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Frontiers of Structural and Civil Engineering

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Front. Struct. Civ. Eng.    2021, Vol. 15 Issue (1) : 227-243    https://doi.org/10.1007/s11709-020-0687-3
RESEARCH ARTICLE
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.
Keywords high-strength steel reinforcement      high-strength concrete      flexural behavior      crack width     
Corresponding Author(s): Xun CHONG   
Just Accepted Date: 03 February 2021   Online First Date: 17 March 2021    Issue Date: 12 April 2021
 Cite this article:   
Qing JIANG,Hanqin WANG,Xun CHONG, et al. Flexural behavior of high-strength, steel-reinforced, and prestressed concrete beams[J]. Front. Struct. Civ. Eng., 2021, 15(1): 227-243.
 URL:  
https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0687-3
https://academic.hep.com.cn/fsce/EN/Y2021/V15/I1/227
Fig.1  Details of the beam specimens (mm). (As: tensile mild steel reinforcement; As': compressive mild steel reinforcement; Ap: prestressed tendons; Av1: stirrup in the bending-shear sections; Av2: stirrup in the bending sections; h: depth of the cross-section; b: width of the cross-section; h0: effective depth of the cross-section; c: thickness of the concrete cover.)
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  Design parameters of the specimens
Fig.2  Test set-up and measuring points of the beam specimens (mm). (1: Linear Variable Differential Transformer (LVDT); 2: strain gauges of the stirrups; 3: strain gauges of the longitudinal reinforcements; 4: force transducer; 5: actuator; 6: load distribution beam.)
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  Mechanical properties of the reinforcement
Fig.3  Typical failure mode for the beam specimens.
Fig.4  Crack patterns for the beam specimens: (a) PCB-1; (b) PCB-2; (c) PCB-3; (d) PCB-4; (e) PCB-5; (f) PCB-6; (g) PCB-7; (h) PCB-8; (i) PCB-9; (j) PCB-10; (k) PCB-11; (l) PCB-12.
Fig.5  Moment–deflection curves produced by the beam specimens: (a) Group 1; (b) Group 2; (c) Group 3; (d) Group 4.
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  Flexural strength of the beam specimens
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  Displacement ductility of the beam specimens
Fig.6  Effect of fc on displacement ductility ratio µ. R2 is the coefficient of determination.
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  Experimental data from other researchers
Fig.7  Effect of ρs on displacement ductility ratio µ
Fig.8  Comparison of ωmaxcand ωmaxt using different methods. ωmaxc and ωmaxt are the calculated and tested maximum crack width, respectively.
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  Comparison of the means, SV, and coefficients of variation (CVs) using different methods
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  The mean values, standard deviations, and CVs of lcrt/lcrc
Fig.9  Comparison of average crack spacings.
Fig.10  Statistical distribution of crack width. wi is the width of every crack, and wm is the mean value of the crack width.
method mean value SD CV
GB50010–2010 0.883 0.211 0.239
modified equation 1.017 0.211 0.207
Tab.8  The means, SD, and CVs of ωmaxt/ωmaxc
Fig.11  Finite element model of the prestressed concrete beam.
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  The initial strain in all specimens
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  Critical parameters of concrete material
Fig.12  Reinforcement material models. (a) Common reinforcements; (b) prestressed tendons.
Fig.13  Mid-span bending moment-deflection curves. (a) PCB-1; (b) PCB-2; (c) PCB-3(d) PCB-4; (e) PCB-5(f) PCB-6; (g) PCB-7; (h) PCB-8; (i) PCB-9; (j) PCB-10; (k) PCB-11; (l) PCB-12.
Fig.14  Mid-span bending moment-steel longitudinal reinforcement strain curves. (a) PCB-1(b) PCB-2; (c) PCB-3; (d) PCB-4; (e) PCB-5; (f) PCB-6; (g) PCB-7; (h) PCB-8; (i) PCB-9; (j) PCB-10; (k) PCB-11; (l) PCB-12.
Fig.15  Crack distribution of PCB-9 and PCB-10. (a) Simulation result of PCB-9; (b) test result of PCB-9; (c) simulation result of PCB-10; (d) test result of PCB-10.
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