桥梁电算.docx
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桥梁电算.docx
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桥梁电算
一、后张法预应力混凝土梁截面见图1.1,T梁截面宽1.8米,梁肋下部为马蹄形,宽0.4米,梁高1.6米;预留孔道6个,每个孔道直径为50毫米;每孔高强钢丝束为24ΦP5;混凝土强度等级为C50;高强钢丝和混凝土的弹性模量分别为Ep=2.05×105MPa和Ec=3.45×104MPa.不计普通钢筋的影响。
划分节线共6条,每个孔道面积Ak=3.14d2/4=1963.5*10-6m2.每束高强钢丝面积Ap=24*19.63-6=471.12*10-6m2。
一、毛截面:
原始数据:
1
1
6
0.4,0.4,0.2,0.2,1.8,1.8
0.0,0.37,0.50,1.37,1.50,1.60
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下
1.2059.6710.59471.0053
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
1.3461.2048.3052.5159
二、净截面:
原始数据:
2
1
6
0.4,0.4,0.2,0.2,1.8,1.8
0.0,0.37,0.50,1.37,1.50,1.60
4
1963.5E-6,0.080,2,1963.5E-6,0.320,2,1963.5E-6,0.790,1,1963.5E-6,1.080,1
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下
1.2005.6592.58471.0153
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
1.3429.1975.2995.5201
三、换算截面:
原始数据:
3
02.0E5,2.05E5,3.45E5
1
6
0.4,0.4,0.2,0.2,1.8,1.8
0.0,0.37,0.50,1.37,1.50,1.60
4
471.12E-6,0.080,2,2,471.12E-6,0.320,2,2,471.12E-6,0.790,2,1,471.12E-6,1.080,2,1
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下
1.2053.6699.59371.0063
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
1.3458.2041.3046.5163
二、一跨径25米的刚接肋梁桥的横截面布置,桥面净空为-7.5+2×0.75.全宽有5根T行截面梁组成。
混凝土强度等级取C45,其弹性模量为3.55×104Mpa,剪变模量取0.4倍的弹性模量值。
求解荷载横向分布系数。
一、跨径和横截面布置形式单根梁的截面细部尺寸见下图示
行车道宽度7.5米,设计车道为2。
剪变模量G=0.4×3.35×104MPa=1.34×107KPa;梁抗扭惯性矩It计算:
翼板,t1/b1=130/1700=0.076,c1=1/3;腹板:
t2/b2=200/1370=0.146,插值求得c2=0.312+0.046*(0.291-0.312)/0.1=0.302;故It=∑cbt3=1/3*1.7*0.133+0.302*1.37*0.23=4555*10-6m4.。
二、原始数据:
2,0.75,0.25
1,5,0,1
25,3.35E7,1.34E7,0.13
4555E-6,0.75,4
0.2,0.2,1.7,1.7
0.0,1.37,1.37,1.5
1,1,1,1,1
三、计算结果:
荷载横向分布影响线
主梁号12345
P=1位置x
.850.6313.3200.1061-.0021-.0554
2.550.3200.3401.2370.1049-.0021
4.250.1061.2370.3137.2370.1061
5.950-.0021.1049.2370.3401.3200
7.650-.0554-.0021.1061.3200.6313
扭矩横向分布影响线
主梁号12345
P=1位置x
.850-.1932-.1649-.0919-.0423-.0252
2.550.0321-.0245-.0828-.0720-.0579
4.250.0780.0752.0000-.0752-.0780
5.950.0579.0720.0828.0245-.0321
7.650.0252.0423.0919.1649.1932
各主梁联结点处截面弯矩影响线
结点号1234
P=1位置x
.850-.1201-.3099-.2105-.0723
2.550.2399.2475-.0460-.0597
4.250.0122.3188.3188.0122
5.950-.0597-.0460.2475.2399
7.650-.0723-.2105-.3099-.1201
主梁号汽车荷载横向分布系数人群荷载横向分布系数
1.5016.7791
2.5084.2425
3.4744.2001
4.5082.2425
5.5006.7791
三、变截面钢筋混凝土肋拱桥结构的某肋,拱轴为悬连线:
y=f[ch(2kx/l)-1]/(m-1),共轴系数m=2.54,跨度l=45米,拱高10米,拱肋为矩形截面,其惯性矩I=Ic/cosΦ,截面面积A=Ac/cosΦ,拱顶截面高度hc=1.5米,截面宽度bc=1米。
假设该肋承受图示荷载,。
一、拱桥立面图及荷载布置如下示:
其中拱肋截面特性:
Ic=1×1.53/12=0.281m4,Ac=1×1.5=1.5m2,
二、拱顶截面下图所示:
三、原始数据:
3,2,4,0,1,10,1
45,10,1,0.281,1.5
1,10,2,100,100,-4,50,-9,130,-13,70
2.54
四、计算结果:
SL=51.8064DS=5.1806
COFiSIFiXIYIEIEA
.684-.730-22.50010.000.4112.194
.773-.634-19.1336.838.3631.940
.868-.496-14.8793.901.3241.728
.942-.336-10.1761.739.2981.592
.986-.167-5.163.434.2851.521
1.000.000.000.000.2811.500
.986.1675.163.434.2851.521
.942.33610.1761.739.2981.592
.868.49614.8793.901.3241.728
.773.63419.1336.838.3631.940
.684.73022.50010.000.4112.194
YS=3.182
X1=1974.415X2=542.827X3=-105.322
IXiMIQINI
0-22.500-81.041-75.036713.883
1-19.133-272.849-6.933696.218
2-14.879-102.87872.305666.523
3-10.176265.91678.230604.117
4-5.163318.6754.047551.289
5.000247.183-105.322542.827
65.163-194.404-63.836561.444
710.176-398.354-12.896580.841
814.879-309.37148.689597.382
919.133113.498114.706607.873
1022.500774.456170.310612.184
R:
HAVAMA
542.827469.678-81.041
HBVBMB
542.827330.322774.456
四、源村大桥为主孔斜拉杆式桁构,采用单杆吊装。
施工最大悬挂阶段上弦最大拉力为7121KN。
主跨105米,矢跨比1/7,俩岸边孔分别为5米和11米刚构,全长125米。
桥宽为净7+2*0.75米人行道。
试分别对其进行施工阶段、营运阶段进行静力反应计算。
此处假设施工阶段和营运阶段仅在梁上作用有均布荷载q=60kN/m。
每个孔道直径为50毫米;每孔高强钢丝束为24ΦP5;混凝土强度等级为C50;高强钢丝和混凝土的弹性模量分别为Ep=2.05×105MPa和Ec=3.45×104MPa.不计普通钢筋的影响.
一、桥型布置图如下所示:
二、各杆件截面设计及截面特性结果如下所示;
计算截面特性如下:
划分节线共6条,每个孔道面积Ak=3.14d2/4=1963.5*10-6m2.每束高强钢丝面积Ap=24*19.63-6=471.12*10-6m2
原始数据:
3
2.05e5,2.05e5,3.45e4
1
10
7.5,7.5,1.98,1.26,0.56,0.56,1.26,1.98,7.5,7.5
0.0,0.16,0.16,0.21,0.26,1.0,1.05,1.1,1.1,1.3
2
471.12e-6,0.07,2,14,471.12e-6,1.23,2,14
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下
1.93443.4326.6128.6872
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
11.52471.3597.3961.4442
计算截面特性如下:
划分节线共6条,每个孔道面积Ak=3.14d2/4=1963.5*10-6m2.每束高强钢丝面积Ap=24*19.63-6=471.12*10-6m2
原始数据:
32.05e5,2.05e5,3.45e4110
7.5,7.5,1.98,1.26,0.56,0.56,1.26,1.98,7.5,7.5
0.0,0.16,0.16,0.21,0.26,0.6,0.65,0.70,0.70,0.90
2471.12e-6,0.07,2,14,471.12e-6,1.23,2,14
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下
1.39343.2086.4235.4765
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
1.9290.8255.2573.2895
计算截面特性如下:
划分节线共6条,每个孔道面积Ak=3.14d2/4=1963.5*10-6m2.每束高强钢丝面积Ap=24*19.63-6=471.12*10-6m2
原始数据:
32.05e5,2.05e5,3.45e4
110
7.5,7.5,1.98,1.26,0.56,0.56,1.26,1.98,7.5,7.5
0.0,0.16,0.16,0.21,0.26,0.7,0.75,0.80,0.80,1.0
2471.12e-6,0.07,2,14,471.12e-6,1.23,2,14
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下
1.50393.2646.4707.5293
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
11.0707.9520.2916.3280
计算截面特性如下:
划分节线共2条,每个孔道面积Ak=3.14d2/4=1963.5*10-6m2.每束高强钢丝面积Ap=24*19.63-6=471.12*10-6m2
原始数据:
32.05e5,2.05e5,3.45e4120.45,0.450.0,0.453471.12e-6,0.065,2,3,471.12e-6,0.225,2,2,471.12e-6,0.385,2,3
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下1.0038.2211.2250.2250
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
1.0168.0168.0759.0759
计算截面特性如下
原始数据:
1120.45,0.450.0,0.45
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下
1.0034.2025.2250.2250
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
1.0152.0152.0750.0750
计算截面特性如下:
原始数据:
1121.0,1.00.0,1.0
计算结果:
截面号N截面惯性矩Ix截面面积AA截面形心距离Y上截面形心距离Y下
1.08331.0000.5000.5000
截面号N上截面模量W上下截面模量W下截面上核心距K上截面下核心距K下
1.1667.1667.1667.1667
三、桥梁结构计算如下:
桥梁在施工中的控制阶段为半跨最大悬臂阶段,取半结构进行计算。
此时上弦杆为连续的,没有断缝。
原始数据:
25,21,3,3,7,0,7
9,0,0,0,13,0,0,0,14,0,0,0
9,13,14
1,2,2,3,3,4,4,5,5,6,12,7,7,8,9,1,13,2,2,10,10,16,16,3,3,11,11,18,18,4,19,5,12,6,21,12,14,15,15,16,16,17,17,18,18,19,19,20,20,21
0.0000,0.0000,5.0000,0.0000,19.0000,0.0000,31.9950,0.0000,32.0050,0.0000,44.5000,0.0000,51.0000,-0.63307,57.5000,-0.63307,0.0000,-9.43327,12.0000,-4.37314,25.5000,-1.96670,44.5000,-0.63307,5.0000,-15.44960,5.98009,-16.03837,12.00978,-12.7632,19.0000,-8.74627,26.04777,-5.88962,31.995,-3.93341,32.0050,-3.93341,38.80297,-2.25752,44.5000,-1.26615
1.107E8,0.382E8,1.107E8,0.382E8,1.107E8,0.382E8,1.107E5,0.382E5,1.107E8,0.382E8,1.184E8,0.409E8,1.184E8,0.409E8,2.0E12,2.0E12,0.345E8,0.119E8,0.076E8,0.026E8,0.076E8,0.026E8,0.070E8,0.024E8,0.076E8,0.026E8,0.076E8,0.026E8,0.070E8,0.024E8,0.070E8,0.024E8,2.0E10,2.0E10,2.0E10,2.0E10,1.126E8,0.389E8,1.126E8,0.389E8,1.126E8,0.389E8,1.126E8,0.389E8,1.126E8,0.389E8,1.126E8,0.389E8,1.126E8,0.389E8
1,3,5,-60,2,3,14,-60,3,3,13,-60,4,3,0.01,-60,5,3,12.5,-60,6,3,6.5,-60,7,3,6.5,-60
计算结果:
1桥梁结构结点位移:
水平位移Δx向右为正;竖向位移Δy向上为正;结点转角φ逆时针为正。
结点号ΔxΔyφ
1.7063E-06-.7181E-09-.1134E-06
2.2223E-03-.2495E-03-.9944E-04
3.8404E-03-.2151E-02-.1755E-03
4.1389E-02-.5089E-02-.2452E-03
5.1795E-02-.5092E-02-.5076E-03
6.2276E-02-.1240E-01-.6230E-03
7.1882E-02-.1831E-01-.1093E-02
8.1882E-02-.2574E-01-.1160E-02
9.0000E+00.0000E+00.0000E+00
10-.2432E-04-.6353E-03-.3363E-04
11.7589E-03-.3078E-02-.1468E-03
12.1882E-02-.1240E-01-.6231E-03
13.0000E+00.0000E+00.0000E+00
14.0000E+00.0000E+00.0000E+00
15-.1941E-03-.3579E-03-.4919E-04
16-.2734E-03-.1025E-02-.1005E-03
17-.7225E-04-.2459E-02-.3021E-03
18.4156E-03-.4869E-02-.4417E-03
19.4152E-03-.4873E-02-.4419E-03
20.1061E-02-.8635E-02-.6361E-03
21.1487E-02-.1240E-01-.6230E-03
2桥梁单元杆端内力:
轴力Ni,Nj以拉伸为正;剪力Qi,Qj以绕杆件顺时针转为正;弯矩Mi,Mj以绕杆件顺时针转为正。
单元号NiQiMiNjQjMj
14906.950152.243-889.4884906.950-147.757878.275
24886.848416.021-1159.7824886.848-423.9791215.491
34673.393432.576-1326.6384673.393-347.424771.415
44494.78943.637-1002.7754494.78943.0371002.341
54264.059432.934-1496.2244264.059-317.066770.465
6.000780.000-5070.000.000390.0001267.500
7.000390.000-1267.500.000.000.000
8-152.2434906.950-47178.070-152.2434906.950889.488
9-557.160-21.13786.683-557.160-21.137239.875
10-4.384-5.06541.632-4.384-5.065.171
11-4.384-5.065-.171-4.384-5.06541.973
12-900.863-4.027-2.972-900.863-4.02738.196
13213.285-18.24272.952213.285-18.24250.930
14213.281-18.288-50.930213.281-18.288175.036
15-391.061-178.603471.161-391.061-178.603231.359
16-389.897-230.730413.673-389.897-230.730493.882
17-317.066-4264.0593469.913-317.066-4264.059-770.465
18-1097.066-4264.0591099.404-1097.066-4264.0591600.087
19-5601.73576.759-542.212-5601.73576.75915.506
20-5601.965-57.601-15.506-5601.965-57.601479.898
21-5214.047-134.771-518.899-5214.047-134.7711543.794
22-5211.305216.224-1543.794-5211.305216.224190.082
23-4494.7891486.964-836.279-4494.7891486.964821.409
24-4402.70144.523-1235.082-4402.70144.523923.354
25-4389.009349.798-923.354-4389.009349.798-1099.404
3桥梁结构支座反力:
水平反力Rx向右为正;竖向反力Ry向上为正;反力矩Rm逆时针为正。
结点号水平反力Rx竖向反力Ry反力矩Rm
9-4906.950152.24347178.070
1321.137557.160-86.683
144885.8132741.198542.212
两边结构合拢成桥后,在上弦杆适当位置断开设缝,成为桁式组合拱桥组,故营运阶段按照全桥模型进行整体分析。
由于结构自重荷载较大,活荷载所占比例较小,所以近似认为荷载是对称的,取半跨结构进行营运阶段的计算
原始数据:
25,21,4,4,7,0,7
9,0,0,0,13,0,0,0,14,0,0,0,8,0,1,0
9,13,14,8
1,2,2,3,3,4,4,5,5,6,12,7,7,8,9,1,13,2,2,10,10,16,16,3,3,11,11,18,18,4,19,5,12,6,21,12,14,15,15,16,16,17,17,18,18,19,19,20,20,21
0.0000,0.0000,5.0000,0.0000,19.0000,0.0000,31.9950,0.0000,32.0050,0.0000,44.5000,0.0000,51.0000,-0.63307,57.5000,-0.63307,0.0000,-9.43327,12.0000,-4.37314,25.5000,-1.96670,44.5000,-0.63307,5.0000,-15.44960,5.98009,-16.03837,12.00978,-12.7632,19.0000
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