簡(jiǎn)支T梁橋設(shè)計(jì)

裝配式鋼筋混凝土簡(jiǎn)支T梁橋設(shè)計(jì)一，設(shè)計(jì)資料1、橋面凈空：凈7+2X0.75M2、設(shè)計(jì)荷載：汽車(chē)“公路一I級(jí)，人群荷載：3KN/M23、材料：主筋：HRB335，構(gòu)造筋：R235混凝土：橋面鋪裝：C25，主梁：C304、結(jié)構(gòu)尺寸：如下圖所示主梁：計(jì)算跨徑：L=1950cm全長(zhǎng)：L=1996cm人行道、欄桿每延米（兩側(cè)）重2.0KN/m（為每片主梁分到的值）。瀝青混凝土厚2匚己混凝土墊層（6?12主梁簡(jiǎn)圖（尺寸單位：cm）橫隔梁簡(jiǎn)圖（尺寸單位：cm）p=140kN，輪壓分布如圖所示。車(chē)輪著地長(zhǎng)度a2=0.20m，寬度氣=0p=140kN，輪壓分布如圖所示。車(chē)輪著地長(zhǎng)度a2=0.20m，寬度氣=0.60m。則作用在1、行車(chē)道板計(jì)算：<1>每米板寬恒載集度：瀝青混凝土面層（容重21kN/m2）g=0.02x1.0x21kN/m=0.42kN/m1C25混凝土墊層（容重24kN/m2）g,=0.09x1.0x24kN/m=2.16kN/mT梁翼板（容重25kN/m2）g3=0.11x1.0x25kN/m=2.75kN/m板的荷載集度：g=0.42kN/m+2.16kN/m+2.75kN/m=5.33kN/m<2>每米板寬恒載內(nèi)力：彎矩：MA=—2gl0=-2x5.33x0.712kN=—1.34kN剪力：Qa=gl=5.33x0.71kN=3.78kN<3>活載內(nèi)力：汽車(chē)荷載產(chǎn)生的內(nèi)力計(jì)算。將車(chē)輪對(duì)中布置在接縫處（如圖）。加重車(chē)兩個(gè)后軸各為板上的壓力面邊長(zhǎng)：a1=a2+2H=0.20m+2x0.11m=0.42m%=?+2H=0.60m+2x0.11m=0.82m荷載對(duì)于懸臂根部的有效分布寬度為a=a1++d+2l0=0.42m+1.4m+2x0.71=3.24m沖擊系數(shù)R=0.3作用在每米寬板上彎矩:Mp=-（1+r）H（l0—勺…2x1400.82、s=—1.3x（0.71—）kN?m4x3.244=—14.18kN?m作用在每米寬板上剪力按自由懸臂板計(jì)算，且Z>10則：Q=(EIap2ab01=1.3x—2^0—x0.71kN■m2x3.24x0.82=48.64kN<4>作用組合：按承載能力極限狀態(tài)設(shè)計(jì)M=1.2M+1.4M=1.2x(-1.34)+1.4x(―14.18)kN■m=—21.46kNQAj=1.2QAs+1.4QAp=1.2x3.78+1.4x48.64kN■m=72.63kN<5>橋面板主筋計(jì)算與配置：行車(chē)道板主要是承受負(fù)彎矩，計(jì)可按單筋矩形截面計(jì)算(bxh=1.0mx0.11m)采用C25混凝土，HRB335鋼筋。設(shè)a=40mm,則h=h-a=110-40=70mm計(jì)算混凝土的受壓區(qū)高度:x=h-'h2-270MAj0V0fb“匚__2x1x21.46x106=70-J70211.5x1000=35.8mm<0.56x1000=56mm計(jì)算受拉鋼筋面積:滿足要求!fbx_11.5x1000x35.8f280=1470.4mm2162可取中14@10,供給A=1539mm2,a=30+=38.1mm,h=h-a=110-38.1=71.9mm…A1539123貝|p=貴=1000I”=2.14%>p.=0.45x遍=0.198%w0.2%0滿足要求!2、主梁設(shè)計(jì)計(jì)算：<1>、計(jì)算主梁1#、2井、3井在汽車(chē)、人群荷載作用下的橫向分布系數(shù)。用杠桿原理法計(jì)算支點(diǎn)橫向分布系數(shù)如下圖所示:車(chē)輛荷載車(chē)輛荷載.車(chē)輛荷載杠桿原理法計(jì)算1#、2#、3#梁

支點(diǎn)橫向分布系數(shù)所以：1#梁橫向分布系數(shù)：汽車(chē)荷載：m=Uq=0竺=0.4375oq22人群荷載：m=門(mén)=1.422

卜0.51.000八卜0.51.000八u0.52汽車(chē)何載：m=2q人群荷載：m=門(mén)=03#梁橫向分布系數(shù)：、一心汽車(chē)荷載：m=qoq2人群荷載：m=門(mén)=0用G---M法計(jì)算跨中橫向分布系數(shù)(8+14)h==11cm2(160-18)x11x11+135x18x135—x18X1353+18x13512口35”Q

——-42.7"22=7362418W=0.07362418^4主梁比擬單寬抗彎慣矩：,I7362418J=—^==46015cm4/cmxb160確定有效寬度4時(shí)，橫隔梁長(zhǎng)度取兩邊主梁軸線的距離，l'=4xb=4x160=640cm％二贍'=0.368/y，_22—=427cm(160-18)x11+135x18.y，_22—=427cm(160-18)x11+135x18.所以主梁抗彎慣矩:=12x(160—18)x113+(160-18)x11查表可得:y11.1002x128x11x+15x100xa=2=21.0cmy2x128x11+15x100所以橫隔梁抗彎慣矩：1(11￥=_x2x128x113+2x128x11x21——2=3220x103cm412"2)—x15x10032=3220x103cm4=Iy=竺2迎=6640cm4/cmb485主梁和橫隔梁的抗扭慣矩：（8+14）對(duì)于主梁梁肋：h=一-一=11cmbt=(135-11)/18=6.8889時(shí)，查表c=0.303則：I'=cbt3=0.303x(135—11)x183=219x103cm4Tx對(duì)于橫隔梁梁肋：bt=(100—11)/15=5.933時(shí)，查表c=0.296則：I’=cbt3=0.296x(100—11)x153=88.61x103cm4Ty所以11,1,J+J所以11,1,J+J=—h2+—I+—ITxTx313Tx3Ty=1x1133219000+16088610+485=1995cm4/cm計(jì)算參數(shù)6和a八160x5B==400cm20.3328J=400146015了一標(biāo)5466400.33280.425Ex19952Ew'46015x6640=0.02430.0243=0.1557影響系數(shù)梁位荷載位置校核B3B/4B/2B/40(-)B/(-)B/2:(-)3B/4-)bK100.950.9711.041.11.0410.970.958.98B/41.061.091.091.09110.940.880.939.11B/21.241.191.161.0810.920.850.790.748.973B/41.421.321.21.0910.870.790.730.669.06B1.711.451.241.080.90.830.740.680.69.25K000.820.920.991.091.11.090.990.920.828.78B/41.631.51.341.231.10.880.640.40.198.89B/22.452.11.751.3710.660.26-0.16-0.538.883B/43.332.752.11.4910.41-0.15-0.57-1.199.12B4.253.452.431.660.80.2-0.55-1.12-1.779.39影響系數(shù)匕和k°用內(nèi)插法求實(shí)際梁位處的七和勺值，實(shí)際梁位與表列梁位關(guān)系圖如下，因此對(duì)于①號(hào)梁:(k'=k+kB\對(duì)于②號(hào)梁:對(duì)于③號(hào)梁:x-^0=0.2k+0.8k100B3B4\-k\1B1BJ24x_6°=0.6k+0.4k1001B2，k=k0以0指表列梁位在0點(diǎn)的K值）梁位關(guān)系圖梁號(hào)算式荷載位置B3B/4B/2B/40(-)B/4(-)B/2(-)3B/4(-)B1k'11.4781.3461.2081.0880.9680.8620.7800.7200.648k'03.5142.8902.1661.5240.9280.368-0.230-0.680-1.306k'1-k'0-2.036-1.544-0.958-0.4360.0400.4941.0101.4001.954(k'1-k'0)a-—217-0.240-0.149-0.0680.0060.0770.1570.2180.304ka3.1972.6502.0171.4560.9340.445-0.073-0.462-1.002n1i0.6390.5300.4030.2910.1870.089-0.015-0.092-0.2002k'11.1681.1501.1321.0841.0120.9520.8860.8260.816k'02.1221.8601.5861.3141.0200.7480.4120.064-0.242k'1-k'0-0.954-0.710-0.454-0.230-0.0080.2040.4740.7621.058(k'1-k'0)a-—249-0.111-0.071-0.036-0.0010.0320.0740.1190.165ka1.9731.7491.5151.2781.0190.7800.4860.183-0.077n2i0.3950.3500.3030.2560.2040.1560.0970.037-0.0153k'10.9500.9701.0001.0401.0601.0401.0000.9700.950k'00.8200.9200.9901.0901.1401.0900.9900.9200.820k'1-k'00.1300.0500.010-0.050-0.080-0.0500.0100.0500.130(k'1-k'0)a0—200.0080.002-0.008-0.012-0.0080.0020.0080.020ka0.8400.9280.9921.0821.1281.0820.9920.9280.840n3i0.1680.1860.1980.2160.2260.2160.1980.1860.168計(jì)算各梁的荷載橫向分布系數(shù)：（如下圖所示）對(duì)于1#梁橫向分布系數(shù)：尸廠"斗^n0.53+0.313+0.177-0.005汽車(chē)荷載：m=—^q=z=0.508(0.530)人群荷載：m=n=0.625對(duì)于2#梁橫向分布系數(shù)：尸尸"斗>n0.35+0.265+0.199+0.103汽車(chē)荷載：m=—^q==0.459人群荷載：m=n=0.389對(duì)于3#梁橫向分布系數(shù)：尸廠"斗>n0.196+0.22+0.22+0.196汽車(chē)荷載：m=—^q==0.416人群荷載：m=2xn=0.340②號(hào)梁③號(hào)梁根據(jù)以上結(jié)果可取荷載橫向分布系數(shù)較大的1#梁作為設(shè)計(jì)梁。對(duì)于1#梁橫向分布系數(shù)：汽車(chē)荷載：m二二二053+。.313+。質(zhì)―°.°°5=0.508做。）oq22人群荷載：m=m=門(mén)=0.625<2>、荷載橫向分布系數(shù)沿橋跨徑方向的變化：自%侄/的區(qū)段內(nèi)，荷載橫向分布系數(shù)取跨中橫向分布數(shù)值；支點(diǎn)截面取支點(diǎn)橫向分布系數(shù)；自支點(diǎn)至心4區(qū)段按直線變化<3>、內(nèi)力計(jì)算恒載集度：瀝青混凝土面層（容重21kN/m2）g=0.02x1.6x21kN/m=0.672kN/miC25混凝土墊層（容重24kN/m2）g.=0.09x1.6x24kN/m=3.456kN/mT梁（容重25kN/m2）g3=（1.6x0.11+1.24x0.15）x25kN/m=9.05kN/m梁荷載集度：g=0.672kN/m+3.456kN/m+9.05kN/m=13.178kN/m人行道、欄桿每延米（兩側(cè)）重2.0KN/m（為每片主梁分到的值）行車(chē)道板及鋪裝層產(chǎn)生恒載內(nèi)力：跨中彎矩：M=igl2=ix（13.178+2）x19.52kN=721.43kNmg，i2808

1/4彎矩：M.4=(1+旦)&m(p^y^+q^。)=1.3x1x0.508x(240x2.438+10.5x47.53)kNm支點(diǎn)剪力：Q=(1+Q&m(1.2p=715.93kNmo,qy+q。+y)+上a(m-m)qycqkkkk20ckTEx]0.508x240x】xL2+10.5x9.75+2x4.875x"75』.508)x以％x0.83]支點(diǎn)剪力：Q=(1+Q&m(1.2po,q人群荷載:跨中彎矩：M12,=mcr]1\一-q12=0.625xIN]1一―、一-x3x19.52kNm=89.12kNm18J14彎矩：Ml4,r=mcr(3、一[32ql2J=0.625x]3一—\_一x3x19.52kNm=66.84kNm132J支點(diǎn)剪力：Q=mx—ql+—{m一m)x"xyxqo,rcr2r2orcr4r=1.422x1x3x19.5+1x(0.625-1.422)x竺x0.83x3kN224=36.76kN作用效應(yīng)組合:跨中彎矩：M日d=1.2x721.43+1.4x1102.26+0.8x1.4x89.12kNm=2508.69kNm1/4彎矩：M心d=1.2x541.07+1.4x715.93+0.8x1.4x66.84kNm=1726.45kNm支點(diǎn)剪力：M膏d=1.2x147.99+1.4x321.33+0.8x1.4x36.76kN=668.62kN<4>、受拉主鋼筋的計(jì)算：采用HRB335鋼筋、C30混凝土①確定受壓翼緣的有效寬度。;Sl=冬0650耐mf33b=1600mmb'<b+12"=180+12x(80+140)=1500mm2根據(jù)《橋規(guī)》取三者之間的最小者，即。技1500^②判斷T型梁類(lèi)型:設(shè)a=120mm,h0=h-a=1350-120=1230mmh)k。-』(13.8x1500x110x1230-k>Ml2,ud\021fcdbfhfh]21=2508.69kN史/h')k。-寸113.8x180x0.56x1230x11230-056X1230'k3869.66kN《>M問(wèn)d=2508.69kN《,"屬于第一類(lèi)T型截面屬于第一類(lèi)T型截面=2675.48kN史(shfbzhh-tcdb0k0(bf-b)hfh+13.8x(1500-180)x110x1230-③截面配筋按bh=1500mmx1350mm單筋矩形截面計(jì)算f求受壓區(qū)高度:h2-Mi2，cd=1230-「12302

0fb*且x=50.3mm<h'=110mmf計(jì)算受拉鋼筋面積:A=ff=Ex1230x50.3=3049.3mm2sfsd280選10①20=3141mm2其布置如右圖:④截面復(fù)合250&69x106=50.3mm<&h=0.56x1230=688.8mm13.8x1500b0a=30+2.5x22.7=86.75mmh=h-a=1350-86.75=1236.25mmx°=l￡=280x3141=42.49mm<&hfp；13.8x1500b0符合要求！=0.56x1236.25=692.3mmM=fbfxh-且：ducdfk02=2617.89kNm>Ml2,ud(13.8x1500x42.49x1236.25-k42249]截面安全!=2508.69S歡<5>、計(jì)算活載撓度及預(yù)拱度：I=7362418mm40對(duì)于恒載：fg5x3850.85EI015.178x19.54x?…‘二……=15.18mm3850.85x3.0x104x0.07362418對(duì)于汽車(chē)活載:M=1102.26kN^pf=Ax工p480.85EI01102.26x19.52匕=蘭x1102.26x19.52=23.26mm―=32.5mm480.85x3.0x104x0.07362418600跨中點(diǎn)預(yù)拱度取D=-(f+0.5f)=—(15.18+0.5x32.5)=31.34mm3、橫隔梁計(jì)算取跨中橫隔梁作計(jì)算：汽車(chē)荷載布滿跨中橫隔梁為最不利，如右圖所將整列車(chē)的均布荷載布滿于跨中橫隔梁。縱向一列汽車(chē)計(jì)算荷載1(1240x1+10.5xx1x2x4.85=145.46kNoq對(duì)于①號(hào)梁：n=0.60,n=—0.201115對(duì)于②號(hào)梁：n=0.40,n=02125對(duì)于③號(hào)梁：n=0.20,n=0.201115繪制橫隔梁彎矩影響線：\用偏心受壓法可算得:對(duì)于跨中彎矩M3p=1作用在①號(hào)梁時(shí)門(mén)m=門(mén)x2d+門(mén)xd—1x2d=—0.4d=—0.64311121p=1作用在⑤號(hào)梁時(shí)門(mén)M=門(mén)M=—0.643531p=1作用在③號(hào)梁時(shí)門(mén)M=nx2d+nxd=0.6d=0.96311323對(duì)于彎矩MJ)p=1作用在①號(hào)梁時(shí)門(mén)M疝=門(mén)]]x1.5d+門(mén)幻x0.5d—1x1.5d=—0.4d=—0.64p=1作用在⑤號(hào)梁時(shí)門(mén)M疝=n15x1.5d+門(mén)方x0.5d=—0.3d=—0.48p=1作用在③號(hào)梁時(shí)門(mén)M3為=門(mén)捋x1.5d+門(mén)23x0.5d=0.4d=0.64繪制剪力影響線：對(duì)于剪力己右：P=1作用在計(jì)算截面以右時(shí)：1己右=人即門(mén)。右=門(mén)p=1作用在計(jì)算截面以左時(shí)：Q右=人-1即門(mén)Q右=門(mén)-1對(duì)于剪力Q:p=1作用在①梁時(shí)：2Q1廣。^%即氣2=0.5qp=1作用在②梁時(shí)：Q12=0.5R2即叫2=0.5門(mén)2.由影響線可以看出:,>M（2-3由影響線可以看出:,>M（2-3）Q右>Q2-3即設(shè)計(jì)只考慮：MJ〉、"bffb設(shè)a=120mm,h=h-a=1000-120=880mm/h)f02V13.8x1470x110x880-V>M(2-3)fbhfh-cdff=1840.95"^③截面配筋罰=320.33kNm屬于第一類(lèi)T型截面oqM(23bffb設(shè)a=120mm,h=h-a=1000-120=880mm/h)f02V13.8x1470x110x880-V>M(2-3)fbhfh-cdff=1840.95"^③截面配筋罰=320.33kNm屬于第一類(lèi)T型截面oq因?yàn)闄M隔梁內(nèi)力很小，計(jì)算可忽略不計(jì)，并考慮汽車(chē)荷載占總效應(yīng)的百分比，則按極限狀態(tài)設(shè)計(jì)的計(jì)算內(nèi)力為M(23)=1.4x228.81=320.33S