MorGain 板式楼梯计算
1板式楼梯:TB-11.1基本资料
1.1.1工程名称: 工程一
1.1.2楼梯类型: 板式 A 型 ( ╱ ),支座条件: 两端固端
1.1.3踏步段水平净长 Lsn = 1150mm,梯板净跨度 Ln = Lsn = 1150mm,
梯板净宽度 B = 1150mm
1.1.4低端支座宽度 dl = 200mm,高端支座宽度 dh = 200mm
计算跨度 Lo = Min{Ln + (dl + dh) / 2, 1.05Ln} = Min{1350, 1208} = 1208mm
1.1.5梯板厚度 h1 = Lo / 27 = 45mm,取 h1 = 70mm
1.1.6踏步段总高度 Hs = 1450mm,楼梯踏步级数 n = 9
1.1.7线性恒荷标准值 Pk = 1kN/m; 楼梯(住宅)均布活荷标准值 qk = 2kN/m?,
ψc = 0.7,ψq = 0.4
1.1.8面层厚度 c1 = 25mm,面层容重 γc1 =20kN/m?; 顶棚厚度 c2 = 20mm,
顶棚容重 γc2 =18kN/m?; 楼梯自重容重 γb = 25kN/m?
1.1.9混凝土强度等级 C20, fc = 9.554N/mm?, ft = 1.101N/mm?, ftk = 1.542N/mm?,
Ec = 25413N/mm?
1.1.10钢筋强度设计值 fy = 210N/mm?, Es = 210000N/mm?; 当纵筋直径不小于 12mm 时,
取 fy = 300N/mm?、Es = 200000N/mm?; 纵筋的混凝土保护层厚度 c = 20mm
1.2楼梯几何参数
1.2.1踏步高度 hs = Hs / n = 1450/9 = 161.1mm
踏步宽度 bs = Lsn / (n - 1) = 1150/(9-1) = 143.8mm
踏步段斜板的倾角 α = ArcTan(hs / bs) = ArcTan(161.1/143.8) = 48.3°
踏步段斜板的长度 Lx = Lsn / Cosα = 1150/Cos48.3° = 1727mm
1.2.2踏步段梯板厚的垂直高度 h1' = h1 / Cosα = 70/Cos48.3° = 105mm
踏步段梯板平均厚度 T = (hs + 2 * h1') / 2 = (161+2*105)/2 = 186mm
1.2.3梯板有效高度 h1o = h1 - as = 70-25 = 45mm
1.3均布永久荷载标准值
1.3.1梯板上的线形荷载换算成均布永久荷载 gk1 = Pk / B = 1/1.15 = 0.87kN/m?
1.3.2梯板自重 gk2 = γb * T = 25*0.186 = 4.64kN/m?
1.3.3踏步段梯板面层自重
gk3 = γc1 * c1 * (n - 1) * (hs + bs) / Ln = 20*0.025*(9-1)*(0.161+0.144)/1.15
= 1.06kN/m?
1.3.4梯板顶棚自重 gk4' = γc2 * c2 = 18*0.02 = 0.36kN/m?
gk4 = gk4' * Lx / Ln = 0.36*1.727/1.15 = 0.54kN/m?
1.3.5均布荷载标准值汇总 gk = gk1 + gk2 + gk3 + gk4 = 7.11kN/m?
1.4均布荷载的基本组合值
由可变荷载控制的 Q(L) = γG * gk + γQ * qk = 1.2*7.11+1.4*2 = 11.34kN/m?
由永久荷载控制的 Q(D) = γG1 * gk + γQ * ψc * qk = 1.35*7.11+1.4*0.7*2
= 11.56kN/m?
最不利的荷载基本组合值 Q = Max{Q(L), Q(D)} = Max{11.34, 11.56} = 11.56kN/m?
1.5梯板的支座反力
永久荷载作用下均布反力标准值 Rk(D) = 4.09kN/m
可变荷载作用下均布反力标准值 Rk(L) = 1.15kN/m
最不利的均布反力基本组合值 R = 6.65kN/m
1.6梯板斜截面受剪承载力计算
V ≤ 0.7 * βh * ft * b * ho
V = 0.5 * Q * Ln * Cosα = 0.5*11.56*1.15*Cos48.3° = 4.4kN
0.7 * βh * ft * b * ho = 0.7*1*1101*1*0.045 = 27.8kN ≥ V = 4.4kN,满足要求。
1.7正截面受弯承载力计算
1.7.1跨中 Mmax = Q * Lo ^ 2 / 24 = 11.56*1.208^2/24 = 0.70kN·m
As = 72mm?,as = 23mm,ξ = 0.034,ρ = 0.15%; ρmin = 0.24%,
As,min = 165mm?; 实配纵筋: φ6@150 (As = 188)
1.7.2支座 Mmin = -Q * Lo ^ 2 / 12 = -11.56*1.208^2/12 = -1.40kN·m
As = 151mm?,as = 24mm,ξ = 0.072,ρ = 0.33%; ρmin = 0.24%,
As,min = 165mm?; 实配纵筋: φ8@200 (As = 251)
1.8板式楼梯平面整体表示方法的注写内容
AT1, h = 70 161.1X9 = 1450 板面:φ8@200, 板底:φ6@150
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【MorGain 结构快速设计程序 V2006.11.1592.1597】 Date:2006-11-07 14:35:44
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