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Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

邮发代号 80-968

2019 Impact Factor: 1.68

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Frontiers of Structural and Civil Engineering  2021, Vol. 15 Issue (1): 227-243   https://doi.org/10.1007/s11709-020-0687-3
  本期目录
Flexural behavior of high-strength, steel-reinforced, and prestressed concrete beams
Qing JIANG1,2,3, Hanqin WANG1, Xun CHONG1,2(), Yulong FENG1,2, Xianguo YE1
1. School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China
2. Anhui Key Laboratory of Civil Engineering and Materials, Hefei 230009, China
3. College of Water Conservancy and Civil Engineering, Xinjiang Agricultural University, Urumqi 830052, China
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Abstract：

To study the flexural behavior of prestressed concrete beams with high-strength steel reinforcement and high-strength concrete and improve the crack width calculation method for flexural components with such reinforcement and concrete, 12 specimens were tested under static loading. The failure modes, flexural strength, ductility, and crack width of the specimens were analyzed. The results show that the failure mode of the test beams was similar to that of the beams with normal reinforced concrete. A brittle failure did not occur in the specimens. To further understand the working mechanism, the results of other experimental studies were collected and discussed. The results show that the normalized reinforcement ratio has a greater effect on the ductility than the concrete strength. The cracking- and peak-moment formulas in the code for the design of concrete (GB 50010-2010) applied to the beams were both found to be acceptable. However, the calculation results of the maximum crack width following GB 50010-2010 and EN 1992-1-1:2004 were considerably conservative. In the context of GB 50010-2010, a revised formula for the crack width is proposed with modifications to two major factors: the average crack spacing and an amplification coefficient of the maximum crack width to the average spacing. The mean value of the ratio of the maximum crack width among the 12 test results and the relative calculation results from the revised formula is 1.017, which is better than the calculation result from GB 50010-2010. Therefore, the new formula calculates the crack width more accurately in high-strength concrete and high-strength steel reinforcement members. Finally, finite element models were established using ADINA software and validated based on the test results. This study provides an important reference for the development of high-strength concrete and high-strength steel reinforcement structures.
Key words： high-strength steel reinforcement    high-strength concrete    flexural behavior    crack width
收稿日期: 2019-12-06      出版日期: 2021-04-12
Corresponding Author(s): Xun CHONG   
 引用本文:   
. [J]. Frontiers of Structural and Civil Engineering, 2021, 15(1): 227-243.
Qing JIANG, Hanqin WANG, Xun CHONG, Yulong FENG, Xianguo YE. Flexural behavior of high-strength, steel-reinforced, and prestressed concrete beams. Front. Struct. Civ. Eng., 2021, 15(1): 227-243.
 链接本文:  
https://academic.hep.com.cn/fsce/CN/10.1007/s11709-020-0687-3
https://academic.hep.com.cn/fsce/CN/Y2021/V15/I1/227
Fig.1  
beam
no.		 concrete
strength grade		 prestressing ratio
λ		 normalized reinforcement ratio ρs (%) mild steel reinforcement As, As'
(mm2)		 Ap
(mm2)		 Av1 Av2
PCB-1 C80 0.600 1.74 2DF 20 628 280 C8@200 C8@150
PCB-2 C80 0.694 1.64 4DF 12 452 280 C8@200 C8@150
PCB-3 C80 0.752 1.52 3DF 12 339 280 C8@200 C8@150
PCB-4 C80 0.600 2.61 3DF 20 942 420 C8@200 C8@120
PCB-5 C80 0.694 2.46 6DF 12 679 420 C8@200 C8@120
PCB-6 C80 0.773 2.21 4DF 12 452 420 C8@200 C8@120
PCB-7 C100 0.600 1.74 2DF 20 628 280 C8@200 C8@150
PCB-8 C100 0.694 1.64 4DF 12 452 280 C8@200 C8@150
PCB-9 C100 0.752 1.52 3DF 12 339 280 C8@200 C8@150
PCB-10 C100 0.600 2.61 3DF 20 942 420 C8@200 C8@120
PCB-11 C100 0.694 2.46 6DF 12 679 420 C8@200 C8@120
PCB-12 C100 0.773 2.21 4DF 12 452 420 C8@200 C8@120
Tab.1  
Fig.2  
reinforcement type diameter
(mm)		 yield strength
fy or fpy
(MPa)		 ultimate strength
fu or fpu
(MPa)		 elongation ratio
A (%)
mild steel stirrup 8 381.0 514.3 22.0
mild steel longitudinal reinforcement 12 499.1 643.3 22.0
20 544.3 693.1 19.3
prestressed tendon 15.2 1828.5 1978.4 5.5
Tab.2  
Fig.3  
Fig.4  
Fig.5  
group no. beam
no.		 Mcrt
(kN·m)		 My?t
(kN·m)		 Mp?t (kN·m) McrtM pt MytMp t Mcrc
(kN·m)		 Mpc Mpc (kN·m) MptMp c
group 1 PCB-1 114.4 261.1 296.2 0.39 0.88 98.4 1.16 287.8 1.03
PCB-2 118.0 172.07 234.1 – – 103.0 – 243.6 –
PCB-3 116.2 142.88 226.0 – – 105.8 – 222.2 –
group 2 PCB-4 139.6 341.2 426.7 0.33 0.80 121.8 1.15 422.4 1.01
PCB-5 141.4 287.2 362.8 0.39 0.79 129.5 1.09 356.3 1.02
PCB-6 139.6 223.72 298.0 0.47 0.75 134.7 1.04 321.0 0.93
group 3 PCB-7 110.8 257.5 312.4 0.35 0.83 103.1 1.07 290.0 1.08
PCB-8 114.4 222.4 276.4 0.41 0.81 107.4 1.07 245.9 1.12
PCB-9 107.2 203.5 250.3 0.43 0.81 109.9 0.98 224.4 1.12
group 4 PCB-10 139.6 365.5 451.0 0.31 0.81 128.6 1.09 427.5 1.06
PCB-11 141.4 296.2 395.2 0.36 0.75 135.5 1.04 361.4 1.09
PCB-12 132.4 270.1 342.1 0.39 0.79 140.1 0.95 326.1 1.05
mean value – – – 0.38 0.78 – 1.06 – 1.05
Tab.3  
group no. beam no. Δy (mm) Δu (mm) m
group 1 PCB-1 23.08 165.11 7.15
PCB-2 – – –
PCB-3 – – –
group 2 PCB-4 31.28 88.4 2.83
PCB-5 25.75 88.13 3.24
PCB-6 21.88 69.56 3.18
group 3 PCB-7 25.59 142.38 5.56
PCB-8 22.08 124.29 5.63
PCB-9 19.46 145.67 7.49
group 4 PCB-10 31.56 99.95 3.17
PCB-11 29.91 95.03 3.18
PCB-12 25.21 100.13 3.97
Tab.4  
Fig.6  
Beam
No.		 fc
(MPa)		 fy/ fpy
(MPa)		 ρs
(%)		 µ
Ashour [14]
B-N2 48.6 530 1.18 3.39
B-N3 48.6 530 1.77 2.5
B-N4 48.6 530 2.37 1.49
B-M2 78.5 530 1.18 3.88
B-H3 78.5 530 1.77 2.43
B-M4 78.5 530 2.37 1.84
B-H2 102.4 530 1.18 3.71
B-M3 102.4 530 1.77 2.7
B-H4 102.4 530 2.37 1.81
Hussien et al. [34]
B1-0.0* 72.0 470/1674 0.87 8.38
B2-0.7* 75.0 470/1674 1.21 7.93
B3-1.0* 76.0 470/1674 0.93 3.18
B4-0.0* 95.0 470/1674 0.87 8.04
B5-0.7* 97.0 470/1674 1.21 6.11
B6-1.0* 94.0 470/1674 0.93 4.93
Pam et al. [15]
B7 45.5 520–580 2.16 3.05
B8 44.2 520–580 2.46 2.79
B9 45.5 520–580 3.02 2.73
B10 38.3 520–580 3.50 2.03
B11 45.7 520–580 3.50 2.05
B12 40.5 520–580 4.02 1.87
B13 45.7 520–580 4.69 1.92
B14 81.3 520–580 1.64 5.54
B15 83.9 520–580 2.46 2.45
B16 88.7 520–580 2.46 2.78
B17 72.6 520–580 2.68 3.11
B18 75.9 520–580 4.02 1.83
B19 77.3 520–580 4.02 1.99
B20 69.1 520–580 4.69 1.81
Tab.5  
Fig.7  
Fig.8  
ωmaxt/ωmaxc GB 50010-2010 EN 1992-1-1: 2004
mean value 0.883 0.974
SD 0.211 0.368
CV 0.239 0.378
Tab.6  
method specimens no. lcrt/lcrc (Eq. (4)) lcrt/lcrc (Eq. (8))
mean value standard deviation CV mean value standard deviation CV
this study 12* 0.910 0.058 0.064 0.976 0.062 0.064
Li and Su [25] 24+ 8* 0.890 0.102 0.115 0.951 0.099 0.104
Gao et al. [26] 15 0.844 0.141 0.167 0.899 0.133 0.148
Jin et al. [27] 8 0.996 0.124 0.124 1.069 0.123 0.115
Xu [28] 11 1.127 0.110 0.098 1.218 0.103 0.085
Total 58+ 20* 0.953 0.107 0.114 1.023 0.104 0.103
Tab.7  
Fig.9  
Fig.10  
method mean value SD CV
GB50010–2010 0.883 0.211 0.239
modified equation 1.017 0.211 0.207
Tab.8  
Fig.11  
beam no. initial strain /10−6
PCB-1 6224
PCB-2 6272
PCB-3 6268
PCB-4 6225
PCB-5 6207
PCB-6 6189
PCB-7 6262
PCB-8 6316
PCB-9 6308
PCB-10 6279
PCB-11 6262
PCB-12 6247
Tab.9  
Concrete grade Ec (×104 MPa) u ft (MPa) fc (MPa) εc εu
C80 4.07 0.2 3.31 56.4 0.00224 0.02
C100 4.40 0.2 3.60 72.1 0.00240 0.02
Tab.10  
Fig.12  
Fig.13  
Fig.14  
Fig.15  
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