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发表于 2005-3-25 02:26:37
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1 双向板:B-1
1.1 基本资料
1.1.1 工程名称:2-11轴 A-B C-D轴
1.1.2 边界条件(左端/下端/右端/上端): 固端 / 铰支 / 固端 / 固端
1.1.3 荷载标准值(按静力计算手册考虑活荷不利布置)
1.1.3.1 永久荷载标准值
楼板自重: gk1 = 0.1*25 = 2.50kN/m?
均布荷载: gk2 = 3.24kN/m?
1.1.3.2 可变荷载标准值
均布荷载: qk1 = 3.5kN/m? γQ = 1.4 ψc = 0.7 ψq = 0.4
1.1.4 计算跨度 Lx = 3600mm 计算跨度 Ly = 6900mm
板厚 h = 100mm (h = Lx / 36)
板底、板面纵筋合力点至近边距离:as = 20mm、as' = 20mm
1.1.5 混凝土强度等级:C25 fc = 11.94N/mm? ft = 1.27N/mm?
ftk = 1.78N/mm? Ec = 27871N/mm?
1.1.6 钢筋抗拉强度设计值 fy = 210N/mm? Es = 210000N/mm?
1.2 弯矩计算结果
1.2.1 平行于 Lx 方向的跨中弯矩 Mx
Mxgk1 = (0.04047+0.2*0.00907)*2.5*3.6^2 = 1.37kN·m
Mxgk2 = (0.04047+0.2*0.00907)*3.24*3.6^2 = 1.78kN·m
Mxqk1 = [(0.04047+0.2*0.00907)*3.5*3.6^2+(0.09333+0.2*0.01897)*3.5*3.6^2]/2
= 3.16kN·m
Mx = Max{Mx(L), Mx(D)} = Max{8.2, 7.34} = 8.20kN·m
Mxk = 6.31kN·m Mxq = 4.41kN·m
Asx = 518mm? ρ = 0.65% φ10@140[/COLOR] (As = 561)
ωmax = 0.104mm
1.2.2 平行于 Ly 方向的跨中弯矩 My
Mygk1 = (0.00907+0.2*0.04047)*2.5*3.6^2 = 0.56kN·m
Mygk2 = (0.00907+0.2*0.04047)*3.24*3.6^2 = 0.72kN·m
Myqk1 = [(0.00907+0.2*0.04047)*3.5*3.6^2+(0.01897+0.2*0.09333)*3.5*3.6^2]/2
= 1.24kN·m
My = Max{My(L), My(D)} = Max{3.27, 2.94} = 3.27kN·m
Myk = 2.52kN·m Myq = 1.77kN·m
Asy = 229mm? ρ = 0.33% ρmin = 0.27% Asy* = 272mm?
φ8@180[/COLOR] (As = 279) ωmax = 0.067mm
1.2.3 沿 Lx 方向的支座弯矩 Mx'
Mx'gk1 = -0.08321*2.5*3.6^2 = -2.70kN·m
Mx'gk2 = -0.08321*3.24*3.6^2 = -3.49kN·m
Mx'qk1 = -0.08321*3.5*3.6^2 = -3.77kN·m
Mx' = Max{Mx'(L), Mx'(D)} = Max{-12.71, -12.06} = -12.71kN·m
Mx'k = -9.96kN·m Mx'q = -7.70kN·m
Asx' = 833mm? ρ = 1.04% φ12@125[/COLOR] (As = 905)
ωmax = 0.125mm
1.2.4 沿 Ly 方向的支座弯矩 My'
My'gk1 = -0.05694*2.5*3.6^2 = -1.84kN·m
My'gk2 = -0.05694*3.24*3.6^2 = -2.39kN·m
My'qk1 = -0.05694*3.5*3.6^2 = -2.58kN·m
My' = Max{My'(L), My'(D)} = Max{-8.7, -8.25} = -8.70kN·m
My'k = -6.82kN·m My'q = -5.27kN·m
Asy' = 551mm? ρ = 0.69% φ10@140[/COLOR] (As = 561)
ωmax = 0.125mm
1.3 跨中挠度验算
1.3.1 挠度验算参数
按《建筑结构静力计算手册》表 4-6,挠度系数 κ = 0.00257(1/M)
Mk = 6.31kN·m Mq = 4.41kN·m
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
Es = 210000N/mm? As = 561mm? Ec = 27871N/mm? ftk = 1.78N/mm?
1.3.2 在荷载效应的标准组合作用下,受弯构件的短期刚度 Bs
1.3.2.1 裂缝间纵向受拉钢筋应变不均匀系数 ψ
σsk = Mk / (0.87 * ho * As) (混凝土规范式 8.1.3-3)
σsk = 6306799/(0.87*80*561) = 162N/mm?
矩形截面, Ate = 0.5 * b * h = 0.5*1000*100 = 50000mm?
ρte = As / Ate (混凝土规范式 8.1.2-4)
ρte = 561/50000 = 0.01122
ψ = 1.1 - 0.65 * ftk / (ρte * σsk) (混凝土规范式 8.1.2-2)
ψ = 1.1-0.65*1.78/(0.01122*162) = 0.462
1.3.2.2 钢筋弹性模量与混凝土模量的比值 αE
αE = Es / Ec = 210000/27871 = 7.53
1.3.2.3 受压翼缘面积与腹板有效面积的比值 γf'
矩形截面,γf' = 0
1.3.2.4 纵向受拉钢筋配筋率 ρ = As / (b * ho) = 561/(1000*80) = 0.00701
1.3.2.5 钢筋混凝土受弯构件的 Bs 按混凝土规范式 8.2.3-1 计算:
Bs = Es * As * ho ^ 2 / [1.15ψ + 0.2 + 6 * αE * ρ / (1 + 3.5γf')]
= 210000*561*80^2/[1.15*0.462+0.2+6*7.53*0.00701/(1+3.5*0)]
= 719.36kN·m?
1.3.3 考虑荷载长期效应组合对挠度影响增大影响系数 θ
按混凝土规范第 8.2.5 条,当 ρ' = 0 时,θ = 2.0
1.3.4 受弯构件的长期刚度 B,可按混凝土规范式 8.2.2 计算:
B = Mk / [Mq * (θ - 1) + Mk] * Bs = 6.31/[4.41*(2-1)+6.31]*719.36
= 423.35kN·m?
1.3.5 挠度 f = κ * Qk * Lx ^ 4 / B =0.00257*9.24*3.6^4/423.35*1000 = 9.4mm
f / Lx = 9.4/3600 = 1/383
2 双向板:B-2
1.1 基本资料
1.1.1 工程名称:BC轴
1.1.2 边界条件(左端/下端/右端/上端): 固端 / 固端 / 固端 / 固端
1.1.3 荷载标准值(按静力计算手册考虑活荷不利布置)
1.1.3.1 永久荷载标准值
楼板自重: gk1 = 0.1*25 = 2.50kN/m?
均布荷载: gk2 = 3.24kN/m?
1.1.3.2 可变荷载标准值
均布荷载: qk1 = 3.5kN/m? γQ = 1.4 ψc = 0.7 ψq = 0.4
1.1.4 计算跨度 Lx = 3600mm 计算跨度 Ly = 2100mm
板厚 h = 100mm (h = Ly / 21)
板底、板面纵筋合力点至近边距离:as = 20mm、as' = 20mm
1.1.5 混凝土强度等级:C25 fc = 11.94N/mm? ft = 1.27N/mm?
ftk = 1.78N/mm? Ec = 27871N/mm?
1.1.6 钢筋抗拉强度设计值 fy = 210N/mm? Es = 210000N/mm?
1.2 弯矩计算结果
1.2.1 平行于 Lx 方向的跨中弯矩 Mx
Mxgk1 = (0.00693+0.2*0.0373)*2.5*2.1^2 = 0.16kN·m
Mxgk2 = (0.00693+0.2*0.0373)*3.24*2.1^2 = 0.21kN·m
Mxqk1 = [(0.00693+0.2*0.0373)*3.5*2.1^2+(0.02313+0.2*0.0844)*3.5*2.1^2]/2
= 0.42kN·m
Mx = Max{Mx(L), Mx(D)} = Max{1.03, 0.9} = 1.03kN·m
Mxk = 0.78kN·m Mxq = 0.53kN·m
Asx = 70mm? ρ = 0.10% ρmin = 0.27% Asx* = 272mm?
φ8@180[/COLOR] (As = 279) ωmax = 0.013mm
1.2.2 平行于 Ly 方向的跨中弯矩 My
Mygk1 = (0.0373+0.2*0.00693)*2.5*2.1^2 = 0.43kN·m
Mygk2 = (0.0373+0.2*0.00693)*3.24*2.1^2 = 0.55kN·m
Myqk1 = [(0.0373+0.2*0.00693)*3.5*2.1^2+(0.0844+0.2*0.02313)*3.5*2.1^2]/2
= 0.99kN·m
My = Max{My(L), My(D)} = Max{2.56, 2.29} = 2.56kN·m
Myk = 1.96kN·m Myq = 1.37kN·m
Asy = 155mm? ρ = 0.19% ρmin = 0.27% Asy* = 272mm?
φ8@180[/COLOR] (As = 279) ωmax = 0.026mm
1.2.3 沿 Lx 方向的支座弯矩 Mx'
Mx'gk1 = -0.0571*2.5*2.1^2 = -0.63kN·m
Mx'gk2 = -0.0571*3.24*2.1^2 = -0.82kN·m
Mx'qk1 = -0.0571*3.5*2.1^2 = -0.88kN·m
Mx' = Max{Mx'(L), Mx'(D)} = Max{-2.97, -2.81} = -2.97kN·m
Mx'k = -2.33kN·m Mx'q = -1.80kN·m
Asx' = 180mm? ρ = 0.23% ρmin = 0.27% Asx'* = 272mm?
φ8@180[/COLOR] (As = 279) ωmax = 0.031mm
1.2.4 沿 Ly 方向的支座弯矩 My'
My'gk1 = -0.08*2.5*2.1^2 = -0.88kN·m
My'gk2 = -0.08*3.24*2.1^2 = -1.14kN·m
My'qk1 = -0.08*3.5*2.1^2 = -1.23kN·m
My' = Max{My'(L), My'(D)} = Max{-4.16, -3.94} = -4.16kN·m
My'k = -3.26kN·m My'q = -2.52kN·m
Asy' = 255mm? ρ = 0.32% ρmin = 0.27% Asy'* = 272mm?
φ8@180[/COLOR] (As = 279) ωmax = 0.089mm
1.3 跨中挠度验算
1.3.1 挠度验算参数
按《建筑结构静力计算手册》表 4-4,挠度系数 κ = 0.00239(1/M)
Mk = 1.96kN·m Mq = 1.37kN·m
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
Es = 210000N/mm? As = 279mm? Ec = 27871N/mm? ftk = 1.78N/mm?
1.3.2 在荷载效应的标准组合作用下,受弯构件的短期刚度 Bs
1.3.2.1 裂缝间纵向受拉钢筋应变不均匀系数 ψ
σsk = Mk / (0.87 * ho * As) (混凝土规范式 8.1.3-3)
σsk = 1964919/(0.87*80*279) = 101N/mm?
矩形截面, Ate = 0.5 * b * h = 0.5*1000*100 = 50000mm?
ρte = As / Ate (混凝土规范式 8.1.2-4)
ρte = 279/50000 = 0.00559 <0.01,取 ρte = 0.01
ψ = 1.1 - 0.65 * ftk / (ρte * σsk) (混凝土规范式 8.1.2-2)
ψ = 1.1-0.65*1.78/(0.01*101) = -0.044
当 ψ<0.2 时,取 ψ = 0.2
1.3.2.2 钢筋弹性模量与混凝土模量的比值 αE
αE = Es / Ec = 210000/27871 = 7.53
1.3.2.3 受压翼缘面积与腹板有效面积的比值 γf'
矩形截面,γf' = 0
1.3.2.4 纵向受拉钢筋配筋率 ρ = As / (b * ho) = 279/(1000*80) = 0.00349
1.3.2.5 钢筋混凝土受弯构件的 Bs 按混凝土规范式 8.2.3-1 计算:
Bs = Es * As * ho ^ 2 / [1.15ψ + 0.2 + 6 * αE * ρ / (1 + 3.5γf')]
= 210000*279*80^2/[1.15*0.2+0.2+6*7.53*0.00349/(1+3.5*0)] = 638.50kN·m?
1.3.3 考虑荷载长期效应组合对挠度影响增大影响系数 θ
按混凝土规范第 8.2.5 条,当 ρ' = 0 时,θ = 2.0
1.3.4 受弯构件的长期刚度 B,可按混凝土规范式 8.2.2 计算:
B = Mk / [Mq * (θ - 1) + Mk] * Bs = 1.96/[1.37*(2-1)+1.96]*638.5
= 375.80kN·m?
1.3.5 挠度 f = κ * Qk * Ly ^ 4 / B =0.00239*9.24*2.1^4/375.8*1000 = 1.1mm
f / Ly = 1.1/2100 = 1/1,835
呵呵,有灌水的嫌疑
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