梁式樓梯設(shè)計(jì)計(jì)算例題

1、3.4梁式樓梯設(shè)計(jì)計(jì)算例題3.4.1 設(shè)計(jì)資料某現(xiàn)澆梁式樓梯結(jié)構(gòu)布置圖如圖3-22所示，樓梯品S步尺寸150mmx300mm。樓梯采用C25混凝土(%=11.9N/mm2,ft=1.27N/mm2)。梁采用HRB335鋼筋(fy=300N/mm2),其余鋼筋采用HPB300鋼筋(fy=270N/mm2)。樓梯圖3-22樓梯結(jié)構(gòu)布置圖上的均布荷載標(biāo)準(zhǔn)值qk=3.5kN/m2。試設(shè)計(jì)該樓梯。3.4.2踏步板設(shè)計(jì)(1)確定踏步板板底底板的厚度底板取4=40mm,踏步高度c=150mm300cos二2_2150300300335=0.894踏步板厚取hc-二40-=120mm2cos：20.894梯段

2、斜梁尺寸取b"=150mmM300mm。踏步板計(jì)算跨度l0=lnba.450.15=1.6m(2)荷載計(jì)算恒荷載20mm厚水泥砂漿面層(0.3+1.5)父0.02x20=0.18kN/m踏步板自重0.120.325=0.9kN/m板底抹灰170.020.3/0.894=0.114kN/m恒荷載標(biāo)準(zhǔn)值0.180.90.114=1.194kN/m恒荷載設(shè)計(jì)值1.21.194=1.433kN/m活荷載3.50.3=1.05kN/m一's=22二1fcbhb=0.021:1fcbh0fy2=27.8mm活荷載標(biāo)準(zhǔn)值活荷載設(shè)計(jì)值1.41.05=1.47kN/m荷載總計(jì)荷載設(shè)計(jì)值p=gq

3、=1.4331.47=2.903kN/m(3)內(nèi)力計(jì)算1919跨中彎矩Mpl：2.9031.62-0.743kNm1010(4)配筋計(jì)算板保護(hù)層厚度15mm,有效高度h0=120-20=100mm。0.7431061.011.9300100WJ=1-.112廠；=1-1-20.02-0.021b-0.6141.011.93000.02110027045ft/fy%=451.27/270%=0.212%0.2%因此踏步板最小配筋率為0.212%。此時(shí)Asmin=0.00212300120=76.3mm2As<Asmin取As=Asmin,踏步板應(yīng)按構(gòu)造配筋。選配每踏步28(As=101mm

4、2>76.3mm2),且滿足踏步板配筋不少于26的構(gòu)造要求。另外，踏步內(nèi)斜板分布鋼筋選用8250。踏步板的配筋見(jiàn)圖3-23。圖3-23踏步板配筋3.4.3梯段斜梁設(shè)計(jì)(1)梯段斜梁計(jì)算參數(shù)板傾斜角taW=150/300=0.5,口=26.6：,cos=0.894,ln=3.9m(2)荷載計(jì)算2903踏步板傳來(lái)：f(1.4520.15)/2=8.468kN/m梯段斜梁自重：1.20.15(0.3-0.04)25/0.894=1.309kN/m梯段斜梁粉刷重：1.20.022(0.3-0.04)17/0.894=0.253kN/m荷載設(shè)計(jì)值：p=8.4681.3090.253=10.03kN

5、/m(3)內(nèi)力計(jì)算取平臺(tái)梁截面寬度b=200mm梁計(jì)算跨度1。=lnb=3.90.2=4.1m以及10=1.051n=1.05M3.9=4.095m,取/、值10=4.095m10_4.09520-20=205mm11一11以及()10=()x4.095=293mm410mm,故取h=300mm101410141o1o跨中彎矩Mpl；10.034.0952=16.82kNm10101 1水平向男力Vpln10.033.9=19.56kN2 2斜向男力V=VcosJ=19.560.894-17.49kN(4)配筋計(jì)算梯段斜梁按倒L形計(jì)算：按梁計(jì)算跨度考慮bf="=4095=683mm6

6、6按梁肋凈距考慮bf=bSn/2=1501450/2=875mm按翼緣高度考慮bf=b5hf=150540=350mm取三者中最小值，因此bf=350mm16.82106=0.06梁有效高度h0=300-40=260mmIfcbfh；1.011.93502602貝U=1-1-21s=1-1-20.06=0.062二b=0.55,hf40h0-260=0.154fcbfhofy1.011.93500.062260cc2=22mm3000.45ft/fy=0.45父1.27/300=0.19%<0.2%,因止匕Pmin=0.2%Asmin=Pmi徜=0.002父150黑300=90mm?,貝

7、UAs>Asmin選配212,As=226mm2箍筋計(jì)算:Vcs=0.7ftbh0=0.71.27150260=34.67kN17.49kN可以按構(gòu)造配箍，選用8200。箍筋直徑、間距及配箍率均滿足要求：dsv,min=6mm,smax=200mm：svmin=0.24工=0.241.27/270=0.113%Ov,IIfyv：%=*=250.3=0.335%bs150200圖3-24梯段斜梁配筋圖梯段斜梁配筋見(jiàn)圖3-24。3.4.4平臺(tái)板計(jì)算(1)確定板厚板厚取h=70mm,板跨度lo=ln+a<ln+0=2200+四=2235mm=2.235m222取1m寬板帶按簡(jiǎn)支單向板進(jìn)行

8、配筋計(jì)算。(2)荷載計(jì)算恒荷載20mm厚水泥砂漿面層0.02201=0.4kN/m平臺(tái)板板底抹灰恒荷載標(biāo)準(zhǔn)值恒荷載設(shè)計(jì)值活荷載活荷載標(biāo)準(zhǔn)值活荷載設(shè)計(jì)值荷載總計(jì)荷載設(shè)計(jì)值0.07251=1.75kN/m0.02171=0.34kN/m0.41.750.34=2.49kN/m1.22.49=2.99kN/m3.5kN/m1.43.5=4.9kN/mpq=2.994.9=7.89kN/m(3)內(nèi)力計(jì)算1212跨中彎矩M=(gq)lo=-7.892.2352=4.927kNm88(4)配筋計(jì)算板保護(hù)層厚度15mm,有效高度h0=70-20=50mmM:1fcbh024.92710621.011.910

9、0050=0.166貝U=1-，1127s=1-1一20.1660.183b=0.614As=1.011.910000.183502702A二4033mmAsminAsmin=7mibnh=0.212%100070-148.4mm2選配8120,As=419mm2。圖3-25平臺(tái)板配筋圖3.4.5平臺(tái)梁設(shè)計(jì)(1)確定平臺(tái)梁尺寸梁寬取b=200mm高h(yuǎn)之c+h'/0.894=150+300/0.894=486mm,取h=500mm梁跨度取10=3.9m。(2)荷載計(jì)算1o1梯段斜梁傳來(lái)：Pplo10.034.095=20.54kN22平臺(tái)板傳來(lái)：7.89(0.22.2/2)=10.26k

10、N/m平臺(tái)梁自重：1.20.2(0.5-0.07)25=2.58kN/m平臺(tái)梁粉刷重:1.20.02(0.20.502-0.072)17=0.43kN/m荷載設(shè)計(jì)值:p=10.262.580.43=13.27kN/m16其平臺(tái)梁計(jì)算簡(jiǎn)圖見(jiàn)圖3-26。圖3-26平臺(tái)梁計(jì)算簡(jiǎn)圖1213.273.92=25.23kNm8(3)內(nèi)力計(jì)算1c由p廣生的彎矩設(shè)計(jì)值Mi=-pl28由梯段斜梁傳來(lái)的P產(chǎn)生的彎矩設(shè)計(jì)值0.310.310.31M2=2P(0.1951.600-)-P(1.6-)-P0.310.310.31=220.54(0.1951.600)-20.54(1.6)-20.54=40.87kNm則

11、M=M1M2=25.2340.87=66.1kNm剪力設(shè)計(jì)值1111V=pln-qP=13.273.66-420.54=65.36kN2222(4)配筋計(jì)算平臺(tái)梁按倒L形計(jì)算，bf=b+5hf=200+5x70=550mm梁有效高度=500-40=460mm判斷截面類型，由于,hf70fcbf(h0)=1.011.955070(460)=194.7kNm66.1kNm2266.1106故屬于第一類T形截面。2=0.048fcbfM1.011.9550460則=1一.112Ts=1-1一20.048=0.049：b=0.55fcbfh01.011.95500.0494602fy=49.17mm300選配316,As-603mm2平臺(tái)梁最小配筋率：在0.2%和45ft/fy%=45父1.27/300%=0.19%問(wèn)取大值0.2%止匕時(shí)Asmin=0.002200500=200mm2：二603m