西建大《公路桥梁电算》作业完整版范文.docx
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西建大《公路桥梁电算》作业完整版范文
1.如图1所示预应力混凝土箱形截面梁。
其顶板宽度2m，地板宽0.85m，两个悬臂长度0.5m，梁高0.8m，顶板厚度0.125m，底板厚度0.08m，腹板厚度0.075m。
顶板预留一排15孔的预应力钢筋孔道，其形心至顶板面0.045m。
Φ28mm金属波纹管成孔，每孔张拉钢绞线12Φ5。
底板配置11根HRB335Φ16mm普通钢筋，其形心至底板面0.04m。
混凝土强度等级为C50。
钢绞线、普通钢筋和混凝土的弹性模量分别为Ep=1.95×105MPa、Ec=2.0×104MPa和Ec=3.45×105MPa，试计算梁的毛截面、净截面及换算截面的几何特性。
图1
解：
根据题意，截面的结线共八根，预应力每个孔道面积615.75×10-6m2，每个普通钢筋孔道面积201.06×10-6m2.。
每束钢绞线面积235.56×10-6m2。
据此列出各项原始数据。
原始数据如下：
当为毛截面时，原始数据：
1
1
8
0.85,0.85,0.15,0.15,0.35,,1.1,2.0,2.0
0,0.08,0.08,0.65,0.7,0.7,0.75,0.8
当为净截面时,原始数据:
2
1
8
0.85,0.85,0.15,0.15,0.35,,1.1,2.0,2.0
0,0.08,0.08,0.65,0.7,0.7,0.75,0.8
2
201.06E-6,0.04,11,615.75E-6,0.755,15
当为换算截面时，原始数据:
3
2.0E5,1.95E5,3.45E4
1
8
0.85,0.85,0.15,0.15,0.35,,1.1,2.0,2.0
0,0.08,0.08,0.65,0.7,0.7,0.75,0.8
2
201.06E-6,0.04,0,11,235.56E-6,0.755,2,15
运行结果如下：
毛截面特性计算结果：
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
1.0256.2710.3468.4532
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截面下核心距K下
1.0738.0565.2083.2723
净截面特性计算结果：
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
1.0244.2596.3540.4460
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
1.0688.0546.2104.2651
换算截面特性计算结果：
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
1.0336.3705.2896.5104
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1.1159.0658.1776.3129
2.如图2所示，跨径为L=19.7m的铰接T型桥面板的横截面布置，桥面净空为-7+2×1.0（人行道）。
全宽为6块预制混凝土T型板组成。
图3为结构横断面布置图，图4为单个T型板的构造图。
混凝土强度等级取C50，其弹性模量为3.45×104Mpa，剪变模量取0.4倍的弹性模量值。
求各梁跨中截面荷载横向分布影响线、汽车荷载横向分布系数和人群荷载横向分布系数。
图2（单位：
mm）
图3（单位：
mm）
图4（单位：
mm）
解：
由题意可知，该桥面设计为2车道，宽度7m。
剪切模量G=1.38×107Kpa。
抗扭惯性矩It计算为：
It=0.00192m4。
原始数据如下：
2,1.0,0
0,6,0,1
19.7,3.45E7,1.38E7,0.15
0.00192,0.7,7
0.2,0.2,0.1,0.1,0.2,1.5,1.5
0.0,0.15,0.2,0.7,0.75,0.75,0.9
1,1,1,1,1,1,1
运行结果如下：
荷载横向分布影响线
主梁号123456
P=1位置x
.750.6288.2894.0638.0141.0031.0008
2.250.2894.4031.2397.0528.0118.0031
3.750.0638.2397.3922.2374.0528.0141
5.250.0141.0528.2374.3922.2397.0638
6.750.0031.0118.0528.2397.4031.2894
8.250.0008.0031.0141.0638.2894.6288
扭矩横向分布影响线
主梁号123456
P=1位置x
.750-.2784-.3397-.0748-.0165-.0036-.0006
2.250.2171-.0135-.2814-.0619-.0135-.0023
3.750.0478.2754-.0006-.2784-.0607-.0105
5.250.0105.0607.2784.0006-.2754-.0478
6.750.0023.0135.0619.2814.0135-.2171
8.250.0006.0036.0165.0748.3397.2784
主梁号汽车荷载横向分布系数
1.3022
2.4135
3.4453
4.4453
5.4117
6.2984
主梁号人群荷载横向分布系数
1.6861
2.2303
3.1140
4.1140
5.2303
6.6861
3.变截面钢筋混凝土肋拱桥的计算简图如图5所示，拱轴为悬链线，y=f[ch（2kx/L）-1]/（m-1）,拱轴系数为m=2.24，跨度L=35m，拱高f=7m，拱肋为矩形截面，其惯性矩I=Ic/cosΦ，截面面积为A=Ac/cosΦ,拱顶截面高为Hc=1.1m，截面宽度为Bc=2.25m。
假设该肋承受如图所示荷载，试计算其内力和支座反力。
图5（单位：
m）
解：
截面惯性矩为：
Ic=2.25×1.13/12=0.2496m4，Ac=1.1×2.25=2.475m2。
原始数据如下：
3,2,5,0,1,10,1
35,7,1,0.2496,2.475
1,10,2,10
0,100,-3.0,60,-7.0,55,-9.0,120,-14.0,75
2.24
计算结果如下：
NG=3Kq=2Kp=5Km=0NJ=1NS=10NN=0
L=35.00f=7.00CN=1.00IC=.250AC=2.475
PQ（i,j）=1.0002.000
10.00010.000
PP（i,j）=.000-3.000-7.000-9.000-14.000
100.00060.00055.000120.00075.000
m0=2.240
SL=39.4271DS=3.9427
COFiSIFiXIYIEIEA
.731-.683-17.5007.000.3423.388
.811-.585-14.7754.753.3083.052
.892-.453-11.4142.701.2802.776
.952-.305-7.7691.203.2622.599
.988-.152-3.931.300.2532.504
1.000.000.000.000.2502.475
.988.1523.931.300.2532.504
.952.3057.7691.203.2622.599
.892.45311.4142.701.2802.776
.811.58514.7754.753.3083.052
.731.68317.5007.000.3423.388
YS=2.254
多于未知力：
X1=1381.133X2=548.602X3=-104.934
截面号XiMIQINI
0-17.500-189.993-23.896728.599
1-14.775-151.57046.300709.831
2-11.414-6.06258.520644.995
3-7.769212.75711.497579.728
4-3.931195.6899.718556.576
5.000144.702-104.934548.602
63.931-180.355-59.004564.172
77.769-312.368-6.609578.163
811.414-222.77253.052588.340
914.775110.332116.012592.751
1017.500617.327170.105591.939
反力:
HAVAMA
548.602480.066-189.993
HBVBMB
548.602279.934617.327
4.如图7所示，为共青大桥的的桥型布置简化计算图，采用悬拼施工法架设。
是分别对其进行施工阶段、营运阶段进行静力反应计算。
假设在施工阶段和营运阶段仅在梁上作用有均布荷载q=60KN/m。
建造采用C55#混凝土，E=.355E+05MPa。
图7为梁体横截面图，图8为桥台断面图。
图6（单位：
m）
图7（单位：
m）
图8（单位：
mm）
图9（单位：
mm）
解：
依题意，先求各杆件的拉压和弯曲刚度。
对于梁体单元：
EA=.172E+09，EI=.953E+08。
13号桥台单元：
EA=.588E+09，EI=.105E+10。
14号竖杆单元：
EA=.710E+08，EI=.592E+07。
其余斜腹杆单元：
EA=.192E+08，EI=.323E+06。
拱圈单元：
EA=.284E+09，EI=.237E+08。
建立原始数据：
（对于施工阶段）
29,25,3,3,11,0,11
14,0,0,0,15,0,0,0,16,0,0,0
14,15,16
1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,14,1,15,3,19,3,19,5,22,5,22,7,23,8,25,11,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25
0,0.5,6,0.5,12,0.5,17.5,0.5,23,0.5,28,0.5,32.9,0.5,33.1,0.5,37.75,0.5,42.5,0.5,42.5,0,47.75,0,53,0,0,-4.5,12,-15.9,12.5,-15.9,15.786,-12.783,19.281,-9.903,23,-7.317,26.22,-5.357,29.580,-3.648,32.9,-2.366,33.1,-2.296,37.737,-1.073,42.5,-0.5
.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,
.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,
.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,
.588E+09,.105E+10,.710E+08,.592E+07,.192E+08,.323E+06,.192E+08,.323E+06,
.192E+08,.323E+06,.192E+08,.323E+06,.192E+08,.323E+06,.172E+09,.953E+08,
.284E+09,.237E+08,.284E+09,.237E+08,.284E+09,.237E+08,.284E+09,.237E+08,
.284E+09,.237E+08,.284E+09,.237E+08,.284E+09,.237E+08,.284E+09,.237E+08,
.284E+09,.237E+08
1,3,6,-60,2,3,6,-60,3,3,5.5,-60,4,3,5.5,-60,5,3,5,-60,6,3,4.9,-60,7,3,0.2,-60,8,3,4.65,-60,9,3,4.75,-60,11,3,5.25,-60,12,3,5.25,-60
运行结果如下：
（对于施工阶段）
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
1.1187E-03-.2363E-05-.3556E-04
2.2233E-03-.1390E-03-.3837E-05
3.3279E-03-.1105E-03-.3146E-05
4.4363E-03-.2069E-03-.2426E-04
5.5447E-03-.3889E-03-.5172E-04
6.6435E-03-.7798E-03-.1048E-03
7.7404E-03-.1484E-02-.1952E-03
8.7443E-03-.1523E-02-.2008E-03
9.8353E-03-.2679E-02-.2819E-03
10.9282E-03-.4092E-02-.3093E-03
11.7723E-03-.4092E-02-.3160E-03
12.7723E-03-.6089E-02-.4223E-03
13.7723E-03-.8366E-02-.4375E-03
14.0000E+00.0000E+00.0000E+00
15.0000E+00.0000E+00.0000E+00
16.0000E+00.0000E+00.0000E+00
17-.1945E-03.1159E-03.5168E-04
18-.2561E-03.9382E-04-.4769E-04
19-.1349E-03-.1881E-03-.4539E-04
20-.1205E-03-.3076E-03-.4757E-04
21.1774E-04-.6900E-03-.1726E-03
22.2449E-03-.1409E-02-.2215E-03
23.2578E-03-.1454E-02-.2197E-03
24.4890E-03-.2557E-02-.2828E-03
25.6151E-03-.4090E-02-.3141E-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
12999.498277.83930.4112999.498-82.161-617.446
22999.498-82.161617.4462999.498-442.161955.520
33389.750309.979-915.7033389.750-20.021118.319
43389.750-20.021-118.3193389.750-350.0211135.935
53399.557146.721-1127.6523399.557-153.2791144.049
63399.557-153.279-1144.0493399.557-447.2792615.418
73382.80453.493-2636.4603382.80441.4932626.961
83364.844517.691-2649.8823364.844238.691891.292
93364.844238.691-891.2923364.844-46.309434.383
10-46.309-3364.844-434.383-46.309-3364.8442116.805
11.000630.000-3307.500.000315.000826.875
12.000315.000-826.875.000.000.000
13-277.8392999.498-14967.080-277.8392999.498-30.411
14-478.2784.866-41.037-478.2784.866-38.765
15-472.781.006.970-472.781.006-1.052
16-493.3362.435-9.777-493.3362.435-9.254
17-8.029-1.22111.615-8.029-1.221.971
18-500.772-16.75426.974-500.772-16.75421.042
19-476.199-17.95927.294-476.199-17.95922.920
20-676.309-3364.844491.727-676.309-3364.8441190.695
21-3847.844-309.046970.269-3847.844-309.046429.456
22-3860.027-39.989-429.456-3860.027-39.989610.555
23-3850.435274.881-610.555-3850.435274.881-634.579
24-3758.987-348.618643.385-3758.987-348.618670.770
25-3774.622-61.221-670.770-3774.622-61.221901.550
26-3761.230323.529-901.550-3761.230323.529-249.864
27-3573.619-29.707211.275-3573.619-29.707-204.981
28-3426.059-204.180177.686-3426.059-204.180801.475
29-3421.535269.566-801.475-3421.535269.566-491.727
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
14-2999.498277.83914967.080
15-4.866478.27841.037
163004.3642423.883-970.269
建立原始数据：
（对于运营阶段）
29,25,4,4,10,0,10
14,0,0,0,15,0,0,0,16,0,0,0,13,0,1,0
14,15,16,13
1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,14,1,15,3,19,3,19,5,22,5,22,7,23,8,25,11,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25
0,0.5,6,0.5,12,0.5,17.5,0.5,23,0.5,28,0.5,32.9,0.5,33.1,0.5,37.75,0.5,42.5,0.5,42.5,0,47.75,0,53,0,0,-4.5,12,-15.9,12.5,-15.9,15.786,-12.783,19.281,-9.903,23,-7.317,26.22,-5.357,29.580,-3.648,32.9,-2.366,33.1,-2.296,37.737,-1.073,42.5,-0.5
.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,
.172E+09,.953E+08,.172E+09,.953E+08,.000E+00,.000E+00,.172E+09,.953E+08,
.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,.172E+09,.953E+08,
.588E+09,.105E+10,.710E+08,.592E+07,.192E+08,.323E+06,.192E+08,.323E+06,
.192E+08,.323E+06,.192E+08,.323E+06,.192E+08,.323E+06,.172E+09,.953E+08,
.284E+09,.237E+08,.284E+09,.237E+08,.284E+09,.237E+08,.284E+09,.237E+08,
.284E+09,.237E+08,.284E+09,.237E+08,.284E+09,.237E+08,.284E+09,.237E+08,
.284E+09,.237E+08
1,3,6,-60,2,3,6,-60,3,3,5.5,-60,4,3,5.5,-60,5,3,5,-60,6,3,4.9,-60,8,3,4.65,-60,9,3,4.75,-60,10,3,5.25,-60,11,3,5.25,-60
运行结果如下：
（对于运营阶段）
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
1.2458E-05-.3217E-05-.1858E-05
2-.5235E-05-.8329E-04-.1235E-04
3-.1293E-04-.1375E-03-.1591E-04
4-.1580E-04-.2663E-03-.2122E-04
5-.1867E-04-.3602E-03-.2067E-04
6-.1833E-04-.4752E-03-.1645E-04
7-.1801E-04-.5016E-03.1729E-05
8.1813E-03-.5
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