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Steel fiber reinforced concrete (SFRC) has gained popularity in the last decades attributed to the improvement of brittleness and low tensile strength of concrete. This study investigates the effect of three shapes of steel fibers (straight, hooked end, and corrugated) with four contents (0.5%, 1%, 1.5%, and 2%) on the mechanical properties (compression, splitting tension, shear, and flexure) of concrete. Thirteen groups of concrete were prepared and investigated experimentally. Test results indicated that steel fiber had significant reinforcement on mechanical properties of concrete. When the steel fiber content increases from 0.5% to 2.0%, the compressive strengths increase about 4–24%, splitting tensile strengths increase about 33–122%, shear strengths increase about 31–79%, and flexural strengths increase about 25–111%. Corrugated steel fiber has the best reinforced effect on strength of SFRC, hooked end steel fiber takes the second place, and straight steel fiber is the least. Calculated formulas of compressive, splitting tensile, shear, and flexural strengths were established with consideration of the bonding properties between concrete and steel fiber. Influence factors of steel fiber

Concrete is the largest amount and the most widely used material; its tensile strength is significantly lower than its compressive strength. Synthetic, glass, basalt, carbon, PVA, and steel fiber have been used in concrete to make up for the low tensile strength of concrete [

It is generally acknowledged that the mechanical property of SFRC increases with the rising of steel fiber content. However, some studies suggest that steel fiber does not significantly affect the compressive strength [

According to manufacturing form, steel fiber is usually classified into three main shapes (straight form, hooked ends form, and corrugated form) [

Although much work has been done about SFRC, there still exists unsolved problem:

Although the reinforced effect of steel fiber on compressive strength is much less than that on tensile strength, shear strength, and flexural strength, the increase ratio of compressive strength still can reach 25% for low or moderately high strength (≤60 MPa) concrete. Some literature studies suggest that steel fiber shape almost has no influence on compressive strength; others indicate that compressive strength can be improved by steel fiber no matter what type steel fiber is. There are still many different conclusions about the reinforced effect of steel fiber on compressive strength, so the reinforced effect of steel fiber with different content and type on compressive strength should be studied further.

Splitting tensile, flexure, and shear strength of SFRC increase with the rising of steel fiber content; some researchers suggest that concrete strength will no longer increase when steel fiber content exceeds a certain value, which means that there exists the most economical steel fiber content for certain strength. But there is no final word on the most economical content of steel fiber.

The shape of steel fiber has significantly influence on the enhancement effect of splitting tensile, flexure, and shear strength of SFRC. At the same time, the reinforced effect of different shapes on various mechanical properties of concrete is also different. So, there is the best shape of steel fiber which can achieve the best enhancement effect on one kind of mechanical property of content.

How to determine the optimal content and shape of steel fiber is an important problem. This would help improve the utilization rate of steel fiber and reduce the cost of SFRC.

In this research, the impact of steel fiber shape and content on the reinforced effect of concrete will be monitored and analyzed through the compressive, splitting tensile, shear, and flexural experiments. Three shapes (straight, hooked end, and corrugated) of steel fiber were used to research the influence on the mechanical performance of concrete with different volume fractions (0, 0.5%, 1%, 1.5%, and 2%). Based on the test result, calculation model of compressive, splitting tensile, shear, and flexural strength of SFRC were put forward.

Portland cement (P. O. 42.5) conforming to GB 175 [

Physical and mechanical properties of cement.

Type | Specific gravity (kg/m^{3}) | Surface area (m^{2}/kg) % | Standard consistency | Stability | Setting time (min) | Compressive strength (MPa) | Flexural strength (MPa) | |||
---|---|---|---|---|---|---|---|---|---|---|

Initial | Final | 3 d | 28 d | 3 d | 28 d | |||||

P. O. 42.5 | 3100 | 352 | 24.7 | Eligibility | 175 | 220 | 23.5 | 45 | 5.6 | 8.5 |

Physical properties of the coarse and fine aggregate.

Aggregate type | Apparent density (kg/m^{3}) | Loose packing density (kg/m^{3}) | Dry-rodded density (kg/m^{3}) | Water absorption (wt %) | Crush index (%) | Void ratio (%) |
---|---|---|---|---|---|---|

Coarse aggregate | 2814 | 1568 | 1630 | 1.40 | 8.8 | 44.3 |

Fine aggregate | 2556 | 1611 | 1486 | 0.56 | — | — |

Geometry and mechanical characteristics of steel fibers.

ST-F | HE-F | CO-F | |
---|---|---|---|

Fiber shape | Straight | Hooked end | Corrugated |

Mean length (_{f}), mm | 32.34 | 32.19 | 32.27 |

Mean diameter (d_{f}), mm | 1.036 | 0.993 | 1.215 |

Aspect ratio (_{f}/d_{f}) | 31.21 | 32.41 | 26.56 |

Density (g/cm^{3}) | 7.9 | 7.9 | 7.9 |

Elastic modulus (GPa) | 200 | 200 | 200 |

Tensile strength (MPa) | 500 | 380 | 500 |

Three shapes of steel fiber and four steel fiber volume fractions (_{f} = 0.5%, 1.0%, 1.5%, and 2%) were chosen as test parameters. Steel fiber volume fraction (_{f}) was defined as the absolute volume of steel fiber in 1 m^{3} concrete. Water-cement ratio was taken as 0.55. The mixture proportion design method conformed to the Chinese Standards JGJ 55-2011 [

Mixture proportions (kg/m^{3}).

Mixture number | Water | Cement | Sand | Stone | Steel fiber |
---|---|---|---|---|---|

PC | 264 | 480 | 716.5 | 989.5 | 0 |

ST-F0.5 | 264 | 480 | 727.8 | 965.8 | 39 |

ST-F1 | 264 | 480 | 739.2 | 942.3 | 78 |

ST-F1.5 | 264 | 480 | 750.5 | 917.3 | 117 |

ST-F2 | 264 | 480 | 761.9 | 895.1 | 156 |

HE-F0.5 | 264 | 480 | 727.8 | 965.8 | 39 |

HE-F1 | 264 | 480 | 739.2 | 942.3 | 78 |

HE-F1.5 | 264 | 480 | 750.5 | 917.3 | 117 |

HE-F2 | 264 | 480 | 761.9 | 895.1 | 156 |

CO-F0.5 | 264 | 480 | 727.8 | 965.8 | 39 |

CO-F1 | 264 | 480 | 739.2 | 942.3 | 78 |

CO-F1.5 | 264 | 480 | 750.5 | 917.3 | 117 |

CO-F2 | 264 | 480 | 761.9 | 895.1 | 156 |

The cubic specimens with side length of 150 mm were cast for the compressive strength (_{cu}, _{fcu}) and splitting tensile strength (_{ts}, _{fts}) test, the prism specimens of 100 mm × 100 mm × 300 mm were cast for shear strength (_{v}, _{fv}) test, the prism specimens of 100 mm × 100 mm × 400 mm were cast for flexural strength (_{tm}, _{ftm}) test, and three specimens were prepared for each group. To distinguish the concrete with and without steel fiber, _{cu}, _{ts}, _{v}, and _{tm} are used to represent the mechanical performance indexes of the plain concrete; _{fcu}, _{fts}, _{fv}, and _{ftm} are used to represent the mechanical performance indexes of SFRC.

A multifunction mixer was used to prepare the concrete. Mixing process of concrete included three steps: firstly, all aggregate and cement were put into a forced concrete mixer to mix for about 2 minutes; secondly, the water was added and mixed continuously for 2 minutes; finally, steel fiber was sprinkled evenly and then mixed for another 3 minutes. Fresh concrete was put rapidly into the moulds which were brushed oil in advance. Specimens were vibrated for 20 seconds. After 24 hours of curing in air, specimens were carefully demoulded and placed in a curing room at approximately 95% RH and 20°C.

All the tests were conducted at the age of 28 days. The compressive strength and splitting tensile strength test were performed according to GB/T50081 [

Test setup of splitting tensile strength.

One steel bearing plate and one plywood bearing strip were placed between specimen and the top and bottom pressure plate, respectively. The section of bearing plate is part of circle radius of 75 mm; thickness is 20 mm. The section of bearing strip is 20 mm × 4 mm. The bearing plate and bearing strip should align with the center line of the top and bottom surface of specimen. The splitting tensile strength of the specimen was calculated as follows:_{fts} is the splitting tensile strength, MPa; ^{2}.

The shear test was also carried on a servohydraulic closed-loop testing machine with capacity of 3000 kN at the loading rate of 0.06 MPa/s; the test setup is shown in Figure

Test setup of shear strength.

The load was recorded with a load transducer. The ultimate shear strength was calculated as follows:_{fv} is the ultimate shear strength; F is the maximum applied load indicated by the testing machine; _{eff} is the effective width of the specimen (the average value of the width of the two shear sections), and _{eff} is its effective depth (the average value of the depth of the two shear sections).

Flexural tests were carried on a MTS810 testing machine with capacity of 500 kN with displacement control at a rate of 0.1 mm/min, according to ASTM C1609 (using beam with third-point loading) [

Test setup of flexural strength.

The specimens were normally rotated an angle of 90° from the casting position to eliminate the eccentricity effect from the roughness of the surface. Calculate the flexural strength of the specimen as follows:_{ftm} is flexural strength, MPa; F is the maximum applied load indicated by the testing machine, N;

At least, three specimens in each group were tested and their mean values were taken as the test results. Test results of _{fcu}, _{fts}, _{fv}, and _{ftm} are listed in Table

Test results of mechanics strength (MPa).

Mixture number | _{fcu} | _{fts} | _{fv} | _{ftm} |
---|---|---|---|---|

PC | 34.6 | 3.15 | 6.85 | 4.32 |

ST-F0.5 | 36 | 4.19 | 9.39 | 5.40 |

ST-F1 | 38.8 | 4.45 | 10.20 | 6.25 |

ST-F1.5 | 38.1 | 4.89 | 11.06 | 7.39 |

ST-F2 | 40.8 | 5.34 | 12.25 | 7.95 |

HE-F0.5 | 38.2 | 4.28 | 10.01 | 6.09 |

HE-F1 | 38.1 | 5.20 | 11.00 | 7.26 |

HE-F1.5 | 40.3 | 5.81 | 12.21 | 7.55 |

HE-F2 | 41.6 | 6.41 | 11.38 | 8.68 |

CO-F0.5 | 35 | 4.64 | 9.80 | 6.58 |

CO-F1 | 37.7 | 5.30 | 10.08 | 7.35 |

CO-F1.5 | 40.1 | 6.55 | 12.01 | 8.51 |

CO-F2 | 42.9 | 7.00 | 11.12 | 9.11 |

Relationship between compressive strength (_{fcu}), compressive strength reinforced ratio (_{fcu}/_{cu}), and steel fiber volume fraction (_{f}) with the different steel fiber shape are shown in Figure

Relationship between _{fcu}, _{fcu}/_{cu}, and _{f}.

In general, _{fcu} increased continuously as _{f} increased from 0 to 2%. However, the increasing trend has slight difference with the different steel fiber shape. When _{f} ≤ 1%, the _{fcu}/_{cu} of ST-F and HE-F was slightly bigger than that of CO-F. But, when _{f} reached 2%, _{fcu}/_{cu} of CO-F reached its maximum value 1.24, which was higher than f_{fcu}/f_{cu} of ST-F and HE-F. It indicated that ST-F and HE-F had better strength reinforcement when _{f} was below 1%, while CO-F had better strength reinforcement when _{f} was above 1%. Although different steel fiber shape has reinforced effect on compressive strength of concrete, the increment is limited and the maximum value of _{fcu}/_{cu} is 1.24.

The steel fiber can limit the lateral expansion and restrain the crack propagation of concrete under compressive load, which can delay the damage of concrete and enhance the compressive performance. The reinforced effect is decided by the bonding performance between steel fiber and concrete. The bonding force is affected by the surface shape of steel fiber. So, the different surface shape has the different effect on the compressive strength of concrete.

Relationship between splitting tensile strength (_{fts}), splitting tensile strength reinforced ratio (_{fts}/_{ts}), and steel fiber volume fraction (_{f}) with the different steel fiber shape is shown in Figure _{fts} increased continuously as _{f} increased from 0 to 2%. When _{f} ≤ 0.5%, ST-F and HE-F have a similar reinforced effect on concrete; CO-F has a slighter better reinforced effect than them. When _{f} ≥ 0.5%, CO-F still has the best reinforced effect and HE-F takes the second place. When _{f} = 2%, _{fts}/_{ts} of CO-F is 2.22, _{fts}/_{ts} of HE-F is 2.03, and _{fts}/_{ts} of ST-F is only 1.7. As shown in

Relationship between _{fts}, _{fts}/_{ts}, and _{f}.

Test results proved that CO-F had the best reinforced effect on _{fts}. This is because the surface of CO-F is the shape of corrugate and it can provide higher interface bonding force than ST-F and HE-F. Similarly, HE-F with the hooked form at both ends can provide better interface bonding force than ST-F with straight surface. ST-F has the smallest reinforced effect on _{fts} because its surface is smooth and can not provide the mechanical occlusive force. It can be seen that because the surface shape of steel fiber has important effect on the interface bonding force between concrete and steel fiber, the surface shape of steel fiber obviously affects the reinforced effect on the splitting tensile strength of concrete. In order to increase the reinforcement of steel fiber on concrete, the rough surface of steel fiber is the best choice.

Relationship between shear strength (_{fv}), shear strength reinforced ratio (_{fv}/_{v}), and steel fiber volume fraction (_{f}) with the different steel fiber shape is shown in Figure _{f} increases from 0 to 0.5%, _{fv} increases rapidly. When _{f} = 0.5%, _{fv}/_{v} = 1.37 for ST-F, _{fv}/_{v} = 1.46 for HE-F, and _{fv}/_{v} = 1.43 for CO-F. Whatever the steel fiber shape is, _{fv} increases about 40% when _{f} increases from 0 to 0.5%. When _{f} increases from 0.5 to 1.5%, _{fv} still increases with the increase of _{f}, but the growth ratio is slowing down. When _{f} is more than 1.5%, f_{fv} of ST-F continuously increases while _{fv} decreases with the increase of _{f} for HE-F and CO-F.

Relationship between _{fv}, f_{fv}/_{v}, and _{f}.

This result indicates that too much steel fiber can cause shear strength reduction. The reason lies in two aspects. One is that the compressive strength of concrete matrix is not high; it leads steel fiber which is pulled out from concrete matrix before concrete failure because of the low bond force between concrete and steel fiber. And steel fiber cannot give full play when the steel fiber volume fraction is big. Some literature gave a similar result: to improve the shear strength, the first way consists in the increase of the compressive strength of the concrete; the second way is obtained with the addition of fiber [_{f} may more easily cause the uneven distribution of steel fiber; the uneven distribution of steel fiber leads to the lower bonding force between some steel fiber and concrete and also produces some weakened region. An optimum steel fiber content exists for a given concrete, beyond which the reinforcing effect of steel fiber on the shear strength becomes weakened with increase of steel fiber content. This result is slightly different to many previous literatures which proved that direct shear capacity of SFRC is clearly related to the amount of fiber [

Relationship between flexural strength (_{ftm}), flexural strength reinforced ratio (_{ftm}/_{tm}), and steel fiber volume fraction (_{f}) with the different steel fiber shape is shown in Figure _{ftm} increased continuously as _{f} increased from 0 to 2%. Whatever the shapes of steel fiber are, the three trend lines are nearly straight upward; this indicates that _{ftm} is all nearly a linear function of _{f}. However, the slopes of three lines are different, the slope of CO-F is the biggest, and the slope of ST-F is the least. This means that when _{f} is fixed, the enhancement effect is different with the different shape of steel fiber. CO-F is the best and HE-F takes the second place. It can be attributed to the bond strength of the matrix and steel fiber. The deformed shape provides better bond property than the straight fiber.

Relationship between _{ftm}, _{ftm}/_{tm}, and _{f}.

When _{f} reaches its maximum value 2%, _{ftm}/_{tm} of CO-F is 2.11 and _{ftm}/_{tm} of HE-F is 2.01; this means that _{ftm} of concrete in corrugated and hooked steel fiber doubles the value of plain concrete. _{ftm}/_{tm} of ST-F is the least, which is 1.84. This proved that steel fiber has excellent enhancement effect on flexural strength. Previous research suggested that the limited volume fraction of HE-F is 1.5% for the economical and efficient use of steel fiber on flexural performance [_{f}, even if _{f} ≥ 1.5%. This may be because the concrete matrix strength in this test is only about 40 MPa. The flexural failure is attributable mostly to pull-out rather than rupture of the steel fiber. The flexural strength of the SFRC increased with the increase of fiber content, which is closely related to the number of steel fibers that provide a bridging action. Then, steel fiber of deformed shape can play more important role than that with straight shape.

The above result analysis proved that steel fiber can improve _{fcu}, _{fts}, _{fv}, and _{ftm} of concrete obviously with the increasing of _{f}. When _{f} is fixed, the reinforcement ratio mainly is influenced by the interface bonding force between concrete and steel fiber. The interface bonding force mainly consists of three parts: chemical cementation force, frictional resistance, and mechanical interaction force. Chemical cementation force is mainly influenced by the strength of concrete matrix (_{cu}). Frictional resistance is mainly affected by surface area and roughness. Mechanical occlusal force is mainly affected by the surface dents of steel fiber. Thus, the important enhancement factors of ffcu, f_{fts}, f_{fv}, and f_{ftm} are concrete matrices (f_{cu}), aspect ratio (l_{f}/d_{f}), content (V_{f}), and shape and surface dents of steel fiber.

Based on the above analysis, reinforcement ratio of _{fcu} is influenced by content, aspect ratio, and shape of steel fiber; it can be expressed as follows:_{fcu} is the compressive strength of SFRC; _{cu} is the compressive strength of plain concrete; _{f} is the influence coefficient of steel fiber shape, which is related to the geometric and surface shape of steel fiber; _{f} is the characteristic coefficient of steel fiber, _{f} = _{f}_{f}/_{f}.

_{f} of these three shapes steel fiber can be obtained through the regression analysis of experiment data in this paper and relative research literature [_{fcu}/_{cu} and _{f} is shown in Figure

Relationship between _{fcu}/_{cu} and _{f} (a) ST-F, (b) HE-F, and (c) CO-F.

As shown in Figure _{fcu} had a linear relationship with _{f} when the surface shape of steel fiber is the same. Value of _{f} can be obtained through regression analysis: _{f} = 0.21 for ST-F; _{f} = 0.27 for HE-F; _{f} = 0.4 for CO-F. _{f} of CO-F is the biggest; this is because corrugated surface not only can increase the surface roughness, but also can provide mechanical interaction force. _{f} of HE-F is in the second place; hooks at the end of steel fiber can increase part of the frictional resistance. Adding surface roughness or uneven of steel fiber can improve its enhancement effect obviously under the condition of keeping content of steel fiber.

Concrete matrix also plays an important role in bonding strength, so it significantly affects the reinforcement ratio of _{fts}, _{fv}, and _{ftm}. The reinforcement ratio of _{fts}, _{fv}, and _{ftm} can be expressed as follows:_{f} is strength reinforced ratio of SFRC; it can represent _{fts}/_{ts}, _{fv}/_{v}, or _{ftm}/_{tm}; _{c} is the influence coefficient of concrete matrix, which is related to compressive strength of concrete matrix.

_{c} can be obtained through the regression analysis of experiment data in this paper and previous literature [_{f} is known: _{f} = 0.21 for ST-F; _{f} = 0.27 for HE-F; _{f} = 0.4 for CO-F. The relationship between _{f} and _{f}_{f} is shown in Figure

Relationship between _{f} and _{f}_{f}.

As shown in Figure _{f} represents different strength reinforcement rates, such as _{fts}/_{ts}, _{fv}/_{v}, or _{ftm}/_{tm}, _{f} showed a linear relationship with _{f}_{f}. This indicates that the reinforced effect of concrete matrix on the strength of SFRC is linear when eliminating the effect of steel fiber. As shown in Figure _{c} can be obtained through linear regression with the experiment data, _{c} = 4.86 and ^{2} = 0.87. This shows that the correlation between _{f} and _{f}_{f} is fairly good. Since the compressive strength of plain concrete in this test is fixed (_{cu} = 34.6 MPa), the value of _{c} could change with the changing of _{cu}. The relationship between _{cu} and _{c} should be studied further for high strength concrete.

Above is the main analysis of the enhancement effect of steel fiber. In order to verify the correctness of the equations (_{f} and _{c}, the strength calculation method of _{fcu}, _{fts}, f_{fv}, and f_{ftm} can be put forward based on equations (_{f} = 0.21 for ST-F; _{f} = 0.27 for HE-F; _{f} = 0.4 for CO-F; _{c} = 4.86; _{f} = _{f}_{f}/d_{f}. Putting the test data of _{cu} in (_{ts} in (_{v} in (_{tm} in (_{fcu}, _{fts}, _{fv}, and _{ftm} and the ratio of calculated value to test value are put into Table

Calculated results and the comparison between calculated results and test results of mechanics strength.

Mixture number | _{fcu} | _{fts} | _{fv} | _{ftm} | ||||
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Cal (MPa) | C/T | Cal (MPa) | C/T | Cal (MPa) | C/T | Cal (MPa) | C/T | |

PC | 34.6 | 1 | 3.15 | 1.00 | 6.85 | 1 | 4.32 | 1.00 |

ST-F0.5 | 35.7 | 0.99 | 3.65 | 0.87 | 7.94 | 0.85 | 5.01 | 0.93 |

ST-F1 | 36.9 | 0.95 | 4.15 | 0.93 | 9.03 | 0.89 | 5.70 | 0.91 |

ST-F1.5 | 38.0 | 1.00 | 4.66 | 0.95 | 10.12 | 0.92 | 6.38 | 0.86 |

ST-F2 | 39.1 | 0.96 | 5.16 | 0.97 | 11.21 | 0.92 | 7.07 | 0.89 |

HE-F0.5 | 36.1 | 0.95 | 3.82 | 0.89 | 8.32 | 0.83 | 5.24 | 0.86 |

HE-F1 | 37.6 | 0.99 | 4.49 | 0.86 | 9.76 | 0.89 | 6.16 | 0.85 |

HE-F1.5 | 39.1 | 0.97 | 5.16 | 0.89 | 11.22 | 0.92 | 7.08 | 0.94 |

HE-F2 | 40.7 | 0.98 | 5.83 | 0.91 | 12.68 | 1.11 | 7.99 | 0.92 |

CO-F0.5 | 36.4 | 1.04 | 3.96 | 0.85 | 8.62 | 0.88 | 5.44 | 0.83 |

CO-F1 | 38.3 | 1.02 | 4.78 | 0.90 | 10.39 | 1.03 | 6.55 | 0.89 |

CO-F1.5 | 40.1 | 1.00 | 5.59 | 0.85 | 12.16 | 1.01 | 7.67 | 0.90 |

CO-F2 | 42.0 | 0.98 | 6.40 | 0.91 | 13.92 | 1.25 | 8.78 | 0.96 |

Note that Cal stands for the calculated result and C/T stands for the ratio of the calculated result with test result.

The ratio of calculated value to test value of _{fcu} varies from 0.95 to 1.04; this indicates that calculated value of _{fcu} coincides with test value quite well. The ratio of calculated value to test value of _{fts} and _{ftm} varies from 0.85 to 1. Although the calculated value is slightly less than test value, the calculated value is still close to the test value. Except CO-F2, the ratio of calculated value to test value of _{fv} varies from 0.83 to 1.11; the calculated value is also close to the test value. According to the previous analysis, when _{f} is larger than 1.5%, the enhancement effect of steel fiber becomes weak, but in the calculation of equation (_{f} is 2%, the calculated value is larger than the test value. Further research should be taken for SFRC with steel fiber volume fraction that is above 2%.

The general objective of this research project was to evaluate the effect of steel fiber shape and content on the mechanical property of SFRC and the calculation method of reinforced effect of steel fiber with different shape and content on compressive strength, splitting strength, shear strength, and flexural strength. The main conclusions are as follows:

Expecting that shear strength gets its maximum value at steel fiber volume ratio which is 1.5%, compressive strength, splitting strength, and flexural strength all express linear increase trend with the increasing of steel fiber volume ratio from 0 to 2%.

)When the steel fiber content is fixed, CO-F has the best reinforced effect on compressive strength, splitting strength, shear strength, and flexural strength of SFRC; HE-F takes the second place and ST-F is the least.

In order to increase the reinforcement of steel fiber on concrete, the steel fiber has rough surface which is the best choice. At least, interface bonding force should be increased as far as possible.

Two influence factors _{f} and _{c} were put forward and their value was obtained by regression analysis of experiment data. The proposed calculated formulas for compressive strength, splitting tensile strength, shear strength, and flexural strength of SFRC have good agreement with the experimental results.

When steel fiber volume fraction is larger than 2%, the reinforced effect of steel fiber on shear strength needs to be studied further. Relationship between _{cu} and _{c} should also be researched further for high strength concrete (_{cu} ≥ 60 MPa).

The experimental data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was supported by China National Natural Science Foundation Youth Fund Project (51808509), Innovation Team Development Plan of China's Ministry of Education (IRT_16R67), Key Scientific Research Projects of Colleges and Universities of Henan Provincial Department of Education (19A560005) and Thousand Talents Plan in Henan Province (ZYQR201912029).

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