无梁楼盖柱帽计算

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
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
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
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
−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：
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：
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
一、设计方法及基本参数
无梁楼盖计算 (中间柱帽) ZM1
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
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
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
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
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
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
"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 0.25
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
= "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
(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
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