AT1板式樓梯計(jì)算書

1、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）(2015版)2.幾何參數(shù)：樓梯凈跨: L1 = 3300 mm樓梯高度: H = 1850 mm梯板厚: t = 130 mm踏步數(shù): n = 12(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 = 1.00kN/m2欄桿荷載：qf = 0.20kN/m永久荷載分項(xiàng)

2、系數(shù): G = 1.30可變荷載分項(xiàng)系數(shù): Q = 1.50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 = 20.00 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

3、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 = 0.1542 m踏步寬度：b = 0.3000 m計(jì)算跨度：L0 = L1(b1b2)/2 = 3.30(0.200.20)/2 = 3.50 m梯段板與水平方向夾角余弦值：cos = 0.889 2. 荷載計(jì)算( 取 B = 1m 寬板帶)：(1) 梯段板：面層：gkm = (BB*h/b)*qm = (11*0.15/0.30)*1.00 = 1.51 kN/m自重：gkt = Rc*B*(t/cosh/2) = 25*1*(0.13/0.8890.15/2) = 5.58 kN/m抹灰：gks = RS*B

4、*c/cos = 20*1*0.02/0.889 = 0.45 kN/m恒荷標(biāo)準(zhǔn)值：Pk = gkmgktgksqf = 1.515.580.450.20 = 7.74 kN/m恒荷控制：Pn(G) = 1.35*PkQ*0.7*B*q = 1.35*7.741.50*0.7*1*3.50 = 14.13 kN/m活荷控制：Pn(L) = G*PkQ*B*q = 1.30*7.741.50*1*3.50 = 15.32 kN/m荷載設(shè)計(jì)值：Pn = max Pn(G) , Pn(L) = 15.32 kN/m3. 正截面受彎承載力計(jì)算：左端支座反力: Rl = 26.81 kN右端支座反力:

5、Rr = 26.81 kN最大彎矩截面距左支座的距離: Lmax = 1.75 m最大彎矩截面距左邊彎折處的距離: x = 1.75 mMmax = Rl*LmaxPn*x2/2 = 26.81*1.7515.32*1.752/2 = 23.46 kN·m考慮支座嵌固折減后的最大彎矩: Mmax' = 1*Mmax = 0.80*23.46 = 18.76 kN·m相對(duì)受壓區(qū)高度：= 0.115068 配筋率：= 0.004571縱筋(1號(hào))計(jì)算面積：As = 502.78 mm2支座負(fù)筋(2、3號(hào))計(jì)算面積：As'=As = 502.78 mm2五、計(jì)算結(jié)

6、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：502.78 mm2采用方案：10100實(shí)配面積： 785 mm22.2號(hào)鋼筋計(jì)算結(jié)果(支座)計(jì)算面積As'：502.78 mm2采用方案：10100實(shí)配面積： 785 mm23.3號(hào)鋼筋計(jì)算結(jié)果采用方案：6250實(shí)配面積： 113 mm2六、跨中撓度計(jì)算: Mq - 按荷載效應(yīng)的準(zhǔn)永久組合計(jì)算的彎矩值1.計(jì)算永久組合彎距值Mq:Mq = 3*(Mgk+Mqk) = 3*(qgk + q*qqk)*L02/8 = 0.80*(7.74 + 0.50*3.500)*3.502/8 = 11.631 kN*m2.計(jì)算受彎構(gòu)

7、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 sq = Mq/(0.87*h0*As) 混規(guī)(7.1.4-3) = 11.631*106/(0.87*110*785) = 154.745 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*130= 65000 mm2 te = As/Ate 混規(guī)(7.1.25) = 785/65000 = 1.208%3) 計(jì)算裂縫間縱向受拉鋼筋應(yīng)變不均勻系數(shù) q = 1.1-0.65*ftk/(te*sq) 混規(guī)(7.1.22) = 1.1

8、-0.65*2.01/(1.208%*154.745) = 0.4014) 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) = 785/(1000*110) = 0.714%7) 計(jì)算受彎構(gòu)件的短期剛度 BS 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*785*1102/1.15*0.401+0.2+6*6.667*0

9、.714%/(1+3.5*0.0) = 20.069*102 kN*m23.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 混規(guī)(7.2.5)2) 計(jì)算受彎構(gòu)件的長期剛度 B Bq = Bsq/ 混規(guī)(7.2.2-2) = 20.069/2.000*102 = 10.035*102 kN*m24.計(jì)算受彎構(gòu)件撓度fmaxk = 5*3*(qgk+q*qqk)*L04/(384*B) = 5*0.80*(7.74+0.5*3.500)*3.504/(384*10.035*102) = 14.790 mm6.驗(yàn)算撓度撓度限值f0=L0/200=3.

10、50/200=17.500 mmfmax=14.790mmf0=17.500mm，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*(7.74 + 0.50*3.500)*3.502/8 = 11.631 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) = 11.631*106/(0.87*110.00*785) = 154.745 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*130= 65000 mm2te = As/Ate 混規(guī)(7.1.25) = 785/65000 = 1.208%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/(1.208%*154.745) = 0.4017.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deqdeq= (ni*di2)/(ni*