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):TB1二、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 500102010）2.幾何參數(shù)：樓梯凈跨: L1 = 2600 mm樓梯高度: H = 1800 mm梯板厚: t = 100 mm踏步數(shù): n = 11(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 = 1.70kN/m2欄桿荷載：qf = 0.20kN/m永久荷載分項(xiàng)系數(shù): G =

2、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 = 20.0 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 = 0.1636

3、 m踏步寬度：b = 0.2600 m計(jì)算跨度：L0 = L1(b1b2)/2 = 2.60(0.200.20)/2 = 2.80 m梯段板與水平方向夾角余弦值：cos = 0.846 2. 荷載計(jì)算( 取 B = 1m 寬板帶)：(1) 梯段板：面層：gkm = (BB*h/b)*qm = (11*0.16/0.26)*1.70 = 2.77 kN/m自重：gkt = Rc*B*(t/cosh/2) = 25*1*(0.10/0.8460.16/2) = 5.00 kN/m抹灰：gks = RS*B*c/cos = 20*1*0.02/0.846 = 0.47 kN/m恒荷標(biāo)準(zhǔn)值：Pk =

4、gkmgktgksqf = 2.775.000.470.20 = 8.44 kN/m恒荷控制：Pn(G) = 1.35*PkQ*0.7*B*q = 1.35*8.441.40*0.7*1*3.50 = 14.83 kN/m活荷控制：Pn(L) = G*PkQ*B*q = 1.20*8.441.40*1*3.50 = 15.03 kN/m荷載設(shè)計(jì)值：Pn = max Pn(G) , Pn(L) = 15.03 kN/m3. 正截面受彎承載力計(jì)算：左端支座反力: Rl = 21.04 kN右端支座反力: Rr = 21.04 kN最大彎矩截面距左支座的距離: Lmax = 1.40 m最大彎矩截面

5、距左邊彎折處的距離: x = 1.40 mMmax = Rl*LmaxPn*x2/2 = 21.04*1.4015.03*1.402/2 = 14.73 kN·m相對(duì)受壓區(qū)高度：= 0.203910 配筋率：= 0.008100縱筋(1號(hào))計(jì)算面積：As = 607.48 mm2支座負(fù)筋(2、3號(hào))計(jì)算面積：As'=*As = 0.25*607.48 = 151.87 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：607.48 mm2采用方案：10100實(shí)配面積： 785 mm22.2/3號(hào)鋼筋計(jì)算結(jié)果(支座)計(jì)算面積As'：15

6、1.87 mm2采用方案：12200實(shí)配面積： 565 mm23.4號(hào)鋼筋計(jì)算結(jié)果采用方案：6200實(shí)配面積： 141 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 = (8.44 + 3.500)*2.802/8 = 11.703 kN*m2.計(jì)算永久組合彎距值Mq:Mq = Mgk+Mqk = (qgk + q*qqk)*L02/8 = (8.44 + 0.50*3.500)*2.802/8 = 9.988 kN*m3.計(jì)算受彎構(gòu)件

7、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) = 11.703*106/(0.87*75*785) = 228.365 N/mm sq = Mq/(0.87*h0*As) 混規(guī)(7.1.4-3) = 9.988*106/(0.87*75*785) = 194.900 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*100= 50000 mm2 te = As/Ate 混規(guī)(7.1.25) = 785/50000

8、 = 1.571%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/(1.571%*228.365) = 0.736 q = 1.1-0.65*ftk/(te*sq) 混規(guī)(7.1.22) = 1.1-0.65*2.01/(1.571%*194.900) = 0.6734) 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/

9、(b*h0) = 785/(1000*75) = 1.047%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*785*752/1.15*0.736+0.2+6*6.667*1.047%/(1+3.5*0.0) = 6.031*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*785*752/1.15*0.673+0.2+6*6.667*1.047%/(1+3.5*0.0) =

10、 6.342*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) = 11.703/(9.988*(2.0-1)+11.703)*6.031*102 = 3.254*102 kN*m2 Bq = Bsq/ 混規(guī)(7.2.2-2) = 6.342/2.000*102 = 3.171*102 kN*m2 B = min(Bk,Bq) = min(3.254,3.171 = 3.171*102 kN*m25.

11、計(jì)算受彎構(gòu)件撓度fmaxk = 5*(qgk+qqk)*L04/(384*Bk) = 5*(8.44+3.500)*2.804/(384*3.171*102) = 10.138 mm6.驗(yàn)算撓度撓度限值f0=L0/200=2.80/200=14.000 mmfmax=10.138mmf0=14.000mm，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 = Mgk+Mqk = (qgk + qqk)*L02/8 = (8.44 + 0.50*3.500)*2.802/8 = 9.988 kN*m2.光面鋼筋,所以取值Vi=0.73.C = 204.計(jì)算按荷載荷載效應(yīng)的準(zhǔn)永久

12、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) = 9.988*106/(0.87*75.00*785) = 194.900 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*100= 50000 mm2te = As/Ate 混規(guī)(7.1.25) = 785/50000 = 1.571%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/(1.571%*194.900) = 0.

13、6737.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*Vi*di) = 10*102/(10*0.7*10) = 149.計(jì)算最大裂縫寬度max =cr*sq/ES*(1.9*C+0.08*deq/te) 混規(guī)(7.1.21) = 1.9*0.673*194.900/2.0*105*(1.9*20+0.08*14/1.571%) = 0.1362 mm 0.30 mm,滿足規(guī)范要求板式樓梯計(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):TB2二、示意圖：三、基本資料：1.依據(jù)規(guī)

14、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 500102010）2.幾何參數(shù)：樓梯凈跨: L1 = 3120 mm樓梯高度: H = 2150 mm梯板厚: t = 120 mm踏步數(shù): n = 13(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 = 1.70kN/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 = 1

15、4.30 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 = 20.0 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 = 0.1654 m踏步寬度：b = 0.2600 m計(jì)算跨度：L0 = L1(b1b2)/2 = 3.12(0.200.20)/2 = 3.

16、32 m梯段板與水平方向夾角余弦值：cos = 0.844 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)*1.70 = 2.78 kN/m自重：gkt = Rc*B*(t/cosh/2) = 25*1*(0.12/0.8440.17/2) = 5.62 kN/m抹灰：gks = RS*B*c/cos = 20*1*0.02/0.844 = 0.47 kN/m恒荷標(biāo)準(zhǔn)值：Pk = gkmgktgksqf = 2.785.620.470.20 = 9.08 kN/m恒荷控制：Pn(G) = 1.35*PkQ

17、*0.7*B*q = 1.35*9.081.40*0.7*1*3.50 = 15.69 kN/m活荷控制：Pn(L) = G*PkQ*B*q = 1.20*9.081.40*1*3.50 = 15.79 kN/m荷載設(shè)計(jì)值：Pn = max Pn(G) , Pn(L) = 15.79 kN/m3. 正截面受彎承載力計(jì)算：左端支座反力: Rl = 26.22 kN右端支座反力: Rr = 26.22 kN最大彎矩截面距左支座的距離: Lmax = 1.66 m最大彎矩截面距左邊彎折處的距離: x = 1.66 mMmax = Rl*LmaxPn*x2/2 = 26.22*1.6615.79*1.

18、662/2 = 21.76 kN·m相對(duì)受壓區(qū)高度：= 0.185891 配筋率：= 0.007384縱筋(1號(hào))計(jì)算面積：As = 701.48 mm2支座負(fù)筋(2、3號(hào))計(jì)算面積：As'=*As = 0.25*701.48 = 175.37 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：701.48 mm2采用方案：10100實(shí)配面積： 785 mm22.2/3號(hào)鋼筋計(jì)算結(jié)果(支座)計(jì)算面積As'：175.37 mm2采用方案：12200實(shí)配面積： 565 mm23.4號(hào)鋼筋計(jì)算結(jié)果采用方案：6200實(shí)配面積： 141 mm2

19、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 = (9.08 + 3.500)*3.322/8 = 17.330 kN*m2.計(jì)算永久組合彎距值Mq:Mq = Mgk+Mqk = (qgk + q*qqk)*L02/8 = (9.08 + 0.50*3.500)*3.322/8 = 14.919 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)

20、混規(guī)(7.1.4-3) = 17.330*106/(0.87*95*785) = 266.976 N/mm sq = Mq/(0.87*h0*As) 混規(guī)(7.1.4-3) = 14.919*106/(0.87*95*785) = 229.832 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*120= 60000 mm2 te = As/Ate 混規(guī)(7.1.25) = 785/60000 = 1.309%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.

21、1.22) = 1.1-0.65*2.01/(1.309%*266.976) = 0.726 q = 1.1-0.65*ftk/(te*sq) 混規(guī)(7.1.22) = 1.1-0.65*2.01/(1.309%*229.832) = 0.6664) 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*95) = 0.827%7) 計(jì)算受彎構(gòu)件的短期剛度 BS Bsk = Es*As*

22、h02/1.15*k+0.2+6*E*/(1+ 3.5*f) 混規(guī)(7.2.3-1) = 2.00*105*785*952/1.15*0.726+0.2+6*6.667*0.827%/(1+3.5*0.0) = 10.380*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*785*952/1.15*0.666+0.2+6*6.667*0.827%/(1+3.5*0.0) = 10.936*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)=

23、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) = 17.330/(14.919*(2.0-1)+17.330)*10.380*102 = 5.578*102 kN*m2 Bq = Bsq/ 混規(guī)(7.2.2-2) = 10.936/2.000*102 = 5.468*102 kN*m2 B = min(Bk,Bq) = min(5.578,5.468 = 5.468*102 kN*m25.計(jì)算受彎構(gòu)件撓度fmaxk = 5*(qgk+qqk)*L04/(384*Bk) = 5*(9.08+3.500

24、)*3.324/(384*5.468*102) = 15.389 mm6.驗(yàn)算撓度撓度限值f0=L0/200=3.32/200=16.600 mmfmax=15.389mmf0=16.600mm，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 = Mgk+Mqk = (qgk + qqk)*L02/8 = (9.08 + 0.50*3.500)*3.322/8 = 14.919 kN*m2.光面鋼筋,所以取值Vi=0.73.C = 204.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) = 14.91

25、9*106/(0.87*95.00*785) = 229.832 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*120= 60000 mm2te = As/Ate 混規(guī)(7.1.25) = 785/60000 = 1.309%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/(1.309%*229.832) = 0.6667.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

26、等效直徑deqdeq= (ni*di2)/(ni*Vi*di) = 10*102/(10*0.7*10) = 149.計(jì)算最大裂縫寬度max =cr*sq/ES*(1.9*C+0.08*deq/te) 混規(guī)(7.1.21) = 1.9*0.666*229.832/2.0*105*(1.9*20+0.08*14/1.309%) = 0.1796 mm 0.30 mm,滿足規(guī)范要求板式樓梯計(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):TB3二、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 500102010）2.幾何參數(shù)：

27、樓梯凈跨: L1 = 3900 mm樓梯高度: H = 2700 mm梯板厚: t = 130 mm踏步數(shù): n = 16(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 = 1.70kN/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/mm2

28、Ec = 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 = 20.0 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 = 0.1688 m踏步寬度：b = 0.2600 m計(jì)算跨度：L0 = L1(b1b2)/2 = 3.90(0.200.20)/2 = 4.10 m梯段板與水平方向夾角余弦值：cos = 0.839 2. 荷載計(jì)算( 取 B = 1m 寬板帶)：(

29、1) 梯段板：面層：gkm = (BB*h/b)*qm = (11*0.17/0.26)*1.70 = 2.80 kN/m自重：gkt = Rc*B*(t/cosh/2) = 25*1*(0.13/0.8390.17/2) = 5.98 kN/m抹灰：gks = RS*B*c/cos = 20*1*0.02/0.839 = 0.48 kN/m恒荷標(biāo)準(zhǔn)值：Pk = gkmgktgksqf = 2.805.980.480.20 = 9.46 kN/m恒荷控制：Pn(G) = 1.35*PkQ*0.7*B*q = 1.35*9.461.40*0.7*1*3.50 = 16.21 kN/m活荷控制：P

30、n(L) = G*PkQ*B*q = 1.20*9.461.40*1*3.50 = 16.26 kN/m荷載設(shè)計(jì)值：Pn = max Pn(G) , Pn(L) = 16.26 kN/m3. 正截面受彎承載力計(jì)算：左端支座反力: Rl = 33.33 kN右端支座反力: Rr = 33.33 kN最大彎矩截面距左支座的距離: Lmax = 2.05 m最大彎矩截面距左邊彎折處的距離: x = 2.05 mMmax = Rl*LmaxPn*x2/2 = 33.33*2.0516.26*2.052/2 = 34.16 kN·m相對(duì)受壓區(qū)高度：= 0.247234 配筋率：= 0.0098

31、21縱筋(1號(hào))計(jì)算面積：As = 1031.17 mm2支座負(fù)筋(2、3號(hào))計(jì)算面積：As'=*As = 0.25*1031.17 = 257.79 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：1031.17 mm2采用方案：12100實(shí)配面積：1131 mm22.2/3號(hào)鋼筋計(jì)算結(jié)果(支座)計(jì)算面積As'：257.79 mm2采用方案：12200實(shí)配面積： 565 mm23.4號(hào)鋼筋計(jì)算結(jié)果采用方案：6200實(shí)配面積： 141 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

32、矩值1.計(jì)算標(biāo)準(zhǔn)組合彎距值Mk:Mk = Mgk+Mqk = (qgk + qqk)*L02/8 = (9.46 + 3.500)*4.102/8 = 27.241 kN*m2.計(jì)算永久組合彎距值Mq:Mq = Mgk+Mqk = (qgk + q*qqk)*L02/8 = (9.46 + 0.50*3.500)*4.102/8 = 23.564 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) = 27.241*106/(0.87*105*1131) = 263.670

33、N/mm sq = Mq/(0.87*h0*As) 混規(guī)(7.1.4-3) = 23.564*106/(0.87*105*1131) = 228.078 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) = 1131/65000 = 1.740%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/(1.740%*263.670) = 0.815

34、 q = 1.1-0.65*ftk/(te*sq) 混規(guī)(7.1.22) = 1.1-0.65*2.01/(1.740%*228.078) = 0.7714) 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) = 1131/(1000*105) = 1.077%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) =

35、 2.00*105*1131*1052/1.15*0.815+0.2+6*6.667*1.077%/(1+3.5*0.0) = 15.901*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*1131*1052/1.15*0.771+0.2+6*6.667*1.077%/(1+3.5*0.0) = 16.436*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 = M

36、k/(Mq*(-1)+Mk)*Bsk 混規(guī)(7.2.2-1) = 27.241/(23.564*(2.0-1)+27.241)*15.901*102 = 8.526*102 kN*m2 Bq = Bsq/ 混規(guī)(7.2.2-2) = 16.436/2.000*102 = 8.218*102 kN*m2 B = min(Bk,Bq) = min(8.526,8.218 = 8.218*102 kN*m25.計(jì)算受彎構(gòu)件撓度fmaxk = 5*(qgk+qqk)*L04/(384*Bk) = 5*(9.46+3.500)*4.104/(384*8.218*102) = 18.042 mm6.驗(yàn)算撓

37、度撓度限值f0=L0/200=4.10/200=20.500 mmfmax=18.042mmf0=20.500mm，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 = Mgk+Mqk = (qgk + qqk)*L02/8 = (9.46 + 0.50*3.500)*4.102/8 = 23.564 kN*m2.光面鋼筋,所以取值Vi=0.73.C = 204.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) = 23.564*106/(0.87*105.00*1131) = 228.078 N/mm5

38、.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) = 1131/65000 = 1.740%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/(1.740%*228.078) = 0.7717.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*Vi*di) = 10*

39、122/(10*0.7*12) = 179.計(jì)算最大裂縫寬度max =cr*sq/ES*(1.9*C+0.08*deq/te) 混規(guī)(7.1.21) = 1.9*0.771*228.078/2.0*105*(1.9*20+0.08*17/1.740%) = 0.1940 mm 0.30 mm,滿足規(guī)范要求板式樓梯計(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):TB4二、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 500102010）2.幾何參數(shù)：樓梯凈跨: L1 = 2080 mm樓梯高度: H = 1475 mm梯板

40、厚: t = 100 mm踏步數(shù): n = 9(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 = 1.70kN/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 =

41、 360 N/mm2 Es = 2.00*105 N/mm2保護(hù)層厚度：c = 20.0 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 = 0.1639 m踏步寬度：b = 0.2600 m計(jì)算跨度：L0 = L1(b1b2)/2 = 2.08(0.200.20)/2 = 2.28 m梯段板與水平方向夾角余弦值：cos = 0.846 2. 荷載計(jì)算( 取 B = 1m 寬板帶)：(1) 梯段板：面層：gkm = (BB*h/b)*qm = (11*0.16

42、/0.26)*1.70 = 2.77 kN/m自重：gkt = Rc*B*(t/cosh/2) = 25*1*(0.10/0.8460.16/2) = 5.00 kN/m抹灰：gks = RS*B*c/cos = 20*1*0.02/0.846 = 0.47 kN/m恒荷標(biāo)準(zhǔn)值：Pk = gkmgktgksqf = 2.775.000.470.20 = 8.45 kN/m恒荷控制：Pn(G) = 1.35*PkQ*0.7*B*q = 1.35*8.451.40*0.7*1*3.50 = 14.84 kN/m活荷控制：Pn(L) = G*PkQ*B*q = 1.20*8.451.40*1*3.5

43、0 = 15.04 kN/m荷載設(shè)計(jì)值：Pn = max Pn(G) , Pn(L) = 15.04 kN/m3. 正截面受彎承載力計(jì)算：左端支座反力: Rl = 17.14 kN右端支座反力: Rr = 17.14 kN最大彎矩截面距左支座的距離: Lmax = 1.14 m最大彎矩截面距左邊彎折處的距離: x = 1.14 mMmax = Rl*LmaxPn*x2/2 = 17.14*1.1415.04*1.142/2 = 9.77 kN·m相對(duì)受壓區(qū)高度：= 0.129921 配筋率：= 0.005161縱筋(1號(hào))計(jì)算面積：As = 387.06 mm2支座負(fù)筋(2、3號(hào))計(jì)

44、算面積：As'=*As = 0.25*387.06 = 96.76 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：387.06 mm2采用方案：10140實(shí)配面積： 561 mm22.2/3號(hào)鋼筋計(jì)算結(jié)果(支座)計(jì)算面積As'：96.76 mm2采用方案：12200實(shí)配面積： 565 mm23.4號(hào)鋼筋計(jì)算結(jié)果采用方案：6200實(shí)配面積： 141 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)*L

45、02/8 = (8.45 + 3.500)*2.282/8 = 7.764 kN*m2.計(jì)算永久組合彎距值Mq:Mq = Mgk+Mqk = (qgk + q*qqk)*L02/8 = (8.45 + 0.50*3.500)*2.282/8 = 6.627 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) = 7.764*106/(0.87*75*561) = 212.100 N/mm sq = Mq/(0.87*h0*As) 混規(guī)(7.1.4-3) = 6.627*106

46、/(0.87*75*561) = 181.035 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*100= 50000 mm2 te = As/Ate 混規(guī)(7.1.25) = 561/50000 = 1.122%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/(1.122%*212.100) = 0.551 q = 1.1-0.65*ftk/(te*sq) 混規(guī)(7.1.22) = 1.1-0.65*2.01/(1.122%*181.035) = 0.4574) 計(jì)算鋼筋彈性模量與混凝土模量的比值 E E =