三桩承台计算算例

ξ
=
x h0
= 0.038
相对界限受压区高度ζb按规范GB50010 − 2010式6.2.7 − 1计算
if(ξ < ξb , "满足要求" , "请重新计算") = "满足要求"
ξb = 0.518
5.配筋计算：
按规范GB50010 − 2010中式6.2.10 − 2和GB50007 − 2011中式8.2.12计算
a0y = min(ay , h0) = 0.499m
受冲切截面高度影响系数：βhp =
1 if h ≤ 800mm
0.9 if h ≥ 2000mm
0.9
+
(1
−
0.9)
2m 2m −
−h 0.8m
otherwise
= 0.942
冲垮比： λ0x =
0.25
if
a0x h0
≤
0.25 =
0.252
1
if
a0x h0
≥
1
a0x h0
otherwise
λ0y =
0.25
if
a0y h0
≤
0.25 =
0.35
1
if
a0y h0
≥
1
a0y h0
otherwise
冲切系数：
α0x
=
0.84 λ0x + 0.2
=
1.858
α0y =
0.84 λ0y + 0.2
=
1.528
承台截面抗冲切承载力计算：
FLc = 2 ⋅ ⎡⎣α0x ⋅ (hb + a0x) + α0y ⋅ (hc + a0y)⎤⎦ ⋅ βhp ⋅ ft ⋅ h0 = 14659.581 ⋅ kN
= 1.297
承台计算端头最小宽度： b01 = 2c + a ⋅ cos(α) = 1.44m
承台计算截面处宽度： b02 = 2⎡⎣c + (ay + 0.5 ⋅ a) ⋅ cos(α)⎤⎦ = 1.939m
承台受剪截面计算宽度，参GB50007 − 2011中附录U.0.2 − 1式近似计算
b0
otherwise
承台截面 = "满足GB50007-2011第8.5.21条"
3.冲切计算：
1）柱对承台的冲切计算：（按GB50007 − 2011中8.5.19条计算）
柱短边至桩内边的距离： ax = 0.5(S2 − hb − a) = 360 ⋅ mm
冲切锥体底部计算边长： a0x = min(ax , h0) = 0.36m
NL
=
1 3
⋅
FN
=
2250
⋅
kN
桩对承台冲切验算 = "满足GB50007-2011第8.5.19-2-2条" if NL ≤ min(NLc1 , NLc2)
"不满足GB50007-2011第8.5.19-2-2条，增加承台高" otherwise 桩对承台冲切验算 = "满足GB50007-2011第8.5.19-2-2条"
上部荷载设计值等效于：FN = 3ρg ⋅ γ ⋅ Ra = 6750 ⋅ kN
上部荷载标准值等效于： FNk
=
3γ γk
⋅ ρg ⋅ Ra = 5000 ⋅ kN
上部荷载永久值等效于： FNqk
=
3γ γqk
⋅
ρg
⋅
Ra
=
4219
⋅
kN
三、承载力计算
1.内力计算（弯矩按GB50007 − 2011中8.5.18条计算）
=
1.114
承台截面抗冲切承载力计算：
底桩：
NLc1
=
α11 ⋅
(2 ⋅
c1
+
a11)
⋅
tan⎛⎝
α 2
⎞ ⎠
⋅
βhp ⋅
ft ⋅
h0
=
4319.41 ⋅
kN
顶桩：
NLc2
=
α12 ⋅
(2 ⋅
c2
+
a12)
⋅
tan⎛⎝
π 2
−
α⎞⎠
⋅ βhp ⋅ ft ⋅
h0 =
4070.056 ⋅ kN
桩平均净反力设计值：
底桩内边至承台边线交点的距离： c1 = 0.5 ⋅ b01 ⋅ tan(α) = 1.247m
顶桩内边至承台边线交点的距 离：
c2
=
c
+
0.5a
⋅
tan⎛⎝
α⎞ 2⎠
tan⎛⎝
α 2
⎞ ⎠
= 1.279m
底桩内边至柱边的距离：
a11 = ax = 360 ⋅ mm
顶桩内边至柱边的距离：
a12 = ay ⋅ sin(α) = 432.346 ⋅ mm
初步假定底部纵筋直径：ds0 = 25mm
承台计算高度： h0 = h − cc − dv0 − 0.5 ⋅ ds0 = 1427.5 ⋅ mm
3.荷载：
荷载综合分项系数： γk = 1.35 (荷载标准值计算用) γqk = 1.60 (荷载永久值计算用)
γ = 1.25 (荷载设计值计算用) 单桩承载力利用率： ρg = 1
根据GB50007 − 2011中8.5.20条，按GB50007 − 2011式8.5.21 − 1计算桩边和柱边连线的抗剪
承载力：
圆桩等效方桩截面边长： a = 0.8 ⋅ D = 480 ⋅ mm
桩边至柱边的最大距离：
ay =
2 3
⋅
S1
⋅
sin(α)
−
0.5(a
+
hc)
=
499.23
⋅
mm
计算截面剪跨比：
三桩承台
CT − 3
一、计算方法及使用的国家规范：
以单桩承载力特征值为依据，反推上部荷载标准值及设计值 ，三桩等腰承台按受弯板带计算 抗
弯、抗剪承载力和正常使用阶段的 裂缝，裂缝按永久荷载作用计算。
设计中使用的国家规范：
《混凝土结构设计规范》（GB50010 − 2010）
《建筑地基基础设计规范》（GB50007 − 2011）
4.截面相对受压区高度
不考虑受压钢筋作用，根据GB50010 − 2010中式6.2.10 − 1，计算混凝土等效受压区高度：
三向板带受弯计算宽度近似取： ba = 1.5D = 900 ⋅ mm
x = h0 ⋅ ⎛⎜1 − ⎝
1−
α1
⋅
2M fc ⋅ ba
⋅
h02
⎞⎟ ⎠
=
54.828 ⋅ mm
混凝土相对受压区高度：
柱对承台冲切验算 = "满足GB50007-2011第8.5.19-1式" if FN ≤ FLc "不满足GB50007-2011第8.5.19-1式，增加承台高" otherwise
柱对承台冲切验算 = "满足GB50007-2011第8.5.19-1式"
2）桩对承台的冲切计算：（按GB50007 − 2011中8.5.19条计算）
裂缝计算 = "满足GB50010-2010中3.4.5条"
五、结果汇总
承台高： h = 1.5m
承台底面纵向钢筋： 8ϕ25
配筋率：
承台底面裂缝： ωmax = 0.088 ⋅ mm
ρsd = 0.291 ⋅ %
最大弯矩设计值：
M=
1 3
FN 3
⋅
⎛⎜⎝S1
−
0.75hc 4 − αc
⎞⎟⎠
=
1155.144
⋅
kN
⋅
m
最大剪力设计值：
V=
1 3
FN
=
2250
⋅
kN
wk.baidu.com
永久荷载作用最大弯矩标准值 ：
Mqk
=
1 3
FNqk 3
⋅
⎛⎜⎝S1
−
0.75hc 4 − αc
⎞⎟⎠
=
721.965 ⋅
kN
⋅
m
2.承台截面的斜截面抗剪承载力
有效受拉混凝土截面面积： Ate = 0.5ba ⋅ h = 675000 ⋅ mm2
实配受拉钢筋面积 HRB400 8ϕ25 di = d = 25 ⋅ mm
受拉钢筋等效直径：
de
=
di vi
= 25 ⋅ mm
按有效受拉混凝土截面计算受 拉钢筋配筋率：
Asd = 3926.991 ⋅ mm2
ρte =
桩边距： c = 1D = 600 ⋅ mm
长桩距与短桩距之比
αc
=
S1 S2
=1
单桩承载力特征值： Ra = 1800kN 桩顶伸入承台内尺寸： cc = 50mm
柱截面尺寸： hc = 600mm
hb = 600mm
承台截面参数： 承台高：h = 1500mm
承台边夹角： α
=
1 3
⋅
π
初步假定分布筋直径：dv0 = 10mm
实配钢筋 8ϕ25 n = 8 d = 25mm
Asd
=
nπ
d2 4
=
3927 ⋅
mm2
ρsd
=
Asd ba ⋅ h
=
0.291 ⋅
%
底部实配钢筋 = "满足要求" if Asd ≥ max(As , Amin) = "满足要求"
"钢筋不足,重新选筋" otherwise
纵筋布置间距 =
"满足要求"
if
ba − asv n− 1
≥ 100mm ∧
ba − asv n− 1
≤ 200mm
"不满足要求,重新选筋" otherwise
纵筋布置间距 = "满足要求"
四、裂缝计算
裂缝按GB50010 − 2010中7.1.2 − 1式计算
1.裂缝计算参数：
构件受力特征系数： αcr = 1.9 钢筋的相对粘接系数： vi = 1.0
As
=
max⎛⎜⎝ α1 ⋅
fc ⋅ b01 ⋅ fy
x
,
M 0.9 ⋅ fy ⋅
h0 ⎞⎟⎠
=
3666.9 ⋅
mm2
最小配筋率按GB50010 − 2010中8.5.1条计算取值
ρmin =
0.2%
if
45
ft 100fy
< 0.2%
45
ft 100fy
otherwise
= 0.2 ⋅ %
Amin = ρmin ⋅ (ba ⋅ h) = 2700 ⋅ mm2
2.裂缝计算
ωmax
=
αcr ⋅
ψ
⋅
σsk Es
⋅
⎛⎜⎝1.9cs
+
0.08 ⋅
de ρte
⎞⎟⎠
=
0.088 ⋅
mm
按三级二a类环境允许裂缝： ωlin = 0.2mm
裂缝计算 = "满足GB50010-2010中3.4.5条" if ωmax ≤ ωlin "不满足GB50010-2010中3.4.5条，增加配筋量" otherwise
冲垮比： λ11 =
0.25
if
a11 h0
≤
0.25 =
0.252
1
if
a11 h0
≥
1
a11 h0
otherwise
λ12 =
0.25
if
a12 h0
≤
0.25 =
0.303
1
if
a12 h0
≥
1
a12 h0
otherwise
冲切系数：
α11
=
0.56 λ11 + 0.2
=
1.238
α12 =
0.56 λ12 + 0.2
《建筑桩基技术规范》（JGJ94 − 2008）
《建筑抗震设计规范》（GB50011 − 2010）
二、 设计资料
1.材料： 混凝土强度度等级
纵向钢筋强度等级
箍筋强度等级
构造措施抗震等级
材料参数程序
钢筋弹性模量： 纵筋抗拉强度设计值： 混凝土强度设计值： 环境类别： 二a类 2.基本参数：
Es = ⋅ N ⋅ mm− 2 fy = 360 ⋅ N ⋅ mm− 2 fc = 16.72 ⋅ N ⋅ mm− 2
λa =
受剪切截面高度影响系数：βhs =
0.25
if
ay h0
≤
0.25
=
0.35
3
if
ay h0
≥
3
ay h0
otherwise
1 if h0 ≤ 800mm
0.7952 if h0 ≥ 2000mm
⎛ 800mm ⎞0.25 ⎝ h0 ⎠
otherwise
= 0.865
剪切系数：
β
=
1.75 λa + 1.0
0.01
if
Asd Ate
<
0.01
Asd Ate
otherwise
= 0.01
受拉钢筋应力：
σsk
=
Mqk 0.87 ⋅ h0Asd
= 148.034 ⋅
N mm2
裂缝间受拉钢筋间距不均匀系 数：
ψ=
0.2 if 1.1 − 0.65 ⋅ ftk < 0.2 ρte ⋅ σsk
otherwise 1 if 1.1 − 0.65 ⋅ ftk > 1 ρte ⋅ σsk
1.1 − 0.65 ⋅ ftk
otherwise
ρte ⋅ σsk
= 0.2
最外层受拉钢筋外边缘至混凝 土受拉区底边的距离：
cs = 20 ⋅ mm if cc + dv0 < 20 ⋅ mm
= 60 ⋅ mm
otherwise
65 ⋅ mm if cc + dv0 ≥ 65 ⋅ mm
cc + dv0 otherwise
混凝土弹性模量： 箍筋抗拉强度设计值： 计算参数 α1 = 1
钢筋混凝土保护层厚度： asv = 50mm
Ec = 31334 ⋅ N ⋅ mm− 2 fyv = 360 ⋅ N ⋅ mm− 2
β1 = 0.8 βc = 1
桩参数： 桩径： D = 600mm 腰桩中心间距： S1 = 1800mm 底桩中心间距： S2 = 1800mm
=
⎡⎢⎣1 −
0.5 ⋅ ⎛⎜⎝1 −
b01 b02
⎞⎟⎠⎤⎥⎦
⋅ b02 =
1.69 m
承台截面的斜截面抗剪承载力： Vca = βhs ⋅ β ⋅ ft ⋅ b0 ⋅ h0 = 4260.418 ⋅ kN
承台截面 = "满足GB50007-2011第8.5.21条" if V ≤ Vca "不满足GB50007-2011第8.5.21条，增加承台高或提高混凝土强度 "