混凝土本构数据.doc

附录一

动力弹塑性分析旳材料非线性参数取值

一 混凝土材料:
混凝土材料采用塑性损伤模型(Plastic-Damaged Model)(1).
根据GB 50010- 混凝土强度分类 如下:
C25, C30, C35, C40, C45, C50, C55, C60, C65, C70, C75, C80

(1) 弹性模量:
按(2)表4.1.5, 单位kN/m2

表1弹性模量
C25
C30
C35
C40
C45
C50
2.8E7
3E7
3.15E7
3.25E7
3.35E7
3.25E7
C55
C60
C65
C70
C75
C80
3.55E7
3.6E7
3.65E7
3.7E7
3.75E7
3.8E7

(2) 泊松比, 统一取 0.2 (参阅(2)旳4.1.8)

(3) 剪切模量: 按(2)表4.1.5中旳0.4 倍采用(参阅(2)旳4.1.8).

(4) 密度(2): 2.5 T/m3

(5) 单轴应力-应变关系
混凝土材料轴心抗压和轴心抗拉强度原则值按(2)表4.1.3采用.
A: 单轴受压, 其应力-应变关系方程如下(参阅(2)C.2.1, P206):
当时

当时

在 0 – 0.7fc 旳应力范畴为线弹性, 其弹性模量按表1. 大于0.7fc为塑性范畴, 应力-塑性应变关系如下:

B: 单轴受拉, 其应力-应变关系方程如下(参阅(2)C.2.2, P208):
当时

当时

在 0 – ft 旳应力范畴为线弹性, 其弹性模量按表1. 大于ft为塑性范畴, 应力-塑性应变关系如下:

据此得到下列各等级混凝土材料在拉和压屈服后旳应力(kN/m2)-塑性应变关系:
*Material, Name=C25
*Concrete compression hardening
应力(kN/m2) 塑性应变
11690., 0
16700., 0.000808693
13239.8, 0.00233739
9841.27, 0.00386389
7674.36, 0.0053464
6248.49, 0.00680245
5255.01, 0.00824305
4527.98, 0.00967414
3974.73, 0.011099
3540.4, 0.0125197
*Concrete tension stiffening
1797.8, 0
1780., 0.000025515
1191.06, 0.000135635
859.483, 0.000236563
684.527, 0.000331898
576.455, 0.000424844
502.469, 0.000516573
448.233, 0.000607596
406.519, 0.000698173
373.278, 0.000788446
131.57, 0.00355876

*Material, Name=C30
*Concrete compression hardening
14070., 0
0., 0.000801898
14636.6, 0.00245591
10073.3, 0.00407992
7500.85, 0.00563756
5931.13, 0.00716179
4889.86, 0.00866839
4153.49, 0.0101648
3607., 0.011655
3186.09, 0.0131409
*Concrete tension stiffening
2030.1, 0
., 0.0000282563
1232.19, 0.00014944
849.073, 0.000257466
660.524, 0.000359008
548.371, 0.000458002
473.404, 0.000555757
419.357, 0.000652815
378.298, 0.00074944
345.892, 0.000845777
118.271, 0.00380631

*Material, Name=C35
*Concrete compression hardening
16380., 0
23400., 0.000789431
15814.6, 0.00256253
10267.4, 0.00427092
7408.77, 0.00589395
5749.74, 0.00747891
4682.74, 0.00904507
3943.69, 0.0106008
3403.29, 0.0121503
2991.69, 0.0136956
*Concrete tension stiffening
2222., 0
2200., 0.0000301427
1253.05, 0.000160189
834.315, 0.000273466
638.442, 0.000379668
524.938, 0.000483255
450.278, 0.000585609
397.041, 0.000687284
356.924, 0.000788541
325.457, 0.000889524
109.188, 0.00399589

*Material, Name=C40
*Concrete compression hardening
18760., 0
26800., 0.000764814
16909.7, 0.00265856
10469.9, 0.00444614
7378.84, 0.00613068
5650.07, 0.0077733
4562.41, 0.0093962
3819.83, 0.0110085
3282.34, 0.0126144
2876.02, 0.0142164
*Concrete tension stiffening
2413.9, 0
2390., 0.0000309422
1263.67, 0.000170079
815.537, 0.000288349
615.229, 0.000398993
501.733, 0.000506966
428.08, 0.000613712
376.039, 0.000719794
337.082, 0.000825474
306.681, 0.00093089
101.338, 0.00417611

*Material, Name=C45
*Concrete compression hardening
20720., 0
29600., 0.00075015
17743.1, 0.00273782
10639.8, 0.00458359
7386.84, 0.00631443
5609.46, 0.00800122
4506.18, 0.00966788
3759.48, 0.0113239
3222.27, 0.0129737
2817.97, 0.0146195
*Concrete tension stiffening
2535.1, 0
2510., 0.0000323044
1265.87, 0.000176673
802.219, 0.000297743
600.343, 0.000410999
487.385, 0.0005216
414.624, 0.000631002
363.47, 0.000739759
325.314, 0.000848128
295.619, 0.000956244
96.8983, 0.0042863

*Material, Name=C50
*Concrete compression hardening
22680., 0
32400., 0.000739885
18515.2, 0.00282136
10800.8, 0.00472398
7406.35, 0.00650139
5586.72, 0.00823314
4469.4, 0.00994455
3718.4, 0.0116453
3180.69, 0.0133399
2777.43, 0.0150306
*Concrete tension stiffening
2666.4, 0
2640., 0.0000336591
1264.64, 0.000183705
786.735, 0.000307738
584.088, 0.000423793
472.094, 0.00053722
400.477, 0.000649477
350.37, 0.00076111
313.124, 0.00087237
284.214, 0.000983389
92.4472, 0.00440455

*Material, Name=C55
*Concrete compression hardening
24850., 0
35500., 0.00072745
19297., 0.00291132
10959.8, 0.00487362
7429.12, 0.00670053
5569.63, 0.00848036
4439.05, 0.0102397
3683.89, 0.0119884
3145.52, 0.013731
2743.03, 0.0154698
*Concrete tension stiffening
2767.4, 0
2740., 0.0000352217
1261.67, 0.00018927
774.457, 0.000315399
571.752, 0.000433514
460.697, 0.000549047
390.039, 0.000663442
340.767, 0.000777235
304.231, 0.000890669
275.923, 0.00100387
89.2809, 0.00449368

*Material, Name=C60
*Concrete compression hardening
26950., 0
38500., 0.000700606
19978.3, 0.00298515
11087.9, 0.00500215
7444.03, 0.00687342
5552.82, 0.008696
4412.21, 0.0104977
3654.2, 0.0122888
3115.66, 0.0140739
2714.07, 0.0158551
*Concrete tension stiffening
2878.5, 0
2850., 0.0000356383
1256.67, 0.000194702
760.756, 0.000323283
558.434, 0.000443708
448.564, 0.000561565
379.016, 0.000678302
330.681, 0.000794449
294.926, 0.000910248
267.272, 0.00102582
86.0337, 0.00458981

*Material, Name=C65
*Concrete compression hardening
29050., 0
41500., 0.000671154
20635.5, 0.00305092
11227.6, 0.00511681
7477.58, 0.00702769
5554.81, 0.00888851
4402.81, 0.0107282
3640.4, 0.0125572
3100.27, 0.0143802
2698.31, 0.0161993
*Concrete tension stiffening
2959.3, 0
2930., 0.0000362462
1252.05, 0.000198738
750.74, 0.000328992
548.949, 0.000451041
440.021, 0.000570546
371.305, 0.000688948
323.655, 0.000806774
288.463, 0.000924259
261.278, 0.00104152
83.8153, 0.00465851

*Material, Name=C70
*Concrete compression hardening
31150., 0
44500., 0.000641177
21274.9, 0.00311276
11377.9, 0.00522413
7526.44, 0.0071721
5571.79, 0.00906881
4407.16, 0.0109442
3639.02, 0.0128088
3096.11, 0.0146674
2692.74, 0.0165221
*Concrete tension stiffening
3019.9, 0
2990., 0.000036979
1248.1, 0.00047
743.23, 0.000333282
541.959, 0.000456512
433.772, 0.000577225
365.689, 0.000696855
318.553, 0.000815919
283.779, 0.000934649
256.941, 0.00105316
82.2252, 0.00470937

*Material, Name=C75
*Concrete compression hardening
33180., 0
47400., 0.000619583
21842.2, 0.00318471
11504.1, 0.00534398
7565.26, 0.00733259
5583.9, 0.00926901
4408.93, 0.0111839
3636.25, 0.0130881
3091.21, 0.0149862
2686.84, 0.0168806
*Concrete tension stiffening
3080.5, 0
3050., 0.0000377117
1243.9, 0.000204919
735.834, 0.000337513
535.156, 0.000461909
427.722, 0.000583819
360.269, 0.000704663
313.639, 0.000824951
279.275, 0.000944913
252.774, 0.00106466
80.7083, 0.00475965

*Material, Name=C80
*Concrete compression hardening
35140., 0
50200., 0.000601539
22358.2, 0.00325681
11618.5, 0.00546203
7601.82, 0.00749032
5596.63, 0.00946568
4412.34, 0.0114194
3635.46, 0.0133625
3088.38, 0.0152995
2683., 0.0172327
*Concrete tension stiffening
3141.1, 0
3110., 0.0000384437
1239.38, 0.000207956
728.476, 0.000341687
528.471, 0.000467236
421.811, 0.000590329
354.989, 0.000712373
308.862, 0.000833873
274.904, 0.000955052
248.735, 0.00107603
79.2484, 0.00480935

(6) 损伤系数:
混凝土材料进入塑性状态随着着刚度旳减少, 如下图示(1):

受拉

受压

文献(3)Fig4. (a), (b) 给出了混凝土材料单轴拉压旳滞回曲线. 该曲线已被实验和计算验证. 通过线性插值, 可以得到混凝土材料各塑性应变所相应旳损伤系数如下:

*Material, Name=C25
*Concrete compression damage
损伤系数(dc) 塑性应变
0, 0
0.01, 0.000808693
0.207199, 0.00233739
0.410702, 0.00386389
0.540458, 0.0053464
0.69718, 0.00680245
0.78611, 0.00824305
0.84114, 0.00967414
0.877465, 0.011099
0.902661, 0.0125197
*Concrete tension damage
损伤系数(dt) 塑性应变
0, 0
0.01, 0.000025515
0.330864, 0.000135635
0.517144, 0.000236563
0.615434, 0.000331898
0.747045, 0.000424844
0.834016, 0.000516573
0.888637, 0.000607596
0.919064, 0.000698173
0.937999, 0.000788446
0.998225, 0.00355876

*Material, Name=C30
*Concrete compression damage
0, 0
0.01, 0.000801898
0.271809, 0.00245591
0.498841, 0.00407992
0.626823, 0.00563756
0.758068, 0.00716179
0.830984, 0.00866839
0.875447, 0.0101648
0.904483, 0.011655
0.924462, 0.0131409
*Concrete tension damage
0, 0
0.01, 0.0000282563
0.386973, 0.00014944
0.577576, 0.000257466
0.671381, 0.000359008
0.78758, 0.000458002
0.862336, 0.000555757
0.908476, 0.000652815
0.933922, 0.00074944
0.949638, 0.000845777
0.998607, 0.00380631

*Material, Name=C35
*Concrete compression damage
0, 0
0.01, 0.000789431
0.324164, 0.00256253
0.561223, 0.00427092
0.683386, 0.00589395
0.796302, 0.00747891
0.858328, 0.00904507
0.89589, 0.0106008
0.92031, 0.0121503
0.937062, 0.0136956
*Concrete tension damage
0, 0
0.01, 0.0000301427
0.430433, 0.000160189
0.620766, 0.000273466
0.709799, 0.000379668
0.814503, 0.000483255
0.880713, 0.000585609
0.921137, 0.000687284
0.943295, 0.000788541
0.956917, 0.000889524
0.998833, 0.00399589

*Material, Name=C40
*Concrete compression damage
0, 0
0.01, 0.000764814
0.369042, 0.00265856
0.609331, 0.00444614
0.72467, 0.00613068
0.823245, 0.0077733
0.877128, 0.0093962
0.90969, 0.0110085
0.930844, 0.0126144
0.945352, 0.0142164
*Concrete tension damage
0, 0
0.01, 0.0000309422
0.471266, 0.000170079
0.658771, 0.000288349
0.742582, 0.000398993
0.836523, 0.000506966
0.895279, 0.000613712
0.930952, 0.000719794
0.95046, 0.000825474
0.962428, 0.00093089
0.998995, 0.00417611

*Material, Name=C45
*Concrete compression damage
0, 0
0.01, 0.00075015
0.40057, 0.00273782
0.640546, 0.00458359
0.750445, 0.00631443
0.840063, 0.00800122
0.888862, 0.00966788
0.918306, 0.0113239
0.937422, 0.0129737
0.950532, 0.0146195
*Concrete tension damage
0, 0
0.01, 0.0000323044
0.495671, 0.000176673
0.680391, 0.000297743
0.760819, 0.000410999
0.849034, 0.0005216
0.903712, 0.000631002
0.936711, 0.000739759
0.954691, 0.000848128
0.965692, 0.000956244
0.999092, 0.0042863

*Material, Name=C50
*Concrete compression damage
0, 0
0.01, 0.000739885
0.428544, 0.00282136
0.666642, 0.00472398
0.771409, 0.00650139
0.853722, 0.00823314
0.898389, 0.00994455
0.9253, 0.0116453
0.942763, 0.0133399
0.954738, 0.0150306
*Concrete tension damage
0, 0
0.01, 0.0000336591
0.52097, 0.000183705
0.701994, 0.000307738
0.778754, 0.000423793
0.861159, 0.00053722
0.911801, 0.000649477
0.942194, 0.00076111
0.958699, 0.00087237
0.968775, 0.000983389
0.999181, 0.00440455

*Material, Name=C55
*Concrete compression damage
0, 0
0.01, 0.00072745
0.456423, 0.00291132
0.691273, 0.00487362
0.790729, 0.00670053
0.866219, 0.00848036
0.907065, 0.0102397
0.93165, 0.0119884
0.947601, 0.013731
0.958541, 0.0154698
*Concrete tension damage
0, 0
0.01, 0.0000352217
0.539536, 0.00018927
0.717351, 0.000315399
0.791331, 0.000433514
0.869789, 0.000549047
0.91763, 0.000663442
0.946178, 0.000777235
0.961623, 0.000890669
0.971027, 0.00100387
0.999246, 0.00449368

*Material, Name=C60
*Concrete compression damage
0, 0
0.01, 0.000700606
0.481084, 0.00298515
0.71, 0.00500215
0.806648, 0.00687342
0.876252, 0.008696
0.913899, 0.0104977
0.936577, 0.0122888
0.951309, 0.0140739
0.961426, 0.0158551
*Concrete tension damage
0, 0
0.01, 0.0000356383
0.559063, 0.000194702
0.733068, 0.000323283
0.804058, 0.000443708
0.877995, 0.000561565
0.922909, 0.000678302
0.949666, 0.000794449
0.964133, 0.000910248
0.972937, 0.00102582
0.999299, 0.00458981

*Material, Name=C65
*Concrete compression damage
0, 0
0.01, 0.000671154
0.502758, 0.00305092
0.729456, 0.00511681
0.819817, 0.00702769
0.884515, 0.00888851
0.919509, 0.0107282
0.940612, 0.0125572
0.95434, 0.0143802
0.96378, 0.0161993
*Concrete tension damage
0, 0
0.01, 0.0000362462
0.572681, 0.000198738
0.743775, 0.000328992
0.812645, 0.000451041
0.883611, 0.000570546
0.926569, 0.000688948
0.952106, 0.000806774
0.965898, 0.000924259
0.974284, 0.00104152
0.999336, 0.00465851

*Material, Name=C70
*Concrete compression damage
0, 0
0.01, 0.000641177
0.521912, 0.00311276
0.744318, 0.00522413
0.830867, 0.0071721
0.891435, 0.00906881
0.924204, 0.0109442
0.943987, 0.0128088
0.956872, 0.0146674
0.965746, 0.0165221
*Concrete tension damage
0, 0
0.01, 0.000036979
0.582576, 0.00047
0.751428, 0.000333282
0.818743, 0.000456512
0.887672, 0.000577225
0.929255, 0.000696855
0.953916, 0.000815919
0.967215, 0.000934649
0.975292, 0.00105316
0.999364, 0.00470937

*Material, Name=C75
*Concrete compression damage
0, 0
0.01, 0.000619583
0.539193, 0.00318471
0.757298, 0.00534398
0.840395, 0.00733259
0.897474, 0.00926901
0.928341, 0.0111839
0.946986, 0.0130881
0.95914, 0.0149862
0.967518, 0.0168806
*Concrete tension damage
0, 0
0.01, 0.0000377117
0.592163, 0.000204919
0.758743, 0.000337513
0.824539, 0.000461909
0.891519, 0.000583819
0.931794, 0.000704663
0.955624, 0.000824951
0.968456, 0.000944913
0.976241, 0.00106466
0.999391, 0.00475965

*Material, Name=C80
*Concrete compression damage
0, 0
0.01, 0.000601539
0.554618, 0.00325681
0.768556, 0.00546203
0.848569, 0.00749032
0.902677, 0.00946568
0.931921, 0.0114194
0.94959, 0.0133625
0.961115,