(shè)計(jì)標(biāo)準(zhǔn)及上部結(jié)構(gòu)設(shè)計(jì)荷載：汽-20，掛-100；橋面凈寬：9+2x0.5m標(biāo)準(zhǔn)跨徑：16m計(jì)算跨徑：15.56m梁長15.96m；上部構(gòu)造：鋼筋混凝土空心板梁。水文地質(zhì)條件（本設(shè)計(jì)為假設(shè)條件）沖刷深度：最大沖刷線為河床線下2.0m處；地質(zhì)條件：亞粘土；按無橫橋向的水平力（漂流物、沖擊力、水壓力等）計(jì)算。材料：鋼筋：蓋梁主筋用II級鋼筋，其它均用I級鋼筋；混凝土：蓋梁用C25,墩柱、系梁及鉆孔樁用C20。計(jì)算方法：容許應(yīng)力法。橋墩尺寸：考慮原有標(biāo)準(zhǔn)圖，選用如圖2-1所示結(jié)構(gòu)尺寸。設(shè)計(jì)依據(jù)：《結(jié)構(gòu)設(shè)計(jì)原理》葉見曙主編，人民交通出版社《橋梁計(jì)算示例集》（梁橋）易建國主編，人民交通出版社《橋梁工程》（1985）姚玲森主編，人民交通出版社《公路橋涵標(biāo)準(zhǔn)圖》公路橋涵標(biāo)準(zhǔn)圖編制組，人民交通出版社《公路橋涵設(shè)計(jì)規(guī)范（合訂本）》（JTJ021-85）人民交通出版社《公路磚石及混凝土橋涵設(shè)計(jì)規(guī)范》（JTJ022-85）

二、蓋梁計(jì)算（一）荷載計(jì)算：1、上部構(gòu)造恒載見表2—1及圖2—1表2表2—1自重一孔上部結(jié)構(gòu)自重每一支座恒載反力（KN）單片11.7212285.61142.8全部15.63042.01521.02、蓋梁的自重及內(nèi)力計(jì)算：（如圖2—2及表2—2）蓋梁自重及產(chǎn)生的彎矩、剪力計(jì)算蓋梁自重及產(chǎn)生的彎矩、剪力計(jì)算表2—2編號重NN自(K彎矩(KN?M)剪力Q左Q右1—1q=l/2(0.8+l)2<lX141X25=35M=-0.8Xl.2X1.4X25X1.2/21-1/2X0.4X1.2X1.4X25X1.2/3=-23.52-35-352—2q=1.2X1.2X1.4X251=50.4M=-0.8X1.2X1.4X25X1.2/22-1/2X0.4X1.2X1.4X25(1.2X1/3+0.5X1.2)-1.2X1.2X1.4X25X0.6=-58.8-50.41403—3q=1.2X0.6X1.4X251=25.2M=190.4X0.6-(50.4+25.2)3X1.8/2-0.8X1.2X1.4X25X2.4-1/2X0.4X1.2X1.4X25X(1.2/3+1.8)=-52.9279.879.84—4q=1.2X1.9X1.4X251=79.8M=190.4X2.5-4(50.4+25.2+79.8)X3.7/2-0.8X1.2X1.4X25X4.3-1/2X0.4X1.2X25X1.4X(1.2/3+3.7)=9.5900q1+q2+q3+q4+q5=190.4KN3、活載計(jì)算：（1）荷載橫向分布系數(shù)，荷載的對稱和對稱布置一律采用杠桿法計(jì)算。①汽—201）雙列車對稱布置如圖2-3TOC\o"1-5"\h\zP/2P/2P/2180130180—122’33’44’55’66'7T88’99'1010’11n，二n=35/80X1/2=0.2199n=n=45/80X1/2=0.2818n，=n=55/80X1/2=0.3447n，=n=25/80X1/2=0.1566其他n=02）雙列車非對稱布置如圖2-4。P/2180P/2P/2130P/2P/2180P/2P/2130P/2180圖2-4n=-10/80X1/2X1/2=-0.03151n=n，=90/80X1/2X1/2=0.281522n=-0.063X1/2=-0.03153n，=10/80X1/2=0.0633n=70/80X1/2=0.4384n，=1/2X1=0.55n=1/2X1=0.57

其他n=03）掛—100對稱布置如圖2-5nnJ=n8=25/80X1/4=0.078n§=n7,=55/80X1/4=0.172n5,=n7=35/80X1/4=0.109n§=n6,=45/80X1/4=0.141其他n=04）掛一100非對稱布置如圖2-6n,=40/80X1/4=0.1252n=40/80X1/4=0.1253n,=50/80X1/4=0.1563n=30/80X1/4=0.0944n,=60/80X1/4=0.18754n=20/80X1/4=0.06255n,=70/80X1/4=0.2195n=10/80X1/4=0.031256其他n=05）三列車布置情況對稱與非對稱情況相同如圖2-7P/2180p/2130P/2180P/?130P/2180P/122'33'44'55'66'7788'99'1010'11圖2—7n=n=-10/80X1/2X1/2=-0.0315111n=n，=90/80X1/2X1/2=0.2815210n，=n=10/80X1/2=0.06339n=n，=70/80X1/2=0.43848n，=n=0.557其他n=0（2）按順橋方向活載移動情況，求得支座活載反力的最大值汽—20考慮到支點(diǎn)外布置荷載，并以車輪順橋向著地寬度邊緣為限（0.2m）,布載長度L為：L=15.56+0.25-0.10=15.71m1)單孔荷載(圖2—8)單列車：取三種情況中最大值B=120X(1.010+0.920)+60X0.663=271.38KN2B，=60X1.010+12X0(0.753+0.66)3+70X0.02=231.92KN2B，=130X1.010+7X00.753+12X0(0.11+0.0)2=199.61KN2取用B=271.38KN2

1307012012060-^4.^_10.0_4.06012012070130行車方向-■軋0口1012012060心1556!B11556B27、-000..601圖2^0當(dāng)為二列車時(shí)則：2B=2X271.38=542.76KN2當(dāng)為三列車時(shí)：3B=3X271.38=814.14KN22）雙孔荷載（圖2—9）單列車時(shí)：B=60X0.663+120X0.920=150.18KN1

B=120X1.010+70X0.367+130X0.02=149.49KN2B+B=150.18+149.49=299.67KN12三列車時(shí)：3(B+B)=3X299.67=899.01KN12掛—100：布載長度L=15.71m1)單孔布載(圖2—10)2502502502501.2葉1.2BB=250X（1.010+0.933+0.676+0.599）=809.5KN2）雙孔荷載時(shí)（按兩種方式布載，取最大值）（圖2—11）1-..1h2'f—I.-LL-Lu1-..1h2'f—I.-LL-Lu圖2—11B=250X0.933=233.25KN1B=250X(1.010+0.7528+0.6757)=609.63KN2

B,=B,=250X(0.8043+0.8814)=421.43KN12兩種布載方式(Bl+B2)之和基本相等，(Bl+B2)=842.85KN表2—3荷載橫向分布情況汽-20荷載（KN）掛-100荷載（KN）荷載布置橫向分布系數(shù)n單孔雙孔單孔雙孔BRBRBRBR汽-20雙列對稱n，=n=0.2191319542.76118.86599.34131.26n=n”,=0.281152.52168.41n”,=n”=0.344186.71206.17n，=n=0.15684.6793.50其他n=0i00汽-20雙列非對稱n=n=-0.0315542.76-17.1599.34-18.88n=n”，=0.2815152.79168.71n”，=0.06334.1937.76n=0.438237.73262.51n，=0.5271.38299.67n7=0.5271.38299.67其他n=000汽-20列布置n=n=-0.0315814.14-25.65899.01-28.32n=n，=0.2815229.18253.07n=n，=0.2815229.18253.07n”，=n”=0.06351.2956.64n=n，=0.438356.59393.77n，=n=0.5407.07449.50其他n=000掛n,，=n”=0.125101.19105.36-100非對稱布置n”,=0.156809.5126.28842.85131.48n=0.09476.0979.23n，=0.1875151.78158.03n=0.062550.5952.68n”,=0.219177.28184.58n”=0.0312525.326.34其他n=000掛-100對稱布置n=n”=0.078809.563.14842.8565.74n”=n”,=0.172139.234144.97n”,=n”=0.10988.2491.87n”=n”,=0.141114.14118.84其他ni=000（3）活栽橫向分布后各梁支點(diǎn)反力（計(jì)算的一般公式R=Bxn）見表2—3iI（4）各梁恒載、活載反力組合：計(jì)算見表2—4（設(shè)計(jì)計(jì)算書第52頁），表中均取用各梁的最大值。其中沖擊系數(shù)為：1+p=1+0.3X（45-31.12/45）=1.093影響長度按雙孔計(jì)，即為2X15.56=31.12m,且表中汽車荷載項(xiàng)已計(jì)入沖擊系數(shù)值。4、雙柱反力G計(jì)算如圖2—11，所引起的各梁反力見表2—5,i由表2—5可知，偏載左邊的立柱反力最大（即G2G）,并由荷載組12合9時(shí)（汽—20雙列非對稱組合）控制設(shè)計(jì)，此時(shí)G=2228.20KN，1G2=2053.71KN。（二）內(nèi)力計(jì)算1、恒載加活載作用下各截面的內(nèi)力（1）彎矩計(jì)算（圖2—11）截面位置見圖示，為求得最大彎矩值支點(diǎn)負(fù)彎矩取用非對稱布置數(shù)值。按（圖2—11）給出截面位置，各

彎矩值計(jì)算式為：M=-RX0.9—RX0.1TOC\o"1-5"\h\z-①12M=-RX1.5-RX0.7-RX0.5-②122M=-RX0.2-RX1.2-R，X1.0+G1X0.5-RX0.2-③1223M=-RX4.9-RX4.1-R，X3.9-R，X2.9-RX2.1-R，X1.9-R-④1223445X1.1-R，X0.9-RX0.1+G1X3.456R2鬥r3R|'R2鬥r3R|'R6J嚴(yán)’G1250孑250—11G2R1圖2-11雙柱反力G計(jì)算i表2一5荷載組合情況計(jì)算式反力G.i(KN)1/5.0X(186.13X6.9+186.13X6.1+186.13X5.9+186.13X5.1+288.27X組合74.9+186.13X4.1+311.16X3.9+242.83X3.1+242.83X2.3+311.16X汽一20雙列對稱布置2.1+186.13X1.3+186.13X1.1+186.13X0.3+265.73X0.1-186.13X1921.121.9T86.13X1.1-186.13X0.9T86.13X0.1)1/5.0X(174.66X6.9+288.45X6.1+288.45X5.9+174.68X5.1+209.03X組合84.9+345.327X4.1+186.13X3.9+186.13X3.1+367.87X2.3+186.13X汽—20雙歹啡對稱布置2.1+186.13X1.3+186.13X1.1+186.13X0.3+186.13X0.1+186.13X2228.201.3+186.13X0.5+186.13X0.3-186.13X1.6T86.13X0.8T86.13X0.6)1/5.0X(174.66X8.3+288.45X7.5+288.45X7.3+186.13X6.5+209.03X組合96.3+345.327X5.5+186.13X5.3+186.13X4.5+367.87X4.3+186.13X汽一20三列布置3.5+186.13X3.3+367.87X2.5+186.13X2.3+186.13X1.5+345.327X1925.821.3+209.03X0.5+186.13X0.3-174.68X1.6-288.45X0.8-288.45X0.6)組合101/5.0X(186.13X8.3+186.13X7.5+236.352X7.3+236.352X6.5+258.04X掛一100非對稱布6.3+214.66X5.5+280.08X5.3+240.79X4.5+302.12X4.3+170.76X2125.15

置3.5+186.13X3.3+186.13X2.5+186.13X2.3+186.13X1.5+186.13X1.3+186.13X0.5+186.13X0.3-186.13X1.6-186.13X0.8-186.13X0.6)組合11掛一100對稱布置186.13+186.13+186.13+186.13+186.13+186.13+203.47+269.23+225.16+247.542062.162各種荷載組合下各截面彎矩計(jì)算見表2—6。其中表內(nèi)計(jì)算未考慮施工荷載影響。各截面彎矩計(jì)算表2-6何載組合墩柱反力(KN)梁的反力(KN)各截面彎矩(KN*m)G1R1R2截面①-①截面②-②截面③-③截面④-④組合7汽一20雙列對稱布置1921.12778.1351061.39-661.41-1283.92-374.421046.03組合8汽20雙列非對稱布置2228.20713.6821134.4-606.63-1177.58-209.1241169組合9汽一20三列布置1925.821014.53754.2-862.35-1673.97-1014.4336.857組合10掛一100非對稱布置2125.15950.08867.2-807.568-567.32-829.348216.432組合11掛一100對稱布置2062.162478.34589.16-406.589-789.261-245.822631.782相應(yīng)于最大彎矩值的剪力計(jì)算。一般公式為截面①-①：Q=Q=-(R+R)左右12-②：Q=-(R+R+R)左123Q=G1-(R+R+R，+R)左1223-③：Q=G1-(R+R+R，+R)左1223Q=G1-(R+R+R，+R+R，)右12233

-④:Q=G1-(R+R+R,+R+R,+R+R,+R+R,+R)左1223344556Q左二Q右計(jì)算值見表2-7。各截面剪力計(jì)算表2-7墩柱反力G1各截面剪力荷載組合情況梁的反力截面①一①截面②一②截面③一③截面④一④截面⑤一⑤R1R2R3Q左Q右組合7汽一201921778.106111840-77-77-778-77816531653637.637.-547雙列對.1214.39.518.18.1.14.14.64.642525.26稱布置組合8-713.68-713.68汽一20雙2228713.1134120.0-713-71317601760626.626.-578列非對稱.2068.437.68.68.82.824242.95布置組合9-1014.53-1014.53汽一2019251014754.764.0-101-10111991199444.444.-319三列布.82.5320404.534.53.16.169696.44置組合10-950.08-950.08掛一1002125950.867.785.0-950-95013421342475.475.-310非對稱.15082026.08.08.33.331313.13布置組合11-478.41-478.41掛一1002062478.589.797.0-478-478988.988.398.398.-398對稱布.162341683.41.4107079191.92置1、蓋梁內(nèi)力匯總表（表2—8）表中各截面內(nèi)力均取表2—7、2—6中的最大值，按2—8表可控制內(nèi)力計(jì)算值的包絡(luò)圖。計(jì)算值詳見表2—8。（三）截面配筋設(shè)計(jì)及承載力校核采用C30號混凝土，主筋用不16錳鋼少25,保護(hù)層用5CM（混凝土邊緣至鋼筋中心的距離），查《橋規(guī)》P得到：139O=210kgf/cm,ow=210000kpa，o=200000kpagg1、彎矩作用時(shí)配筋計(jì)算：各截面所需鋼筋量，見表2—9，實(shí)際配筋見施工圖，對比可知：原有標(biāo)準(zhǔn)圖紙（灌注樁雙柱式橋墩，跨徑20M，汽一20,掛一100，凈9+2X0.5）的墩帽鋼筋用量是足夠的均大于計(jì)算值（參見《鋼筋混凝土結(jié)構(gòu)原理》P90）。2、剪力作用時(shí)配筋計(jì)算：各截面主拉應(yīng)力計(jì)算。在離梁懸臂部分變高度區(qū)主拉應(yīng)力計(jì)算式：T=l/b?zX（Q—M/HXtga）=O0zl其他等高度區(qū)間計(jì)算式：T=l/b?zXQ=oZL具體計(jì)算見表2—10查橋規(guī)30號混凝土容許拉應(yīng)力值為[o]=850KpaZL蓋梁內(nèi)力匯總表表2—8截面內(nèi)力?①一①②一②③一③④一④彎矩(KN?m)M白重-11.538.149.98114.65M荷載-372.25608.16222.17-58.251654.04M計(jì)算-383.75646.30232.14-58.251759.69剪力(KN)Q自重左-12.75-32.395.70右-12.75112.4595.750Q荷載左-463.12-751.531337.75-186.27右-463.12-1523.881131.52-186.27Q計(jì)算左-475.87-783.871433.45-186.27右-475.871636.331227.22-186.27

各截面鋼筋量計(jì)算表2—9截面號M計(jì)算(KN?m)B(m)H0(m)T=[j]?b?Hg0/M計(jì)算含筋率p=p%鋼筋面積A=p%bHg0所需申25根數(shù)實(shí)際用申25根數(shù)Ag①一①-383.751.201.05689.50.15419.403.95629.45②一②646.301.201.05409.01.26132.896.71839.27③一③232.151.201.051139.80//629.45-58.254542.5629.45④一④1759.591.201.05150.40.74565.9713.441468.73各截面主拉應(yīng)力表表2—10截面號Q計(jì)算(KN)b(m)h0(m)實(shí)際用筋量A含筋率p=p%參數(shù)a入Z=Ah0O=l/b?zXzl(Q-M/hXtga)①一①-475.871.201.0529.450.2340.1900.9360.983403.42-475.87②一②-783.871.201.0539.270.3120.2210.9270.973671.351636.331401.44③一③1433.451.201.0529.450.2340.1900.9360.9831215.201227.221040.37④一④-186.271.201.0568.730.5450.2800.9070.952163.05-186.27三、橋墩、墩柱計(jì)算：墩柱一般尺寸見圖2—1所示，墩柱直徑為120CM，用25號砼、II級鋼筋。(一)荷載計(jì)算：1、恒載計(jì)算(由前算得)上部結(jié)構(gòu)恒載，一孔重2427.36KN蓋梁自重(半根蓋梁)144.75KN橫系梁重1.00X0.7X5.8X2.5=101.5KN墩柱自重：3.14X0.62X29X2.5=81.95KN作用墩柱底面的恒載垂直力：N恒=0.6X2427.36+144.75+81.95=1683.12KN2、活載計(jì)算，荷載布置及行駛情況見圖2-8和圖2-9，由蓋梁計(jì)算得知(1)汽—20單孔荷載1)雙列車：B=01B=554.28KN2則B+B=554.28KN12相應(yīng)的制動力為T=(300+200)X0.1=50KNT=300X0.3=90KN2)三列車3B=831.42KN2雙孔荷載：單列車時(shí)：B=156.18KNB=193.31KN12B+B=349.31KN12相應(yīng)制動力：T=(300+200)X0.1=50KN<90KN(1)掛—100單孔荷載B=0B=843.75KN12B+B=843.75KN12雙孔荷載B=236.50KNB=638.00KN12

B+B=874.50KN12活載中雙孔荷載產(chǎn)生支點(diǎn)處最大反力值，產(chǎn)生最大墩柱垂直力活載中單孔荷載產(chǎn)生最大偏心彎矩，即產(chǎn)生最大墩柱底彎矩。n=0.292三列車：n=250/500=0.51n=0.292掛—100：n=（160+250）/500=0.821n=0.1824、荷載組合：（1）最大、最小垂直反力計(jì)算（如表3—1活載組合垂直反力計(jì)算表3—1編號荷載情況B最大垂直反力最小垂直反力n1n1”n2n1汽雙列349.490.72523.400.29210.812—20三列349.490.5545.200.5545.203掛一100874.510.82717.100.18157.41表中汽一20項(xiàng)內(nèi)已沖擊系數(shù)1+p=1.093

2）最大彎矩計(jì)算見表3—2，表內(nèi)水平力由兩墩柱平均分配活載組合最大彎矩計(jì)算（單孔）表3—2編號荷載情況墩柱反力BXn（i+m）垂直力水平力HKN對柱頂中彎矩B1B2B1+B2（B1-B2）X0.25H1X1.141上部構(gòu)造與蓋梁恒載///1936.13///2汽一20雙列554.28X0.72X1.17466.930466.9345116.7351.33汽一20三列8.31X0.5X1.17486.380486.3845121.6051.34掛一100843.75X0.82X1.17691.880691.88/172.97/（二）截面配鋼筋計(jì)算及應(yīng)力驗(yàn)算作用于墩柱頂?shù)耐饬Γ▓D3—2）1）垂直力最大垂直力N=1936.13+717.10=2653.29KNmax掛N=1936.13+545.20=2481.33KNmin2653.29/1.25=2122.63KN〈2481.33KN故N=2481.33KNmax最小垂直力（需考慮最大彎矩值相適應(yīng)）由表3-2得到N=1936.13+486.38=2422.51KNmin（2）水平力H=45KN（3）彎矩M=121.6+51.3=172.9KN?M〉172.9/1.25=138.38KN?Mmax2、作用于墩柱底的外力N=2481.33+56.94=2538.27KNmaxN=2422.51+56.94=2479.45KNminM=172.9+45X2.9=303.4KN?Mmax3、截面配鋼筋計(jì)算已知墩柱用25號砼[o]=90kgf/cm2,采用16少20鋼筋[oa]=200kgf/cm2,A=3.14X162=50.27cm2。由于I/d=2X2.9/1.0=5.8〈7ggp不計(jì)偏心彎矩的增大系數(shù)影響。雙孔荷載,最大垂直反力時(shí),墩柱按軸心受壓構(gòu)件驗(yàn)算:o=N/屮(A+MA,)

hmaxhs式中：屮=1.0,A=3.14X0.52=0.785cm2hm—鋼筋強(qiáng)度與砼軸心抗壓極限強(qiáng)度比值，按II級鋼筋與25號砼可查表得m=20.6故O=25387.27/1.0X(0.785+20.6X50.27X104)h=2856.62KPa〈[o]a單孔載體最大彎矩時(shí),墩柱按最小偏心受壓構(gòu)件驗(yàn)算：e=M/N=303.4/2479.45=0.122m〈d/6=0.167m0eWkk為軸心受壓構(gòu)件截面的核心距0y=y=R=0.5m121y—取換算截面重心軸到截面邊緣的距離A=n?R2+nA=nX602+16XnX1=11354.24cm20gI=I+nI=nX604/4+nX16/4=11145612.56cm20ngK=11145612.56/11354.24X60=0.19e,=e/r=0.19/0.60=0.32001e=0.19〈0.32,故按小偏心構(gòu)件計(jì)算.025號砼n=10,r=60-5=55,A=50.27cm2ggp二A/n?R2=50.27/3.14X3600=0.45%g1np=10X0.45%=0.045,r/R=55/60=0.92g1按圓形鋼筋砼截面桿件強(qiáng)度計(jì)算公式：O，二N/A土M,/W=N/n?R(T土e?s)h0020O二-no?2k?R-(R-r)/2k?Rk=o/(o-o,)

gh1g1hhh上式中T、S可查有關(guān)表格，可按下式求得：T=1/(1+np)=1/(1+0.045)=0.956S=4/1+2np(r/R,)=4/(1+2X0.045X0.922)=3.7g1代入上式后可得到:o=2479.45X(0.956+0.32X3.62)/3.14X0.62h=4637.78KPa<9000Kpa拉應(yīng)力o,=2479.45X(0.956-0.32X3.62)/nX0.62h=-443.77KPa<[o]=850Kpazl則k=o(o-o,)=4637.78/(4637.78-179.15)=1hhho=-10X4637.78X[2X1X0.6-(0.6-0.55)]/2X1X0.6g=16000.34KPa<[o]=200000Kpag砼拉應(yīng)力小于容許應(yīng)力。表明墩柱不會出現(xiàn)裂縫,墩柱配筋滿足規(guī)范要求,箍筋可按要求配置。四、鉆孔灌注樁計(jì)算：鉆孔灌注樁直徑為1.5m，用25號砼少2011級鋼筋，灌注樁樁身砼受壓彈性模量Eh=2.85X104Mpa荷載計(jì)算每一根樁承受的荷載為:1、兩孔恒重反力N=1/2X2427.36=1213.68KN12、蓋梁恒重反力N=144.75KN23、系梁恒重反力N=1/2X101.5=50.75KN3maxmax4、一根墩柱恒重N=81.95KN4作用于樁恒載反力N為：N二N+N+N+N=1491.13KN恒恒12345、灌注樁每延米自重q二nX1.52X15/4=16.96KN（已扣除浮力）6、活載反力1）兩跨活載反力N=545.20KN（汽一20雙列）5N,=717.10KN（掛—100）52）單跨活載反力N,=523.40KN（汽一20三列）5N=486.38KN（汽一20雙列）N,=466.93KN（汽一20三列）66N,=691.88KN（掛一100）63）制動力T=45KN，作用在支座中心，距樁距離為：（1/2X0.042+1.1+2.9）=4.021m4）縱向風(fēng)力風(fēng)壓取0.7X400=280Pa由蓋梁引起的風(fēng)力：W=1/2X10.5X280X103=1.47KN1對樁頂引起的力臂為：1.10X1/2+2.9=3.45m由樁頂引起的風(fēng)力：W=2.9X3.14X0.62X0.28=0.92KN2對樁頂?shù)牧Ρ蹫椋?/2X2.9=1.45m由于墩柱橫向剛度較大，橫向風(fēng)力可不考慮。7、作用于樁頂?shù)耐饬Γㄒ妶D3一3）N=2027.82+545.20=2573.02KN（雙孔）maxN=2027.82+486.38=2514.2KN（單孔）minH=45+1.47+0.92=47.38KNM=NX0.36+TX4.021+WX3.45+WX1.45612=362.45KN?M（單跨荷載）8、作用于地面外樁頂上的外力N=2573.02+16.96=2589.98KNZZN=2514.20+16.96=2531.16KNminH=47.11KN0M=NX0.36+TX(4.021+1)+WX4.45+WX2.45=409.84KN?M061H-1NH-1NJ、7圖3-3樁長計(jì)算：假設(shè)樁長h,采用確定單樁容許承載力的經(jīng)驗(yàn)公式計(jì)算樁長。灌注樁最大沖刷線以下樁長為h。0[N]=l/2u?工l?T+入?m?A{[o]+k?r?(h-3)}iio0223式中：u樁周長u=n?1.2=3.77m,考慮用旋轉(zhuǎn)式鉆機(jī)，成孔直徑應(yīng)增大5cm，則有p=4.08。見《基礎(chǔ)工程》l——土層厚度取l=25.58miiT——樁壁極限阻力T=55kpaii入——考慮樁入土深度影響系數(shù)入=0.7m――考慮孔底沉淀層厚度影響的清底系數(shù)取m=0.8ooA——樁底截面積A=n?R2=n?0.752=1.77cm2[o]——樁底土層容許承載力取o=260kpa00k――深度修正系數(shù)取1.52r――土層容重取8KN/m32h――一般沖刷線以下深度(m)3代入可得：[N]=l/2X[3.93X(2.0+h)X55]+0.70X0.80Xl.77X[260+1.5X8X(2.0+h-3)]代入上式計(jì)算結(jié)果得:樁長h~20m,即地面以下樁長為22m。由上式反求，可知樁的軸向承載力能滿足要求。、樁的內(nèi)力計(jì)算(m法)1、樁的計(jì)算寬度b1b=k(d+1)=0.9(1.5+1.0)=2.25m1f2、樁的變形系數(shù)a?=5'mbi式中：E=2.6X107(KN/M2)ElhI=0.0491?d4=0.189(m4)受彎構(gòu)件，EI=0.67EIh3、地面以下深度Z處樁身截面上的彎矩Mz與水平壓應(yīng)力j的計(jì)已知作用于地面處樁頂上的外力為：N=2566.78KN,H=47.11KN,M=409.84KN?M000(1)樁身彎矩M111MZ=—0?A+M?BZam0mzxa—bzxa—bxaM?z?bbx式中無量綱系數(shù)Am、Bm可由表格查得，計(jì)算見表3-3樁身彎矩Mz計(jì)算(單位：kNm)表3-3zz=azh=ahAmBm-—oAmaMo?BmMz0.350.14.00.099600.9997432.32483.37515.690.700.24.00.196960.9980663.91482.56546.471.400.44.00.377390.98617122.45476.81599.262.100.64.00.529380.95861171.76463.49635.252.800.84.00.645610.91324209.48441.55651.033.501.04.00.723050.85089234.60411.406464.551.34.00.767610.73161249.