混凝土本构数据(陈家勇)

附录一

动力弹塑性分析的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 50010-2002 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/m 2

(2) 泊松比, 统一取 0.2 (参阅(2)的4.1.8)

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

(4) 密度(2): 2.5 T/m 3

(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标准值按(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1≤x 时

32)2()23(x αx ααy a a a -+-+=

当1≥x 时 x

x αx y d +-=2)1( c

εεx = *=

c f σy

在 0 – 0.7f c 的应力范围为线弹性, 其弹性模量按表1. 大于0.7f c

为塑性范围, 应力-塑性应变关系如下:

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

当1≤x 时

62.02.1x x y -=

当1≥x 时 x

x αx y t +-=7.1)1( t

εεx = *=

t f σy 在 0 – f t 的应力范围为线弹性, 其弹性模量按表1. 大于f t 为塑性

范围, 应力-塑性应变关系如下:

E σεεt t ck t -=

据此得到下列各等级混凝土材料在拉和压屈服后的应力(kN/m 2)-塑性应变关系:

*Material, Name=C25

*Concrete compression hardening

应力(kN/m 2) 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

20100., 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

2010., 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