地下室底板(车库位置)
双向板:B-1
一、基本资料:
1、工程名称:工程一
2、边界条件 (左端/下端/右端/上端): 固端 / 固端 / 固端 / 固端
3、荷载:
永久荷载标准值:
楼板自重: gk1 = 26.15kN/m
可变荷载标准值
均布荷载: qk1 = 3.00kN/m γQ = 1.4 ψc = 0.7 ψq = 0.4
4、其他:
计算跨度 Lx = 7800mm 计算跨度 Ly = 7800mm
板厚 h = 400mm (h = Lx / 20)
板底、板面纵筋合力点至近边距离: as = 50mm as' = 50mm
混凝土强度等级: C30
fc = 14.33 ft = 1.43 ftk = 2.01N/mm Ec = 29791N/mm
钢筋抗拉强度设计值 fy = 210N/mm Es = 210000N/mm
二、计算结果:
Mxgk1 = (0.01760+0.2*0.01760)*26.15*7.800^2 = 33.60kN·M
Mxqk1 = (0.01760+0.2*0.01760)*3.00*7.800^2 = 3.85kN·M
Mx = Max{Mx(L), Mx(D)} = Max{45.72, 49.14} = 49.14kN·M
Mxk = 37.46kN·M Mxq = 35.14kN·M
Asx = 475mm ρ = 0.14% ρmin = 0.21% Asx* = 860mm
(Ⅱ)Φ12@125 (As = 905) ωmax = 0.051mm ωs,max = 0.061mm
Mygk1 = (0.01760+0.2*0.01760)*26.15*7.800^2 = 33.60kN·M
Myqk1 = (0.01760+0.2*0.01760)*3.00*7.800^2 = 3.85kN·M
My = Max{My(L), My(D)} = Max{45.72, 49.14} = 49.14kN·M
Myk = 37.46kN·M Myq = 35.14kN·M
Asy = 489mm ρ = 0.14% ρmin = 0.21% Asy* = 860mm
(Ⅱ)Φ12@125 (As = 905) ωmax = 0.058mm ωs,max = 0.072mm
Mx'gk1 = -0.05130*26.15*7.800^2 = -81.62kN·M
Mx'qk1 = -0.05130*3.00*7.800^2 = -9.36kN·M
Mx' = Max{Mx'(L), Mx'(D)} = Max{-111.05, -119.36} = -119.36kN·M
Mx'k = -90.98kN·M Mx'q = -85.36kN·M
Asx' = 1178mm ρ = 0.34%
(Ⅱ)Φ14@125 (As = 1232) ωmax = 0.278mm ωs,max = 0.331mm
My'gk1 = -0.05130*26.15*7.800^2 = -81.62kN·M
My'qk1 = -0.05130*3.00*7.800^2 = -9.36kN·M
My' = Max{My'(L), My'(D)} = Max{-111.05, -119.36} = -119.36kN·M
My'k = -90.98kN·M My'q = -85.36kN·M
Asy' = 1178mm ρ = 0.34%
(Ⅱ)Φ14@125 (As = 1232) ωmax = 0.278mm ωs,max = 0.331mm
三、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
(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 = 0.00127(1/M)
Mk = 37.46kN·M Mq = 35.14kN·M
Es = 200000N/mm As = 905mm
Ec = 29791N/mm ftk = 2.01N/mm
(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、裂缝间纵向受拉钢筋应变不均匀系数 ψ,按下列公式计算:
ψ = 1.1 - 0.65 * ftk / ρte / σsk (混凝土规范式 8.1.2-2)
σsk = Mk / 0.87 / ho / As (混凝土规范式 8.1.3-3)
σsk = 37456023/0.87/350/905 = 136N/mm
矩形截面,Ate = 0.5 * b * h = 0.5*1000*400 = 200000mm
ρte = As / Ate (混凝土规范式 8.1.2-4)
ρte = 905/200000 = 0.45%
ψ = 1.1 - 0.65*2.01/0.00452/136 = -1.020
当 ψ<0.2 时,取ψ = 0.2
②、钢筋弹性模量与混凝土模量的比值 αE:
αE = Es / Ec = 200000/29791 = 6.71
③、受压翼缘面积与腹板有效面积的比值 γf':
矩形截面,γf' = 0
④、纵向受拉钢筋配筋率 ρ = As / b / ho = 905/1000/350 = 0.00259
⑤、钢筋混凝土受弯构件的 Bs 按公式(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')]
Bs = 200000*905*350^2/[1.15*0.200+0.2+
6*6.71*0.00259/(1+3.5*0.000)] = 41501.50kN·M
(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
(4)、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 (混凝土规范式 8.2.2)
B = 37.46/[35.14*(2-1)+37.46]*41501.50 = 21411.84kN·M
(5)、挠度 f = κ * Qk * Lx ^ 4 / B
f =0.00127*29.15*7.800^4/21411.84*1000 = 6.4mm
f / Lx = 6.4/7800 = 1/1,219