1 Introduction
2 Experimental Investigations
Beam designation | Longitudinal rebar diameter (mm) | Reinforcing ratio (%) | Number of longitudinal rebars | Steel fiber fraction by volume |
---|---|---|---|---|
L2.33%-1.5%-1/2 | 20 | 2.33 | 3 | 1.5% hooked end |
L2.33%-2.0%-1/2 | 20 | 2.33 | 3 | 2.0% hooked end |
L2.33%-3.0%-1/2 | 20 | 2.33 | 3 | 2.0% hooked end + 1.0% straight |
L1.48%-2.0%-1/2 | 16 | 1.48 | 3 | 2.0% hooked end |
L2.83%-2.0%-1/2 | 22 | 2.83 | 3 | 2.0% hooked end |
2.1 Material Properties
2.2 Specimen Preparation
2.3 Bending Tests
3 Crack Width Prediction from Different Codes
3.1 GB 50010, CECS38 and JTG 3362
3.2 NF P18-710
3.3 MC
3.4 Rebar Stress
3.5 Modified Crack Width Prediction Based on GB50010-2010
3.5.1 Rebar Stress
3.6 Average Crack Spacing
3.7 Nonuniformity Distribution Coefficient of Rebar Strain
3.8 Member Characteristic Coefficient
3.9 Modified Crack Width Prediction
4 Results and Discussion
4.1 Crack Width Prediction from Existing Codes
4.2 Rebar Stress
4.3 Average Crack Spacing
Specimens | Wmax = 0.05 (mm) | Average | Wmax = 0.10 (mm) | Average | Wmax = 0.20 (mm) | Average |
---|---|---|---|---|---|---|
L2.33%-1.5%-1 | 62.40 | 56.60 | 47.10 | 40.20 | 29.10 | 25.05 |
L2.33%-1.5%-2 | 50.80 | 33.30 | 21.00 | |||
L2.33%-2.0%-1 | 63.30 | 58.30 | 30.90 | 30.65 | 23.90 | 21.7 |
L2.33%-2.0%-2 | 53.30 | 30.40 | 19.50 | |||
L2.33%-3.0%-1 | 45.10 | 48.35 | 30.10 | 31.2 | 18.50 | 19.85 |
L2.33%-3.0%-2 | 51.60 | 32.30 | 21.20 | |||
L1.48%-2.0%-1 | 78.30 | 82.45 | 26.00 | 27.5 | 24.50 | 24.20 |
L1.48%-2.0%-2 | 86.60 | 29.00 | 23.90 | |||
L2.83%-2.0%-1 | 45.40 | 51.45 | 21.40 | 22.55 | 18.70 | 18.80 |
L2.83%-2.0%-2 | 57.50 | 23.70 | 18.90 |
Average crack spacing (mm) | |||||||
---|---|---|---|---|---|---|---|
Specimens | Crack numbers | Measured① | Average | Equation 27 Predicted② | Equation 28 Predicted③ | ②/① | ③/① |
L2.33%-1.5%-1 | 10 | 66.67 | 63.33 | 76.22 | 60.36 | 1.20 | 0.95 |
L2.33%-1.5%-2 | 11 | 60.00 | |||||
L2.33%-2.0%-1 | 12 | 54.55 | 52.27 | 76.22 | 54.42 | 1.46 | 1.04 |
L2.33%-2.0%-2 | 13 | 50.00 | |||||
L2.33%-3.0%-1 | 13 | 50.00 | 48.08 | 76.22 | 47.59 | 1.59 | 0.99 |
L2.33%-3.0%-2 | 14 | 46.15 | |||||
L1.48%-2.0%-1 | 11 | 60.00 | 63.33 | 85.76 | 63.96 | 1.35 | 1.01 |
L1.48%-2.0%-2 | 10 | 66.67 | |||||
L2.83%-2.0%-1 | 13 | 50.00 | 50.00 | 72.74 | 50.95 | 1.45 | 1.02 |
L2.83%-2.0%-2 | 13 | 50.00 | |||||
Standard deviation | 0.13 | 0.03 | |||||
Average | 1.41 | 1.00 | |||||
Coefficient of variance | 0.09 | 0.03 |
4.4 Modified Crack Width
Specimens | Rebars | Cover thick (mm) | Cross-sectional size (mm2) | Rebar area (mm) | Rebar ratio | Tensile strength UHPC | Elastic modulus UHPC |
---|---|---|---|---|---|---|---|
B-1 | 4Φ20 | 20 | 350 × 160 Wang et al., (2017) | 1256 | 0.0513 | 14.1 MPa | 59 GPa |
B-2 | 20 | 1256 | 0.0513 | ||||
B-5 | 20 | 1256 | 0.0513 | ||||
B-6 | 20 | 1256 | 0.0513 | ||||
C-1 | 6Φ16 | 20 | 1206 | 0.0492 | |||
C-4 | 20 | 1206 | 0.0492 | ||||
C-6 | 20 | 1206 | 0.0492 | ||||
C-8 | 20 | 1206 | 0.0492 | ||||
D-2 | 4Φ18 | 20 | 1018 | 0.0416 | |||
D-3 | 20 | 1018 | 0.0416 | ||||
D-6 | 20 | 1018 | 0.0416 | ||||
E-1 | 4Φ22 | 20 | 1520 | 0.0620 | |||
L1 | 2Φ25 | 20 | 150 × 250 Wu et al., (2014) | 982 | 0.0524 | 7.6 MPa | 42 GPa |
L2 | 3Φ25 | 20 | 1473 | 0.0786 | |||
L3 | 4Φ25 | 20 | 1964 | 0.1047 | |||
L4 | 2Φ25 + 2Φ18 | 20 | 982 | 0.0524 | |||
L5 | 2Φ25 | 20 | 982 | 0.0524 | |||
L6 | 2Φ25 + 2Φ16 | 20 | 1384 | 0.0738 | |||
L7 | 2Φ25 | 20 | 982 | 0.0524 | |||
L8 | 2Φ18 + 2Φ16 | 20 | 911 | 0.0486 | |||
L-2 | 2Φ14 | 25 | 150 × 200 Li et al., (2010) | 308 | 0.0210 | 10.2 MPa | 48.1 GPa |
L-3 | 2Φ22 | 25 | 760 | 0.0510 | |||
L-4 | 3Φ18 | 25 | 763 | 0.0510 | |||
L-5 | 2Φ25 + 1Φ22 | 25 | 1362 | 0.0910 | |||
L-6 | 2Φ22 + 1Φ40 | 25 | 2017 | 0.1340 |
5 Conclusions
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From experimental observations, multiple cracking behavior and localized crack are further confirmed in the steel reinforced UHPC beams. Although both increasing steel reinforcing ratio and fiber volume reduce average crack spacing along with more even distribution of cracks, steel reinforcing ratio shows better improvement effectiveness in controlling crack width development.
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Normal concrete codes (GB50010 and JTG 3362) show conservative crack width predictions with high scattering. Although CECS 38 generally underestimates crack width and MC underestimates crack width after 0.1 mm, the predictions from AFGC are in the safety side, especially for the beams with large fiber volume and low reinforcement ratio.
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The residual tensile strength of UHPC shows an important influence on the rebar stress calculation in the mechanics-based model. The residual tensile strength of is 0.8 \({f}_{tk}\) for the equivalent stress block shows accurate rebar stress predictions.
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With the calibrated equations for calculating average crack spacing and nonuniformity distribution coefficient of rebar strain, the modified crack width equation shows prediction accuracy of 0.97–1.03 and standard deviation of 0.11–0.21 in this study and other investigations. Therefore, the modified equations are expected to be validated in future studies to promote structural design and crack control of steel reinforced UHPC beams.