型钢混凝土梁与十字型钢混凝土柱连接节点计算书

箍筋体积配筋量：
Hc
Hc s2 s1 acs
c
hc
c
c
hc
c
tcf
tcf
bc
tcw
tcf
tcf tcw bc
Bc
acs s1 s2
Bc s2 s1 acs
acs s1 s2
Acv := 2π ⋅ dcv2 ⋅ (Hc − 2 ⋅ acs) = 560963 ⋅ mm3
型钢混凝土柱截面
fc与ft的参数的的 fcc := fc = 21.1 ⋅ N ⋅ mm− 2
柱翼缘塑性截面模量 Wpcf := bc ⋅ tcf ⋅ (hc − tcf) = 1.421 × 106 ⋅ mm3
全截面塑性模量： 型钢截面面积：
Wpc :=
Wpcf +
⎛ ⎝
hc
− 2tcf 2
2
⎞ ⎠
⋅
tcw
+
1 2
(bc
−
tcw)2 ⋅ tcf =
2.424 ×
106 ⋅ mm3
Asc = 26240 ⋅ mm2
Ab := Bb ⋅ Hb = 199500 ⋅ mm2
3.焊缝截面参数：
tf
（1）腹板焊缝截面：
h1 := h − 2 ⋅ tf − ω1 − ω2 = 253 ⋅ mm hf := 13mm
lw := h1 − 2hf = 227 ⋅ mm 焊缝有效高度：he := 0.5 2hf = 9.2 ⋅ mm
弯矩传递途径： 梁翼缘——翼缘对接焊缝——柱 梁腹板——腹板连接角焊缝——柱
剪力传递途径： 梁腹板——腹板连接角焊缝——柱 2.梁端与柱连接方式： H型钢梁与十字型钢柱刚性连接 ，梁翼、腹板均缘采用对接焊缝与柱翼 缘焊接，详见下图
MV
VM
R35
型钢混凝土节点 25
6 19 10 35°
R10~15
ω2=50
ξb :=
1+
0.8 fsf + f 2 ⋅ 0.003Es
= 0.513
if(ξ < ξb , "满足要求" , "请重新计算") = "满足要求"
(4)型钢混凝土梁抗弯承载力
抗弯承载力抗震调整系数 γRE1 := 0.75
柱型钢截面 = "满足JGJ138-2001中6.1.9-4式"
柱截面含钢率：
ρsc :=
Asc Ac
=
5.355 ⋅ %
柱纵筋配筋率：
ρc :=
Acs Ac
=
1.087 ⋅ %
柱截面含钢率、配筋率 := "满足JGJ138-2001中6.2.4条" if ρsc ≥ 4% ∧ ρsc ≤ 10% ∧ ρc ≥ 0.8%
梁配筋量：
Abs :=
1 4
⋅
π
⋅
n3
⋅
d2
=
804 ⋅ mm2
梁箍筋配筋量：
Abபைடு நூலகம் :=
1 4
⋅
π
⋅
n4
⋅
dbv2
=
226 ⋅
mm2
型钢混凝土梁截面
fc与ft的参数的的 fcb := fc = 19.1 ⋅ N ⋅ mm− 2
梁截面柱性
ftb := ft = 1.71 ⋅ N ⋅ mm− 2
型钢截面柱性
全截面惯性矩
Ix = 1.827 × 108 ⋅ mm4 翼缘截面惯性矩
Ifx = 1.505 × 108 ⋅ mm4
腹板截面惯性矩 Iwx = 3.218 × 107 ⋅ mm4 端头腹板净截面惯性矩 Inwx1 = 1.35 × 107 ⋅ mm4
端头净截面惯性矩 Inx1 = 1.64 × 108 ⋅ mm4 端头净截面抵抗矩
Wnx1 = ⋅ mm3
全截面抵抗矩
Wx = 9.874 × 105 ⋅ mm3 翼缘截面抵抗矩
Wfx = 8.134 × 105 ⋅ mm3
腹板截面抵抗矩 Wwx = 1.904 × 105 ⋅ mm3
梁翼缘塑性截面模量 Wpf := b ⋅ tf ⋅ (h − tf)
Wpf = 8.496 × 105 ⋅ mm3
fck = 29.6 ⋅ N ⋅ mm− 2
fycv := 210N ⋅ mm− 2
柱截面柱性
型钢截面柱性
全截面惯性矩
Icx = 5.246 × 108 ⋅ mm4 抗弯计算方向截面惯性矩 Icsx = 4.201 × 108 ⋅ mm4
全截面抵抗矩
Wcx = 2.281 × 106 ⋅ mm3 抗弯计算方向截面抵抗矩 Wcsx = 1.826 × 106 ⋅ mm3
c1 := 100mm c2 := Hb − h − c1 = 100 ⋅ mm
Hb
h
tw
tf
b1 := 0.5(Bb − b) b2 := b1 = 100 ⋅ mm
材质：Q345
f := 310N ⋅ mm− 2
fv := 180N ⋅ mm− 2
fy := 345N ⋅ mm− 2 fu := 470N ⋅ mm− 2
fwf := 200N ⋅ mm− 2
βf := 1.22
（2）翼缘焊缝截面：
梁端翼缘采用加强版加强，加强板厚10mm
h
hf tw hf
b
梁端头焊缝截面
tf
lw
翼缘对接焊缝高度： fwt := 295N ⋅ mm− 2
（3）焊缝截面柱性：
tsf := tf + 10mm = 26 ⋅ mm fwv := 170N ⋅ mm− 2
c2
b
梁净跨：
Ln := 7700mm
Bb
混凝土强度度等级 C := 40
梁纵向钢筋采用三级钢
Es := 200000N ⋅ mm− 2
梁实际配筋： 上下各4Φ16 d := 16mm n3 := 4
梁端箍筋： Φ12 @100(2) n4 := 2
dbv := 12mm sbv := 100mm fybv := 210N ⋅ mm− 2
柱型钢外混凝土保护层厚度 = "满足JGJ138-2001中4.3.3条"
柱型钢截面 :=
"满足JGJ138-2001中6.1.9-4式"
if
f⋅
(tcw ⋅ hcw + fcc ⋅ Bc ⋅
2tcf ⋅ Hc0
bc)
≥
0.1
"不满足JGJ138-2001中6.1.9-4，增大型钢截面面积" otherwise
25 25
梁与十字型柱连接节点
6 R20 10
35°
tf 62
6
6 19
1=35 tf ω 29 6 2
二、截面及焊缝参数
1.柱截面参数
Hc := 700mm Bc := 700mm acs := 40mm
hc := 460mm bc := 200mm Hc0 := Hc − acs
tcw := 16mm tcf := 16mm hcw := hc − 2tcf
梁型钢外混凝土保护层厚度 = "满足JGJ138-2001中4.3.3条"
梁型钢截面 :=
"满足JGJ138-2001中5.1.4-4式"
if
f ⋅ tw ⋅ hw fcb ⋅ Bb ⋅ H0
≥
0.1
"不满足JGJ138-2001中5.1.4-4，增大型钢截面面积" otherwise
梁型钢截面 = "满足JGJ138-2001中5.1.4-4式"
aa := c1 + 0.5tf = 108 ⋅ mm
按承载力极限状态型钢受拉翼 缘达到屈服，钢筋屈服计算
h0 :=
Abs ⋅ fsf ⋅ (Hb − as) + b ⋅ tf ⋅ (h + c1 −
Abs ⋅ fsf + b ⋅ tf ⋅ f
0.5tf) ⋅ f
=
484 ⋅ mm
( 2)腹板上下端距受压区上边缘的 距离与h0 的比值
c :=
Hc − 2
hc
材质：Q345
=
120 ⋅
mm f :=
310N ⋅
mm− 2
fv := 180N ⋅ mm− 2 fy := 345N ⋅ mm− 2 fu := 470N ⋅ mm− 2
柱高
Hn := 5600mm
混凝土强度度等级
C := 45
β1 := 0.8
柱纵向钢筋采用三级钢 fsf := 360N ⋅ mm− 2
柱实际配筋： 4Φ20（角筋） + 16Φ18
节点区内柱箍筋： Φ12 @100 dcv := 12mm scv := 100mm
d1 := 20mm
d2 := 18mm n1 := 4 n2 := 16
( ) 柱配筋量：
Acs :=
1 4 ⋅π⋅
n1 ⋅ d12 + n2 ⋅ d22
= 5328 ⋅ mm2
H型钢混凝土梁与十字型钢混凝 土柱刚性连接节点一
一、设计方法及连接方式 1.设计方法 按8度抗震设防，抗震等级一级，型钢梁与型钢柱等强连接设计 ，弯矩由翼缘、腹板承担，剪力由腹
板承担，梁端翼缘与腹板所承担的弯矩 按各自的刚度比分配。对翼缘连接焊缝计算正应力，对腹板连接角 焊缝计算弯剪共同作用下的综 合应力。
梁箍筋配筋率： ρbv :=
Abv Bb ⋅ sbv
= 0.646 ⋅ %
梁箍筋配筋率 :=
"满足JGJ138-2001中5.4.7-2式"
if
ρbv ≥ 0.3 ⋅
ftb fybv
"不满足JGJ138-2001中5.4.7-2式，重新设计" otherwise
梁箍筋配筋率 = "满足JGJ138-2001中5.4.7-2式" 2.型钢混凝土梁端抗弯承载力 （1）受拉区钢筋与型钢翼缘合力点 至混凝土受压区边缘的距离h0 型钢翼缘形心至最近混凝土边 的距离：
焊缝截面柱性
全截面惯性矩
Isx = 2.491 × 108 ⋅ mm4
腹板有效截面惯性矩 Iswx = 1.792 × 107 ⋅ mm4
翼缘截面抵抗矩 Wsfx = 1.25 × 106 ⋅ mm3
腹板焊缝有效面积： Assw = 4173.344 ⋅ mm2
焊缝截面面积： Ass = 11973.344 ⋅ mm2
全截面塑性模量： 腹板面积：
Wp
:=
Wpf
+
⎛h ⎝
− 2tf ⎞2 2⎠
⋅
tw
Aw = 3380 ⋅ mm2
翼缘面积：
Wp = 1.135 × 106 ⋅ mm3 Af = 4800 ⋅ mm2
型钢截面面积： Asb = 8180 ⋅ mm2
型钢截面净面积：
Asbn = 7330 ⋅ mm2
梁截面面积：
柱截面面积
Ac = 490000 ⋅ mm2
2.梁截面参数：
c1
Hb := 570mm Bb := 350mm as := 30mm
H0 := Hb − as
tf
h := 370mm b := 150mm ω1 := 35mm ω2 := 50mm
tw := 10mm tf := 16mm hw := h − 2tf
三、承载力计算
翼缘截面惯性矩 全截面抵抗矩 腹板截面有效抵抗矩 翼缘焊缝面积：
Isfx = 2.312 × 108 ⋅ mm4 Wsx = 1.347 × 106 ⋅ mm3 Wswx = 1.579 × 105 ⋅ mm3 Assf = 7800 ⋅ mm2
1.截面构造
(1)型钢混凝土柱
柱型钢外混凝土保护层厚度 := "满足JGJ138-2001中4.3.3条" if c ≥ 120mm "不满足JGJ138-2001中4.3.3条，重新设计" otherwise
柱节点区体积配箍率 = "满足JGJ138-2001中7.2.1条"
(2)型钢混凝土梁 梁型钢外混凝土保护层厚度 :=
"满足JGJ138-2001中4.3.3条"
if
min(c1 , c2) ≥ 100mm ∧ b1 ≥
Bb 6
"不满足JGJ138-2001中4.3.3条，重新设计" otherwise
"不满足JGJ138-2001中6.2.4，重新设计" otherwise
柱截面含钢率、配筋率 = "满足JGJ138-2001中6.2.4条"
柱节点区体积配箍率：
ρvc :=
Acv
(Hc − 2acs)2 ⋅ scv
=
1.459 ⋅ %
柱节点区体积配箍率 := "满足JGJ138-2001中7.2.1条" if ρvc ≥ 0.6% "不满足JGJ138-2001中7.2.1，重新设计" otherwise
梁截面含钢率：
ρsb :=
Asb Ab
=
4.1 ⋅ %
梁纵筋配筋率：
ρb :=
Abs Ab
=
0.403 ⋅ %
梁纵筋配筋率 := "满足JGJ138-2001中5.4.2条" if ρb ≥ 0.3% "不满足JGJ138-2001中5.4.2，重新设计" otherwise
梁纵筋配筋率 = "满足JGJ138-2001中5.4.2条"
fcb ⋅ Bb tw ⋅ f
+
2.5
=
122 ⋅
mm
aa + tf = 124 ⋅ mm
x := x if x ≥ aa + tf aa + tf otherwise
= 124 ⋅ mm
ξ :=
x h0
=
0.256
Asb'
相对界限受压区高度ζb按JGJ138-2001式5.1.2-7计算
x
δ1h0
δ1 :=
c1 + tf h0
= 0.24
δ2 :=
c1 +
tf + h0
hw
=
0.938
(3)混凝土相对受压区高度x
型钢混凝土梁实际配筋为对称配筋，受拉钢筋与受压钢筋量相同，按JGJ138 − 2001中5.1.2 − 4式
和5.1.2 − 5式计算受压区高度。
混凝土相对受压区高度：
x :=
(δ1 + δ2) ⋅ h0