現(xiàn)澆板式樓梯計(jì)算-4

1、TB1板式樓梯計(jì)算書項(xiàng)目名稱設(shè)構(gòu)件編旦 校日期審核設(shè)計(jì)示意圖Lr./4Ln/4L i-rl )x1:blbzL匸 L1"Xif基本資料樓梯混凝土容重：b = 25.00 kN/m 3 樓梯面層容重：c1 = 25.00 kN/m 3樓梯頂棚抹灰容重：c2 = 20.00 kN/m 3樓梯欄桿自重：qf = 0.50 kN/m樓梯均布活荷載標(biāo)準(zhǔn)值可變荷載組合值系數(shù)：可變荷載準(zhǔn)永久值系數(shù)4 .材料參數(shù)混凝土強(qiáng)度等級：C30混凝土抗壓強(qiáng)度設(shè)計(jì)值混凝土抗拉強(qiáng)度標(biāo)準(zhǔn)值混凝土抗拉強(qiáng)度設(shè)計(jì)值q = 3.50 kN/m 2 c = 0.70q = 0.50fc = 14.30 N/mm 2 ftk

2、= 2.01 N/mm 2 ft= 1.43 N/mm 22混凝土彈性模量：Ec = 3.00 104 N/mm 鋼筋強(qiáng)度等級：HRB335(20MnSi) 鋼筋彈性模量：Es = 200000 N/mm 2 受拉縱筋合力點(diǎn)到斜梯段板底邊的距離三、荷載計(jì)算過程1.樓梯幾何參數(shù)梯段板與水平方向夾角余弦值2fy = 300.00 N/mmas = 15 mm280COS = 22 = '22 = 0.88Qb2 + h22802 + 1502斜梯段的計(jì)算跨度:L0 = Min Ln + (b1 + b2)/2,1.05Ln = Min2520 + (200 + 200) / 2,1.052

3、520 = Min 2720,2646 = 2646 mm梯段板的平均厚度：T = (h + C / cosX2) / 2 = (150 + 100 / 0.882) / 2 X=188 mm2 .荷載設(shè)計(jì)值2.1均布恒載標(biāo)準(zhǔn)值2.1.1L1段梯板自重gk1' = b XT / 1000 = 25.00188X1000 = 4.71 kN/m 2混凝土結(jié)構(gòu)設(shè)計(jì)規(guī)范(GB50010 2002)gk1=gk1' X1 / Ln = 4.712520 / 2520 =4.71 kN/m 2幾何參數(shù)L1段梯板面層自重樓梯類型板式A型樓梯(/ )gk3'=c1 XC2 XH +

4、L1) / L1 / 1000 = 25.0030 逐500 + 2520) / 2520 / 1000約束條件兩端彈性=1.20 kN/m 2斜梯段水平投影長度：L1 =2520 mmgk3=gk3' L1 / Ln = 1.202520 / 2520 =1.20 kN/m 2梯段凈跨Ln :=L1 = 2520 =2520 mm樓梯頂棚自重樓梯高度H =:1500 mm樓梯寬度：W = 1150 mmgk5'=c2 >C3 / 1000 = 20.0020 /1000=0.40 kN/m 2踏步高度h =150 mm踏步寬度：b =280 mmgk5=gk5'

5、 Ln + L1 >(1 / cos - 1) / Ln=0.402520 + 2520(1X0.88 - 1) /樓梯級數(shù)n =10 (級)梯段板厚：C=100 mm2520 = 0.45 kN/m 2面層厚度C2=30 mm將欄桿自重由線荷載折算成面荷載抹灰厚度C3=20 mmgk6=qf / W X1000 = 0.50 / 11501000 X 0.43 kN/m 22.永久荷載標(biāo)準(zhǔn)值1設(shè)計(jì)規(guī)范建筑結(jié)構(gòu)荷載規(guī)范(GB50009 2001)上部平臺(tái)梯梁寬度：下部平臺(tái)梯梁寬度：3.荷載參數(shù)bi = 200 mm b2 = 200 mmgk = gk1 + gk3 + gk5 + gk

6、6 = 4.71 + 1.20 + 0.45 + 0.43 = 6.80 kN/m2.2均布荷載設(shè)計(jì)值由活荷載控制的梯段斜板荷載設(shè)計(jì)值Pl = 1.2gk + 1.4q = 1.26)80 + 1.43.50=13.06 kN/m由恒荷載控制的梯段斜板荷載設(shè)計(jì)值pD = 1.35gk + 1.4 cq = 1.356.801)相對界限受壓區(qū)高度cu = 0.0033 - ( fcu,k - 50) 取 cu = 0.0033b10<5 = 0.0033 - (30 - 50)10-5 = 0<0035 > 0.0033+ 1.40.703.50 = 12.60 kN/m按規(guī)范

7、公式（7.1.4-1）最不利的梯段斜板荷載設(shè)計(jì)值p = Max pl，pd = Max13.06,12.60=13.06 kN/m四、正截面承載能力計(jì)算1,fy1 + pEs cu1 + 2.000.80300105 >0.00330=0.551 斜梯段配筋計(jì)算h0 = T - as = 100 - 15 = 85 mm11跨中最大彎矩，Mmax = 10pL2 = 10 X 13.0620462 010-62) 受壓區(qū)高度x按規(guī)范公式(7.2.1-1), As = 0, Ap = 0x|M| =1fcbx h0 - =9.14 kN m-1)相對界限受壓區(qū)高度cu = 0.0033 -

8、 (fcu,k - 50)b1X5 = 0.0033 - (30 - 50)10-5 = 00035 > 0.00332 2M22 為-2.29|x = h0 -: h0 -=85 -, 85 - 1.00 松.301000 = j90mm取 cu = 0.0033按規(guī)范公式(7.1.4-1)< bh0 = 0.5585 = 46.75mm,按計(jì)算不需要配置受壓鋼筋3）受拉鋼筋截面積As按規(guī)范公式（7.2.1-2）1fcbx = fyAs1,fy1 + EEs cu1 + 2.000.80300X05 X0.00330=0.55得As =1fcbx1.0014.3010001.90

9、300.002=91mm24）驗(yàn)算配筋率2) 受壓區(qū)高度x按規(guī)范公式(7.2.1-1), As = 0, Ap = 0Asbh911000 >100X 100% = 0.09% <max = 2.62%不超筋xM = 1fcbx h0 - 2匚_2M/22 X9.14_1X-_x = h0 - - ；' h0 -花=85 - = 85 - 1.00 X4.30000 = 7.89mm< bh0 = 0.5580= 46.75mm,按計(jì)算不需要配置受壓鋼筋3)受拉鋼筋截面積As按規(guī)范公式(7.2.1-2)min = 0.2%min = 0.214% >min =

10、0.451.43 / 300.00 = 0.214%按最小配筋率要求配筋，As = minbh = 0.2141000 100 / 100 = 214mm2梯段板支座截面實(shí)際配置受拉鋼筋為B8200,每米寬板實(shí)際配筋面積為五、斜截面承載能力驗(yàn)算1fcbx = fyAs得As =1fcbxfy1.00 14.30X00300.00X.89=376mm 2251mm24）驗(yàn)算配筋率As=bh3761000 X00X100% = 0.38% <max = 2.62%不超筋min = 0.2%min = 0.451X3 / 300.00 = 0.214%min = 0.214% <滿足最小

11、配筋率要求梯段中間截面實(shí)際配置受拉鋼筋為B8130,每米寬板實(shí)際配筋面積為387mm2V = 0.5pL0 = 0.513.062646 / 1000 = 17.3 kN1) 復(fù)核截面條件按規(guī)范公式(7.5.1)0.25 cfcbh0 = 0.25 1.00 14.30 1000 85 = 303.9103 NV = 17.3 kN < 303.9 kN,截面尺寸滿足要求2) 驗(yàn)算構(gòu)造配筋條件按規(guī)范公式(7.5.7-2) 取=31.751.753+10ftbh0 = 3 + 1 0 X 1.43 1000 85 = 53.2103 N > V = 17.3kN斜截面承載力滿足要求六

12、、跨中撓度驗(yàn)算支座最大負(fù)彎矩,Mmax = - 40pL2 = - 40 X 13.06 26462 X10-6=-2.29 kN m -1 .荷載效應(yīng)的標(biāo)準(zhǔn)組合值pk = gk + q = 6.80 + 3.50 = 10.30 kN/mMk =和kL0 =希 X 10.3026462 X10"6根據(jù)規(guī)范公式（）,可得MkB = Mq( - 1) + MkBs=7.21 kN m-2 荷載效應(yīng)的準(zhǔn)永久組合值5.987.21(2.00 - 1) + 7.21X 637.59= 348.41 kN m2pq = gk + qq = 6.80 + 0.503.50<= 8.55 k

13、N/mMq = ：10pqL0 =希 X8.5526462 X10"68)跨中撓度：f3 pkL4 f =f 384 B310.30 V384 X348.41264 X 10-9= 11.32 mm=5.98 kN m-9）容許撓度:3 撓度驗(yàn)算裂縫間縱向受拉鋼筋應(yīng)變不均勻系數(shù)1)因計(jì)算跨度L0小于7000mm,所以容許撓度L。= 益2646"20013.00 mm2)3)4)5)由規(guī)范公式（）,縱向受拉鋼筋的應(yīng)力7208647.9220.8785386.66 = 252.11 N/mm對矩形截面受彎構(gòu)件，有效受拉混凝土截面面積=0.51000 W0 = 50000 mm

14、2按規(guī)范公式（）計(jì)算縱向鋼筋配筋率=7.733210-3混凝土抗拉強(qiáng)度標(biāo)準(zhǔn)值按規(guī)范公式（）=0.43ftk = 2.01 N/mm 2=1.1 - 0.65 ftk鋼筋彈性模量和混凝土彈性模量的比值e =巨=200000 =667Ec 300006.6受壓翼緣面積與腹板有效面積的比值對于矩形截面，f' = 0.00縱向受拉鋼筋配筋率：bAs = 100087藥 =0.004549bh01000 >85受彎構(gòu)件的短期剛度：Bs由規(guī)范公式（） , Bs =Mksk =sk0.87h0AsAte = 0.5bhAste = Ate38750000跨中最大撓度小于容許撓度，滿足要求。七、

15、裂縫寬度驗(yàn)算1 裂縫寬度驗(yàn)算1）裂縫間縱向受拉鋼筋應(yīng)變不均勻系數(shù)由規(guī)范公式（）,縱向受拉鋼筋的應(yīng)力：7208647.9220.8785386.66 = 252.11 N/mm=1.1 - 0.65te sk2 01 10007.7§32_252.11對矩形截面受彎構(gòu)件，有效受拉混凝土截面面積21000100 = 50000 mm=0.5按規(guī)范公式（）計(jì)算縱向鋼筋配筋率：2)EsAsh23)1.15 + 0.2 + E1 + 3.5 f'200000 >387 852 921.150.43 + 0.2 + 6 施70.004549 X10= 637.59 kNm，4)1

16、+ 3.50 旳06）考慮荷載長期效應(yīng)組合對撓度增大的影響系數(shù) 根據(jù)混凝土結(jié)構(gòu)設(shè)計(jì)規(guī)范條規(guī)定：5)=0, 取 = 2.007）受彎構(gòu)件的長期剛度：BMksk =sk0.87h0AsAte = 0.5bhAste = Ae3875000010-3時(shí),取 te = 0.01=7.73當(dāng) te < 0.01混凝土抗拉強(qiáng)度標(biāo)準(zhǔn)值按規(guī)范公式（）ftk = 2.01 N/mm 2ftk=1.1 - 0.65= 1.1 - 0.65te sk2.0110.00001000252.11=0.58構(gòu)件受力特征系數(shù)cr根據(jù)表8.1.2-1,對于受彎的鋼筋混凝土構(gòu)件，其構(gòu)件受力特征系數(shù) 取為2.1受拉區(qū)縱向鋼

17、筋的等效直徑deq根據(jù)表8.1.2-2,對于帶肋鋼筋，其相對粘結(jié)特性系數(shù)=1.0yn*d2根據(jù)規(guī)范公式（） , deq =1 ；2J1i idi最外層縱向受拉鋼筋外邊緣至受拉區(qū)底邊的距離 取鋼筋保護(hù)層厚度25mm最大裂縫寬度max根據(jù)規(guī)范公式得max =skcrcr252.11=2.1 0.58200000 X81.0=8.00 mmdeq匸 1.9c + 0.08Este8.00任 15 + °.°8 硫=0.1053 mm6）容許裂縫寬度TB2板式樓梯計(jì)算書根據(jù)規(guī)范第條,樓梯所處環(huán)境取為一類環(huán)境，裂縫控制等級取為三級，所以容許裂縫寬度 =0.3 mm最大裂縫寬度小于裂縫

18、寬度限值,滿足要求。項(xiàng)目名稱構(gòu)件編號(hào)日期設(shè) 計(jì)校 對審核八、梯段中間截面施工圖實(shí)際配置受拉鋼筋代換為0R9130,每米寬板實(shí)際配筋面積為489mm2、設(shè)計(jì)示意圖、基本資料1 設(shè)計(jì)規(guī)范建筑結(jié)構(gòu)荷載規(guī)范（GB50009 2001）混凝土結(jié)構(gòu)設(shè)計(jì)規(guī)范（GB50010 2002）2 .幾何參數(shù)樓梯類型：板式A型樓梯（/）約束條件：兩端彈性斜梯段水平投影長度：Li = 1540 mm梯段凈跨Ln :=Li = 1540 =1540 mm樓梯高度H =:1500 mm樓梯寬度：W=870 mm踏步高度h =187 mm踏步寬度：b =220 mm樓梯級數(shù)n =8 （級）梯段板厚：C =100 mm面層厚度

19、C2=30 mm抹灰厚度C3=20 mm上部平臺(tái)梯梁寬度：bi = 200 mm下部平臺(tái)梯梁寬度3. 荷載參數(shù)樓梯混凝土容重： 樓梯面層容重： 樓梯頂棚抹灰容重b2 = 200 mmgk = gk1 + gk3 + gk5 + gk6 = 5.62 + 1.48 + 0.52 + 0.57 = 8.20 kN/m2.2均布荷載設(shè)計(jì)值clb = 25.00 kN/m 3=25.00 kN/m 3c2 = 20.00 kN/m 3由活荷載控制的梯段斜板荷載設(shè)計(jì)值=14.74 kN/m由恒荷載控制的梯段斜板荷載設(shè)計(jì)值pL = 1.2gk + 1.4q = 1.28.20 + 1.4pD = 1.35

20、gk + 1.4 cq = 1.358.203.50樓梯欄桿自重：qf = 0.50 kN/m樓梯均布活荷載標(biāo)準(zhǔn)值： 可變荷載組合值系數(shù)： 可變荷載準(zhǔn)永久值系數(shù)：4. 材料參數(shù)混凝土強(qiáng)度等級：C30混凝土抗壓強(qiáng)度設(shè)計(jì)值：混凝土抗拉強(qiáng)度標(biāo)準(zhǔn)值：混凝土抗拉強(qiáng)度設(shè)計(jì)值：q = 3.50 kN/m 2c = 0.70q = 0.50fc = 14.30 N/mm 2ftk = 2.01 N/mm 22ft= 1.43 N/mm2混凝土彈性模量：Ec = 3.00 104 N/mm 鋼筋強(qiáng)度等級：HRB335（20MnSi） 鋼筋彈性模量：Es = 200000 N/mm 2 受拉縱筋合力點(diǎn)到斜梯段板底

21、邊的距離fy = 300.00 N/mm 2as = 15 mm+ 1.40.703.50 = 14.50 kN/m最不利的梯段斜板荷載設(shè)計(jì)值=14.74 kN/m 2四、正截面承載能力計(jì)算p = Max pL,pD = Max14.74,14.50三、荷載計(jì)算過程1 .斜梯段配筋計(jì)算h0 = T - as = 100 - 15 = 85 mm11跨中最大彎矩，Mmax =石pL2 = 10 X 14.74 1為172 X 10-6=3.85 kN m-1)相對界限受壓區(qū)高度bcu = 0.0033 - (fcu,k - 50)10<5 = 0.0033 - (30 - 50)10-5

22、= 0<0035 > 0.0033取 cu = 0.0033按規(guī)范公式(7.1.4-1)1.樓梯幾何參數(shù)梯段板與水平方向夾角余弦值2201,fy1 + pEs cu1 + 2000.80300=0.55105 >0.00330=.b2 + h2 = . 2202 + 1872 = 0.76斜梯段的計(jì)算跨度:L0 = Min Ln + (b1 + b2)/2,1.05Ln = Min1540 + (200 + 200) / 2,1.051540 = Min 1740,1617 = 1617 mm梯段板的平均厚度：T = (h + C / cos >2) / 2 = (18

23、7 + 100 / 0.762) / 2 X=225 mm2.荷載設(shè)計(jì)值2.1均布恒載標(biāo)準(zhǔn)值2.1.1 L1段梯板自重gk1' = b 燈 / 1000 = 25.00225 *1000 = 5.62 kN/m 2gk1 = gk1' L1 / Ln = 5.621540 / 1540 = 5.62 kN/m 22.1.2 L1段梯板面層自重gk3' = " >C2 »(H + L1) / L1 / 1000 = 25.0030 >51500 + 1540) / 1540 / 1000=1.48 kN/m 2cos2) 受壓區(qū)高度x按規(guī)范

24、公式(7.2.1-1), As = 0, Ap = 0x1fcbx h0 -x = h0 -2M1fcb=85 -2 X3.85 1旳6_1.0014.301000 = 3.23mm< bh0 = 0.5585 = 46.75mm,按計(jì)算不需要配置受壓鋼筋3）受拉鋼筋截面積As按規(guī)范公式（7.2.1-2）1fcbx = fyAs得As =1fcbxfy4）驗(yàn)算配筋率1.0014.3010003.23300.00=154mm2gk3 = gk3'區(qū)1 / Ln = 1.481540 / 1540 = 1.48 kN/m 2樓梯頂棚自重gk5' = c2 >C3 / 1

25、000 = 20.0020 /1000 = 0.40 kN/m 2gk5 = gk5' Ln + L1 凡1 / cos - 1) / Ln = 0.401540 + 1540(1 *0.76 - 1) /1540 = 0.52 kN/m 2將欄桿自重由線荷載折算成面荷載gk6 = qf / W X1000 = 0.50 / 8701000>= 0.57 kN/m 2永久荷載標(biāo)準(zhǔn)值A(chǔ)s=bh1541000 >100X 100% = 0.15% <max = 2.62%不超筋min = 0.2%min = 0.214% >min = 0.451.43 / 300.

26、00 = 0.214%按最小配筋率要求配筋,As = minbh = 0.214 1000 100 / 100 = 214mm2梯段中間截面實(shí)際配置受拉鋼筋為B8200,每米寬板實(shí)際配筋面積為251mm2支座最大負(fù)彎矩，Mmax1 2 1-40pL0 =-亦 < 147416172 < 10-61 .荷載效應(yīng)的標(biāo)準(zhǔn)組合值pk = gk + q = 8.20 + 3.50 = 11.70 kN/m=-0.96 kN m 1)相對界限受壓區(qū)高度cu = 0.0033 - (fcu，k - 50) 取 cu = 0.0033b1係5 = 0.0033 - (30 - 50)10-5 =

27、0.0035 > 0.0033按規(guī)范公式（7.1.4-1）0.80300=0.551 + 200105 >0.003302） 受壓區(qū)高度x按規(guī)范公式（7.2.1-1），As = 0, Ap = 0x|M| =1fcbx h0 - 2x = h0 -h0 -理=85 -1fcb22 X|-0.96|10<85 - 10014.30_1000 = 0.80mm< bh0 = 0.5585 = 46.75mm,按計(jì)算不需要配置受壓鋼筋3）受拉鋼筋截面積As按規(guī)范公式（7.2.1-2）1fcbx = fyAs得As =1fcbx1.00 杯3°1000°.8

28、0 = 38mm2300.004）驗(yàn)算配筋率As38bh 1000 XI00 < 100% = 0.04% < max = 2.62% 不超筋min = 0.2%min = 0.214% >min = 0.451.43 / 300.00 = 0.214%按最小配筋率要求配筋 ，As = minbh = 0.2141000100 / 100 = 214mm2梯段板支座截面實(shí)際配置受拉鋼筋為B8200,每米寬板實(shí)際配筋面積為251mm2五、斜截面承載能力驗(yàn)算V = 0.5pL0 = 0.5 14C74 1)617 / 1000 = 11.9 kN1)復(fù)核截面條件按規(guī)范公式(7.5

29、.1)0.25 cfcbh0 = 0.25 1.00 14.301000 85 = 303.9103 NV = 11.9 kN < 303.9 kN,截面尺寸滿足要求2）驗(yàn)算構(gòu)造配筋條件按規(guī)范公式（7.5.7-2）節(jié)即創(chuàng)。=31+7|50 < 1.43 1000 85 = 53.2103 N > V = 11.9kN斜截面承載力滿足要求六、跨中撓度驗(yàn)算Mk =詁2 =3.06 kN m-X11.7016172 < 10-62 荷載效應(yīng)的準(zhǔn)永久組合值pq = gk + qq = 8.20 + 0.50=2.60 kN m-3.50<= 9.95 kN/m16172

30、<10-63 撓度驗(yàn)算裂縫間縱向受拉鋼筋應(yīng)變不均勻系數(shù)1)2)3)4)5)6)由規(guī)范公式（）,縱向受拉鋼筋的應(yīng)力：3058874.85° 208785251.33 = 164.58 N/mm對矩形截面受彎構(gòu)件，有效受拉混凝土截面面積=0.51000100 = 50000 mm 2按規(guī)范公式（）計(jì)算縱向鋼筋配筋率：Mksk =sk0.87h0AsAte = 0.5bhAste = 一Ate25150000=5.0266 訶3混凝土抗拉強(qiáng)度標(biāo)準(zhǔn)值按規(guī)范公式（）=-0.48ftk = 2.01 N/mm 2=1.1 - 0.65=1.1 - 0.65te sk201 1000當(dāng) < 0.2 時(shí)，取=0.2 ;鋼筋彈性模量和混凝土彈性模量的比值Es200000 門“E = Ec = 30000 = 6.67受壓翼緣面積與腹板有效面積的比值對于矩形截面，f' = 0.00縱向受拉鋼筋配筋率：As251 = =0 002957bh01000 >85 0.002957受彎構(gòu)件的短期剛度：Bs由規(guī)范公式（）, Bs =f'EsAsh21 15+ 0 2 + -1 + 3.5 f'200000 <51<521.15 0- + 0.2 + 6 篤§ 瞪7 < 1八 6