梁式楼梯计算.doc

结构构件计算书梁式楼梯计算项目名称_日 期_设 计 者_校 对 者_一、工程名称: LT-1二、示意图三、基本资料1依据规范：建筑结构荷载规范（GB 500092002）混凝土结构设计规范（GB 500102010）2几何参数：楼梯类型： 梁式楼梯（ 型）支座条件： 两端铰支斜梯段水平长度： L1 = 2700 mm梯段净跨： Ln = L1 = 2700 mm楼梯高度：H = 1500mm楼梯宽度：W = 3000 mm梯板厚：t = 70 mm楼梯级数：n = 10(阶)踏步宽度：b = 300 mm踏步高度：h = 150 mm上平台楼梯梁宽度: b1 = 200 mm下平台楼梯梁宽度: b2 = 200 mm楼梯梁高度：h3 = 300 mm楼梯梁宽度： b3 = 200 mm3荷载标准值：可变荷载：q = 2.50kN/m2面层荷载：qm = 4.00kN/m2栏杆荷载：qf = 0.20kN/m永久荷载分项系数: G = 1.20可变荷载分项系数: Q = 1.40准永久值系数: q = 0.504材料信息：混凝土强度等级: C30fc = 14.30 N/mm2ftk = 2.01 N/mm2ft = 1.43 N/mm2梯梁纵筋强度等级: HPB300ES = 210000000 N/mm2fy = 270.0 N/mm2受拉区纵向钢筋类别：光面钢筋其余钢筋选用HPB300钢fyv = 270.0 N/mm2保护层厚度: c = 20 mm顶棚厚度 c1 20mm顶棚容重 Rs 20.0 kN/m3混凝土容重 Rc 25.0 kN/m3混凝土弹性模量 Ec = 3.00104 N/mm2钢筋弹性模量 Es = 2.1105 N/mm2梯段板纵向受力钢筋合力点至近边距离as1 = 25 mm梯梁纵向受力钢筋合力点至近边距离as2 = 30 mm四、计算过程：说明：本计算书中所有的剪力、弯矩、挠度均由建筑结构静力计算手册中 单跨梁的内力及变位计算公式所得。1楼梯几何参数：梯段倾角余弦值：cos = b/sqrt(b2h2) = 300.00/sqrt(300.002150.002) =0.89梯梁计算跨度:L0 = Ln = 2700 mm梯段板计算跨度:B0 = W2*b3 = 30002*200 =2600 mm梯段板平均厚度:ht = (h2t/cos)/2 = (150.002*70.00/0.89)/2 = 153.26 mm2荷载设计值：(1) 梯段板荷载设计值（取一个踏步宽板带）：自重：gkb = Rc*ht*b = 25.0*0.15*0.30 = 1.15 kN/m面层：gkm = qm*(hb) = 4.00*(0.150.30) = 1.80 kN/m抹灰：gks = Rs*c1*b/cos = 20.0*0.02*0.30/0.89 = 0.13 kN/m恒荷标准值：Pkb = gkbgkmgks = 1.151.800.13 = 3.08 kN/m恒荷控制：Pb(G) = 1.35*PkbQ*0.7*b*q = 1.35*3.081.40*0.7*0.30*2.50 = 4.90 kN/m活荷控制：Pb(L) = G*PkbQ*b*q = 1.20*3.081.40*0.30*2.50 = 4.75 kN/m荷载设计值：Pb = max Pb(G) , Pb(L) = 4.90 kN/m(2) 斜梯段梯梁荷载设计值：自重放大系数（考虑面层）:b=1.1自重：gkl = b*Rc*b3*h3/cos = 1.1*25.0*0.20*0.30/0.89 = 1.84 kN/m恒荷标准值：Pkl = Pkb/b*W/2gklqf = 3.08/0.30*3.00/21.840.20 = 17.46 kN/m恒荷控制：Pl(G) = 1.35*PklQ*0.7*q*W/2 = 1.35*17.461.40*0.7*2.50*3.00/2 = 27.25 kN/m活荷控制：Pl(L) = G*PklQ*q*W/2 = 1.20*17.461.40*2.50*3.00/2 = 26.21 kN/m荷载设计值：Pl = max Pl(G) , Pl(L) = 27.25 kN/m3梯梁斜截面受剪承载力计算：Vmax = 36.79 kNVmax0.7*ft*b3*(h3as2)= 0.7*1430.00*0.20*(0.300.03)= 54.05 kN按构造配置箍筋。4正截面受弯承载力计算：(1) 梯段斜板计算：计算高度：H = (t+h*cos)/2 = 102.08 mm计算宽度：b0 = b/cos = 335.41 mmMmax = Pb*B02/8 = 4.90*2.602/8 = 4.14 kNm = 0.5894%纵筋/计算面积：As = 156.95 mm2(2) 梯梁计算：M中 = 24.83 kNm = 0.2882%纵筋计算面积：As = 350.15 mm2左支座：按构造配筋。钢筋计算面积：As = 120.00 mm2右支座：按构造配筋。钢筋计算面积：As = 120.00 mm2五、计算结果：1纵筋计算结果：计算面积：350.15 mm2采用方案：510实配面积：Ag = 393mm2实际配筋率： = 0.3232%2钢筋计算结果：计算面积：120.00 mm2采用方案：210实配面积：Ag = 157mm2实际配筋率： = 0.2909%3箍筋计算结果：采用方案：2d61504钢筋计算结果：计算面积：120.00 mm2采用方案：210实配面积：Ag = 157mm25纵筋/计算结果：计算面积：As = 156.95 mm2采用方案：d880实配面积：Ag = 211mm2六、跨中挠度验算：Mk - 按荷载效应的标准组合计算的弯矩值Mq - 按荷载效应的准永久组合计算的弯矩值取准永久值系数 q = 0.5梯段梯梁标准荷载：Qk =Pklq*W/2=17.462.50*3.00/2=21.21 kN/m梯段梯梁准永久荷载：Qq =Pklq*q*W/2=17.460.5*2.50*3.00/2=19.34 kN/m(1) 挠度验算参数：Mk = 19.33 kNmMq = 17.62 kNm(2) 短期刚度Bs与长期刚度B：按下列公式计算：k 1.10.65*ftk/(te*sk)(混规(7.1.2-2)q 1.10.65*ftk/(te*sq)(混规(7.1.2-2)sk = Mk/(0.87*h0*AS)(混规(7.1.4-3)sq = Mq/(0.87*h0*AS)(混规(7.1.4-3)te = (AsAp)/Ate (混规(7.1.2-4)Bsk = Es*As*h02/1.15k0.26*E*/(13.5f)(混规(7.2.3-1)B = Mk/Mq*(1)Mk*Bsk(混规(7.2.2-1)Bsq = Es*As*h02/1.15q0.26*E*/(13.5f)(混规(7.2.3-1)B = Bsq/(混规(7.2.2-2)B = min(Bsk,Bsq)sk = Mk/(0.87*h0*Ag) = 19.33*106/(0.87*270*393) = 209.55 N/mmte = Ag/(0.5h3*b3) = 393/(0.5*300*200) = 1.31% sq = Mq/(0.87*h0*Ag) = 17.62*106/(0.87*270*393) = 191.03 N/mmte = Ag/(0.5h3*b3) = 393/(0.5*300*200) = 1.31% q = 1.10.65*ftk/(te*sq) = 1.10.65*2.01/(1.31%*191.03) = 0.58钢筋弹性模量与混凝土模量的比值E = Es/Ec = 7.00受拉翼缘面积与腹板有效面积的比值：f 0纵向受拉钢筋配筋率 = 0.7272%Bsk = Es*Ag*h02/1.15k0.26*E*/(13.5f) = 210*393*0.272/1.15*0.620.26*7.00*0.7272%/(13.5*0) = 4916.87 kNm2Bsq = Es*Ag*h02/1.15q0.26*E*/(13.5f) = 210*393*0.272/1.15*0.580.26*7.00*0.7272%/(13.5*0) = 5140.14 kNm2荷载长期作用对挠度增大的影响系数：当 = 0 时， = 2.0Bk = Mk/Mq*(1)Mk*Bs = 19.33/17.62*(21)19.33*4916.87 = 2572.11 kNm2Bq = Bs/ = 5140.14/2 = 2570.07 kNm2B = min(dBk,dBq) = min(2570.07,2570.07) = 2570.07(3) 跨中挠度：f = 5.71 mm梯梁计算长度L0 = 2.70mf/L0 = 1/473 1/200，满足要求。七、梯梁裂缝宽度验算:1.计算荷载效应Mq = 17.622.C = 20 mm3.计算按荷载荷载效应的准永久组合作用下，构件纵向受拉钢筋应力sq = Mq/(0.87*h0*As) 混规(7.1.4-3) = 17.62106/(0.87*270*393) = 191.031 N/mm4.计算按有效受拉混凝土截面面积计算的纵向受拉钢筋配筋率矩形截面积: Ate = 0.5*b3*h3 = 0.5*200*300= 30000 mm2te = As/Ate 混规(7.1.2-4) = 393/30000 = 1.309%5.计算裂缝间纵向受拉钢筋应变不均匀系数 = 1.1-0.65*ftk/(te*sq) 混规(7.1.2-2) = 1.1-0.65*2.01/(1.309%*191.031) = 0.5786.计算最大裂缝宽度max =cr*sq/ES*(1.9*C+0.08*deq/te) (混规(7.1.2-1) = 1.9*0.578*191.031/2100.0105*(1.9*20+0.08*10/1.309%) = 0.0001 mm 0.30 mm满足规范要求八、跨中挠度计算: Mk - 按荷载效应的标准组合计算的弯矩值Mq - 按荷载效应的准永久组合计算的弯矩值1.计算标准组合弯距值Mk:Mk = Mgk+Mqk = (qgk + qqk)*L02/8 = (3.08 + 2.500)*2.602/8 = 4.718 kN*m2.计算永久组合弯距值Mq:Mq = Mgk+Mqk = (qgk + q*qqk)*L02/8 = (3.08 + 0.50*2.500)*2.602/8 = 3.662 kN*m3.计算受弯构件的短期刚度 Bs1) 计算按荷载荷载效应的两种组合作用下，构件纵向受拉钢筋应力 sk = Mk/(0.87*h0*As) 混规(7.1.4-3) = 4.718106/(0.87*77*211) = 333.845 N/mm sq = Mq/(0.87*h0*As) 混规(7.1.4-3) = 3.662106/(0.87*77*211) = 259.108 N/mm2) 计算按有效受拉混凝土截面面积计算的纵向受拉钢筋配筋率 矩形截面积: Ate = 0.5*b*h = 0.5*1000*102= 51041 mm2 te = As/Ate 混规(7.1.2-4) = 211/51041 = 0.413%3) 计算裂缝间纵向受拉钢筋应变不均匀系数 k = 1.1-0.65*ftk/(te*sk) 混规(7.1.2-2) = 1.1-0.65*2.01/(0.413%*333.845) = 0.152 q = 1.1-0.65*ftk/(te*sq) 混规(7.1.2-2) = 1.1-0.65*2.01/(0.413%*259.108) = -0.121 因为k 0.2，所以取k = 0.2 因为q 0.2，所以取q = 0.24) 计算钢筋弹性模量与混凝土模量的比值 E E = ES/EC = 2100.00105/(3.00104) = 7000.0005) 计算受压翼缘面积与腹板有效面积的比值 f 矩形截面，f = 06) 计算纵向受拉钢筋配筋率 = As/(b*h0) = 211/(1000*77) = 0.273%7) 计算受弯构件的短期刚度 BS BSk = ES*As*h02/1.15*k+0.2+6*E*/(1+ 3.5*f)(混规(7.2.3-1) = 2100.00105*211*772/1.15*0.200+0.2+6*7000.000*0.273%/(1+3.5*0.0) = 22.814102 kN*m2 BSq = ES*As*h02/1.15*q+0.2+6*E*/(1+ 3.5*f)(混规(7.2.3-1) = 2100.00105*211*772/1.15*0.200+0.2+6*7000.000*0.273%/(1+3.5*0.0) = 22.814102 kN*m24.计算受弯构件的长期刚度B1) 确定考虑荷载长期效应组合对挠度影响增大影响系数 当=0时，=2.0 混规(7.2.5)2) 计算受弯构件的长期刚度 B Bk = Mk/(Mq*(-1)+Mk)*BSk (混规(7.2.2-1) = 4.718/(3.662*(2.0-1)+4.718)*22.814102 = 12.845102 kN*m2 Bq = BSq/ (混规(7.2.2-2) = 4.718/3.7102 = 11.407102 kN*m2 B = min(Bk,Bq) = min(12.845,11.407 = 11.407102 kN*m25.计算受弯构件挠度fmax = 5*(qgk+qqk)*L04/(384*B) = 5*(3.08+2.500)*2.604/(384*11.407102) = 2.913 mm6.验算挠度挠度限值f0=L0/200=2600.00/200=13.000 mmfmax=2.913mmf0=13.000mm，满足规范要求!九、裂缝宽度验算: 1.计算标准组合弯距值Mk:Mk = Mgk+Mqk = (qgk + qqk)*