1、3荷载标准值: 可变荷载:q = 2.50kN/m2 面层荷载:qm = 1.70kN/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: C30 fc = 14.30 N/mm2 ftk = 2.01 N/mm2 ft = 1.43 N/mm2 梯梁纵筋强度等级: HPB235 ES = 210000000 N/mm2 fy = 210.0 N/mm2 受拉区纵向钢筋类别:光面钢筋 其余钢筋选用HPB235钢 fyv = 210.0 N/mm2 保护层厚度: c
2、 = 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
3、梯梁计算跨度: L0 = Ln = 3800 mm 梯段板计算跨度: B0 = W2*b3 = 18002*200 =1400 mm 梯段板平均厚度: ht = (h2t/cos)/2 = (150.002*40.00/0.89)/2 = 119.72 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*0.12*0.30 = 0.90 kN/m 面层:gkm = qm*(hb) = 1.70*(0.150.30) = 0.77 kN/m 抹灰:gks = Rs*c1*b/cos = 20.0*0.02*0.30/0.89 = 0
4、.13 kN/m 恒荷标准值:Pkb = gkbgkmgks = 0.900.770.13 = 1.80 kN/m 恒荷控制: Pb(G) = 1.35*PkbQ*0.7*b*q = 1.35*1.801.40*0.7*0.30*2.50 = 3.16 kN/m 活荷控制: Pb(L) = G*PkbQ*b*q = 1.20*1.801.40*0.30*2.50 = 3.21 kN/m 荷载设计值:Pb = max Pb(G) , Pb(L) = 3.21 kN/m (2) 斜梯段梯梁荷载设计值: 自重放大系数(考虑面层):b=1.1gkl = b*Rc*b3*h3/cos = 1.1*25.
5、0*0.20*0.30/0.89 = 1.84 kN/m Pkl = Pkb/b*W/2gklqf = 1.80/0.30*1.80/21.840.20 = 7.44 kN/m Pl(G) = 1.35*PklQ*0.7*q*W/2 = 1.35*7.441.40*0.7*2.50*1.80/2 = 12.24 kN/m Pl(L) = G*PklQ*q*W/2 = 1.20*7.441.40*2.50*1.80/2 = 12.07 kN/mPl = max Pl(G) , Pl(L) = 12.24 kN/m (3) 平台板荷载设计值(取 B = 1m 宽板带):gkb = Rc*h4*B
6、= 25.0*0.07*1.0 = 1.75 kN/mgkm = qm*B = 1.70*1 = 1.70 kN/mgks = Rs*c1*B = 20.0*0.02*1 = 0.40 kN/mPkb = gkbgkmgks = 1.751.700.40 = 3.85 kN/m Pb(G) = 1.35*PkbQ*0.7*B*q = 1.35*3.851.40*0.7*1.0*2.50 = 7.65 kN/m Pb(L) = G*PkbQ*B*q = 1.20*3.851.40*1.0*2.50 = 8.12 kN/mPb = max Pb(G) , Pb(L) = 8.12 kN/m (4)
7、 平台段梯梁荷载设计值:gkl = b*Rc*b3*h3 = 1.1*25.0*0.20*0.30 = 1.65 kN/m Pkl = Pkb/B*W/2gklqf = 3.85/1.0*1.80/21.650.20 = 5.32 kN/m Pl(G) = 1.35*PklQ*0.7*q*W/2 = 1.35*5.321.40*0.7*2.50*1.80/2 = 9.38 kN/m Pl(L) = G*PklQ*q*W/2 = 1.20*5.321.40*2.50*1.80/2 = 9.53 kN/mPl = max Pl(G) , Pl(L) = 9.53 kN/m3梯梁斜截面受剪承载力计算
8、: Vmax = 23.17 kN Vmax0.7*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 = 87.08 mm 计算宽度:b0 = b/cos = 335.41 mm Mmax = Pb*B02/8 = 3.21*1.402/8 = 0.79 kNm = 0.1487% min = max0.002,(0.45*ft/fyv) = 0.3064% = min = 0.3064% 纵筋/计算面积:As = 89.50
9、mm2 (2) 梯梁计算: M中 = 21.93 kNm = 0.2301% min = max0.002,(0.45*ft/fy) = 0.3064% = min = 0.3064% 纵筋计算面积:As = 582.21 mm2 左支座: 按构造配筋。钢筋计算面积:As = 145.55 mm2 右支座:钢筋计算面积:五、计算结果:1纵筋计算结果: 计算面积:582.21 mm2 采用方案:4d14 实配面积:Ag = 616mm2 实际配筋率: = 0.3601%2钢筋计算结果:145.55 mm2Ag = 308mm2 = 1.1403%3箍筋计算结果:2d61504钢筋计算结果:2d1
10、0Ag = 157mm25纵筋/计算结果:d680Ag = 119mm2六、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=7.442.50*1.80/2=9.69 kN/m 梯段梯梁准永久荷载:Qq =Pklq*q*W/2=7.440.5*2.50*1.80/2=8.56 kN/m 平台梯梁标准荷载:Qk =Pklq*W/2=5.322.50*1.80/2=7.57 kN/m 平台梯梁准永久荷载:Qqq*q*W/2=5.320.5*2.50*1.80/2=6.
11、44 kN/m (1) 挠度验算参数: Mk = 17.35 kNm Mq = 15.32 kN (2) 短期刚度Bs与长期刚度B: 按混凝土结构设计规范(GB 50010-2002)下列公式计算: 1.10.65*ftk/(te*sk) (8.1.22) sk = Mk/(0.87*h0*AS) (8.1.33) te = (AsAp)/Ate (8.1.24) Bs = Es*As*h02/1.150.26*E*/(13.5f) (8.2.31) B = Mk/Mq*(1)Mk*Bs (8.2.2) sk = Mk/(0.87*h0*Ag) = 17.35*106/(0.87*270*61
12、6) = 119.96 N/mm te = Ag/(0.5h3*b3) = 616/(0.5*300*200) = 2.05% = 1.10.65*ftk/(te*sk) = 1.10.65*2.01/(2.05%*119.96) = 0.57 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 = 1.1403% Bs = Es*Ag*h02/1.150.26*E*/(13.5f) = 210*616*0.272/1.15*0.570.26*7.00*1.1403%/(13.5*0) = 7068.05 kNm2 荷载
13、长期作用对挠度增大的影响系数:当 = 0 时, = 2.0 B = Mk/Mq*(1)Mk*Bs = 17.35/15.32*(21)17.35*7068.05 = 3753.68 kN (3) 跨中挠度:f = 6.94 mm 梯梁计算长度L0 = 3.80m f/L0 = 1/547 1/200,满足要求。七、梯梁裂缝宽度验算: 1.计算荷载效应 Mk = 17.35 2.C = 20 mm 3.计算按荷载荷载效应的标准组合作用下,构件纵向受拉钢筋应力 sk = Mk/(0.87*h0*As) (混凝土规范式 8.1.33) = 17.35106/(0.87*270*616) = 119.
14、957 N/mm 4.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 mm2 te = As/Ate (混凝土规范式 8.1.24) = 616/30000 = 2.053% 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*sk) (混凝土规范式 8.1.22) = 1.1-0.65*2.01/(2.053%*119.957) = 0.569 6.计算最大裂缝宽度 max =cr*sk/ES*(1.9*C+0.08*deq/te) (混凝土规范式 8.1.21) = 2
15、.1*0.569*119.957/2100.0105*(1.9*20+0.08*14/2.053%) = 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 = (1.80 + 2.500)*1.402/8 = 1.053 kN*m 2.计算永久组合弯距值Mq: Mq = Mgk+Mqk = (qgk + q*qqk)*L02/8 = (1.80 + 0.50*2.500)*1.402/8 = 0
16、.747 kN*m 3.计算受弯构件的短期刚度 Bs 1) 计算按荷载荷载效应的标准组合作用下,构件纵向受拉钢筋应力 = 1.053106/(0.87*62*119) = 164.428 N/mm 2) 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 Ate = 0.5*b*h = 0.5*1000*87= 43541 mm2 = 119/43541 = 0.272% 3) 计算裂缝间纵向受拉钢筋应变不均匀系数 = 1.1-0.65*2.01/(0.272%*164.428) = -1.818 因为 0.2,所以取 = 0.2 4) 计算钢筋弹性模量与混凝土模量的比值 E E = ES/
17、EC = 2100.00105/(3.00104) = 7000.000 5) 计算受压翼缘面积与腹板有效面积的比值 f 矩形截面,f = 0 6) 计算纵向受拉钢筋配筋率 = As/(b*h0) = 119/(1000*62) = 0.191% 7) 计算受弯构件的短期刚度 BS BS = ES*As*h02/1.15*+0.2+6*E*/(1+ 3.5*f)(混凝土规范式8.2.3-1)105*119*622/1.15*0.200+0.2+6*7000.000*0.191%/(1+3.5*0.0) = 11.900102 kN*m2 4.计算受弯构件的长期刚度B 1) 确定考虑荷载长期效应
18、组合对挠度影响增大影响系数 当=0时,=2.0 (混凝土规范第 8.2.5 条) 2) 计算受弯构件的长期刚度 B B = Mk/(Mq*(-1)+Mk)*BS (混凝土规范式 8.2.2) = 1.053/(0.747*(2.0-1)+1.053)*11.900102 = 6.963 5.计算受弯构件挠度 fmax = 5*(qgk+qqk)*L04/(384*B) = 5*(1.80+2.500)*1.404/(384*6.963102) = 0.309 mm 6.验算挠度 挠度限值f0=L0/200=1400.00/200=7.000 mm fmax=0.309mmf0=7.000mm,
19、满足规范要求!九、裂缝宽度验算: 2.光面钢筋,所以取值Vi=0.7 3.C = 20 4.计算按荷载荷载效应的标准组合作用下,构件纵向受拉钢筋应力 5.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 因为te 1.000%,所以取te = 1.000% 6.计算裂缝间纵向受拉钢筋应变不均匀系数 = 1.1-0.65*2.01/(1.000%*164.428) = 0.305 7.计算单位面积钢筋根数n n = 1000/s = 1000/80 = 12 8.计算受拉区纵向钢筋的等效直径deq deq= (ni*di2)/(ni*Vi*di) = 12*62/(12*0.7*6) = 8 9.计算最大裂缝宽度 = 2.1*0.305*164.428/2.1105*(1.9*20+0.08*8/1.000%) = 0.0512 mm 0.30 mm,满足规范要求类型二 梁式楼梯( 型) 支座条件: L1 = 3300 mm Ln = L1 = 3300 mm L0 = Ln = 3300 mmgkl = b*Rc*b3*h3/cos = 1.1*25
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