发布于:2011-01-17 14:27:17
来自:建筑结构/探索者
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以下是TSSD计算独立基础的计算书,再计算完弯矩后,为什么要乘以折减系数Ks是什么意思啊?为什么会有这个系数,出处在哪?
阶梯柱基计算书
一、示意图
基础类型:阶梯柱基 计算形式:验算截面尺寸
平面:
剖面:
二、基本参数
1.依据规范
《建筑地基基础设计规范》(GB 50007-2002)
《混凝土结构设计规范》(GB 50010-2002)
《简明高层钢筋混凝土结构设计手册(第二版)》
2.几何参数:
已知尺寸:
B1 = 1000 mm, A1 = 1000 mm
H1 = 200 mm, H2 = 200 mm
B = 400 mm, A = 400 mm
B3 = 700 mm, A3 = 700 mm
无偏心:
B2 = 1000 mm, A2 = 1000 mm
基础埋深d = 2.00 m
钢筋合力重心到板底距离as = 80 mm
3.荷载值:
(1)作用在基础顶部的基本组合荷载
F = 200.00 kN
Mx = 20.00 kN•m
My = 30.00 kN•m
Vx = 50.00 kN
Vy = -70.00 kN
折减系数Ks = 1.35
(2)作用在基础底部的弯矩设计值
绕X轴弯矩: M0x = Mx-Vy•(H1+H2) = 20.00--70.00×0.40 = 48.00 kN•m
绕Y轴弯矩: M0y = My+Vx•(H1+H2) = 30.00+50.00×0.40 = 50.00 kN•m
(3)作用在基础底部的弯矩标准值
绕X轴弯矩: M0xk = M0x/Ks = 48.00/1.35 = 35.56 kN•m
绕Y轴弯矩: M0yk = M0y/Ks = 50.00/1.35 = 37.04 kN•m
4.材料信息:
混凝土: C30 钢筋: HPB235(Q235)
5.基础几何特性:
底面积:S = (A1+A2)(B1+B2) = 2.00×2.00 = 4.00 m2
绕X轴抵抗矩:Wx = (1/6)(B1+B2)(A1+A2)2 = (1/6)×2.00×2.002 = 1.33 m3
绕Y轴抵抗矩:Wy = (1/6)(A1+A2)(B1+B2)2 = (1/6)×2.00×2.002 = 1.33 m3
三、计算过程
1.修正地基承载力
修正后的地基承载力特征值 fa = 118.00 kPa
2.轴心荷载作用下地基承载力验算
计算公式:
按《建筑地基基础设计规范》(GB 50007-2002)下列公式验算:
pk = (Fk+Gk)/A (5.2.2-1)
Fk = F/Ks = 200.00/1.35 = 148.15 kN
Gk = 20S•d = 20×4.00×2.00 = 160.00 kN
pk = (Fk+Gk)/S = (148.15+160.00)/4.00 = 77.04 kPa ≤ fa,满足要求。
3.偏心荷载作用下地基承载力验算
计算公式:
按《建筑地基基础设计规范》(GB 50007-2002)下列公式验算:
当e≤b/6时,pkmax = (Fk+Gk)/A+Mk/W (5.2.2-2)
pkmin = (Fk+Gk)/A-Mk/W (5.2.2-3)
当e>b/6时,pkmax = 2(Fk+Gk)/3la (5.2.2-4)
X、Y方向同时受弯。
偏心距exk = M0yk/(Fk+Gk) = 37.04/(148.15+160.00) = 0.12 m
e = exk = 0.12 m ≤ (B1+B2)/6 = 2.00/6 = 0.33 m
pkmaxX = (Fk+Gk)/S+M0yk/Wy
= (148.15+160.00)/4.00+37.04/1.33 = 104.81 kPa
偏心距eyk = M0xk/(Fk+Gk) = 35.56/(148.15+160.00) = 0.12 m
e = eyk = 0.12 m ≤ (A1+A2)/6 = 2.00/6 = 0.33 m
pkmaxY = (Fk+Gk)/S+M0xk/Wx
= (148.15+160.00)/4.00+35.56/1.33 = 103.70 kPa
pkmax = pkmaxX+pkmaxY-(Fk+Gk)/S = 104.81+103.70-77.04 = 131.48 kPa
≤ 1.2×fa = 1.2×118.00 = 141.60 kPa,满足要求。
4.基础抗冲切验算
计算公式:
按《建筑地基基础设计规范》(GB 50007-2002)下列公式验算:
Fl ≤ 0.7•βhp•ft•am•h0 (8.2.7-1)
Fl = pj•Al (8.2.7-3)
am = (at+ab)/2 (8.2.7-2)
pjmax,x = F/S+M0y/Wy = 200.00/4.00+50.00/1.33 = 87.50 kPa
pjmin,x = F/S-M0y/Wy = 200.00/4.00-50.00/1.33 = 12.50 kPa
pjmax,y = F/S+M0x/Wx = 200.00/4.00+48.00/1.33 = 86.00 kPa
pjmin,y = F/S-M0x/Wx = 200.00/4.00-48.00/1.33 = 14.00 kPa
pj = pjmax,x+pjmax,y-F/S = 87.50+86.00-50.00 = 123.50 kPa
(1)柱对基础的冲切验算:
计算冲切截面超出基础冲切范围。故柱对基础冲切满足要求。
(2)变阶处基础的冲切验算:
H0 = H1-as = 0.20-0.08 = 0.12 m
X方向:
Alx = 1/4•(A3+2H0+A1+A2)(B1+B2-B3-2H0)
= (1/4)×(0.70+2×0.12+2.00)(2.00-0.70-2×0.12)
= 0.78 m2
Flx = pj•Alx = 123.50×0.78 = 96.22 kN
ab = min{A3+2H0, A1+A2} = min{0.70+2×0.12, 2.00} = 0.94 m
amx = (at+ab)/2 = (A3+ab)/2 = (0.70+0.94)/2 = 0.82 m
Flx ≤ 0.7•βhp•ft•amx•H0 = 0.7×1.00×1430.00×0.820×0.120
= 98.50 kN,满足要求。
Y方向:
Aly = 1/4•(B3+2H0+B1+B2)(A1+A2-A3-2H0)
= (1/4)×(0.70+2×0.12+2.00)(2.00-0.70-2×0.12)
= 0.78 m2
Fly = pj•Aly = 123.50×0.78 = 96.22 kN
ab = min{B3+2H0, B1+B2} = min{0.70+2×0.12, 2.00} = 0.94 m
amy = (at+ab)/2 = (B3+ab)/2 = (0.70+0.94)/2 = 0.82 m
Fly ≤ 0.7•βhp•ft•amy•H0 = 0.7×1.00×1430.00×0.820×0.120
= 98.50 kN,满足要求。
5.基础受压验算
计算公式:《混凝土结构设计规范》(GB 50010-2002)
Fl ≤ 1.35•βc•βl•fc•Aln (7.8.1-1)
局部荷载设计值:Fl = 200.00 kN
混凝土局部受压面积:Aln = Al = B×A = 0.40×0.40 = 0.16 m2
混凝土受压时计算底面积:Ab = min{B+2A, B1+B2}×min{3A, A1+A2} = 1.44 m2
混凝土受压时强度提高系数:βl = sq.(Ab/Al) = sq.(1.44/0.16) = 3.00
1.35βc•βl•fc•Aln
= 1.35×1.00×3.00×14300.00×0.16
= 9266.40 kN ≥ Fl = 200.00 kN,满足要求。
6.基础受弯计算
计算公式:
按《简明高层钢筋混凝土结构设计手册(第二版)》中下列公式验算:
MⅠ=β/48•(L-a)2(2B+b)(pjmax+pjnx) (11.4-7)
MⅡ=β/48•(B-b)2(2L+a)(pjmax+pjny) (11.4-8)
(1)柱根部受弯计算:
G = 1.35Gk = 1.35×160.00 = 216.00kN
Ⅰ-Ⅰ截面处弯矩设计值:
pjnx = pjmin,x+(pjmax,x-pjmin,x)(B1+B2+B)/2/(B1+B2)
= 12.50+(87.50-12.50)×(2.00+0.40)/2/2.00
= 57.50 kPa
MⅠ = β/48•(B1+B2-B)2[2(A1+A2)+A](pjmax,x+pjnx)
= 1.0946/48×(2.00-0.40)2×(2×2.00+0.40)×(87.50+57.50)
= 37.24 kN•m
Ⅱ-Ⅱ截面处弯矩设计值:
pjny = pjmin,y+(pjmax,y-pjmin,y)(A1+A2+A)/2/(A1+A2)
= 14.00+(86.00-14.00)×(2.00+0.40)/2/2.00
= 57.20 kPa
MⅡ = β/48•(A1+A2-A)2[2(B1+B2)+B](pjmax,y+pjny)
= 1.0919/48×(2.00-0.40)2×(2×2.00+0.40)×(86.00+57.20)
= 36.69 kN•m
Ⅰ-Ⅰ截面受弯计算:
相对受压区高度: ζ= 0.012799 配筋率: ρ= 0.000872
ρ < ρmin = 0.001500 ρ = ρmin = 0.001500
计算面积:600.00 mm2/m
Ⅱ-Ⅱ截面受弯计算:
相对受压区高度: ζ= 0.012608 配筋率: ρ= 0.000859
ρ < ρmin = 0.001500 ρ = ρmin = 0.001500
计算面积:600.00 mm2/m
(2)变阶处受弯计算:
Ⅰ-Ⅰ截面处弯矩设计值:
pjnx = pjmin,x+(pjmax,x-pjmin,x)(B1+B2+B3)/2/(B1+B2)
= 12.50+(87.50-12.50)×(2.00+0.70)/2/2.00
= 63.13 kPa
MⅠ = β/48•(B1+B2-B3)2[2(A1+A2)+A3](pjmax,x+pjnx)
= 1.0694/48×(2.00-0.70)2×(2×2.00+0.70)×(87.50+63.13)
= 26.65 kN•m
Ⅱ-Ⅱ截面处弯矩设计值:
pjny = pjmin,y+(pjmax,y-pjmin,y)(A1+A2+A3)/2/(A1+A2)
= 14.00+(86.00-14.00)×(2.00+0.70)/2/2.00
= 62.60 kPa
MⅡ = β/48•(A1+A2-A3)2[2(B1+B2)+B3](pjmax,y+pjny)
= 1.0675/48×(2.00-0.70)2×(2×2.00+0.70)×(86.00+62.60)
= 26.25 kN•m
Ⅰ-Ⅰ截面受弯计算:
相对受压区高度: ζ= 0.066964 配筋率: ρ= 0.004560
计算面积:547.19 mm2/m
Ⅱ-Ⅱ截面受弯计算:
相对受压区高度: ζ= 0.065914 配筋率: ρ= 0.004488
计算面积:538.61 mm2/m
四、计算结果
1.X方向弯矩验算结果:
计算面积:600.00 mm2/m
采用方案:d10@110
实配面积:714.00 mm2/m
2.Y方向弯矩验算结果:
计算面积:600.00 mm2/m
采用方案:d10@110
实配面积:714.00 mm2/m
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