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 500092012）混凝土結(jié)構(gòu)設(shè)計(jì)規(guī)范（gb 500102010）2.幾何參數(shù)：樓梯凈跨: l1 = 2700 mm樓梯高度: h = 1800 mm梯板厚: t = 110 mm踏步數(shù): n = 10(階)上平臺(tái)樓梯梁寬度: b1 = 200 mm下平臺(tái)樓梯梁寬度: b2 = 200 mm3.荷載標(biāo)準(zhǔn)值：可變荷載：q = 3.50kn/m2面層荷載：qm = 1.50kn/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 = 3.00*104 n/mm2鋼筋強(qiáng)度等級(jí): hrb400 fy = 360 n/mm2 es = 2.00*105 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：光面鋼筋梯段板縱筋合力點(diǎn)至近邊距離：as = 25.00 mm考慮支座嵌固作用求配筋時(shí)彎矩折減1 = 0.8求裂縫時(shí)彎矩折減2 = 0.8求撓度時(shí)彎矩折減3 = 0.8四、計(jì)算過程：1. 樓梯幾何參數(shù)：踏步高度：h = 0.1800 m踏步寬度：b = 0.3000 m計(jì)算跨度：l0 = l1(b1b2)/2 = 2.70(0.200.20)/2 = 2.90 m梯段板與水平方向夾角余弦值：cos = 0.857 2. 荷載計(jì)算( 取 b = 1m 寬板帶)：(1) 梯段板：面層：gkm = (bb*h/b)*qm = (11*0.18/0.30)*1.50 = 2.40 kn/m自重：gkt = rc*b*(t/cosh/2) = 25*1*(0.11/0.8570.18/2) = 5.46 kn/m抹灰：gks = rs*b*c/cos = 20*1*0.02/0.857 = 0.47 kn/m恒荷標(biāo)準(zhǔn)值：pk = gkmgktgksqf = 2.405.460.470.20 = 8.52 kn/m恒荷控制：pn(g) = 1.35*pkq*0.7*b*q = 1.35*8.521.40*0.7*1*3.50 = 14.94 kn/m活荷控制：pn(l) = g*pkq*b*q = 1.20*8.521.40*1*3.50 = 15.13 kn/m荷載設(shè)計(jì)值：pn = max pn(g) , pn(l) = 15.13 kn/m3. 正截面受彎承載力計(jì)算：左端支座反力: rl = 21.94 kn右端支座反力: rr = 21.94 kn最大彎矩截面距左支座的距離: lmax = 1.45 m最大彎矩截面距左邊彎折處的距離: x = 1.45 mmmax = rl*lmaxpn*x2/2 = 21.94*1.4515.13*1.452/2 = 15.90 knm考慮支座嵌固折減后的最大彎矩: mmax = 1*mmax = 0.80*15.90 = 12.72 knm相對(duì)受壓區(qū)高度：= 0.131833 配筋率：= 0.005237縱筋(1號(hào))計(jì)算面積：as = 445.12 mm2支座負(fù)筋(2、3號(hào))計(jì)算面積：as=as = 445.12 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：445.12 mm2采用方案：12150實(shí)配面積： 754 mm22.2號(hào)鋼筋計(jì)算結(jié)果(支座)計(jì)算面積as：445.12 mm2采用方案：10150實(shí)配面積： 524 mm23.3號(hào)鋼筋計(jì)算結(jié)果采用方案：8200實(shí)配面積： 251 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 = 3*(mgk+mqk) = 3*(qgk + qqk)*l02/8 = 0.80*(8.52 + 3.500)*2.902/8 = 10.112 kn*m2.計(jì)算永久組合彎距值mq:mq = 3*(mgk+mqk) = 3*(qgk + q*qqk)*l02/8 = 0.80*(8.52 + 0.50*3.500)*2.902/8 = 8.640 kn*m3.計(jì)算受彎構(gòu)件的短期剛度 bsk1) 計(jì)算按荷載荷載效應(yīng)的兩種組合作用下，構(gòu)件縱向受拉鋼筋應(yīng)力 sk = mk/(0.87*h0*as) 混規(guī)(7.1.4-3) = 10.112*106/(0.87*85*754) = 181.354 n/mm sq = mq/(0.87*h0*as) 混規(guī)(7.1.4-3) = 8.640*106/(0.87*85*754) = 154.958 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*110= 55000 mm2 te = as/ate 混規(guī)(7.1.25) = 754/55000 = 1.371%3) 計(jì)算裂縫間縱向受拉鋼筋應(yīng)變不均勻系數(shù) k = 1.1-0.65*ftk/(te*sk) 混規(guī)(7.1.22) = 1.1-0.65*2.01/(1.371%*181.354) = 0.574 q = 1.1-0.65*ftk/(te*sq) 混規(guī)(7.1.22) = 1.1-0.65*2.01/(1.371%*154.958) = 0.4854) 計(jì)算鋼筋彈性模量與混凝土模量的比值 e e = es/ec = 2.00*105/(3.00*104) = 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) = 754/(1000*85) = 0.887%7) 計(jì)算受彎構(gòu)件的短期剛度 bs bsk = es*as*h02/1.15*k+0.2+6*e*/(1+ 3.5*f) 混規(guī)(7.2.3-1) = 2.00*105*754*852/1.15*0.574+0.2+6*6.667*0.887%/(1+3.5*0.0) = 8.964*102 kn*m2 bsq = es*as*h02/1.15*q+0.2+6*e*/(1+ 3.5*f) 混規(guī)(7.2.3-1) = 2.00*105*754*852/1.15*0.485+0.2+6*6.667*0.887%/(1+3.5*0.0) = 9.793*102 kn*m24.計(jì)算受彎構(gòu)件的長(zhǎng)期剛度b1) 確定考慮荷載長(zhǎng)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 混規(guī)(7.2.5)2) 計(jì)算受彎構(gòu)件的長(zhǎng)期剛度 b bk = mk/(mq*(-1)+mk)*bsk 混規(guī)(7.2.2-1) = 10.112/(8.640*(2.0-1)+10.112)*8.964*102 = 4.834*102 kn*m2 bq = bsq/ 混規(guī)(7.2.2-2) = 9.793/2.000*102 = 4.897*102 kn*m2 b = min(bk,bq) = min(4.834,4.897 = 4.834*102 kn*m25.計(jì)算受彎構(gòu)件撓度f(wàn)maxk = 5*3*(qgk+qqk)*l04/(384*bk) = 5*0.80*(8.52+3.500)*2.904/(384*4.834*102) = 14.261 mm6.驗(yàn)算撓度撓度限值f0=l0/200=2.90/200=14.500 mmfmax=14.261mmf0=14.500mm，滿足規(guī)范要求!七、裂縫寬度驗(yàn)算: 1.計(jì)算準(zhǔn)永久組合彎距值mq:mq = 2*(mgk+mqk) = 2*(qgk + qqk)*l02/8 = 0.80*(8.52 + 0.50*3.500)*2.902/8 = 8.640 kn*m2.光面鋼筋,所以取值vi=0.73.c = 154.計(jì)算按荷載荷載效應(yīng)的準(zhǔn)永久組合作用下，構(gòu)件縱向受拉鋼筋應(yīng)力sq = mq/(0.87*h0*as) 混規(guī)(7.1.43) = 8.640*106/(0.87*85.00*754) = 154.958 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*110= 55000 mm2te = as/ate 混規(guī)(7.1.25) = 754/55000 = 1.371%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*sq) 混規(guī)(7.1.22) = 1.1-0.65*2.01/(1.371%*154.958) = 0.4857.計(jì)算單位面積鋼筋根數(shù)nn = 1000/s = 1000/150 = 68.計(jì)算受拉區(qū)縱向鋼