# Experimental Investigation of Flexural Behavior of Ultra-High-Performance Concrete with Coarse Aggregate-Filled Steel Tubes

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Test Design

_{e}, was fixed at 1200 mm. The tubes were fabricated using seamless steel tube with the same external diameter of 114 mm, but different nominal wall thicknesses (t) of 4.5 mm, 6 mm, 8 mm and 10 mm were considered. Two steel plates with dimensions of 140 mm × 140 mm × 10 mm were welded at the both ends to avoid the relative slip between the steel tube and CA-UHPC infill during the loading process. The nomenclature of the specimen is as follows: BC32S6, where ‘B’ represents the bending specimen, ‘C32’ is defined as the type of CA-UHPC, with the mixture containing 30% coarse aggregate and 2% steel fiber by the volume fraction, and ‘S6’ indicates that the nominal thickness of steel tube is 6 mm. The details of all specimens used in the present study are summarized in Table 1.

#### 2.2. Materials Properties

#### 2.2.1. Steel

_{y}), ultimate tensile strength (f

_{u}) and elastic modulus (E

_{s}), are summarized in Table 2.

#### 2.2.2. UHPC with Coarse Aggregate

^{3}, and tensile strength of 400 MPa was adopted in the mixture. River sand with an apparent density of 2650 kg/m

^{3}and grain size below 2 mm was applied. Polycarboxylate superplasticizer (SP) with a water-reducing ratio of 30% and a solid content of 40% was applied to reduce the water consumption and improve the flowability of CA-UHPC. Crushed granite with particle size ranging from 5 mm to 20 mm was used, and the apparent density is about 2725 kg/m

^{3}. The grading curves of fine and coarse aggregates are shown in Figure 2.

#### 2.3. Experimental Setup and Loading Procedure

_{e}/15).

## 3. Test Results and Discussion

#### 3.1. Failure Modes

#### 3.2. Overall Deflection Curves

#### 3.3. Moment–Curvature Relationship

_{m}represents the vertical deflection at the mid-span, L

_{e}denotes the clear span between the supports, and x is the distance to the left support. The sectional curvature (ϕ) can be deduced by taking the second derivative:

_{e}, the curvature at the mid-span section (ϕ

_{m}) can be expressed as $\frac{{\pi}^{2}}{{L}_{\mathrm{e}}^{2}}{u}_{\mathrm{m}}$.

_{m}) curve is presented in Figure 6. It is clear that the moment–curvature curves can be divided into three phases: the elastic stage (OB), the elastic–plastic stage (BC) and the plastic hardening stage (CD). Several characteristic points are also labeled in the figure, in which point A represents the initial cracking of the CA-UHPC infill at the tensile zone edge; point B stands for the initial yielding of the steel tube at the tensile flange, corresponding to the proportional limit; point C refers to the tensile strain of the steel tube at the tensile side of the mid-span section, reaching 10,000 με; while point D corresponds to the mid-span maximum deflection, up to L

_{e}/15.

- (1)
- Elastic stage: the moment increases linearly with the curvature until the moment reaches 70~80% of ultimate flexural capacity. The moment increases sharply in this stage, while the increase of the curvature is mild. The stiffness remains almost constant, while the steel tube and the compression zone of the CA-UHPC infill remain in an elastic state during this stage. When the load reaches 30~40% of ultimate flexural capacity, the tensile stress in the tensile flange of the concrete exceeds the tensile strength, resulting in transverse cracking. With regard to the core CA-UHPC infilled with steel fiber, the steel fiber is able to restrain the initiation and extension of tensile cracks triggered during this stage, thus enhancing the flexural performance of the concrete core.
- (2)
- Elastic–plastic stage: the moment increases moderately while the curvature increases rapidly. The specimen presents nonlinear response as the gradient of the curves decreases. The yield zone at the bottom flange of the steel tube gradually extends to the compression zone, while the top region of the steel tube and the CA-UHPC are still in an elastic state. The yielding of steel tube tensile flange and the cracking of the concrete core in the tensile zone accelerate the degradation of the section flexural stiffness of the CA-UHPCFST beam. The interaction between the steel tube and the UHPC infill is triggered in this stage, and this can restrict the development of cracks in the CA-UHPC core along the height of the section.
- (3)
- Plastic hardening stage: there is a nearly linear relationship between the bending moment and curvature; however, the slope of the curve is much lower than during the elastic stage. The moment increases at a moderate rate, but nevertheless the curvature increases rapidly. Near point C, the top edge of the steel tube has yielded and the compressive top fiber of CA-UHPC infill is crushed. The stiffness of the specimen decreases dramatically due to the gradual yielding of the steel tube from the tensile flange and the compression edge to the neutral axis. Until the termination of the test, the curve still increases continually, and no distinct softening stage can be observed; the increasing rate of moment in plastic hardening stage is distinctly higher than that of the normal- and high-strength concrete-filled steel tubes or stainless steel tubes. It is demonstrated that the CA-UHPCFST beams under pure bending have better ductility than conventional CFSTs [18,34,35]. This may be ascribed to the higher flexural strength of UHPC and the interaction effect between the steel tube and the CA-UHPC core, where the CA-UHPC prevents the inward local buckling of the steel tube, and accordingly, the further strength degradation and cracking of the core CA-UHPC is restricted due to the confinement provided by the external steel tube.

#### 3.4. Moment–Strain Relationship

#### 3.5. Ultimate Flexural Capacity

_{u}) [34]. Figure 10 presents a comparison of the ultimate flexural capacity of CA-UHPCFSTs with different steel tube thicknesses and CA-UHPC types. The ultimate flexural capacity increases obviously with increasing steel tube thickness. For instance, with an increase in steel tube thickness from 4.5 mm to 10 mm, the ultimate flexural capacity was increased by 38.0%, 57.5% and 92.1%, respectively. This can be ascribed to the increase in steel tube thickness inducing an improvement in composite section strength, while the confinement effect provided by the steel tube on the compression zone of the CA-UHPC infill is also strengthened, thus resulting in a higher compressive strength of the CA-UHPC core at the compressive flange being achieved.

#### 3.6. Flexural Stiffness

_{i}) is defined as the secant stiffness corresponding to the moment of 0.2M

_{u}, while the serviceability-level section flexural stiffness (K

_{s}) represents the secant stiffness corresponding to the moment of 0.6M

_{u}, according to the mechanical model proposed by Han [34]. The initial and serviceability-level flexural stiffness of the tested specimens are summarized in Table 1, and the effects of steel tube thickness and CA-UHPC type on flexural stiffness are plotted in Figure 11. It can be seen from the comparison that the initial flexural stiffness is higher than the serviceability-level section flexural stiffness for the same specimen, indicating that there is an obvious degradation of flexural stiffness of CA-UHPCFSTs in service. Both the initial and serviceability-level flexural stiffness improve significantly with increasing steel tube thickness. This is in agreement with the findings of Li et al. [21], who found that initial flexural stiffness and service-level flexural stiffness increased with an increase in the steel ratio. Furthermore, the initial and serviceability-level flexural stiffness are generally increased with CA-UHPC strength, but this enhancement is not as significant as that obtained with increasing steel tube thickness. The comparison between the CA-UHPC type of C30 and C32 shows that the initial flexural stiffness and the flexural stiffness at the serviceability limit state were also enhanced by the incorporation of 2% steel fiber. Furthermore, the comparison of the C32 and C02 specimens indicates that the incorporation of moderate coarse aggregate in UHPC core also enhances the flexural stiffness of CA-UHPCFST beam, since the coarse aggregate can increase the stiffness and elastic modulus of concrete [36].

#### 3.7. Ductility and Energy Dissipation Capacity

_{u}represents the mid-span deflection at the ultimate capacity, and δ

_{y}denotes the mid-span deflection corresponding to the yield load, which is the applied load corresponding to the yield strain of the steel tube at the tensile flange.

_{u}) and the yield load (E

_{y}), and the ratio of E

_{u}/E

_{y}are listed in Table 5 and Figure 12. The energy dissipation capacity increases with increasing steel tube thickness, with an increase in steel tube thickness from 4.5 mm to 10 mm resulting in an improvement in the energy dissipation capacity corresponding to ultimate capacity by 25.6%, 57.3% and 79.8%, respectively. The addition of steel fiber to CA-UHPC improves the energy dissipation capacity, in a manner similar to that of fiber-reinforced concrete-filled steel tubes subjected to bending [30], since the bridging effect of steel fiber can significantly enhance the tensile strength, crack resistance and deformability of concrete. However, the values of E

_{u}/E

_{y}decrease with the steel tube thickness and CA-UHPC strength, in a manner similar to the ductility index.

#### 3.8. Strain Ratio

## 4. Design Guidelines

#### 4.1. Comparisons of Flexural Stiffness

_{e}represents the flexural stiffness, E

_{s}and E

_{c}are the elastic modulus of steel and concrete core, respectively, I

_{s}and I

_{c}denote the moment of inertia of steel tube and concrete infill, respectively, and α is the contribution ratio of concrete core to the section flexural stiffness of the CFST beam.

_{c}/K

_{i}, and the mean value and standard deviation (coefficient of variation, COV) of this ratio for the different design codes. It is clear that the predictions obtained using EC 4 and AS 5100-6 were conservative, with mean values of 0.926 and 0.925 and COV of 0.077 and 0.078, which are lower than of the values obtained from the experimental results by about 7.4% and 7.5%, respectively. The predictions provided by AIJ were much lower than the test results, since this code mainly considers the contribution of steel tube to the flexural stiffness. BS 5400-6 gave a flexural stiffness about 2.7% higher than the value obtained from testing, and AISC/LRFD gave an initial flexural stiffness about 2.3% lower than the test results. It can be seen from Figure 14a that the predictions provided using Equation (6), proposed in this paper, were in good agreement with the experimental results, making it acceptable for the calculation of the initial flexural stiffness of CA-UHPCFST members.

_{s}) is compared with the predictions (K

_{sc}) obtained using various design guidelines, as shown in Figure 14b. The predictions, the ratio value of the predictions to the experimental values, the mean value, and the coefficient of variation (COV) of K

_{sc}/K

_{s}are summarized in Table 8. Additionally, on the basis of the fitting of the current experimental results, a prediction model for the serviceability-level flexural stiffness of CA-UHPCFST beams is proposed as follows:

_{sc}/K

_{s}for Equation (7) are also listed in Table 8. The comparisons in the table clearly indicate that AIJ presents conservative results for the serviceability-level flexural stiffness, with a mean value of 0.912 and a COV of 0.079. The predicted values of serviceability-level flexural stiffness of EC 4 and AS 5100 were slightly higher than of the values obtained from the test results. BS 5400 and AISC/LRFD overestimate the serviceability-level section flexural stiffness of the CA-UHPCFST specimen, with values about 13.8% and 8.2% higher than those obtained during the test, respectively. The prediction obtained using Equation (7) provides the most accurate estimation for the serviceability-level flexural stiffness, with a mean value of 0.997 and a COV of 0.085.

#### 4.2. Comparisons of Ultimate Flexural Capacity

_{uc}) of the CA-UHPCFST beams using the various design methods presented in Table 9 were compared with the current experimental results (M

_{u}). The predictions (M

_{uc}), the ratios of the predictions to the tested values (M

_{uc}/M

_{u}), and the mean values and the coefficients of variation (COV) of the ratio M

_{uc}/M

_{u}are listed in Table 10. It can be seen that AIJ underestimated the flexural capacity of the circular CA-UHPCFST beam, with a mean value of 0.890 and a COV of 0.083. This can be attributed to AIJ only considering the contribution of the steel tube to the flexural capacity, while ignoring the improvement to flexural strength provided by the concrete infill, thus resulting in a lower predicted flexural capacity. Specifically, as mentioned above, the addition of steel fiber improves the flexural capacity of the CA-UHPCFST member. EC 4 overestimated the moment capacity by a range of approximately 8% to 36%, with a mean value of 24.2% and a COV of 0.077. GB 50936 gave a mean value of 1.103 and a COV of 0.226, with the prediction being about 10.3% higher than of the values obtained from the test results; notably, the thicker steel tube led to lower prediction and results with a greater coefficient of variation. The method proposed by Han overestimated the test results, with a mean value of 1.137 and a COV of 0.090. The prediction of BS 5400 was conservative, with a mean value of 0.895 and a COV of 0.073. Since the lowest deviation and coefficient of variation among these design guidelines was obtained using BS 5400-5, we propose that the ultimate flexural capacity of CA-UHPCFST members can be achieved by modifying the design formula of BS 5400-5. Overall, the current design methods for normal-strength and high-strength concrete-filled steel tube beams are inapplicable for calculating the ultimate flexural capacity of CA-UHPCFST beams. Further research needs to be carried out to propose accurate design formulas for the ultimate flexural capacity of CA-UHPCFSTs.

## 5. Conclusions

- (1)
- All the CA-UHPCFST members behaved in a good ductile manner. The failure mode of specimens was similar to that of conventional CFST specimens. The addition of steel fiber had a limited effect on the global failure mode, whereas it was able to effectively reduce the number and depth of the tensile cracks, as well as mitigating the crushing in the compressive zone of the CA-UHPC infill.
- (2)
- The flexural stiffness, ultimate flexural capacity and hardening stage flexural moment were significantly enhanced with increased steel tube thickness. The increase in concrete strength for CA-UHPC without steel fiber had a limited effect on the flexural capacity. The incorporation of steel fiber was able to moderately increase the ultimate flexural capacity of the CA-UHPCFST members as well as lengthen the elastic stage of moment-versus-curvature curve.
- (3)
- The yield flexural moment of the CA-UHPCFST members under bending was approximately 0.7 times the ultimate flexural strength. The confinement effect in the compressive zone and the centroidal plane was triggered after the specimen entered the elastic–plastic stage, while the confinement effect in the tensile flange was minor or even negligible throughout the whole loading process.
- (4)
- Two empirical formulas were developed to predict the initial flexural stiffness and serviceability-level flexural stiffness of circular CA-UHPCFSTs. EC 4, AIJ, AS 5100 presented conservative results for the initial flexural stiffness, BS 5400-5 and AISC/LRFD gave the most accurate prediction on the value of K
_{i}. Additionally, EC 4, AS 5100, BS 5400-5 and AISC/LRFD overestimated the serviceability-level flexural stiffness. - (5)
- The current design rules are imprecise for calculating the ultimate flexural moment of CA-UHPCFSTs, with AIJ and BS 5400 presenting conservative results for the flexural capacity of circular CA-UHPCFST beams subjected to pure bending load, while EC 4, GB 50936, and the formula proposed by Han overestimate the ultimate flexural capacity. Further research is still required to propose accurate design formulas for the ultimate flexural capacity of CA-UHPCFSTs.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Ellobody, E.; Young, B.; Lam, D. Behaviour of Normal and High Strength Concrete-Filled Compact Steel Tube Circular Stub Columns. J. Constr. Steel Res.
**2006**, 62, 706–715. [Google Scholar] [CrossRef] - Yoo, D.; Banthia, N. Mechanical Properties of Ultra-High-Performance Fiber-Reinforced Concrete: A Review. Cem. Concr. Compos.
**2016**, 73, 267–280. [Google Scholar] [CrossRef] - Yoo, D.; Kim, S.; Park, J. Comparative Flexural Behavior of Ultra-High-Performance Concrete Reinforced with Hybrid Straight Steel Fibers. Constr. Build. Mater.
**2017**, 132, 219–229. [Google Scholar] [CrossRef] - Yoo, D.; Yoon, Y. Structural Performance of Ultra-High-Performance Concrete Beams with Different Steel Fibers. Eng. Struct.
**2015**, 102, 409–423. [Google Scholar] [CrossRef] - Hassan, A.M.T.; Jones, S.W.; Mahmud, G.H. Experimental Test Methods to Determine the Uniaxial Tensile and Compressive Behaviour of Ultra High Performance Fibre Reinforced Concrete (UHPFRC). Constr. Build. Mater.
**2012**, 37, 874–882. [Google Scholar] [CrossRef] - Xu, L.; Wu, F.; Chi, Y.; Cheng, P.; Zeng, Y.; Chen, Q. Effects of Coarse Aggregate and Steel Fibre Contents On Mechanical Properties of High Performance Concrete. Constr. Build. Mater.
**2019**, 206, 97–110. [Google Scholar] - Hannawi, K.; Bian, H.; Prince-Agbodjan, W.; Raghavan, B. Effect of Different Types of Fibers On the Microstructure and the Mechanical Behavior of Ultra-High Performance Fiber-Reinforced Concretes. Compos. Part B Eng.
**2016**, 86, 214–220. [Google Scholar] [CrossRef] [Green Version] - Wang, Q.; Shi, Q.; Lui, E.M.; Xu, Z. Axial Compressive Behavior of Reactive Powder Concrete-Filled Circular Steel Tube Stub Columns. J. Constr. Steel Res.
**2019**, 153, 42–54. [Google Scholar] [CrossRef] - Hoang, A.L.; Fehling, E.; Lai, B.; Thai, D.; Chau, N.V. Experimental study on structural performance of UHPC and UHPFRC columns confined with steel tube. Eng. Struct.
**2019**, 187, 457–477. [Google Scholar] [CrossRef] - Xiong, M.; Xiong, D.; Liew, J.Y.R. Behaviour of Steel Tubular Members Infilled with Ultra High Strength Concrete. J. Constr. Steel Res.
**2017**, 138, 168–183. [Google Scholar] [CrossRef] - Guler, S.; Çopur, A.; Aydogan, M. Axial capacity and ductility of circular UHPC-filled steel tube columns. Mag. Concr. Res.
**2013**, 65, 898–905. [Google Scholar] [CrossRef] - An, L.H.; Fehling, E. Analysis of Circular Steel Tube Confined UHPC Stub Columns. Steel Compos. Struct.
**2017**, 23, 669–682. [Google Scholar] - Huang, W.; Fan, Z.; Shen, P.; Lu, L.; Zhou, Z. Experimental and Numerical Study On the Compressive Behavior of Micro-Expansive Ultra-High-Performance Concrete-Filled Steel Tube Columns. Constr. Build. Mater.
**2020**, 254, 119150. [Google Scholar] [CrossRef] - Chen, S.; Zhang, R.; Jia, L.; Wang, J.; Gu, P. Structural Behavior of UHPC Filled Steel Tube Columns Under Axial Loading. Thin Wall. Struct.
**2018**, 130, 550–563. [Google Scholar] [CrossRef] - Yan, Y.; Xu, L.; Li, B.; Chi, Y.; Yu, M.; Zhou, K.; Song, Y. Axial Behavior of Ultra-High Performance Concrete (UHPC) Filled Stocky Steel Tubes with Square Sections. J. Constr. Steel Res.
**2019**, 158, 417–428. [Google Scholar] [CrossRef] - Xu, L.; Lu, Q.; Chi, Y.; Yang, Y.; Yu, M.; Yan, Y. Axial Compressive Performance of UHPC Filled Steel Tube Stub Columns Containing Steel-Polypropylene Hybrid Fiber. Constr. Build. Mater.
**2019**, 204, 754–767. [Google Scholar] [CrossRef] - Wei, J.; Xie, Z.; Zhang, W.; Luo, X.; Yang, Y.; Chen, B. Experimental Study On Circular Steel Tube-Confined Reinforced UHPC Columns Under Axial Loading. Eng. Struct.
**2021**, 230, 111599. [Google Scholar] [CrossRef] - Xiong, M.; Xiong, D.; Liew, J.Y.R. Flexural Performance of Concrete Filled Tubes with High Tensile Steel and Ultra-High Strength Concrete. J. Constr. Steel Res.
**2017**, 132, 191–202. [Google Scholar] [CrossRef] - EN 1994-1-1. Eurocode 4: Design of Composite Steel and Concrete Structures—Part 1-1: General Rules and Rules for Buildings; European Committee for Standardization: Brussels, Belgium, 2004. [Google Scholar]
- Guler, S.; Copur, A.; Aydogan, M. Flexural Behaviour of Square UHPC-filled Hollow Steel Section Beams. Struct. Eng. Mech.
**2012**, 43, 225–237. [Google Scholar] [CrossRef] - Li, J.; Deng, Z.; Sun, T. Flexural Behavior of Ultra-High Performance Concrete Filled High-Strength Steel Tube. Struct. Concr.
**2021**, 22, 1688–1707. [Google Scholar] [CrossRef] - Yang, I.; Joh, C.; Kim, B. Flexural Response Predictions for Ultra-High-Performance Fibre-Reinforced Concrete Beams. Mag. Concr. Res.
**2012**, 64, 113–127. [Google Scholar] [CrossRef] - Wu, Z.; Khayat, K.H.; Shi, C. How Do Fiber Shape and Matrix Composition Affect Fiber Pullout Behavior and Flexural Properties of UHPC? Cem. Concr. Comp.
**2018**, 90, 193–201. [Google Scholar] [CrossRef] [Green Version] - AISC/LRFD. Load and Resistance Factor Design Specification for Structural Steel Buildings; American Institute of Steel Construction: Chicago, IL, USA, 2005. [Google Scholar]
- AIJ. Recommendations for Design and Structures of Concrete Filled Steel Tubular Structures; Architectural Institute of Japan: Tokyo, Japan, 1997. [Google Scholar]
- AS 5100.6. Bridge Design—Part 6: Steel and Composite Construction; Australian Standards: Sydney, Australia, 2004. [Google Scholar]
- BS 5400-5. Steel, Concrete and Composite Bridges—Part 5: Code of Practice for Design of Composite Bridges; British Standards Institution: London, UK, 2005. [Google Scholar]
- GB 50936-2014. Technical Code for Concrete-Filled Steel Tubular Structures; Architecture & Buliding Press: Beijing, China, 2014. (In Chinese) [Google Scholar]
- GB/T228. 1–2010. Metallic Materials-Tensile Testing—Part1: Method of Test at Room Temperature; China Standard Press: Beijing, China, 2010. (In Chinese) [Google Scholar]
- Lu, Y.; Liu, Z.; Li, S.; Li, W. Behavior of steel fibers reinforced self-stressing and self-compacting concrete-filled steel tube subjected to bending. Constr. Build. Mater.
**2017**, 156, 639–651. [Google Scholar] [CrossRef] - Han, L. Flexural behaviour of concrete-filled steel tubes. J. Constr. Steel Res.
**2004**, 60, 313–337. [Google Scholar] [CrossRef] - Al-Shaar, A.A.M.; Göğüş, M.T. Flexural behavior of lightweight concrete and self-compacting concrete-filled steel tube beams. J. Constr. Steel Res.
**2018**, 149, 153–164. [Google Scholar] [CrossRef] - Li, G.; Liu, D.; Yang, Z.; Zhang, C. Flexural Behavior of High Strength Concrete Filled High Strength Square Steel Tube. J. Constr. Steel Res.
**2017**, 128, 732–744. [Google Scholar] [CrossRef] - Han, L.; Lu, H.; Yao, G.; Liao, F. Further Study On the Flexural Behaviour of Concrete-Filled Steel Tubes. J. Constr. Steel Res.
**2006**, 62, 554–565. [Google Scholar] [CrossRef] - Chen, Y.; Feng, R.; Wang, L. Flexural Behaviour of Concrete-Filled Stainless Steel SHS and RHS Tubes. Eng. Struct.
**2017**, 134, 159–171. [Google Scholar] [CrossRef] - Wu, F.; Xu, L.; Chi, Y.; Zeng, Y.; Deng, F.; Chen, Q. Compressive and flexural properties of ultra-high performance fiber-reinforced cementitious composite: The effect of coarse aggregate. Compos. Struct.
**2020**, 236, 111810. [Google Scholar] [CrossRef] - Zhang, T.; Gong, Y.; Ding, F.; Liu, X.; Yu, Z. Experimental and Numerical Investigation On the Flexural Behavior of Concrete-Filled Elliptical Steel Tube (CFET). J. Build. Eng.
**2021**, 41, 102412. [Google Scholar] [CrossRef]

**Figure 1.**Test setup and stress-strain curves of steel tensile coupons. (

**a**) Tensile coupon test setup; (

**b**) stress-strain curves of steel tensile coupons.

**Figure 3.**Experimental setup and locations of strain gauges. (

**a**) Experimental setup; (

**b**) schematic diagram (Unit: mm); (

**c**) strain gauge locations.

**Figure 5.**Typical overall lateral deflection curves. (

**a**) BC20S6; (

**b**) BC30S6; (

**c**) BC32S6; (

**d**) BC02S6; (

**e**) BC32S4.5; (

**f**) BC32S8.

**Figure 7.**Moment (M)-versus-curvature (ϕ) curves. (

**a**) The effect of steel tube wall thickness; (

**b**) the effect of CA-UHPC type.

**Figure 8.**Moment-versus-strain curves of specimens. (

**a**) BC32S4.5; (

**b**) BC32S6; (

**c**) BC32S8; (

**d**) BC32S10; (

**e**) BC30S6; (

**f**) BC02S6.

**Figure 9.**Typical longitudinal strain distribution along the sectional height of the specimen. (

**a**) BC32S6; (

**b**) BC32S10.

**Figure 10.**Ultimate flexural capacity of CA-UHPCFST beams. (

**a**) The effect of steel tube thickness; (

**b**) the effect of CA-UHPC type.

**Figure 11.**The flexural stiffness of CA-UHPCFSTs. (

**a**) The effect of steel tube thickness; (

**b**) the effect of CA-UHPC type.

**Figure 12.**The energy dissipation capacity of CA-UHPCFST members. (

**a**) The effect of steel tube thickness; (

**b**) the effect of CA-UHPC type.

**Figure 14.**Comparisons of flexural stiffness. (

**a**) Initial section flexural stiffness; (

**b**) serviceability-level section flexural stiffness.

Specimen | L (mm) | D (mm) | t (mm) | f_{y}(MPa) | A_{s}(mm ^{2}) | f_{ck}(MPa) | A_{c}(mm ^{2}) | ξ | M_{u}(kN∙m) | K_{e} (kN∙m^{2}) | |
---|---|---|---|---|---|---|---|---|---|---|---|

K_{i} | K_{s} | ||||||||||

BC20S6 | 1400 | 114 | 6 | 406 | 2035 | 101 | 8167 | 1.00 | 30.52 | 709 | 636 |

BC30S6 | 1400 | 114 | 6 | 406 | 2035 | 108 | 8167 | 0.94 | 30.66 | 749 | 671 |

BC32S6 | 1400 | 114 | 6 | 406 | 2035 | 124 | 8167 | 0.82 | 38.52 | 924 | 809 |

BC02S6 | 1400 | 114 | 6 | 406 | 2035 | 112 | 8167 | 0.90 | 33.68 | 819 | 728 |

BC32S4.5 | 1400 | 114 | 4.5 | 420 | 1547 | 124 | 8655 | 0.61 | 27.72 | 706 | 587 |

BC32S8 | 1400 | 114 | 8 | 400 | 2662 | 124 | 7539 | 1.14 | 43.66 | 940 | 879 |

BC32S10 | 1400 | 114 | 10 | 429 | 3285 | 124 | 6936 | 1.63 | 53.24 | 1154 | 1132 |

_{y}and A

_{s}denote the yield strength and sectional area of steel tube, and f

_{ck}and A

_{c}stand for the 28-day prismatic compressive strength and cross-sectional area of the CA-UHPC core. ξ represents the confinement index, $\xi ={f}_{\mathrm{y}}{A}_{\mathrm{s}}/{f}_{\mathrm{c}}{A}_{\mathrm{c}}$; greater values of ξ indicate a stronger confinement effect provided by the steel tube on the concrete core. M

_{u}refers to the ultimate flexural capacity, and K

_{i}and K

_{s}represent the initial and serviceability-level flexural stiffness, respectively.

Thickness (mm) | f_{y} (MPa) | f_{u} (MPa) | E_{s} (GPa) |
---|---|---|---|

4.5 | 420 | 603 | 205 |

6 | 406 | 589 | 206 |

8 | 400 | 592 | 206 |

10 | 429 | 587 | 205 |

Mix | Content (kg/m^{3}) | f_{cu}(MPa) | f_{ck}(MPa) | E_{c}(GPa) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Cement | Silica Fume | Fly Ash | Steel Fiber | PPF | Water | SP | Sand | Granite | ||||

C20 | 599.24 | 138.29 | 184.38 | 0.0 | 0.9 | 165.94 | 23.05 | 1014.10 | 430 | 113 | 101 | 39 |

C30 | 493.49 | 113.88 | 151.84 | 0.0 | 0.9 | 136.66 | 18.98 | 835.14 | 817 | 117 | 108 | 42 |

C32 | 449.22 | 103.67 | 138.22 | 157.0 | 0.9 | 124.40 | 17.28 | 760.22 | 817 | 139 | 124 | 48 |

C02 | 660.72 | 152.47 | 203.30 | 157.0 | 0.9 | 182.97 | 25.41 | 1118.13 | 0 | 126 | 112 | 41 |

_{cu}and f

_{ck}represent the cubic and prismatic compressive strength, respectively, E

_{c}represents the elastic modulus of the CA-UHPC infill.

Composition | Na_{2}O | MgO | Al_{2}O_{3} | SiO_{2} | SO_{3} | Fe_{2}O_{3} | P_{2}O_{5} | CaO | K_{2}O | MnO | ZnO | SrO |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Cement | 0.079 | 2.14 | 4.5 | 19.58 | 3.06 | 3.119 | 0.128 | 64.94 | 0.75 | 0.127 | 0.024 | 0.148 |

Silica fume | 0.068 | 0.224 | 0.354 | 92.87 | 1.26 | 0.113 | 0.11 | 0.213 | 0.332 | 0.008 | 0.019 | 0.005 |

Fly ash | 0.552 | 0.575 | 30.63 | 48.74 | 0.706 | 2.611 | 0.247 | 2.44 | 1.25 | 0.016 | 0.013 | 0.060 |

Specimen | M_{y} (kN∙m) | M_{u} (kN∙m) | δ_{y} (mm) | δ_{u} (mm) | E_{y} (kN∙m) | E_{u} (kN∙m) | M_{y}/M_{u} | μ = δ_{u}/δ_{y} | E_{u}/E_{y} |
---|---|---|---|---|---|---|---|---|---|

BC20S6 | 20.04 | 30.52 | 5.14 | 20.22 | 254.42 | 2313.45 | 0.66 | 3.93 | 9.09 |

BC30S6 | 20.8 | 30.66 | 5.63 | 20.43 | 277.05 | 2330.89 | 0.68 | 3.63 | 8.41 |

BC32S6 | 28.96 | 38.52 | 6.28 | 20.04 | 464.46 | 2845.67 | 0.75 | 3.19 | 6.13 |

BC02S6 | 22.63 | 33.68 | 5.92 | 21.16 | 325.15 | 2562.51 | 0.67 | 3.57 | 7.88 |

BC32S4.5 | 18.91 | 27.72 | 5.63 | 21.41 | 259.34 | 2264.70 | 0.68 | 3.80 | 8.73 |

BC32S8 | 32.72 | 43.66 | 8.34 | 23.78 | 640.45 | 3561.25 | 0.75 | 2.85 | 5.56 |

BC32S10 | 38.52 | 53.24 | 10.56 | 23.70 | 944.75 | 4072.25 | 0.72 | 2.24 | 4.31 |

Design Codes | Formula |

EC 4 (2005) [19] | ${K}_{\mathrm{e}}={E}_{\mathrm{s}}{I}_{\mathrm{s}}+0.6{E}_{\mathrm{c}}{I}_{\mathrm{c}}$ |

AISC/LRFD (1999) [24] | ${K}_{\mathrm{e}}={E}_{\mathrm{s}}{I}_{\mathrm{s}}+0.8{E}_{\mathrm{c}}{I}_{\mathrm{c}}$ |

AS 5100.6 (2004) [26] | ${K}_{\mathrm{e}}=0.9{E}_{\mathrm{s}}{I}_{\mathrm{s}}+0.9{E}_{\mathrm{c}}{I}_{\mathrm{c}}$ |

AIJ (1997) [25] | ${K}_{\mathrm{e}}={E}_{\mathrm{s}}{I}_{\mathrm{s}}+0.2{E}_{\mathrm{c}}{I}_{\mathrm{c}}$ |

BS 5400-5 (2005) [27], GB 50936 (2014) [28] | ${K}_{\mathrm{e}}={E}_{\mathrm{s}}{I}_{\mathrm{s}}+{E}_{\mathrm{c}}{I}_{\mathrm{c}}$ |

**Table 7.**Comparisons of the measured initial flexural stiffness with the predictions of the design guidelines.

Specimen Label | K_{i}(kN∙m ^{2}) | EC 4 | AIJ | AS 5100 | BS 5400 | AISC/LRFD | Equation (6) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

K_{ic} | K_{ic}/K_{i} | K_{ic} | K_{ic}/K_{i} | K_{ic} | K_{ic}/K_{i} | K_{ic} | K_{ic}/K_{i} | K_{ic} | K_{ic}/K_{i} | K_{ic} | K_{ic}/K_{i} | ||

BC20S6 | 707 | 730 | 1.03 | 652 | 0.92 | 728 | 1.03 | 809 | 1.14 | 769 | 1.09 | 789 | 1.12 |

BC30S6 | 749 | 732 | 0.98 | 653 | 0.87 | 730 | 0.98 | 811 | 1.08 | 772 | 1.03 | 792 | 1.06 |

BC23S6 | 924 | 760 | 0.82 | 662 | 0.72 | 772 | 0.84 | 858 | 0.93 | 809 | 0.87 | 833 | 0.90 |

BC02S6 | 819 | 707 | 0.86 | 644 | 0.79 | 693 | 0.85 | 770 | 0.94 | 739 | 0.90 | 754 | 0.92 |

BC23S4.5 | 706 | 643 | 0.91 | 533 | 0.76 | 678 | 0.96 | 753 | 1.07 | 698 | 0.99 | 726 | 1.03 |

BC23S8 | 940 | 900 | 0.96 | 816 | 0.87 | 885 | 0.94 | 983 | 1.05 | 942 | 1.00 | 963 | 1.02 |

BC23S10 | 1116 | 1024 | 0.92 | 953 | 0.85 | 985 | 0.88 | 1094 | 0.98 | 1059 | 0.95 | 1077 | 0.97 |

Mean value | 0.926 | 0.825 | 0.925 | 1.027 | 0.977 | 1.002 | |||||||

COV | 0.077 | 0.090 | 0.078 | 0.078 | 0.076 | 0.077 |

**Table 8.**Comparisons of the measured serviceability-level flexural stiffness with the predictions of design guidelines.

Specimen Label | K_{s}(kN∙m ^{2}) | EC 4 | AIJ | AS 5100 | BS 5400 | AISC/LRFD | Equation (7) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

K_{sc} | K_{sc}/K_{s} | K_{sc} | K_{sc}/K_{s} | K_{sc} | K_{sc}/K_{s} | K_{sc} | K_{sc}/K_{s} | K_{sc} | K_{sc}/K_{s} | K_{sc} | K_{sc}/K_{s} | ||

BC20S6 | 636 | 730 | 1.15 | 652 | 1.02 | 728 | 1.14 | 809 | 1.27 | 769 | 1.21 | 711 | 1.12 |

BC30S6 | 671 | 732 | 1.09 | 653 | 0.97 | 730 | 1.09 | 811 | 1.21 | 772 | 1.15 | 712 | 1.06 |

BC23S6 | 809 | 760 | 0.94 | 662 | 0.82 | 772 | 0.95 | 858 | 1.06 | 809 | 1.00 | 735 | 0.91 |

BC02S6 | 728 | 707 | 0.97 | 644 | 0.89 | 693 | 0.95 | 770 | 1.06 | 739 | 1.02 | 692 | 0.95 |

BC23S4.5 | 587 | 643 | 1.10 | 533 | 0.91 | 678 | 1.15 | 753 | 1.28 | 698 | 1.19 | 616 | 1.05 |

BC23S8 | 879 | 900 | 1.02 | 816 | 0.93 | 885 | 1.01 | 983 | 1.12 | 942 | 1.07 | 879 | 1.00 |

BC23S10 | 1132 | 1024 | 0.90 | 953 | 0.84 | 985 | 0.87 | 1094 | 0.97 | 1059 | 0.94 | 1006 | 0.89 |

Mean value | 1.025 | 0.912 | 1.024 | 1.138 | 1.082 | 0.997 | |||||||

COV | 0.088 | 0.079 | 0.105 | 0.105 | 0.096 | 0.085 |

Codes | Formulation |

EC4 [19] | ${M}_{\mathrm{u}}={f}_{\mathrm{y}}[{A}_{\mathrm{s}}(D-2t-{d}_{\mathrm{c}})/2+Dt(t+{d}_{\mathrm{c}})]$$,{d}_{\mathrm{c}}=\left({A}_{\mathrm{s}}-2dt\right)/[(d-2t)\rho +4t]$$,d=0.6{f}_{\mathrm{ck}}/{f}_{\mathrm{y}}$ |

AIJ [25] | ${M}_{\mathrm{u}}=Z{f}_{\mathrm{y}}$$,Z=({D}^{3}-{(D-2t)}^{3})/6$ |

BS 5400-5 [27] | ${M}_{\mathrm{u}}=0.91S{f}_{\mathrm{y}}(1+0.01m)$$,S={t}^{3}{({D}_{\mathrm{e}}/t-1)}^{2}$ |

GB 50936 [28] | ${M}_{\mathrm{u}}={\gamma}_{\mathrm{m}}{W}_{\mathrm{sc}}{f}_{\mathrm{sc}}$$,{f}_{\mathrm{sc}}=\left(1.212+B\theta +C{\theta}^{2}\right){f}_{\mathrm{c}}$$,{W}_{\mathrm{sc}}=\pi \left({r}_{0}^{4}-{r}_{\mathrm{ci}}^{4}\right)/4{r}_{0}$$,\theta ={A}_{\mathrm{s}}{f}_{\mathrm{y}}/{A}_{\mathrm{c}}{f}_{c}$ |

Han [34] | ${M}_{\mathrm{u}}={\gamma}_{\mathrm{m}}\cdot {W}_{\mathrm{scm}}\cdot {f}_{\mathrm{scy}}$$,{f}_{\mathrm{scy}}=\left(1.14+1.02\xi \right)\cdot {f}_{\mathrm{ck}}$$,{\gamma}_{\mathrm{m}}=1.1+0.48\cdot \mathrm{ln}(\xi +0.1)$$,\xi ={A}_{\mathrm{s}}{f}_{\mathrm{y}}/{A}_{\mathrm{c}}{f}_{c}$ |

Specimen Label | M_{u}(kN∙m) | EC 4 | AIJ | BS 5400-5 | GB 50936 | Han | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

M_{uc} | M_{uc}/M_{u} | M_{uc} | M_{uc}/M_{u} | M_{uc} | M_{uc}/M_{u} | M_{uc} | M_{uc}/M_{u} | M_{uc} | M_{uc}/M_{u} | ||

BC20S6 | 30.5 | 41.5 | 1.36 | 29.5 | 0.97 | 29.5 | 0.97 | 38.6 | 1.27 | 36.4 | 1.19 |

BC30S6 | 30.6 | 41.5 | 1.35 | 29.5 | 0.96 | 29.7 | 0.97 | 39.1 | 1.28 | 36.6 | 1.19 |

BC32S6 | 38.5 | 41.7 | 1.08 | 29.5 | 0.77 | 30.1 | 0.78 | 41.3 | 1.07 | 37.6 | 0.98 |

BC02S6 | 33.7 | 41.6 | 1.23 | 29.5 | 0.88 | 29.9 | 0.89 | 39.9 | 1.19 | 36.9 | 1.10 |

BC32S4.5 | 27.7 | 33.5 | 1.21 | 23.2 | 0.84 | 23.9 | 0.86 | 36.8 | 1.33 | 29.6 | 1.07 |

BC32S8 | 43.6 | 52.3 | 1.20 | 38.1 | 0.87 | 38.2 | 0.87 | 42.7 | 0.98 | 49.9 | 1.14 |

BC32S10 | 53.2 | 67.1 | 1.26 | 50.1 | 0.94 | 48.9 | 0.92 | 32.6 | 0.61 | 68.8 | 1.29 |

Mean value | 1.242 | 0.890 | 0.895 | 1.103 | 1.137 | ||||||

COV | 0.077 | 0.083 | 0.073 | 0.226 | 0.090 |

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**MDPI and ACS Style**

Wu, F.; Zeng, Y.; Li, B.; Lyu, X.
Experimental Investigation of Flexural Behavior of Ultra-High-Performance Concrete with Coarse Aggregate-Filled Steel Tubes. *Materials* **2021**, *14*, 6354.
https://doi.org/10.3390/ma14216354

**AMA Style**

Wu F, Zeng Y, Li B, Lyu X.
Experimental Investigation of Flexural Behavior of Ultra-High-Performance Concrete with Coarse Aggregate-Filled Steel Tubes. *Materials*. 2021; 14(21):6354.
https://doi.org/10.3390/ma14216354

**Chicago/Turabian Style**

Wu, Fanghong, Yanqin Zeng, Ben Li, and Xuetao Lyu.
2021. "Experimental Investigation of Flexural Behavior of Ultra-High-Performance Concrete with Coarse Aggregate-Filled Steel Tubes" *Materials* 14, no. 21: 6354.
https://doi.org/10.3390/ma14216354