梯形钢屋架设计.docx
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梯形钢屋架设计.docx
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梯形钢屋架设计
1设计资料·····························································································································1
2屋架形式及几何尺寸···········································································································1
3支撑的布置··························································································································2
4荷载计算·····························································································································3
5内力计算·····························································································································4
6杆件复核·····························································································································5
7节点复核····························································································································10
采用PKPM软件进行设计,对杆件和部分节点进行手算复核。
1设计资料
1.1结构形式
跨度为21m,总长90m,柱距6m,采用梯形钢屋架。
1.2屋架尺寸及选材
屋架端部高度设计为1.8m,屋面坡度为1/10,采用Q235钢,E43型焊条。
1.3荷载标准值
恒载有:
防水层、找平层、保温层等1.7kN/m2预应力混凝土屋面板(含灌缝1.5kN/m2屋架及支撑自重(20.120.011kN/mkgL=+0.351kN/m2
活载有:
屋面均布活载0.5kN/m2雪荷载0.35kN/m2积灰荷载0.5kN/m2
屋面为重屋面,不考虑风荷载;抗震设防烈度为6度,不考虑地震作用。
2屋架形式及几何尺寸
(1计算跨度0215021000215020700mmLL=-⨯=-⨯=;(2屋架中部高度2100018000.1=2850mm
2
H=+⨯
;
(3屋架跨中起拱高度L/500=42mm,实取50mm;(4几何尺寸如下图1所示:
1508
135********81508150815082850
3000
3000
30001815
2100
2400
2700
2850
2376
2709
2964
3226
24
5526
9929
5342
A
B
C
D
E
FG
H
IJ
K
L
M
屋架几何尺寸示意图(单位:
mm
图1屋架几何尺寸示意图(单位:
mm3支撑的布置
根据车间长度、屋架跨度和荷载情况,上、下弦各设两道横向水平支撑,具体见支撑布置图2。
a上弦支撑
11
b下弦支撑
CC1CC3CC1
LG2
GG2
c1-1剖面垂直支撑
图2屋面支撑布置(单位:
mm
SC-上弦支撑;XC-下弦支撑;CC-垂直支撑;GG-刚性系杆;LG-柔性系杆
4荷载计算
屋面活荷载与雪荷载不同时组合,屋面活荷载大于雪荷载,故只取屋面活荷载进行计算。
由于屋面坡度较小,可以将沿斜面分布的荷载均视为水平投影面上的荷载。
计算时,竖向节点荷载取1.5m×6.0m面积的荷载。
详见表1、表2。
表1恒载计算
表2活载计算节点荷载标准值:
3.5511.5631.96P=⨯⨯=恒kN,11.569P=⨯⨯=活
kN
5内力计算
按由可变荷载效应控制的组合计算:
1.231.961.40.9949.69
P=⨯+⨯⨯=kN
按由永久荷载效应控制的组合计算:
1.3531.961.40.7951.97
P=⨯+⨯⨯=kN
因此计算按永久荷载效应控制的组合进行,采用PKPM软件将内力、参数输入,初步选定截面进行计算,直到PKPM计算无不符合要求的杆件。
活荷载输入时应该按互斥荷载分别输入“全跨荷载”与“半跨荷载”两组数据。
内力图如图3所示。
-481.4
-1.3
-481.5-717.9-718.0-770.4-770.4258.7
616.5
734.6
-36.3
-57.2
-57.2
-57.2
1.5
-467.5
-267.0
-105.0
72.3
351.4
17
3.7
-13
.7A
B
C
D
E
FGHIJK
LM杆件内力图(单位:
kN
37.3
图3杆件内力图(单位:
kN
根据腹杆的最大设计内力467.5AGN=-kN,取中间节点板厚为10mm,支座节点板厚为12mm。
6杆件复核
Q235钢,厚度不大于16mm时,215f=N/mm2,
235yf=N/mm26.1上弦杆
图4上弦杆截面
整个上弦杆采用同一种截面类型,为2L140×90×12不等边角钢短肢相并。
(图4
max770.4N=-kN
由角钢间距a=10mm查表得
A=2640×2=5280mm2,xi=2.54cm,yi=6.81cm,压杆的容许长细比[]150λ=计算长度:
1508oxl=mm(节点间轴线长度
x
3016oyl=mm(按大型屋面板与屋架保证三点焊接考虑,取oy
l为两块屋面板宽
(1刚度验算:
0150859.37
25.4
xxx
liλ=
==<[]150λ=(满足
0301644.2968.1
yyy
liλ=
=
=<[]150λ=(满足
因为
011
1400.563016
11.670.56
12.0612
140
ylbt
b⨯==≤=
=,所以44.29
yzyλλ==<
[]150λ=(满足
(2整体稳定性验算:
截面对x轴为b类,对y轴为b
类,由max
59.37
λ=,查表得:
min0.8070.37(0.8130.8070.809ϕ=+⨯-=
因此3
min770.410
180.36
0.8095280
N
A
σϕ⨯==
=⨯N/mm2<215f=N/mm2(满足
6.2下弦杆
图8下弦杆截面
整个下弦杆采用同一种截面类型,为2L125×80×10不等边角钢短肢相并。
(图8
max751.7N=kN
由角钢间距a=10mm查表得
A=1970×2=3940mm2,xi=2.26cm,yi=6.11cm,拉杆的容许长细比[]350λ=计算长度:
1508oxl=mm(节点间轴线长度,20700103502
oyl==mm(跨中有通长细杆
(1刚度验算:
01508134.5322.6
xxx
liλ=
==<[]350λ=(满足
010350169.3961.1
yyy
liλ=
=
=<[]350λ=(满足
(2强度验算:
3
751.710190.793940
NAσ⨯=
=
=N/mm2<215f=N/mm2
(满足
6.3端斜杆AG
图9端斜杆截面
端斜杆采用2L110×70×10不等边角钢长肢相并(图9
467.5AGN=-kN
由角钢间距a=10mm查表得
A=1720×2=3440mm2,xi=3.48cm,yi=2.96cm,压杆的容许长细比[]150λ=计算长度:
2376
oxoyll==mm
(1刚度验算:
0237668.2834.8
xxx
liλ=
==<[]150λ=(满足
0237680.2729.6
yyy
liλ=
=
=<[]150λ=(满足
因为
022
700.482376
70.48
16.7910
70
ylbtb⨯==≤=
=
所以4
42222
2
01.091.0970
(180.27(183.99237610
yzyy
blt
λλ⨯=+
=⨯+
=⨯<[]150λ=(满足
(2整体稳定型验算:
截面对x轴为b类,对y轴为b
类,由max
83.99
λ=,查表得:
min0.661ϕ=
因此3
min467.510
205.6
0.6613440
N
A
σϕ⨯==
=⨯N/mm2<215f=N/mm2(满足
6.4竖杆
图10竖杆截面
竖杆采用同一种截面类型(除了中竖杆,中竖杆是采用2L63×8十字型截面,选用2L63×8等边角钢,取DL杆复核。
(图10
DL57.2N=-kN
由角钢间距a=10mm查表得
A=951×2=1902mm2,xi=1.9cm,yi=3.02cm,压杆的容许长细比[]150λ=计算长度:
27000.82160oxl=⨯=mm,2700
oyl=mm
(1刚度验算:
02160113.6819
xxx
liλ=
==<[]150λ=(满足
0270089.430.2
yyyliλ=
=
=<[]150λ=(满足
因为
0630.582700
7.880.58
24.868
63
ylbt
b
⨯=
=≤=
=
所以4
4
222
2
00.4750.47563(189.4(190.8327008
yzyy
blt
λλ⨯=+
=⨯+
=⨯<[]150λ=(满足
(2整体稳定型验算:
截面对x轴为b类,对y轴为b
类,由max
90.83
λ=,查表得:
min0.6140.83(0.6210.6140.62ϕ=+⨯-=
因此3
min57.210
48.510.621902
N
A
σϕ⨯=
=
=⨯N/mm
2
<215f=N/mm2(满足
6.5其他斜腹杆
图11其他斜腹杆截面
其他斜腹杆采用同一种截面类型2L80×10等边角钢,取BI杆进行复核。
(图11
BI267N=-kN
由角钢间距a=10mm查表得
A=1510×2=3020mm2,xi=2.42cm,yi=3.74cm,压杆的容许长细比[]150λ=计算长度:
27090.82167.2
oxl=⨯=mm,2709oyl=mm
(1刚度验算:
02167.289.5524.2
xxx
liλ=
==<[]150λ=(满足
0270972.4337.4
yyyliλ=
=
=<[]150λ=(满足
因为
0800.582709
80.58
19.6410
80
ylbt
b
⨯=
=≤=
=
所以4
4222
2
00.4750.47580(172.43(174.35270910
yzyy
blt
λλ⨯=+
=⨯+
=⨯<[]150λ=(满足
(2整体稳定型验算:
截面对x轴为b类,对y轴为b
类,由max
89.55
λ=,查表得:
min0.6210.55(0.6280.6210.625ϕ=+⨯-=
因此3
min26710
141.460.6253020
N
A
σϕ⨯=
=
=⨯N/mm
2
<215f=N/mm2(满足
7节点复核
Q235钢,E43型焊条,160wff=N/mm27.1下弦节点B复核
具体尺寸如图12所示,焊缝尺寸见表4。
图12下弦节点B
表4B节点焊缝尺寸
(1BG杆(2L80×10等边角钢,10.7K=,20.3K=
肢背所需要焊缝长度:
3
110.7351.410
2212115.5120.720.712160
fw
ff
KNlhhf
⨯⨯=
+=
+⨯=⨯⨯⨯⨯<120mm(满足
肢尖所需要焊缝长度:
3
220.3351.410
22690.4420.720.76160
fwff
KNlhhf
⨯⨯=
+=
+⨯=⨯⨯⨯⨯<120mm(满足
(2BH杆(2L63×8等边角钢,10.7K=,20.3K=
肢背所需要焊缝长度:
3
110.757.210
22641.7920.720.76160
fw
ff
KNlhhf
⨯⨯=
+=
+⨯=⨯⨯⨯⨯<95mm(满足
肢尖所需要焊缝长度:
3
220.357.210
22624.7720.720.76160
fwff
KNlhhf
⨯⨯=
+=
+⨯=⨯⨯⨯⨯<95mm(满足
(3BI杆(2L80×10等边角钢,10.7K=,20.3K=
肢背所需要焊缝长度:
3
110.726710
221293.5320.720.712160
fw
ff
KNlhhf
⨯⨯=
+=
+⨯=⨯⨯⨯⨯<120mm(满足
肢尖所需要焊缝长度:
3
220.326710
22671.6020.720.76160
fw
ff
KNlhhf⨯⨯=
+=
+⨯=⨯⨯⨯⨯<120mm(满足
(4ABC杆(2L125×80×10不等边角钢短肢相并,10.75K=,20.25K=
杆件所受内力差616.5258.7357.8N∆=-=kN肢背所需要焊缝长度:
3
110.75357.810226211.6720.720.76160
fw
ff
KNlhhf
∆⨯⨯=
+=
+⨯=⨯⨯⨯⨯<212mm(满足
肢尖所需要焊缝长度:
3
220.3357.810
22678.5620.720.76160
fwff
KNlhhf
∆⨯⨯=
+=
+⨯=⨯⨯⨯⨯<120mm(满足
7.2上弦节点I复核
具体尺寸如图13所示,焊缝尺寸见表5。
图13上弦节点I
表5I节点焊缝尺寸
(1BI杆(2L80×10等边角钢,在下弦节点B复核时已经算过,满足要求。
(2CI杆(2L80×10等边角钢,10.7K=,20.3K=
肢背所需要焊缝长度:
3
110.7173.710
221269.2320.720.712160
fw
ff
KNlhhf⨯⨯=
+=
+⨯=⨯⨯⨯⨯<120mm(满足
肢尖所需要焊缝长度:
3
220.3173.710
22650.7720.720.76160
fw
ff
KNlhhf⨯⨯=
+=
+⨯=⨯⨯⨯⨯<120mm(满足
(3HIJ杆(2L140×90×12不等边角钢短肢相并
上弦杆与节点板的连接焊缝是由角钢肢背的槽焊缝和角钢肢尖的两条角焊缝组成,假定角钢肢背的槽焊缝承受节点荷载P,角钢肢尖的两条角焊缝承担N∆和由于
N
∆与肢尖焊缝的偏心距e而产生的弯矩eNM⋅∆=∆。
当屋面坡度较缓时,角钢肢背槽焊缝的强度可按下式计算:
0.820.7w
fffw
Pfhlβ≤⨯
角钢肢背的槽焊缝近似按两条0.5tfh=(t为节点板厚度的角焊缝计算;上式中的系数0.8是考虑到槽焊缝的质量不易保证,而将角焊缝的强度设计值降低20%。
对承受静力荷载和间接承受动力荷载的结构,22.1=fβ;对直接承受动力荷载的结构,
.1=f
β
。
角钢肢背槽焊缝的强度验算:
51.97
P=kN,0.50.5105fht==⨯=mm,135wl=mm,22.1=fβ
3
51.9710
54.990.80.81.22160156.1620.720.75135
w
fffw
Pfhlβ⨯=
=≤=⨯⨯=⨯⨯⨯⨯kN(满足
角钢肢尖焊缝的强度验算:
717.9481.5236.4
N∆=-=kN
9021.968.1e=-=mm,6fh=mm,314wl=
mm
3
236.410
89.6320.720.76314
f
fw
Nhlτ
∆⨯=
=
=⨯⨯⨯⨯N/mm2
3
2
2
66236.41068.1116.6320.720.76314
f
fw
Mhlσ
∆⨯⨯⨯=
=
=⨯⨯⨯⨯N/mm
2
131==N/mm2
160wff≤=N/mm2(满足
7.3屋脊拼接节点M复核
具体尺寸如图14所示,焊缝尺寸见表6。
图14屋脊拼接节点M
表6M节点焊缝尺寸
(1拼接角钢与弦杆之间的连接焊缝复核:
弦杆都采用同号角钢进行拼接,为使拼接角钢与弦杆之间能够密合,且便于施焊,需要将拼接角钢的尖角削除,并截去垂直肢的一部分宽度(为51010525fth++=++=mm。
拼接角钢的部分削弱,可以借助节点板来补偿。
按上弦杆力770.4LMN=kN计算拼接角钢与上弦的焊缝,每边共有4条焊缝平均
承受此力,则一条焊缝的计算长度为:
3
770.410
171.940.740.710160
ww
ff
Nlhf⨯=
=
=⨯⨯⨯⨯mm
拼接角钢需要的长度为:
(22(171.9210230413.8
wfllh=+⨯+=+⨯⨯+=弦杆杆端空隙mm<430mm(满
足
(2上弦与节点板之间的焊缝复核:
角钢肢背槽焊缝的强度验算:
上弦与节点间在节点两侧共4条焊缝,共同承受节点荷载P与两侧上弦内力的合力。
近似地取sinα=tanα=0.1,该合力的数值为:
3
3
3
2sin2770.4100.151.9710102.1110NPα-=⨯⨯⨯-⨯=⨯kN
0.50.5105fht==⨯=
mm,135wl=mm,22.1=fβ
3
2sin102.1110
54.030.80.81.22160156.1620.740.75135
w
fffw
NPfhlαβ-⨯=
=≤=⨯⨯=⨯⨯⨯⨯kN(满
足
角钢肢尖焊缝的强度验算:
上弦角钢肢尖与节点板的连接焊缝按上弦杆最大内力的15%计算
0.15770.4115.56N=⨯=kN
9021.968.1e=-=mm,6fh=mm,212
wl=mm
3
115.5610
64.8920.720.76212
f
fw
Nhlτ
⨯=
=
=⨯⨯⨯⨯N/mm2
3
22
66115.561068.1125.0720.720.76212
f
fw
Mhl
σ
⨯⨯⨯=
=
=⨯⨯⨯⨯N/mm
2
121.33==N/mm2
160wff≤=N/mm2(满足(3其他杆件受力均比较小,这里不进行复核。
7.4支座节点A复核
具体尺寸如图15所示。
支座节点
A
图15支座节点A
(1支座底板复核:
(支座节点板厚度为12mm,底板厚度为18mm
支座反力R(31.951.3591.40.75.5(33.31.3591.40.7=⨯+⨯⨯⨯+⨯+⨯⨯(23.211.354.51.40.7+⨯+⨯⨯=375.26kN支座底板尺寸采用280mm×360mm,承压面积为:
2
A280360(252503095837.5
π=⨯-⨯+⨯⨯=mm2
验算柱顶混凝土的抗压强度:
(选用C30混凝土,14.3cf=N/mm2
3
375.26103.9295837.5
RAσ⨯=
=
=N/mm214.3cf≤=N/mm2(满足
验算底板厚度:
底板的厚度按屋架反力作用下的弯距计算,节点板和加劲肋将底板分成四块,每块板为两相邻边支承,而另两相邻边自由的板,每块板单位宽度的最大弯距为:
2
1
Maβσ=
底板的平均应力3.92σ=N/mm2两相邻支承边的对角线长度(图16
1219.6a=
=mm
a1
由相似三角形关系得支承边的交点至对角线的垂直距离1174134
106.2219.6
b
⨯
==mm
11106.2
0.48219.6
ba==,查表得0.06β=
所以
17.79
t===mm
18
≤mm(满足
(2加劲肋与节点板的连接焊缝复核:
见图17,焊缝长度等于加劲肋高度,也等于
节点板高度。
焊缝长度为399mm,计算长度
3991510374
w
l=--=mm(焊脚尺寸hf=5mm,
每块加劲肋近似的按承受1
4
R计算,
1
4
R作用点到
焊缝的距离为175151595
2
e
-
=+=mm。
则焊缝所
受剪力V及弯矩M为:
375.26
93.82
44
R
V===kN
3
93.8210958912900Nmm
MVe
=⨯=⨯⨯=⋅
57.34
==160
w
f
f
≤=N/mm2(满足(3加劲肋与节点板、底板的焊缝复核:
焊缝
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