Flexural Performance of Steel–GFRP Strips–UHPC Composite Beam in Negative Moment Region

Abstract

This study aims to clarify the longitudinal flexural cracking characteristics in hogging moment regions and propose a practical calculation method for the cracking load and ultimate bearing capacity for a steel–GFRP strips–UHPC composite deck structure. The longitudinal flexural behavior of two steel–GFRP strips–UHPC composite beams in the hogging moment region is determined through a three-point loading test method. Their failure modes and mechanisms, crack propagation and distribution characteristics are analyzed considering the influence of the reinforcement ratio. The variation of the law of mid-span displacement, maximum crack width, strains and interface slip with load are discussed. Calculation methods for the cracking load and ultimate bearing capacity of steel–GFRP strips–UHPC composite beams are proposed. The results show that with the increase of the reinforcement ratio, the cracking load and ultimate bending capacity are improved by 11.1% and 6.0%, respectively. However, the development of cracks is inhibited, as the crack width, average crack spacing and strain of the reinforcement bars are reduced as the reinforcement ratio increases. The maximum crack width changes linearly with the load as it is less than 0.2 mm. The theoretical cracking load and ultimate bearing capacity of the composite beams considering the tensile contribution of UHPC achieve good agreement with the experimental values.

1. Introduction

Glass-fiber-reinforced polymer (GFRP) is a high-performance material with high specific strength, corrosion resistance, and fatigue resistance. Therefore, it is a good option for replacing steel and has been applied widely in bridges, ocean engineering, disaster prevention and mitigation engineering [1,2]. However, due to the low elastic modulus and high project cost of FRP, it is mainly introduced to reinforce old bridges and partly replace tensile members. Recently, lots of research has been conducted on GFRP–concrete composite structures, including the effect of interface connection methods on the mechanical properties of composite structures [3,4,5,6], structural combination forms and the static and fatigue performance. Research results show that the shear strength of the interface can be improved effectively by the treatment of applying epoxy resin adhesive and laying crushed stone, and the GFRP–concrete composite structure can effectively reduce the self-weight and welding workload, and it has good durability and fatigue performance [7,8].

Ultra-high-performance concrete (UHPC) is the most innovative cement-based material with ultra-high compressive strength, ultra-long durability, ultra-high toughness and good crack resistance [9,10,11]. Currently, UHPC has been widely used in the deck system of long-span bridge structures [12]. However, due to the differences in mechanical properties and composition between UHPC and ordinary concrete, the existing research on the GFRP–UHPC composite structure is limited, and the prediction formula for the crack width of UHPC cannot accurately reflect the actual engineering stress situation. Al-Ramahee [13] proposed a novel lightweight and lower profile UHPC–FRP composite deck for accelerated bridge construction. The use of UHPC instead of concrete can significantly enhance the cracking strength, maximum stiffness and ductility of an FRP–concrete composite beam in the hogging moment [14].

Researchers have carried out related research on the cracking characteristics and crack width calculation methods of UHPC composite structures, such as Kwahk et al. [15] and Deng et al. [16], who conducted research on the crack resistance of UHPC beams, and the results show that the existing codes are too conservative in the design of the crack load. Luo et al. [17] investigated the crack resistance of steel–UHPC composite beams in negative moment regions. The results show that increasing the reinforcement ratio and the thickness of the UHPC layer, and reducing the spacing of the shear connectors, could inhibit and delay the development of cracks in the UHPC layer. The bending stiffness of a UHPC–OSD composite deck was increased and the tensile strain of the UHPC layer was decreased with the increase of the reinforcement ratio [18]. Tan et al. [19] studied the transverse hogging moment of a steel–UHPC composite deck considering the influence of steel reinforcement and the shear connector wet joint. The results showed that the nominal crack strength and ultimate capacity were improved with the increase in the diameter of the steel reinforcement. Subsequently, Rahdar et al. [20], Xu et al. [21] and Jin et al. [22] analyzed the effects of reinforcement types and reinforcement ratios on the cracking strength and crack width of the UHPC beams. Choi et al. [23] conducted research on the flexural behavior of inverted T-shaped steel–UHPC composite beams. The results show that the cracking strength of the composite beam was improved with the reducing space of the shear members and the increasing of the thickness of the UHPC layer. Wang et al. [24] designed a fully prefabricated UHPC composite beam. The research results show that fully dry connection joints could effectively improve the crack resistance and stiffness of the composite beams. Wang et al. [25] put forward a steel strips–UHPC composite bridge deck structure, and the fatigue life assessment method for this composite structure was proposed. Qiu et al. [26] developed a simplified formula for calculating reinforcement stress considering the tensile contribution of UHPC. Therefore, the cracking issue of composite beams under the hogging moment has been one of the main concerns for researchers, especially the factors affecting the cracking properties of UHPC composite beams. However, the theoretical calculation methods, considering the tension contribution of UHPC, for predicting the crack load of UHPC composite beams require further research.

In order to realize the efficient utilization and combination of materials, solve the welding fatigue cracking of existing composite bridges, and effectively improve the crack resistance of composite bridge deck in hogging moment regions, two new materials, GFRP and UHPC, were used in the design of composite bridges, and a steel–GFRP strips–UHPC lightweight composite beam bridge was proposed, as shown in Figure 1. The GFRP strips used in this structure were placed on the tension side to enhance the cracking strength in the positive moment regions, and the UHPC was applied to the compression side. It was an innovative bridge deck structure connected by high-strength arc-shaped shear connectors and special interface reinforcement treatment. The latest literature was reviewed and a comparative analysis conducted. References [27,28] focused on the prediction methods for the mechanical properties of advanced structural materials, which lay the foundation for the subsequent research on structural performance. Compared with the steel–UHPC composite structure, the steel–GFRP strips–UHPC composite structure enhances its anti-corrosion performance, further reduces its self-weight, and decreases the welding fatigue stress and residual stress [29], etc. Compared with the UHPC–GFRP structure [30] and GFRP–concrete structures, this structure can improve its stiffness, ductility and shear resistance. This bridge deck structure has the characteristics of a light weight, good durability and crack resistance. Therefore, the steel–GFRP strips–UHPC composite deck structure can better meet the major needs of bridge engineering, such as a light weight, high strength, and good durability.

This study investigates the longitudinal flexural cracking characteristics of the steel–GFRP strips-–UHPC lightweight composite beam, and the effects of the reinforcement ratio on the failure mode, mid-span displacement, interface slip, strain, maximum crack width and crack distribution of the composite beam are analyzed. The characteristics and distribution of crack propagation are thoroughly investigated. Calculation methods are proposed for predicting the cracking load of UHPC composite beams at the Serviceability Limit State [31] and their ultimate bearing capacity.

2. Experimental Program

2.1. Specimen Design

Considering the influence of the reinforcement ratio on the flexural response of steel–GFRP strips–UHPC under the negative moment, two composite beam specimens were designed. As shown in Figure 1, the reinforcement ratios of specimens L-1 and L-2 were set at 3.91% and 5.03%, respectively, based on Eurocode 4 [32]. The number of longitudinal reinforcements in specimen L-1 was 7, while that in specimen L-2 was 9. The composite beams had a total length of 2000 mm and a height of 280 mm. The width and height of the UHPC flange plate were 500 mm and 55 mm, respectively. The width and height of the I-steel beam were 130 mm and 225, respectively, and the thicknesses of its lower flange, web and upper flange were 12 mm, 8 mm and 10 mm, respectively. In order to withstand the transverse load composite structure, the GFRP strips with a thickness of 10 mm and a width of 130 mm were arranged on the upper flange surface of the steel beam at 290 mm intervals, and they were connected with the upper flange of the steel beam via transverse bolted connectors.

The shear connectors were fabricated from HRB400 reinforcement bars with a diameter of 14 mm. The inner diameter of the arc-shaped shear connectors was 31 mm. The two longitudinal arc-shaped shear connectors were welded on the upper flange of the steel beam at 290 mm intervals. Transverse arc-shaped shear connectors were bolted to connect the GFRP strip and the upper flange of the I-steel beam. The placement details of the shear connectors are shown in Figure 2 and

Table 1. Design parameters of the specimens.

Specimen	Interface Processing		Longitudinal Reinforcement Ratio	Steel Fiber Content of UHPC Layer
	UHPC and I-Steel Beam	GFRP and UHPC
L-1	Unbonded interface	Gravel and adhesive bond interface	3.9%	1.5%
L-2		Gravel and adhesive bond interface	5.0%

. The diameters of the longitudinal and transverse reinforcement were 14 mm and 10 mm, respectively, and the specific layout is shown in Figure 2c,d. The transverse reinforcement bars had a diameter of 10 mm and were spaced at 150 mm intervals. The thickness of the protective layer for the longitudinal reinforcement was 22 mm.

2.2. Materials

The UHPC layer designed for the purpose of this study consisted of Portland cement, silica fume, fly ash, quartz sand, quartz powder, mineral powder, super plasticizer, steel fibers and water. The type of steel fiber was straight steel fiber with a length of 13 mm and a diameter of 0.2 mm, and the steel fiber content of the UHPC was 1.5%. The water–cement ratio of the UHPC was fixed at 0.18 [33].

Table 2. Mix proportions of the UHPC.

Ingredient	Amount (kg/m3)
Portland cement (52.5 R)	773.2
Silica fume (2–280 mm)	215.3
Quartz sand (450–900 μm)	848.4
Fly ash	78.2
Steel fibers (1.5% Vol.)	118.5
Mineral powder (S95)	78.2
Quartz powder (50.2 μm)	77.3
Super plasticize (1.5% Vol)	20.1
Water	192

shows the mix proportions of the UHPC. When the UHPC layer was cast, three UHPC cubes (100 mm × 100 mm × 100 mm), three prisms (100 mm × 100 mm × 400 mm) and six prisms (100 mm × 100 mm × 300 mm) were made and cured under the same conditions as the composite beam specimens to test the compressive strength, flexural strength and elastic modulus of the UHPC material, respectively. The weight of the GFRP strips was 19 kN/m³. The tensile strength of the steel fiber was 2850 MPa, and the elasticity modulus was 200 GPa. The mechanical parameters of the materials obtained experimentally are shown in

Table 3. Main material properties.

Material		Elasticity Modulus (GPa)	S	Compressive Strength (MPa)	S	Flexural Strength (MPa)	S	Tensile Strength (MPa)	S	Yield Strength (MPa)
UHPC (steel fiber content 1.5%)		44.1	3.4	123.4	12.3	29.8	4.8	8.2	5.3	-
Q345C steel plate		206.0	-	-	-	-	-	-	-	385.0
HRB400 ribbed bar		206.0						540.0		400.0
HRB400 plain bar		206.0	-	-	-	-	-	540.0	-	400.0
GFRP	Fiber direction	32.6	-	270.0	-	-	-	415.0	-	-
	Perpendicular fiber direction	11.2	-	80.9	-	-	-	113.5	-	-

Note: S is the standard deviation.

.

2.3. Specimen Fabrication

Figure 3 illustrates the fabrication sequence for the steel–GFRP strips–UHPC composite beam. The process commenced with prefabrication of I-section steel beams and arc-shaped shear connectors based on the design specifications in Figure 2. Subsequently, longitudinal arc-shaped shear connectors were double-sided welded at uniform intervals onto the upper flange plate surface of the I-section steel beam. Following this, GFRP strips were connected equally spaced with the upper flange plate of the I-section steel beam via the transverse arc-shaped reinforcement shear connector. Specifically, each connector was welded with top-mounted gaskets on the upper surface of the GFRP strips and bolted to the lower surface, as detailed in Figure 3a.

Prior to UHPC casting, the GFRP strip surface was coated with a high-temperature-resistant epoxy resin (effective range: 150–200 °C). A particle size of 4.75–9.5 mm gravel was then uniformly distributed over the resin-coated surface, achieving 50% area coverage through mass-to-area proportional control (Figure 3a).

In the formwork assembly phase, the steel reinforcement meshes comprising 14 mm longitudinal bars and 10 mm transverse bars were positioned within templates made according to the specimen design (Figure 3b). The UHPC, mixed at a designated proportion, was subsequently cast into the formwork to encapsulate the steel meshes (Figure 3c).

For the curing protocol, the cast specimens were first covered with plastic film and cured at room temperature for 24 h, followed by a 48 h steam curing at 90–100 °C under 95% relative humidity (Figure 3d).

Figure 3. Construction procedures: (a) installation of shear connector and GFRP strip; (b) installation of reinforcement and template; (c) casting UHPC; and (d) curing.

Figure 3. Construction procedures: (a) installation of shear connector and GFRP strip; (b) installation of reinforcement and template; (c) casting UHPC; and (d) curing.

2.4. Layout of Measuring Point and Loading Scheme

Figure 4 shows the layout of the measuring point for the composite beams. The strain gauges were arranged at equal intervals along the height of the I-steel beam to measure the strain of the I-steel beam, and they were mounted on the surface and side of the UHPC flange plate, and on the surface of the longitudinal reinforcement to measure the strain of the UHPC and reinforcement. The width of the crack on the UHPC flange plate was measured by a crack observation instrument. Dial gauges were mounted to measure the interfacial slip between the UHPC flange plate and the I-steel beam, and the deflection of the composite beam at the mid-span supports.

A three-point bending loading method was adopted for the composite beams, and a 100 T jack was utilized for loading equipment [26], as indicated in Figure 5. The test loading process was divided into the pre-loading stage and the formal stage. At the pre-loading stage, 5% of the estimated ultimate load was pre-loaded five times to eliminate the gap between the components and ensure the proper function of the jack, dial gauges, and strain gauges. During formal loading, the force-based control was used to apply the static load with a 20 kN load increment. When the load reached about 70% of the ultimate load, it was changed to displacement control with 1 mm per step. Each step lasted for 5–10 min. When each step of the load was stable, the deflection at the mid-span and the end of the beam, the interface slip value of the beam end, the strain value, the crack width and length, and the crack distribution were recorded.

Figure 4. Loading schematic and layout of the measuring points.

Figure 4. Loading schematic and layout of the measuring points.

Figure 5. Loading setup.

Figure 5. Loading setup.

3. Results and Discussion

The test results are presented in Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 and Table 4. The failure mode and mechanism, load–deflection response, load–interface slip response, strain distribution characteristic and crack propagation characteristics are addressed.

3.1. Failure Mode and Mechanism

The failure modes of the specimens are shown in Figure 4. During the initial loading process, the load was small and the I-steel beam worked cooperatively with the UHPC slab and GFRP plate. The GFRP plate was not detached from the UHPC slab. There were no cracks on the surface of the UHPC slab, because the surface stress of the UHPC slab did not reach its tensile strength. With the increase in the load, the UHPC slab remained working well together with the I-steel beam and GFRP plate. When the stress of the UHPC slab reached its tensile strength value, several visible short and tiny cracks appeared on the upper surface of the UHPC slab, and the cracks were mainly distributed near the mid-span position of the composite beam. During this stage, the cracks were tiny but numerous because of the bridging action of the steel fibers. As the load increased to 85% of the ultimate value, the number of cracks on the upper surface of the UHPC slab gradually increased, and its width gradually increased linearly, and the cracks extended in the depth direction of the UHPC slab. The interface relative slip between the UHPC slab and the I-steel beam gradually became larger. When the load reached 85% of the ultimate value, the I-section steel beam started to yield at the lower flange of the I-steel beam. Two significant main cracks had formed. As the load continued to increase, the I-steel beam showed signs of yielding, and the maximum width of the crack and the interface relative slip increased dramatically. When the load achieved the ultimate value, the composite beam failed. There were two main cracks, and other small and short cracks on the surface of the UHPC slab. The cracks were mainly distributed in the range of 300 mm on both sides of the middle span of the composite beam. The maximum main crack width for specimen L-1 and L-2 was 2.3 mm and 1.24 mm, respectively. The steel fibers inside the main crack were pulled out. Obvious yielding deformation at the lower flange of the I-section steel beam occurred. The arc-shaped reinforcement shear connector remained intact without shearing off.

Table 4 summarizes the main test results of the composite beams. It can be seen from Table 3 that the ultimate bearing capacity of the specimens increased by 5.95% when the reinforcement ratio was increased from 3.91% to 5.03%. Therefore, increasing the longitudinal reinforcement ratio of the UHPC slab could improve the ultimate bending capacity of composite beams.

Table 4. The main test results of the composite beam.

Specimen	Put (kN)	ωut (mm)	μ (mm)	Failure Characteristics
L-1	487	36.84	2.30	Two main cracks on the UHPC layer, and yielding deformation at the lower flange of the I-section steel beam
L-2	516	35.54	1.24

Note: P_ut is the maximum measured load, ω_ut is the mid-span deflection corresponding to the ultimate load, and μ is the maximum crack width corresponding to the maximum load.

Table 4. The main test results of the composite beam.

Specimen	Put (kN)	ωut (mm)	μ (mm)	Failure Characteristics
L-1	487	36.84	2.30	Two main cracks on the UHPC layer, and yielding deformation at the lower flange of the I-section steel beam
L-2	516	35.54	1.24

Note: P_ut is the maximum measured load, ω_ut is the mid-span deflection corresponding to the ultimate load, and μ is the maximum crack width corresponding to the maximum load.

Figure 6. Failure mode of composite beams.

Figure 6. Failure mode of composite beams.

3.2. Load–Deflection Response

Figure 7 indicates the mid-span load–deflection curve of the composite beams in the hogging moment regions. They are divided into three stages: elastic stage, crack development stage and yield stage. In the elastic stage, the load–deflection curves showed a linear trend, and no visible cracks were detected on the surface of the specimens. With the increase in the load, visible cracks (crack width about 0.05 mm) initiated and developed on the upper surface of the UHPC layer, and the composite beam entered the crack development stage. At this stage, fine cracks initiated and developed on the upper surface of the UHPC, while the stiffness of the composite beam gradually decreased, indicated by the change in slope of the load–deflection curve. At the end of this stage, the I-section steel beam yielded. Once the load reached about 85% of its ultimate value, the composite beam entered the yield stage. During this stage, due to the steel beam having yielded, the crack width on the upper surface of the UHPC layer increased rapidly. When the specimens were destroyed, there was obvious buckling deformation at the lower flange of the middle span of the I-section steel beam, the stress of the longitudinal reinforcement bar had reached its yield strength, and the mid-span deflection of L-1 and L-2 specimens were 36.84 mm and 35.54 mm, respectively, as shown in Figure 7. Therefore, the composite beam lost its bearing capacity due to the successive yielding of the steel beams and longitudinal reinforcement bars; meanwhile, the UHPC layer reached its ultimate tensile stress value.

Figure 7. Load–deflection curve of composite beam.

Figure 7. Load–deflection curve of composite beam.

3.3. Strain Characteristic Analysis

3.3.1. Load–Strain Response

Figure 8a depicts the load–strain curves at the lower flange of an I-section steel beam. It can be seen from Figure 8a that the load–strain curve of the lower flange of the I-section steel beam presents two obvious stages: elastic stage and yield stage. When the load was small, the strain changed linearly with the increase in the load. When the load reached 80–85% of the maximum load, the strain at the lower flange of the I-section steel beam increased sharply, and the I-section steel beam yielded. Meanwhile, the slope of the load–strain curves decreased.

The average value of the measured strain of each longitudinal reinforcement bar was obtained. The load–strain curve of the reinforcement bar is shown in Figure 8b. It can be seen from Figure 8b that the curve of the load–reinforcement bar strain presents three stages: elastic stage, crack development stage and yield stage. When the load was relatively small, the curve changed linearly, there were no cracks on the surface of the UHPC layer, and the reinforcement bars and UHPC layer worked together. As the load reached about 20% of the ultimate load, due to the UHPC layer reaching its tensile strength and cracking, the load borne by the reinforcement bar improved and the strain of the reinforcement bar increased quickly, while the slope of the load–strain curve decreased. When the load reached about 85% of the ultimate load, the I-section steel beam yielded, the strain of the reinforcement bars increased sharply, the load–strain curve of the reinforcement bars changed nonlinearly, and the slope decreased. Comparing the load–strain curves of the two specimens, it was found that the strain of the reinforcement bar for L-2, with a high reinforcement ratio, was slightly less than that of L-1; therefore, increasing the reinforcement ratio could reduce the strain of the reinforcement bar.

Figure 8. Load–strain curve.

Figure 8. Load–strain curve.

3.3.2. Strain Distribution Along the Height of the Mid-Span Section

Figure 9 depicts the strain distribution along the height of the mid-span section under different loads. It can be seen from Figure 8 that the strain distribution along the height of the mid-span section changed linearly during the initial loading process. As the load continued to increase, the upper surface stress of the UHPC layer reached its cracking strength value first and entered the strain hardening state. The strain distribution along the height of the mid-span section changed nonlinearly gradually, and the neutral axis moved down along the height of the composite beam. Based on the experimental analysis results in Figure 9, when the load was less than 80% of the ultimate load, the strain distribution along the height of the mid-span section basically conformed to the plane-section assumption. With the continued increase in the load due to the upper surface crack width exceeding the maximum value of the strain gauge, it was unable to measure the strain value corresponding to the ultimate load. When the I-section steel beam yielded, there were obvious interface slips between the I-section beam and the UHPC layer, and due to the redistribution of the cross-section stress, the UHPC layer and the I-section steel beam presented obvious bending deformation around their own neutral axes, respectively, and the distribution of the cross-section strain was no longer continuous. However, the cross-section strain along the height of the composite beam still approximately satisfied the plane cross-section assumption under low load levels.

Figure 9. Strain distribution along the height of the mid-span section: (a) L-1; and (b) L-2.

Figure 9. Strain distribution along the height of the mid-span section: (a) L-1; and (b) L-2.

3.4. Load–Interface Slip Response

The interface slip between the I-section steel beam and the UHPC layer was measured, and Figure 10 demonstrates the load–interface slip curves of the specimens. It can be seen from Figure 10 that the change trends of the load–interface slip curves were basically similar. When the load was less than 100 kN, the interface slip value was very small, and the horizontal shear load at the interface was mainly borne by the friction force and mechanical bite force between the UHPC layer and the I-section steel beam. As the load continued to increase, the UHPC layer of the composite beam cracked, the curves increased almost linearly, while the slope of the curve decreased. During this stage, the interface friction and mechanical bite force gradually quit the working state, and the horizontal shear load was mainly borne by the shear members. When the load approached the ultimate value, due to the interfacial arc-shaped shear connector having yielded, the interface slip value increased rapidly. Meanwhile, from the load–interface slip curve of the two specimens in Figure 10, it can be seen that under the same load, the interface slip value of L-1 was less than L-2. Thus, the longitudinal tensile reinforcement bar could effectively restrain the development of cracks. Under the same load, due to the specimen with a high reinforcement ratio having better deformation resistance, the interface relative slip value was large.

Figure 10. Load–interface slip curve.

Figure 10. Load–interface slip curve.

3.5. Crack Propagation Characteristics

The maximum crack widths on the upper surface of the UHPC layer for the composite beams were measured, and the load–maximum crack width curves of specimens L-1 and L-2 were obtained, as shown in Figure 11. It can be seen from Figure 11 that the load–maximum crack width curve is distributed in two stages: crack propagation stage and yield stage. When the maximum crack width was less than 0.2 mm, the maximum crack width changed linearly with the increase in load. With the increase in load, the steel tended to yield and the load increasing rate was slowed down, while the crack width increased rapidly. Comparing the crack propagation trends of specimens L-1 and L-2 in Figure 12, it can be seen that the curve slope of L-2 was greater than that of L-1. Meanwhile, the maximum crack width of specimen L-1 was greater than that of specimen L-2 with the same load. When the reinforcement ratio of the composite beams increased from 3.91% to 5.03%, the load values corresponding to the characteristic crack width were improved by 16.7%, 11.1%, 15.4%, 13.6% and 6.0%, respectively, as shown in Figure 12. Therefore, increasing the reinforcement ratio could effectively inhibit the propagation of cracks and reduce the maximum crack width.

Figure 11. Load–maximum crack width curve.

Figure 11. Load–maximum crack width curve.

Figure 12. Loads at characteristic crack widths.

Figure 12. Loads at characteristic crack widths.

Based on the regulation of the crack width design in the ultra-high-performance fiber-reinforced concretes of French [25,26,29,31,32,33,34], the crack distribution on the surface of the UHPC layer with main crack widths of 0.02 mm, 0.05 mm, 0.1 mm, 0.2 mm and failure was, respectively, measured, as shown in Figure 13. It can be seen from Figure 13 that with the increase in load, the number of cracks gradually rose and the cracks propagated from the mid-span to both ends of the specimen. When the maximum crack width increased to 0.2 mm, the number of cracks gradually tended to stabilize and the specimen lost its bearing capacity subsequently. The cracks were mainly distributed in the range of 300 mm at the mid-span, and there were two main cracks. This phenomenon was mainly due to the uneven distribution of the internal force and reinforcement stress for the composite beams and the layout position of the shear connectors. With the action of the concentrated load, the bending moment decreased gradually from the mid-span to both ends of the specimen, the stress distribution of reinforcement bars was uneven, and the stress concentration occurred at the layout position of the shear connectors.

Figure 13. Crack distribution of composite beams: (a) crack width 0.02 mm; (b) crack width 0.05 mm; (c) crack width 0.1 mm; (d) crack width 0.2 mm; and (e) final distribution of cracks.

Figure 13. Crack distribution of composite beams: (a) crack width 0.02 mm; (b) crack width 0.05 mm; (c) crack width 0.1 mm; (d) crack width 0.2 mm; and (e) final distribution of cracks.

4. Flexural Calculation of Steel–GFRP Strips–UHPC Composite Beam

Based on the experimental results, the UHPC layer exhibited post-cracking strength and the steel fiber took on the bridge role after cracking; thus, the stress of the reinforcement bar was reduced to a certain extent, the development of cracks was inhibited and the cracking load value was increased. Therefore, the tensile contribution of UHPC and the bridging role of steel fiber could not be ignored in the calculation of the cracking load and ultimate bearing capacity of steel–GFRP strips–UHPC composite beams. Based on the existing experimental results, the tensile constitutive model of UHPC materials could be assumed to be a bilinear elastic–plastic constitutive model.

4.1. Load Corresponding to 0.05 mm Crack Width

Since UHPC has a high elastic modulus and tensile strength, and as steel fiber can restrain the propagation of cracks, when the crack width on the surface of the UHPC layer was smaller than 0.05 mm, according to Rafiee et al. [35] and Yoo et al. [36], the effect of the crack width on the tensile behavior and durability of UHPC could be ignored. Therefore, the visible crack width of 0.05 mm was often regarded as a crack control index affecting the long-term services of the UHPC layer. Based on the test results, when the crack width of the UHPC layer improved to 0.05 mm, deformation of the composite beam still varied linearly with the load due to the strain hardening characteristics of UHPC, and the cross-section strain distribution along the height of composite beams changed linearly on the whole. Therefore, it can be assumed that the cross-section strain distribution of the composite beams satisfied the plane cross-section assumption.

Figure 14 demonstrates a calculation model of the cracking load Fcr. Based on the calculation formula for the cracking strain in NFP18-710 [27] and the measured strain data on the surface of the UHPC layer in this study, when the crack width improved to 0.05 mm, the tensile strain on the top surface of the UHPC layer could be calculated as shown in Formula (1):

$${\epsilon }_{0.05}={\displaystyle \frac{f_{ut}}{E_c}}+{\displaystyle \frac{\Delta \omega }{l_0}}$$

(1)

where f_ut is the tensile strength of UHPC; Δω is the increment of the crack width from first visible crack to 0.05 mm crack width; and l₀ is the characteristic length related to the size of the specimen, which is considered as ${\displaystyle \frac{2}{3}}$ of the beam height.

Note: Although the UHPC layer and the I-section steel beam had small interface slip with the increase in the load, the curvature of the UHPC layer and the I-section steel beam remained equal. Based on the plane section assumption and geometric deformation coordination relationship, it can be determined that:

$${\epsilon }_{st}={\epsilon }_g={\displaystyle \frac{y_c-h_c-h_g}{y_c}}{\epsilon }_{0.05}$$

(2)

$${\epsilon }_{sb}={\displaystyle \frac{y_s}{y_c}}{\epsilon }_{0.05}$$

(3)

$${\epsilon }_s={\displaystyle \frac{y_c-a_s}{y_c}}{\epsilon }_{0.05}$$

(4)

where ε_g is the strain of the lower surface of the GFRP; ε_st, ε_sb are the strains of the upper flange and the under flange of the I-section steel beam, respectively; ε_s is the strain of the reinforcement bar; y_s is the distance from the neutral axis to the lower flange of the I-section steel beam; and y_c is the distance from the neutral axis to the upper surface of the UHPC layer.

According to the calculation model in Figure 13, the bending moment value corresponding to the crack width of 0.05 mm can be obtained, as shown in Formula (5):

$$\begin{array}{ll}{M}_{cr}=& E_s{A}_s{\epsilon }_s{y}_1+f_{ut}{b}_e{h}_c{y}_2+E_g{b}_e{h}_g{\epsilon }_g{\mathrm{y}}_3+E_{st}{A}_{st}{\epsilon }_{st}{\mathrm{y}}_4\\ & +{\displaystyle \frac{1}{2}}{E}_{st}{\epsilon }_{st}{A}_{s1}{y}_5+{\displaystyle \frac{1}{2}}{E}_{sb}{\epsilon }_{sb}{A}_{s2}{y}_6+E_{sb}{\epsilon }_{sb}{A}_{sb}{y}_7\end{array}$$

(5)

Based on the formula for the structural mechanics, the cracking load of the composite beams can be obtained:

$$F_{cr}={\displaystyle \frac{4M_{cr}}{l}}$$

(6)

where A_s is the reinforcement area; A_s1 is the area of the web above the neutral axis of the I-section steel beam; A_s2 is the area of the web below the neutral axis of the I-section steel beam; A_st and A_sb are the area of the upper flange and bottom flange of the I-section steel beam, respectively; y₁–y₇ are the distances from the force centroid of each part to the neutral axis; h_c and h_g are the height of UHPC plate and GFRP plate, respectively; b_e is the equivalent width of the UHPC slab; E_s is the elastic modulus of the longitudinal reinforcement bar; E_st = E_sb is the elastic modulus of the I-section steel beam; E_g is the elastic modulus of the GFRP strips; and l is the calculation of the span for the composite beams.

4.2. Calculation of Ultimate Bearing Capacity

Based on the above analysis of the test results, when the composite beam reached the ultimate bearing capacity, both the compression side and the tension side of the I-section steel beam had yielded, the reinforcement bar had reached its tensile yielding value, the GFRP strips had achieved their design tensile strength, and the stress of the UHPC layer was in the plastic hardening state. Based on the plastic theory of composite structure, the calculation model of the ultimate bearing capacity for the composite beam under the hogging moment is shown in Figure 15.

On the basis of the internal force balance condition, the neutral axis of a composite beam under the ultimate state can be obtained:

$$f_{ut}{b}_c{h}_c+f_s{A}_s+f_g^{\prime }{b}_g{h}_g+f_s^{\prime }{b}_0(y_0-h_c-h_g)=f_s^{\prime }{b}_0(h_c+h_g+t_1-y_0)+f_s^{\prime }{h}_w{t}_w+f_s^{\prime }{b}_0{t}_2$$

(7)

The moment of the forces about the neutral axis location for a composite beam under the ultimate state can be obtained:

$$M_u=f_{ut}{b}_c{h}_c{k}_1+f_s{A}_s{k}_2+f_g^{\prime }{b}_g{h}_g{k}_3+f_s^{\prime }\left[b_0(y_0-h_c-h_g)k_4+b_0(h_c+h_g+t_1-y_0)k_5+h_w{t}_w{k}_6+b_0{t}_2{k}_7\right]$$

(8)

$$F_u={\displaystyle \frac{4M_u}{l}}$$

(9)

where y₀ is the distance from the upper surface of the UHPC layer to the neutral axis of the composite beam; and k₁–k₇ are the distances from the force centroid of each part to the neutral axis; The meanings of the other parameters are shown in Figure 15.

4.3. Validation

The theoretical calculated results of the ultimate bearing capacity were obtained. In order to verify the reliability of the theoretical calculation method, the experimental data in this study and in Zhang et al. [37] were comparative analyzed. The theoretical values without the tensile contribution of UHPC are presented. The results are listed in

Table 5. Comparison between the theoretical calculated and tested results.

Specimen			Calculated Results ①/kN	Calculated Results ②/kN	Tested Results ③/kN	①/③	②/③
L-1		Fcr	163.82	-	180	0.910	-
		Fu	473.82	434.70	487	0.973	0.893
L-2		Fcr	172.07	-	200.00	0.860	-
		Fu	481.98	454.43	515.9	0.934	0.881
Reference [37]	SU-S	Fcr	177.66	-	160.43	1.107	-
		Fu	499.39	466.72	578.89	0.863	0.806
	SU-B	Fcr	192.78	-	204.45	0.943	-
		Fu	475.30	434.48	536.89	0.885	0.809

Note: Calculated results ① represents the calculated ultimate flexural capacity considering the tensile contribution of UHPC; Calculated results ② represents the calculated ultimate flexural capacity without the tensile contribution of UHPC; and Tested results ③ represents the experimental results in this paper.

. It can be seen from Table 4 that the calculated values of the method proposed in this study agree with the tested values. When the contribution of the tensile strength to the UHPC was considered, the ratios of the calculated values for the cracking load and ultimate load to the tested values were 0.860–1.107 and 0.863–0.973, respectively. The average values were 0.956 and 0.914, respectively. The coefficient of variation was 0.093 and 0.043, respectively. However, when the contribution of the tensile strength to the UHPC was ignored, the ratio of the calculated ultimate load to the tested value was 0.806–0.893, the average value was 0.847, and the coefficient of variation was 0.040. Therefore, considering the tensile contribution of UHPC, the theoretical calculation results were in better agreement with the tested ones. Thus, the calculation method and assumptions proposed in this study better conformed to engineering practice, and the theoretical formulas proposed in this study could be potentially used to predict the flexural capacity of steel–GFRP strips–UHPC composite beams. However, the authors suggest that more flexural test data for steel–GFRP strips–UHPC composite beams with different design parameters are needed to further verify the applicability of the proposed theoretical equations.

5. Conclusions

This study investigated the flexural behavior of the steel–GFRP strips–UHPC composite beam under hogging moment regions. The influence of the reinforcement ratio on the failure mode, mid-span deflection, interface slip, strain and maximum crack width of this composite beam was analyzed. The crack propagation characteristics and distribution law were clarified, and the calculation methods for the cracking load and ultimate bearing capacity of composite beam were presented. The following conclusions can be drawn:

(1)

The composite beams presented two obvious main cracks on the upper surface of the UHPC layer, and there was obvious buckling deformation at the lower flange of the I-steel beam.

(2)

Increasing the reinforcement ratio appropriately could improve the cracking load, ultimate bearing capacity and interface slip value corresponding to the ultimate load. Moreover, it could effectively inhibit the development of cracks and reduce the strain of the reinforcement bars, crack width and average crack spacing.

(3)

When the maximum crack width was less than 0.2 mm, the maximum crack width of the specimens changed linearly with the increase in load. However, it increased rapidly once the reinforcement bar yielded.

(4)

Considering UHPC’s tensile contribution, the theoretical calculation method for the cracking load and flexural ultimate bearing capacity for the steel–GFRP strips–UHPC composite beam was established, and the theoretical calculation results show a correlation with the relevant test results, indicating that they can predict the flexural capacity of the composite beams.

(5)

Due to the limited number of test specimens, more flexural test data are needed to verify the applicability of the proposed calculation method of the cracking load and flexural ultimate bearing capacity for the steel–GFRP strips–UHPC composite beam. Therefore, further experimental studies, such as the depth–thickness ratio of the composite beam and the UHPC layer, and finite element analysis of the flexural performance of this composite beam should be carried out in the future.