CT2板式樓梯計(jì)算書.doc

結(jié)構(gòu)構(gòu)件計(jì)算書板式樓梯計(jì)算書項(xiàng)目名稱_日 期_設(shè) 計(jì) 者_(dá)校 對(duì) 者_(dá)一、構(gòu)件編號(hào):LT-1二、示意圖：三、基本資料：1.依據(jù)規(guī)范：建筑結(jié)構(gòu)荷載規(guī)范（GB 500092001）混凝土結(jié)構(gòu)設(shè)計(jì)規(guī)范（GB 500102002）2.幾何參數(shù)：樓梯凈跨: L1 = 4160 mm樓梯高度: H = 2900 mm梯板厚: t = 180 mm踏步數(shù): n = 17(階)上平臺(tái)樓梯梁寬度: b1 = 200 mm下平臺(tái)樓梯梁寬度: b2 = 200 mm上平臺(tái)寬: L3 = 300 mm3.荷載標(biāo)準(zhǔn)值：可變荷載：q = 3.50kN/m2面層荷載：qm = 1.00kN/m2欄桿荷載：qf = 0.20kN/m永久荷載分項(xiàng)系數(shù): G = 1.20可變荷載分項(xiàng)系數(shù): Q = 1.40準(zhǔn)永久值系數(shù): q = 0.504.材料信息：混凝土強(qiáng)度等級(jí): C30fc = 14.30 N/mm2ft = 1.43 N/mm2Rc=25.0 kN/m3ftk = 2.01 N/mm2Ec = 3.00104 N/mm2鋼筋強(qiáng)度等級(jí): HRB400 fy = 360 N/mm2 Es = 2.00105 N/mm2保護(hù)層厚度：c = 15.0 mmRs=20 kN/m3受拉區(qū)縱向鋼筋類別：帶肋鋼筋梯段板縱筋合力點(diǎn)至近邊距離：as = 25.00 mm支座負(fù)筋系數(shù)： = 0.25四、計(jì)算過程：1. 樓梯幾何參數(shù)：踏步高度：h = 0.1706 m踏步寬度：b = 0.2600 m計(jì)算跨度：L0 = L1L3(b1b2)/2 = 4.160.30(0.200.20)/2 = 4.66 m梯段板與水平方向夾角余弦值：cos = 0.836 2. 荷載計(jì)算( 取 B = 1m 寬板帶)：(1) 梯段板：面層：gkm = (BB*h/b)*qm = (11*0.17/0.26)*1.00 = 1.66 kN/m自重：gkt = Rc*B*(t/cosh/2) = 25*1*(0.18/0.8360.17/2) = 7.51 kN/m抹灰：gks = RS*B*c/cos = 20*1*0.02/0.836 = 0.48 kN/m恒荷標(biāo)準(zhǔn)值：Pk = gkmgktgksqf = 1.667.510.480.20 = 9.85 kN/m恒荷控制：Pn(G) = 1.35*PkQ*0.7*B*q = 1.35*9.851.40*0.7*1*3.50 = 16.73 kN/m活荷控制：Pn(L) = G*PkQ*B*q = 1.20*9.851.40*1*3.50 = 16.72 kN/m荷載設(shè)計(jì)值：Pn = max Pn(G) , Pn(L) = 16.73 kN/m(2) 平臺(tái)板：面層：gkm = B*qm = 1*1.00 = 1.00 kN/m自重：gkt = Rc*B*t = 25*1*0.18 = 4.50 kN/m抹灰：gks = RS*B*c = 20*1*0.02 = 0.40 kN/m恒荷標(biāo)準(zhǔn)值：Pk = gkmgktgksqf = 1.004.500.400.20 = 6.10 kN/m恒荷控制：Pl(G) = 1.35*PkQ*0.7*B*q = 1.35*6.101.40*0.7*1*3.50 = 11.67 kN/m活荷控制：Pl(L) = G*PkQ*B*q = 1.20*6.101.40*1*3.50 = 12.22 kN/m荷載設(shè)計(jì)值：Pl = max Pl(G) , Pl(L) = 12.22 kN/m3. 正截面受彎承載力計(jì)算：左端支座反力: Rl = 37.25 kN右端支座反力: Rr = 38.89 kN最大彎矩截面距左支座的距離: Lmax = 2.33 m最大彎矩截面距左邊彎折處的距離: x = 1.93 mMmax = Rl*LmaxPl*L3*(xL3/2)Pn*x2/2 = 37.25*2.3312.22*0.40*(1.930.40/2)16.73*1.932/2 = 45.22 kNm相對(duì)受壓區(qū)高度：= 0.141663 配筋率：= 0.005627縱筋(1號(hào))計(jì)算面積：As = 872.21 mm2支座負(fù)筋(2、3號(hào))計(jì)算面積：As=*As = 0.25*872.21 = 218.05 mm2五、計(jì)算結(jié)果：(為每米寬板帶的配筋)1.1號(hào)鋼筋計(jì)算結(jié)果(跨中)計(jì)算面積As：872.21 mm2采用方案：f14100實(shí)配面積：1539 mm22.2/3號(hào)鋼筋計(jì)算結(jié)果(支座)計(jì)算面積As：218.05 mm2采用方案：f14200實(shí)配面積： 770 mm23.4號(hào)鋼筋計(jì)算結(jié)果采用方案：d6200實(shí)配面積： 141 mm24.5號(hào)鋼筋計(jì)算結(jié)果采用方案：f12100實(shí)配面積：1131 mm2六、跨中撓度計(jì)算: Mk - 按荷載效應(yīng)的標(biāo)準(zhǔn)組合計(jì)算的彎矩值Mq - 按荷載效應(yīng)的準(zhǔn)永久組合計(jì)算的彎矩值1.計(jì)算標(biāo)準(zhǔn)組合彎距值Mk:Mk = Mgk+Mqk = (qgk + qqk)*L02/8 = (9.85 + 3.500)*4.662/8 = 36.235 kN*m2.計(jì)算永久組合彎距值Mq:Mq = Mgk+Mqk = (qgk + q*qqk)*L02/8 = (9.85 + 0.50*3.500)*4.662/8 = 31.485 kN*m3.計(jì)算受彎構(gòu)件的短期剛度 Bs1) 計(jì)算按荷載荷載效應(yīng)的標(biāo)準(zhǔn)組合作用下，構(gòu)件縱向受拉鋼筋應(yīng)力 sk = Mk/(0.87*h0*As) (混凝土規(guī)范式 8.1.33) = 36.235106/(0.87*155*1539) = 174.555 N/mm2) 計(jì)算按有效受拉混凝土截面面積計(jì)算的縱向受拉鋼筋配筋率 矩形截面積: Ate = 0.5*b*h = 0.5*1000*180= 90000 mm2 te = As/Ate (混凝土規(guī)范式 8.1.24) = 1539/90000 = 1.710%3) 計(jì)算裂縫間縱向受拉鋼筋應(yīng)變不均勻系數(shù) = 1.1-0.65*ftk/(te*sk) (混凝土規(guī)范式 8.1.22) = 1.1-0.65*2.01/(1.710%*174.555) = 0.6624) 計(jì)算鋼筋彈性模量與混凝土模量的比值 E E = ES/EC = 2.00105/(3.00104) = 6.6675) 計(jì)算受壓翼緣面積與腹板有效面積的比值 f 矩形截面，f = 06) 計(jì)算縱向受拉鋼筋配筋率 = As/(b*h0) = 1539/(1000*155) = 0.993%7) 計(jì)算受彎構(gòu)件的短期剛度 BS BS = ES*As*h02/1.15*+0.2+6*E*/(1+ 3.5*f)(混凝土規(guī)范式8.2.3-1) = 2.00105*1539*1552/1.15*0.662+0.2+6*6.667*0.993%/(1+3.5*0.0) = 54.427102 kN*m24.計(jì)算受彎構(gòu)件的長期剛度B1) 確定考慮荷載長期效應(yīng)組合對(duì)撓度影響增大影響系數(shù) 當(dāng)=0時(shí)，=2.0 (混凝土規(guī)范第 8.2.5 條)2) 計(jì)算受彎構(gòu)件的長期剛度 B B = Mk/(Mq*(-1)+Mk)*BS (混凝土規(guī)范式 8.2.2) = 36.235/(31.485*(2.0-1)+36.235)*54.427102 = 29.122102 kN*m25.計(jì)算受彎構(gòu)件撓度fmax = 5*(qgk+qqk)*L04/(384*B) = 5*(9.85+3.500)*4.664/(384*29.122102) = 28.145 mm6.驗(yàn)算撓度撓度限值f0=L0/200=4.66/200=23.300 mm七、裂縫寬度驗(yàn)算: 1.計(jì)算標(biāo)準(zhǔn)組合彎距值Mk:Mk = Mgk+Mqk = (qgk + qqk)*L02/8 = (9.85 + 3.500)*4.662/8 = 36.235 kN*m2.帶肋鋼筋,所以取值Vi=1.03.C = 154.計(jì)算按荷載荷載效應(yīng)的標(biāo)準(zhǔn)組合作用下，構(gòu)件縱向受拉鋼筋應(yīng)力sk = Mk/(0.87*h0*As) (混凝土規(guī)范式 8.1.33) = 36.235106/(0.87*155.00*1539) = 174.555 N/mm5.計(jì)算按有效受拉混凝土截面面積計(jì)算的縱向受拉鋼筋配筋率矩形截面積: Ate = 0.5*b*h = 0.5*1000*180= 90000 mm2te = As/Ate (混凝土規(guī)范式 8.1.24) = 1539/90000 = 1.710%6.計(jì)算裂縫間縱向受拉鋼筋應(yīng)變不均勻系數(shù) = 1.1-0.65*ftk/(te*sk) (混凝土規(guī)范式 8.1.22) = 1.1-0.65*2.01/(1.710%*174.555) = 0.6627.計(jì)算單位面積鋼筋根數(shù)nn = 1000/s = 1000/100 = 108.計(jì)算受拉區(qū)縱向鋼筋的等效直徑deq