钢筋混凝土中承式拱桥几何非线性计算

1、钢筋混凝土中承式拱桥几何非线性计算例题为一钢筋混凝土中承式拱桥，采用有限元程序软件对其在恒载作用下的内力分别进行线性与非线性计算，非线性分析过程中只考虑几何非线性因素，采用Newton-Raphson法进行求解。并对结果进行分析和比较，得出线形和非线形计算结果的差异、基本概况 本计算模型为一钢筋混凝土中承式拱桥，拱肋线形为悬链线型，跨径42m，矢跨比为1/4.375，拱轴系数为1.167。全桥立面如图1所示。主拱圈为两片等截面钢筋混凝土拱肋，拱肋截面如图2所示。高110cm，宽60cm，其中布置有沿拱圈方向的纵向钢筋和横向截面的箍筋。拱肋通过吊杆与加劲纵梁联接，两根拱肋横向间距为5.6m。每根

2、拱肋设10根厂制吊杆，吊杆间距为3.0m。吊杆采用PE7-127半平行钢丝成品索，外包双层高密度聚乙烯（PE）护套，配套锚具采用带有纠偏装置的DS(K)7-127镦头锚，吊杆标准强度Ryb =1670MPa，破断力Nb=8162kN。桥面横向布置为：0.65（纵梁）+ 0.5m（防撞墙）+4.5m(双车道)+0.5 m（防撞墙）+0.65（纵梁），桥面全宽6.80m。如图3主要建筑材料：（） C40混凝土（） 拱肋、纵梁及桥面板配筋（） 桥面铺装：10cm沥青混凝土（） 吊杆采用Ryb=1670Mpa的7mm低松弛镀锌高强钢丝，外包双层高密度聚乙烯材料。 图1图2图3、 结构离散本计算以恒载组

3、合作用下的单片拱肋为对象，将拱肋划分为84个单元，其中拱脚两端为固结，横系梁可当作为集中荷载作用在2片拱肋上，其荷载值为75.3KN，对称作用在距拱脚水平距离为3.0m的拱肋上纵梁及桥面板以集中荷载的形式传递给每跟吊杆，其中最外侧吊杆受244.8KN拉力,其余吊杆受71.4KN的拉力。桥面铺装等荷载以集中荷载的形式传递给吊杆，两侧为12KN拉力，其余为9KN拉力。如图所示。 计算模型示意图3、 结果分析 轴力、剪力、弯矩结果比较 非线性计算线性计算单元轴向 (kN)剪力(kN)弯矩(kN*m)轴向 (kN)剪力(kN)弯矩(kN*m)1-1083.13-10.83-181.29-1083.35

4、-10.85-1832-1082.89-26.4-177.94-1083.11-26.45-179.643-1082.5-41.93-166.79-1082.71-42.01-168.474-1087.3315.97-147.87-1087.5415.87-149.55-1088.22.61-157.94-1088.422.48-159.536-1088.93-14.99-161.32-1089.14-15.15-162.847-1089.56-28.18-155.85-1089.77-28.38-157.298-1090.1-41.27-143.71-1090.3-41.49-145.059

5、-1090.34-58.47-124.91-1090.53-58.71-126.1410-1104.8-1.28-97.29-1105.02-1.55-98.3911-1106.4-14.21-98.74-1106.61-14.49-99.7112-1107.87-29.08-93.58-1108.07-29.39-94.413-1109.13-45.82-80.74-1109.32-46.15-81.414-1110.56-56.14-59.16-1110.74-56.48-59.6415-1111.59-72.41-32.11-1111.77-72.76-32.4116-1135.17-1

6、6.553.64-1135.38-16.923.5217-1137.46-32.7510.18-1137.65-33.1210.2518-1139.77-44.6325.36-1139.95-4525.6319-1141.95-58.2746.99-1142.13-58.6347.4520-1147.5163.38112.69-1147.6963.73113.5321-1146.14-84.69112.69-1146.31-85.02113.5322-1178.12-32.62156.7-1178.31-32.94157.7223-1181.31-45.62172.39-1181.49-45.

7、91173.5924-1184.45-58.3195.44-1184.63-58.57196.8125-1187.47-72.54225.8-1187.65-72.77227.3226-1190.7-82.73264.51-1190.88-82.91266.1627-1193.68-96.27309.37-1193.87-96.39311.1228-1322.14102.63362.49-1322.32102.6364.3129-1328.887.62300.35-1328.9787.65302.1930-1335.2674.87246.38-1335.4274.95248.231-1341.

8、6862.43199.45-1341.8462.55201.2232-1348.1448.48159.5-1348.348.64161.233-1354.5534.92127.57-1354.7235.1129.1834-1360.9123.51103.61-1361.0723.71105.135-1367.2910.6886.47-1367.4610.987.8436-1373.67-1.7777.18-1373.84-1.5478.4137-1427.2546.575.69-1427.446.7776.7738-1434.5632.3843.21-1434.7132.6644.1239-1

9、441.8320.3919.49-1441.9920.6720.2240-1449.148.763.37-1449.39.043.9141-1456.48-2.49-5.21-1456.64-2.22-4.8442-1463.87-13.38-6.31-1464.03-13.12-6.1343-1083.13-10.83-181.29-1083.35-10.85-18344-1082.89-26.4-177.94-1083.11-26.45-179.6445-1082.5-41.93-166.79-1082.71-42.01-168.4746-1087.3315.97-147.87-1087.

10、5415.87-149.547-1088.22.61-157.94-1088.422.48-159.5348-1088.93-14.99-161.32-1089.14-15.15-162.8449-1089.56-28.18-155.85-1089.77-28.38-157.2950-1090.1-41.27-143.71-1090.3-41.49-145.0551-1090.34-58.47-124.91-1090.53-58.71-126.1452-1104.8-1.28-97.29-1105.02-1.55-98.3953-1106.4-14.21-98.74-1106.61-14.49

11、-99.7154-1107.87-29.08-93.58-1108.07-29.39-94.455-1109.13-45.82-80.74-1109.32-46.15-81.456-1110.56-56.14-59.16-1110.74-56.48-59.6457-1111.59-72.41-32.11-1111.77-72.76-32.4158-1135.17-16.553.64-1135.38-16.923.5259-1137.46-32.7510.18-1137.65-33.1210.2560-1139.77-44.6325.36-1139.95-4525.6361-1141.95-58

12、.2746.99-1142.13-58.6347.4562-1147.5163.38112.69-1147.6963.73113.5363-1146.14-84.69112.69-1146.31-85.02113.5364-1178.12-32.62156.7-1178.31-32.94157.7265-1181.31-45.62172.39-1181.49-45.91173.5966-1184.45-58.3195.44-1184.63-58.57196.8167-1187.47-72.54225.8-1187.65-72.77227.3268-1190.7-82.73264.51-1190

13、.88-82.91266.1669-1193.68-96.27309.37-1193.87-96.39311.1270-1322.14102.63362.49-1322.32102.6364.3171-1328.887.62300.35-1328.9787.65302.1972-1335.2674.87246.38-1335.4274.95248.273-1341.6862.43199.45-1341.8462.55201.2274-1348.1448.48159.5-1348.348.64161.275-1354.5534.92127.57-1354.7235.1129.1876-1360.

14、9123.51103.61-1361.0723.71105.177-1367.2910.6886.47-1367.4610.987.8478-1373.67-1.7777.18-1373.84-1.5478.4179-1427.2546.575.69-1427.446.7776.7780-1434.5632.3843.21-1434.7132.6644.1281-1441.8320.3919.49-1441.9920.6720.2282-1449.148.763.37-1449.39.043.9183-1456.48-2.49-5.21-1456.64-2.22-4.8484-1463.87-

15、13.38-6.31-1464.03-13.12-6.13挠度结果比较非线性计算线性计算节点DX (m)DZ (m)RY (rad)DX (m)DZ (m)RY (rad)100.00014000.000161022.5E-050.000129-4.1E-052.5E-050.00015-4.2E-0535.2E-059.8E-05-8.1E-055.2E-050.000119-8.2E-0548E-054.7E-05-0.0001188E-056.7E-05-0.00011950.00011-1.8E-05-0.0001530.000112E-06-0.00015460.000143-0.0

16、00101-0.000190.000144-8.2E-05-0.00019270.000181-0.000202-0.0002270.000181-0.000185-0.00022980.000224-0.000323-0.0002620.000224-0.000306-0.00026490.000271-0.00046-0.0002930.000272-0.000445-0.000296100.000325-0.000612-0.0003190.000326-0.000599-0.000322110.000384-0.000772-0.0003420.000386-0.00076-0.000

17、345120.00045-0.000944-0.0003650.000452-0.000934-0.000368130.000522-0.001127-0.0003850.000524-0.001119-0.000389140.000601-0.00132-0.0004020.000604-0.001313-0.000406150.000686-0.00152-0.0004130.00069-0.001515-0.000417160.000778-0.001724-0.0004160.000782-0.001722-0.00042170.000873-0.001924-0.0004150.00

18、0878-0.001924-0.000419180.000974-0.002123-0.000410.000979-0.002124-0.000414190.001077-0.002319-0.0004010.001084-0.002322-0.000405200.001183-0.002509-0.0003860.001191-0.002514-0.000389210.00129-0.002689-0.0003620.001298-0.002697-0.000366220.001395-0.002856-0.0003280.001404-0.002865-0.000331230.001495

19、-0.002999-0.0002860.001505-0.003009-0.000289240.001587-0.003119-0.0002380.001598-0.003132-0.000241250.00167-0.003215-0.0001840.001682-0.003228-0.000186260.001741-0.003281-0.000120.001753-0.003296-0.000122270.001794-0.003312-4.4E-050.001807-0.003328-4.5E-05280.001826-0.0033034.6E-050.001838-0.0033194

20、.5E-05290.001825-0.0032310.0001350.001838-0.0032480.000135300.001798-0.0031190.000210.001811-0.0031360.00021310.001749-0.0029730.0002710.001762-0.0029890.000271320.001679-0.0027990.0003210.001691-0.0028150.000322330.00159-0.0026030.0003610.001602-0.0026190.000363340.001485-0.0023890.0003940.001497-0

21、.0024030.000396350.001366-0.0021590.0004220.001377-0.0021730.000424360.001232-0.0019170.0004450.001243-0.001930.000448370.001086-0.0016630.0004680.001095-0.0016750.000471380.000924-0.0013940.0004860.000932-0.0014040.000489390.000752-0.0011190.0004950.000759-0.0011260.000499400.000572-0.0008390.00049

22、90.000577-0.0008450.000503410.000386-0.0005590.0004990.000389-0.0005630.000503420.000195-0.0002790.0004970.000197-0.0002810.00050143000.000496000.000544-2.5E-050.0001294.1E-05-2.5E-050.000154.2E-0545-5.2E-059.8E-058.1E-05-5.2E-050.0001198.2E-0546-8E-054.7E-050.000118-8E-056.7E-050.00011947-0.00011-1

23、.8E-050.000153-0.000112E-060.00015448-0.000143-0.0001010.00019-0.000144-8.2E-050.00019249-0.000181-0.0002020.000227-0.000181-0.0001850.00022950-0.000224-0.0003230.000262-0.000224-0.0003060.00026451-0.000271-0.000460.000293-0.000272-0.0004450.00029652-0.000325-0.0006120.000319-0.000326-0.0005990.0003

24、2253-0.000384-0.0007720.000342-0.000386-0.000760.00034554-0.00045-0.0009440.000365-0.000452-0.0009340.00036855-0.000522-0.0011270.000385-0.000524-0.0011190.00038956-0.000601-0.001320.000402-0.000604-0.0013130.00040657-0.000686-0.001520.000413-0.00069-0.0015150.00041758-0.000778-0.0017240.000416-0.00

25、0782-0.0017220.0004259-0.000873-0.0019240.000415-0.000878-0.0019240.00041960-0.000974-0.0021230.00041-0.000979-0.0021240.00041461-0.001077-0.0023190.000401-0.001084-0.0023220.00040562-0.001183-0.0025090.000386-0.001191-0.0025140.00038963-0.00129-0.0026890.000362-0.001298-0.0026970.00036664-0.001395-

26、0.0028560.000328-0.001404-0.0028650.00033165-0.001495-0.0029990.000286-0.001505-0.0030090.00028966-0.001587-0.0031190.000238-0.001598-0.0031320.00024167-0.00167-0.0032150.000184-0.001682-0.0032280.00018668-0.001741-0.0032810.00012-0.001753-0.0032960.00012269-0.001794-0.0033124.4E-05-0.001807-0.00332

27、84.5E-0570-0.001826-0.003303-4.6E-05-0.001838-0.003319-4.5E-0571-0.001825-0.003231-0.000135-0.001838-0.003248-0.00013572-0.001798-0.003119-0.00021-0.001811-0.003136-0.0002173-0.001749-0.002973-0.000271-0.001762-0.002989-0.00027174-0.001679-0.002799-0.000321-0.001691-0.002815-0.00032275-0.00159-0.002603-0.000361-0.001602-0.002619-0.00036376-0.001485-0.002389-0.000394-0.001497-0.002403-0.00039677-0.001366-0.002159-0.000422-0.001377-0.002173-0.00042478-0.001232-0.001917-0.00044