无梁楼盖柱帽计算

一、设计方法及基本参数
无梁楼盖计算 (中间柱帽) Zwenku.baidu.com1
1.设计方法：
受弯计算按等代框架多跨连续 梁计算总弯矩，再按柱上板带和跨中板带弯矩 分配系数分配弯矩，
无梁楼盖与柱顶铰接连接。冲切计算当混凝土板厚不满足 时，配置冲切钢筋。
2.柱帽构造：
柱帽构造详见下图
L ≥35
45°
a 2 ≥0.175L
hc hc 22
= 0.055
γs4 := "请重新计算" if 1 − 2αs4 < 0
1+
1 − 2 ⋅ αs4 2
otherwise
ξ4 := "请重新计算" if 1 − 2αs4 < 0
(1 − 1 − 2 ⋅ αs4) otherwise
= 0.972 = 0.056
if(ξ4 < ξb , "满足要求" , "请重新计算") = "满足要求"
(2)砼受压区等效高度计算
x1 := ξ1 ⋅ h0 if ξ1 ⋅ h0 < ξb ⋅ h0 = 72 ⋅ mm
ξb ⋅ h0 otherwise
(3)配筋计算
As1 :=
α1 ⋅ fcd ⋅ B ⋅ h0 ⋅ ξ1 fsd
= 2976 ⋅ mm2
最小配筋率按GB50010 − 2002中9.5.1条和GB50038 − 2005中4.11.7条计算取值
(2)砼受压区等效高度计算
x4 := ξ4 ⋅ h0 if ξ4 ⋅ h0 < ξb ⋅ h0 = 24.199 ⋅ mm
ξb ⋅ h0 otherwise
(3)配筋计算
As4 :=
α1 ⋅ fcd ⋅ B ⋅ h0 ⋅ ξ4 fsd
= 998 ⋅ mm2
最小配筋率按GB50010 − 2002中9.5.1条计算取值
跨中板带弯矩分配系数： 板支座： ηcb := 0.55
板跨中： ηbb := 0.45
配筋计算单元宽度： B := 1m
柱上板带柱帽上每米弯矩：
Mx :=
ηc ⋅ B 0.5Ly
⋅ MxC =
−570 ⋅ kN ⋅ m
My :=
ηc ⋅ B 0.5Lx
⋅ MyC =
−671 ⋅ kN ⋅ m
Ly
−224 ⋅ kN ⋅ m
跨中板带下部每米弯矩：
Mx1中 :=
ηbb ⋅ B 0.5Ly
⋅
Mx1
=
203 ⋅
kN
⋅
m
My1中 :=
ηbb ⋅ B 0.5Lx
⋅
My1
=
239 ⋅
kN
⋅
m
（三）、配筋计算
Ly Ly Ly
2
2
2
Lx Lx Lx
2
2
2
Lx
【一】、X向配筋计算
1.X向柱上板带上部配筋计算
(1)相对受压区等效高度计算：
π 4
=
2011 ⋅ mm2
X向柱上板带下部实配钢筋 := "满足要求" if Asb2 ≥ As2
= "满足要求"
"钢筋不足,重新选筋" otherwise
3.X向跨中板带支座上部配筋计算
(1)相对受压区等效高度计算：
αs3 :=
Mx11 fcd ⋅ B ⋅ h02
= 0.051
γs3 :=
"请重新计算" if 1 − 2αs3 < 0
Asb3 :=
B sb3
⋅ db32 ⋅
π 4
=
2454 ⋅ mm2
X向跨中板带支座上实配钢筋 := "满足要求" if Asb3 ≥ As3
= "满足要求"
"钢筋不足,重新选筋" otherwise
4.X向跨中板带下部配筋计算
(1)相对受压区等效高度计算：
αs4 :=
Mx1中 fcd ⋅ B ⋅ h02
βc := 1.0
Es := 200000N ⋅ mm− 2
γds := 1.35
γdc := 1.5
ft = 1.57 ⋅ N ⋅ mm− 2
fc = 16.7 ⋅ N ⋅ mm− 2
fcd := γc ⋅ γdc ⋅ fc fsd := γds ⋅ fsy ftd := γc ⋅ γdc ⋅ ft
ρmin :=
0.25%
if
45
ftd 100fsd
< 0.25%
= 0.25 ⋅ %
Amin := ρmin ⋅ (B ⋅ h) = 1125 ⋅ mm2
45
ft 100fsd
otherwise
As1 :=
As1 if Amin < As1 Amin otherwise
= 2976 ⋅ mm2
实配钢筋 ϕ25＠200 + ϕ25＠200
qx1 := (γQ1 ⋅ qe1 + γG ⋅ Gk) ⋅ Ly = 900.15 ⋅ kN ⋅ m− 1 qy1 := (γQ1 ⋅ qe1 + γG ⋅ Gk) ⋅ Lx = 857.79 ⋅ kN ⋅ m− 1
（二）、内力计算
计算跨数： X向：5跨 Y向：5跨
计算简图如下：
A
1
B2
C3
D4
E5
柱上板带跨中下每米弯矩：
Mx中 :=
ηcb ⋅ B 0.5Ly
⋅
Mx1
=
248
⋅
kN
⋅
m
My中 :=
ηcb ⋅ B 0.5Lx
⋅
My1
=
292
⋅
kN
⋅
m
跨中板带支座上每米弯矩：
Mx11 :=
ηb ⋅ B 0.5Ly
⋅ MxC =
−190 ⋅ kN ⋅ m
My11 :=
ηb ⋅ B 0.5Lx
⋅ MyC =
1+
1 − 2 ⋅ αs3 2
otherwise
= 0.974
ξ3 := "请重新计算" if 1 − 2αs3 < 0 = 0.053
(1 − 1 − 2 ⋅ αs3) otherwise
if(ξ3 < ξb , "满足要求" , "请重新计算") = "满足要求"
(2)砼受压区等效高度计算
x3 := ξ3 ⋅ h0 if ξ3 ⋅ h0 < ξb ⋅ h0 = 22.632 ⋅ mm
= "满足要求"
"钢筋不足,重新选筋" otherwise
【二】、Y向配筋计算
1.Y向柱上板带上部配筋计算
(1)相对受压区等效高度计算：
αs11 :=
My fcd ⋅ B ⋅ h02
= 0.181
F
Ln
Ln
Ln
Ln
Ln
MB
MC
MD
ME
M1
M2
M3
M4
M5
A
B
C
D
E
F
Ln
Ln
Ln
Ln
Ln
计算净跨度： Lxn :=
Lx −
2 3
⋅
bex =
6.733m
Lyn :=
Ly −
2 3
⋅ bey =
7.133m
各截面最大弯矩系数： η1 := 0.0782 η2 := 0.0332 η3 := 0.0469 ηB := −0.105 ηC := −0.0791
ξb ⋅ h0 otherwise
(3)配筋计算
As3 :=
α1 ⋅ fcd ⋅ B ⋅ h0 ⋅ ξ3 fsd
= 933 ⋅ mm2
最小配筋率按GB50010 − 2002中9.5.1条计算取值
As3 := As3 if Amin < As3 = 1125 ⋅ mm2
Amin otherwise
实配钢筋 ϕ25＠200 sb3 := 200mm db3 := 25mm
= 1227.778 ⋅ mm2
最小配筋率按GB50010 − 2002中9.5.1条计算取值 As2 := As2 if Amin < As2 = 1228 ⋅ mm2
实配钢筋
Amin otherwise ϕ16＠100 sb2 := 100mm
db2 := 16mm
Asb2 :=
B sb2
⋅ db22 ⋅
if(ξ2 < ξb , "满足要求" , "请重新计算") = "满足要求"
(2)砼受压区等效高度计算
x2 := ξ2 ⋅ h0 if ξ2 ⋅ h0 < ξb ⋅ h0 = 29.775 ⋅ mm ξb ⋅ h0 otherwise
(3)配筋计算
As2 :=
α1 ⋅ fcd ⋅ B ⋅ h0 ⋅ ξ2 fsd
fcukd := γdc ⋅ fcuk
4.柱截面参数
hc := 450mm bc := 800mm 柱高 Hn := 3450mm
hc := min(hc , bc) = 450 ⋅ mm
5.楼板参数
计算跨度： Lx1 := 8.1m Ly1 := 8.5m 相邻跨计算跨度 Lx2 := 8.1m Ly2 := 8.5m
"不满足要求，重新设计" otherwise
二、战时分析
（一）、荷载
二等人员掩蔽所,乙类防空地下室,防核武器抗力等级级别6级,采用等效静荷载设计,等效静荷载
按《人民防空地室设计规范》GB50038-2005查表取用：
作用于顶板上等效荷载标准值查表 4.7.2
qe1 := 60kN ⋅ m− 2
覆土厚 H1 := 1.5m 填土的容重： γ := 18kN ⋅ m− 3
柱上板带宽度： Bcx := 0.5 ⋅ Lx = 4.05m
Bcy := 0.5 ⋅ Ly = 4.25m
跨中板带宽度： B1x := 0.5 ⋅ Lx = 4.05m
B1y := 0.5 ⋅ Ly = 4.25m
柱上板带弯矩分配系数： 柱帽上： ηc := 0.75
板支座： ηb := 0.25
αs1 :=
Mx fcd ⋅ B ⋅ h02
= 0.154
γs1 :=
"请重新计算" if 1 − 2αs1 < 0
1+
1 − 2 ⋅ αs1 2
otherwise
= 0.916
ξ1 := "请重新计算" if 1 − 2αs1 < 0 = 0.168
(1 − 1 − 2 ⋅ αs1) otherwise
Lx := 0.5 ⋅ (Lx1 + Lx2) = 8.1m
Ly := 0.5 ⋅ (Ly1 + Ly2) = 8.5m
板厚：
h := 450mm as := 20mm
h0 := h − as = 430 ⋅ mm
柱帽有效宽度： bex := 2050mm
bey := 2050mm
be := max(bex , bey) = 2.05m
sb1 := 200mm db11 := 25mm
db12 := 25mm
( ) Asb1 :=
B sb1 ⋅
db112 + db122
⋅
π 4
=
4909 ⋅
mm2
X向柱上板带上部实配钢筋 := "满足要求" if Asb1 ≥ As1 "钢筋不足,重新选筋" otherwise
= "满足要求"
2.X向柱上板带下部配筋计算
跨中最大总弯矩： Mx1 := η3 ⋅ qx1 ⋅ Lxn2 = 1914.027 ⋅ kN ⋅ m
My1 := η3 ⋅ qx1 ⋅ Lyn2 = 2148.19 ⋅ kN ⋅ m
支座最大总弯矩： MxC := ηC ⋅ qx1 ⋅ Lxn2 = −3228.134 ⋅ kN ⋅ m
MyC := ηC ⋅ qx1 ⋅ Lyn2 = −3623.067 ⋅ kN ⋅ m
柱帽宽度： 柱帽高度： 柱帽构造 :=
ax := 3500mm
ay := 3500mm
h1 :=
be −
hc − h 2
=
575 ⋅ mm
H0 :=
3 2
⋅
h
−
as
=
0.655m
"满足要求" if be ≥ 0.2max(Lx , Ly) ∧ be ≤ 0.3min(Lx , Ly) = "满足要求"
混凝土容重 γcg := 25kN ⋅ m− 3
恒荷载分项系数 恒荷载标准值：
γG := 1.2 等效静荷载分项系数：γQ1 := 1.0 Gk := H1 ⋅ γ + h ⋅ γcg = 38.25 ⋅ kN ⋅ m− 2
计算单元荷载设计值 , 按GB50038 − 2005中4.10.2条计算：
As4 := As4 if Amin < As4 = 1125 ⋅ mm2
实配钢筋
Amin otherwise ϕ16＠100 sb4 := 100mm
db4 := 16mm
Asb4 :=
B sb4
⋅ db42 ⋅
π 4
=
2011 ⋅ mm2
X向跨中板带下部实配钢筋 := "满足要求" if Asb4 ≥ As4
(1)相对受压区等效高度计算：
αs2 :=
Mx中 fcd ⋅ B ⋅ h02
= 0.067
γs2 :=
"请重新计算" if 1 − 2αs2 < 0
1+
1 − 2 ⋅ αs2 2
otherwise
= 0.965
ξ2 := "请重新计算" if 1 − 2αs2 < 0 = 0.069 1 − 1 − 2 ⋅ αs2 otherwise
a 2 ≥0.175L
3.材料参数：
混凝土强度度等级
C := 35
混凝土的动力强度折减系数 γc := 0.8
fc与ft的参数的的
主要受拉钢筋采用三级钢 fsy := 360N ⋅ mm− 2
箍筋采用一级钢 fvy := 210N ⋅ mm− 2
fcuk := C
α1 := 1.0
β1 := 0.8
εcu := 0.0033 − (fcuk − 50) ⋅ 10− 5
0.0033 otherwise
ξb :=
1+
β1 fsd
Es ⋅ εcu
= 0.461
if 0.0033 − (fcuk − 50) ⋅ 10− 5 < 0.0033
= 0.003
if(ξ1 < ξb , "满足要求" , "请重新计算") = "满足要求"