1. Introduction
Steel is one of the most widely used materials in construction engineering. However, in severe environments (strong acid and alkali, seaports and chemical structures, etc.), and after 10–15 years, structures generally show serious cracks along the rebar direction caused by steel corrosion. This soon evolves into serious damage if effective measures are not taken. To enhance the anti-corrosion properties of steel bars, various techniques have been proposed. Fiber reinforced polymer (FRP) is a non-metal material that has evolved to an effective substitution for steel rebar in severe environments. Furthermore, FRPs can be suitable for use in extreme conditions such as fire or blast loading [
1,
2]. Because of the highly desirable properties of FRP, such as high strength, light weight and high anti-corrosion, the application of FRP as reinforcement in concrete structures has been growing rapidly [
3,
4,
5,
6]. A potential application of FRP reinforcement is in reinforced concrete (RC) frames. However, due to FRP’s predominantly elastic behavior, FRP-RC members exhibit low ductility and energy dissipation, thus restricting its application in construction [
7,
8]. In recent years, it has been reported that RC members reinforced by hybrid conventional steel bars and FRP bars can improve their seismic performance [
9,
10,
11].
A hybrid rod made with FRP skin over a steel core was first proposed by Nanni et al. [
12] to achieve good anti-corrosion performance for concrete beams, where the FRP skin is made of braided epoxy-impregnated aramid or vinylon fiber. Combining the advantages of FRP and steel bar, the new composite bar is expected to have high strength, high elastic modulus, good ductility and anti-corrosion properties. The factory-produced steel-FRP composite bar (SFCB) was proposed by Wu et al. [
13]. According to the composition rule, the stress-strain relationship of the SFCB can be appropriately simulated as the linear superposition of steel reinforcement and FRP. The schematic stress-strain relationship of this composite bar can be seen in
Figure 1.
Suppose that the outside fiber has fine interface bonding and harmonious deformation with the inner steel bar in the process of loading, that is, they have the same strain in one section. The stress-strain relationship of a SFCB under uniaxial tensile loading can be accurately simulated by the composite superposition principle [
14] using Equation (1).
where,
σsf and
εsf are tensile stress and strain of composite bar, respectively;
Ef and
Af are elastic modulus and cross-sectional area of the composite bar’s outer FRP, respectively; and
A is the total cross-sectional area of the composite bar.
The stress-strain relation of compression is described as Equation (2).
where,
σ’sf and
ε’sf are compressive stress and strain of composite bar, while
f’y and
E’s are compressive yield stress and elastic modulus of inner steel bar.
By comparing test curves of SFCB specimens and conventional steel bar specimens, it was found that the residual deformation of SFCB was less than that of a conventional steel bar when unloading from peak strain after yielding. Further, the stress-strain relationship of SFCB under a cyclic tensile load is provided through monotonic tensile and reciprocating tensile tests according to composition rule, providing the inner steel bar has same deformation with the composite bar.
Previous studies have indicated that compared with conventional steel bar, steel-fiber composite bar has good anti-corrosion performance and designable post-yield stiffness. When the conventional RC member encounters seismic excitation, it is difficult to achieve stable post-yield stiffness due to the large plastic deformation of the steel bar. For the purpose of achieving the seismic fortification goals of “reparable after a medium earthquake” and “collapse after a major earthquake”, SFCB is considered to be the ideal replacement for steel bar in concrete members for structural design and application. Up to now, many experimental studies have been conducted on the mechanical performance of the SFCB [
15] and concrete members reinforced with SFCB, including simply supported beams [
16], columns [
17], column-beam connections [
18], and the bonding behavior of SFCB with concrete by pull-out performance [
19]. To date, the material has been investigated primarily through experiments, while few effective numerical simulations have been conducted to study the seismic behaviors of the frame beam members [
20]. It is essential to explore a simulation framework due to the limited number of experiments.
RC frame beams are an important supporting member of frame structure. They also play a crucial role in resisting horizontal seismic action. Frame beams not only support bending moments, but also support large shear forces and small axial forces, and they can be viewed as a special form of column without axial force. Meanwhile, they have their own characteristics, such as a small cracking load and a complex nonlinear deformation and failure mode after plastic hinge forms, etc. Since the increase in span and the load case has become more and more complex, the design principle of “strong column weak beam” for ordinary RC frame structures has gradually evolved into “strong column and beam”. At present, the research on the seismic performance of components is mainly focused on columns, and less on beams. In this paper, the seismic performance test of concrete beams reinforced with SFCB was introduced. After that, a numerical simulation study was carried out by the finite element software OpenSees. The simulation results were compared with the test results for specimens with the same geometric and mechanical properties as the numerical models. Then, parametric studies were carried out to analyze the seismic behaviors of the concrete beams reinforced with SFCBs. The main variable parameters were the FRP type in composite bars (i.e., basalt, carbon FRP or E-glass FRP), the concrete strength, the steel/FRP ratio of the SFCB and shear span ratio. Seismic behaviors such as skeleton curves, seismic ultimate capacity and the corresponding drift ratio (defined as ultimate drift ratio, its value is equal to the beam’s top horizontal displacement at the peak load divided by the beam’s length) of the SFCB reinforced concrete beams were also evaluated.
4. Parametric Study
After verifying the validity of the numerical modeling method in this paper, the numerical analysis can be carried out through the numerical simulation and changing parameters to consider their influence on the seismic performance of concrete beams. In the parametric study, the geometric dimensions and reinforcement layout are assumed to be the same as the beam discussed above. The influence of different parameters, including the outer fiber types of composite bars, concrete strength grades, shear span ratios of components and the relationship with the change of outer fibers area are discussed.
4.1. Effect of the Outer Fiber Types
One of the key points of the seismic design of beams reinforced with composite bars is how to choose the suitable FRP type (different FRPs have different elastic moduli, ultimate strengths, and elongation rates). In this paper, three types of FRP fiber, including carbon fiber, basalt fiber and glass fiber, are considered to study the mechanical properties of reinforced concrete beams.
When the diameter of inner steel is 12 mm, the number of outer fiber bundles in the composite bar is 30, 50 and 70 respectively. The concrete mechanical performance parameters are assumed to be the same as the beam discussed above. By changing the area of the outer FRP in longitudinal composite bar, the seismic performance of the beam is compared. The BFRP type is CBF13-4000tex, which is different from the properties of BFRP (2400tex) in contrast to the test above. The combination of CFRP and GFRP to steel is similar to BFRP. All the types and mechanical properties of the outer fiber in composite bars are cited from test data in [
16], shown in
Table 5. However, the mechanical properties of FRP in composite bars, such as the ultimate strength and the elongation at break are not the same as the mechanical properties of FRP filament. Generally speaking, the ultimate strength and elongation of composite bars are much less than that of the original fiber, which may be caused by the uneven force of the fiber when the composite bars are stretched.
As shown in
Figure 15, the yield displacement and initial stiffness are relatively close for each fiber type of SFCBs concrete beams. With the increase in fiber content, the post-yield stiffness of beam members increases gradually, and the FRP fracture point gradually moves backward. After FRP fracture, the beam load drops sharply. When the fiber content was increased to 70 bundles, the peak load of steel-BFRP reinforced concrete beam was the highest among the three FRP types beam models, about 120 kN. The beam reinforced with steel-GFRP composite bars was second, at 115.58 kN. The beam reinforced with steel-CFRP was last, about 75.80 kN. As the ultimate strain of CFRP is smaller than the other two fiber types, the damage caused by fiber fracture occurs firstly in steel-CFRP components. At this point, the concrete has not reached the ultimate compressive strain and the failure mode is brittle failure. The capacity of CFRP-related beam is smaller than the other two fiber types because the area per bundle is smaller. In addition, when the outer fiber of the composite bar breaks, taking the content of each type fiber bundle as 70 as an example, the horizontal drift ratio of the CFRP reinforced beam is only about 2.0%, the GFRP reinforced beam is 4.5%, while the BFRP composite beam is nearly 5.0%, with the best ductility. It was found that the post-yield stiffness and displacement ductility of components can be effectively improved by sound design of fiber content in composite bars. By comparing and analyzing the three kinds of FRP types, the concrete beams reinforced with steel-BFRP composite bars were found to have better ductility and maintain high ultimate capacity.
4.2. Effect of Concrete Strength
The comparison of beams reinforced with different types of fibers in
Section 4.1 indicates that concrete beams reinforced with steel-BFRP composite bars have both good ductility and ultimate capacity. The following numerical simulation studies focus on the variable parameters based on beams reinforced with steel-BFRP composite bars.
In order to better compare the test beam specimens, the numerical simulation in
Section 4.2 and
Section 4.3 adopt the mechanical properties of the tested materials verified in
Section 3.1 into the simulation model. In the model, BFRP original fiber is 2400tex, and its mechanical performance parameters are shown in
Table 6 The load-horizontal displacement curve of the S12B50 beam is analyzed by changing the strength of concrete. The strength values are 30 MPa, 50 MPa and 70 MPa, respectively.
Figure 16 shows the influence of different concrete strength values on load-horizontal displacement curve of S12B50” beams. It can be seen that the curves coincide at the pre-yield stage, indicating that the change in concrete strength has a very limited impact on the strength and horizontal displacement of specimens at the initial elastic stage. However, the peak load and the post-yield stiffness increased gradually with the increase in concrete strength at the post-yield stage. As a result, when the concrete strength value is more than doubled, the seismic ultimate capacity of the beam increases by only 10% and the horizontal displacement at FRP fracture point decreased by only 2.7%, that is, the ductility did not change significantly.
Figure 17 shows the influence of concrete strength and fiber content on the seismic ultimate capacity and corresponding drift ratio of the component. The range of BFRP bundles in composite bars is from 50 to 90. As shown in
Figure 17a, it is concluded that with the increase in concrete strength, the seismic ultimate capacity of concrete beam with different fiber content increases significantly.
Figure 17b shows the effect of concrete strength on the ultimate drift ratio, with the increase in concrete strength, the drift ratio at the BFRP fracture point decreases gradually. Due to the elastic behavior of the FRP, all curves are linear to the fiber content. Under the same concrete strength, the ultimate drift ratio decreases more obviously with the increase of the fiber area in composite bars. However, the overall variation range is from 3.6 to 4.4, showing good ductility. It indicates that increasing the concrete strength of components blindly can improve the seismic ultimate capacity, but also reduce the ductility of components.
4.3. Effect of Shear Span Ratio
Since the shear span ratio and fiber content (area) are designable and have great effect on seismic performance of beam, the monotonic pushover analysis was carried out for concrete beams with different shear span ratios, from 3.5 to 5.5 to ensure that the beam is damaged mainly by bending failure. The range of BFRP bundles in composite bars is from 50 to 90.
Figure 18a shows the effect of the shear span ratio and fiber content on seismic ultimate capacity. For each fiber bundle reinforced beam, as the shear span ratio of beam increases, its seismic ultimate capacity decreases gradually.
Figure 18b shows the effect of the shear span ratio and fiber content on the ultimate drift ratio. For each fiber bundle reinforced beam, the ultimate drift ratio increases significantly with the increase of the shear span ratio of beam. Due to elastic behavior of the BFRP, all curves are linear to the fiber content. When the shear span ratio is 3.5, the ultimate drift ratio of each beam is greater than 3%. When the shear span ratio is 5.5, the ultimate drift ratio of each beam is greater than 5%, and the increase is about 57%, showing good ductility.
5. Conclusions
In this paper, the seismic ultimate capacity of beams reinforced with SFCBs is studied by testing and numerical simulation. First, the method and main results of the experiment are briefly introduced, and based on the OpenSees software, a simplified constitutive model of composite bar material was applied to simulate the seismic behaviors of the concrete beams reinforced with SFCBs by fiber element modeling. The validity of the model was verified with the experimental results for the concrete beams reinforced with composite bars under monotonic loading and a low reversed cyclic load. Based on the numerical simulation method, a parametric study was then conducted to illustrate the effects of the FRP types in composite bars (i.e., basalt, carbon FRP and E-glass FRP), the concrete strength, FRP content of the SFCBs and shear span ratio. The results showed that (1) the fiber type of the composite bar has a great impact on the mechanical properties of the frame beam, with beam reinforced with BFRP composite bar having higher seismic ultimate capacity and better ductility; With the increase of the fiber bundle in the composite bar, the post-yield stiffness and ultimate capacity of the component increases and the ductility strengthens; (2) at pre-yield stage, concrete strength has little influence on seismic performance of concrete beam while after yielding, the seismic ultimate capacity and post-yielding stiffness of specimens are increased slowly with the increase in concrete strength, however, the ductility is reduced accordingly; (3) as the shear span ratio of beams increases from 3.5 to 5.5, the seismic ultimate capacity decreases gradually while the ultimate drift ratio increases by more than 50%. Through sensible setting of the fiber content and shear span ratio of the composite bar reinforced concrete beam, concrete beams reinforced with composite bars can have good ductility while maintaining high seismic ultimate capacity. Due to the limited number of the tested beams, more tests and analyses are needed to derive sound conclusions concerning the use of SFCB in concrete structural members in seismic prone regions.