基本资料Array楼梯类型:板式 A 型 (╱ ) 支座条件:两端弹性
梯段水平投影长度 Lo1 =3080mm
梯段净跨 Ln = Lo1 =3080mm
梯板净宽度 B =1470mm
下支座宽度 d1 =200mm
上支座宽度 d2 =200mm
计算跨度 Lo = Min{Ln + (d1 + d2) / 2, 1.05Ln} = Min{3280,3234
=3234mm
梯板厚度 h1 =120mm
梯段高度 Hv =1880mm楼梯级数 n =12
线性恒荷 Pk =0kN/m均布活荷 qk = 3.5kN/m 可变荷载组合值系数ψc =0.7可变荷载准永久值系数ψq =0.4
面层厚度 c1 =50mm顶棚厚度 c2 =20mm 面层、顶棚容重 γ c =20kN/m
楼梯自重容重 γ b =25kN/m
混凝土强度等级: C30
fc =14.3N/mm ft = 1.43N/mm
ftk = 2.01N/mm Ec =30000N/mm
fck =20.1N/mm
钢筋强度等级:3级
钢筋强度设计值 fy =360N/mm Es =200000N/mm 纵筋合力点至近边距离 as =15mm
楼梯几何参数
踏步高度 t = Hv / n =156.7mm
踏步宽度 w = Lo1 / (n - 1) =280mm
梯段斜板的倾角 α = ArcTan(t / w) = ArcTan(0.56)=0.51
梯段斜板的长度 Lx = Lo1 / Cosα =3529.35mm
梯板板厚的垂直高度 h1' = h1 / Cosα =137.507mm
梯板平均厚度 T = (t + 2 * h1') / 2 =215.84mm
梯板有效高度 h1o = h1 - as =105mm
均布永久荷载标准值
梯板上的线形荷载换算成均布永久荷载gk1=Pk / B =0kN/m
梯板自重 gk2 = γ b * T = 5.39601kN/m
Lo1段梯板面层自重gk3=γc*c1*[n*t+(n-1)*w]/Ln= 1.61039kN/m
梯板顶棚自重 gk4' =γ c * c2 =0.4kN/m
gk4 = gk4' * Lx / Ln =0.45836kN/m
均布荷载标准值汇总 gk = gk1+gk2+gk3+gk4 =7.46475kN/m
均布荷载设计值
由可变荷载控制的 p(L) = 1.2 * gk + 1.4 * qk =13.8577kN/m
由永久荷载控制的 p(D)=1.35*gk+1.4*ψc*qk =13.5074kN/m
最不利的荷载设计值 p = Max{p(L), p(D)} =13.8577kN/m
梯板斜截面受剪承载力计算
Vmax = 0.5 * p * Ln * Cosα =18623.8N
0.7 * ft * b * ho =105105N>Vmax =18624N
满足要求
正截面受弯承载力计算
跨中 Mmax = p * Lo ^ 2 / x =14.4934kN·M支座条件(简支=1,半简支
a s=Mmax/(
b * ho *fc) =0.09193m弯距系数x=10
ξ =1-√(1-2a s)=
As=ξ* b * ho * fc/fy =
配筋率 ρ = As / b / ho =
最小配筋率ρmin=Max{0.20%, 0.45ft/fy} = Max{
支座 Mmin = - p * Lo ^ 2 / 12 =
a s=Mmin/(
b * ho *fc) =
ξ =1-√(1-2a s)=
As=ξ* b * ho * fc/fy =
配筋率 ρ = As / b / ho =
最小配筋率ρmin=Max{0.20%, 0.45ft/fy} = Max{0.20%,0.18%} =0.20%<ρ=
跨中挠度验算
挠度验算参数
Mk =11.468kN·M按荷载效应的标准组合计算的弯矩值
Mq =9.2714kN·M按荷载效应的准永久组合计算的弯矩值
在荷载效应的标准组合作用下,受弯构件的短期刚度 Bs
裂缝间纵向受拉钢筋应变不均匀系数 ψ
σsk = Mk / 0.87 / ho / As =239.757N/mm
矩形截面, Ate = 0.5 * b * h =60000mm
ρte = As / Ate =0.87%
ψ = 1.1 - 0.65 * ftk / ρte / σsk=0.47556
钢筋弹性模量与混凝土模量的比值 αE
αE = Es / Ec = 6.66667
受压翼缘面积与腹板有效面积的比值 γf'
矩形截面,γf' = 0
纵向受拉钢筋配筋率 ρ = As / b / ho =0.50%
钢筋混凝土受弯构件的 Bs 按公式计算:
Bs=Es*As*ho^2/[1.15ψ+0.2+6*αE*ρ/(1+3.5γf')]=938.707kN·M
考虑荷载长期效应组合对挠度影响增大影响系数 θ
当 ρ' = 0 时,θ =2
受弯构件的长期刚度 B,可按下列公式计算:
B = Mk / [Mq * (θ - 1) + Mk] * Bs =519.059kN·M
跨中挠度 f = 3.0 / 384 * Qk * Lo ^ 4 / B =18.0523mm
f / Lo =0.005582>0.005不满足要求
裂缝宽度验算
构件受力特征系数αcr= 2.1(钢筋混凝土受弯构件)钢筋表面(光圆钢筋=1,带肋钢筋=2)=
钢筋的相对粘结特性系数v i=1
d eq=d/v i=10
最大裂缝宽度(mm)ωmax=αcr*ψ*σsk/Es*(1.9*c+0.08*deq/ρte)=0.1098
满足要求
}
半简支=2)=2
523.5988
0.50%
604.1524
0.58%
带肋钢筋=2)=2