Numerical analysis of high-strength reinforcing steel with conventional strength in reinforced concrete beams under monotonic loading

Ibrahim S. I. Harba; Abdulkhalik J. Abdulridha; Ahmed A. M. AL-Shaar

doi:10.1515/eng-2022-0365

Article Open Access

Numerical analysis of high-strength reinforcing steel with conventional strength in reinforced concrete beams under monotonic loading

Ibrahim S. I. Harba , Abdulkhalik J. Abdulridha and Ahmed A. M. AL-Shaar

Published/Copyright: December 2, 2022

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From the journal Open Engineering Volume 12 Issue 1

Abstract

This work presents finite element (FE) modeling using the ABAQUS program to investigate the effect of steel reinforcement with three different types of high-strength steels, grades 420, A1035, and SD685 on the flexural behavior of RC beams under monotonic loading. Experimental findings from the literature have been used to validate the proposed model. The numerical load, deflection, mode of failure, failure concrete strain, and bottom steel strain at failure of 24 numerical specimens with collapsed conditions of tension-controlled, balanced, and compression-controlled are recorded. Also, the effect of compression reinforcement is being investigated. The results reveal that the flexural behavior of the experimental test for the three steel grades is well validated by FE analysis. The ductile and brittle behavior features of yield strength (YS) larger than 420 can be predicted for specimens designed according to current standards ACI-318M-19. Also, the compression reinforcement improves load capacity while reducing displacement. It may be argued that when YS decreases, tensile stress and strain of flexural rebar rise, causing the beam to become more ductile. When the YS increased, the brittle behavior was induced.

Keywords: high-strength rebar; flexural behavior; ABAQUS; FE; reinforced concrete beam

1 Introduction

The use of high-strength steel reinforcement (HSSR) (yield stress greater than 60 Ksi or 420 MPa) could permit designers to reduce material quantities, thus leading to reduced construction costs and reinforcement congestion. Additionally, HSSR reinforcement improves the long-term endurance of concrete structures subjected to adverse weather conditions owing to its natural corrosion-resistant feature. The stress in steel at service load levels is projected to be higher with HSSR than with normal steel in concrete, also, a potential significant contribution of HSSR which still remains largely unrealized. The requirements of elongation and strain hardening of these higher grades is not a match with A706 grade 60 steel [1] (ASTM A706 2016). This raises concerns about the performance of reinforced concrete (RC) structures utilizing higher grade reinforcement.

Theoretically, the ultimate curvature capacity is reduced with reinforcement’s lower elongation capacity. While certain HSSR have a lower tensile strength to yield strength (TS/YS) ratio, this might theoretically reduce the strength at ultimate moment corresponding to the strength at yield moment, reducing the spread of plasticity down the length of the beam once yielding begins. The beams constructed with HSSR in theory, could reduce its deformation capacity because of these factors, which affect negatively the ductility of member. This is especially critical for tension-controlled parts like beams, where tension steel should surpass the yield limit and attain a minimum strain of 0.005 before ACI-318-19 [2] at the ultimate condition. For such beams, steel reinforcement reach yield before concrete reach crushing compressive strength, enabling large increases in deflections and providing ample notice before failure. As a result, beams are regarded as totally ductile when tensile strain reaches a minimum of 0.005. An unanticipated rise in YS may therefore alter a beam’s tension control and cause it to breach the minimal 0.005 strain criterion. While in the beginning with ACI-318M-19 [2], the segment is considered as tension-controlled failure when the yield of steel reaches the limit (≥ε _ty + 0.003), where ε _ty = f _y/E _s is net tensile strain of longitudinal tension reinforcement. This expression provides adequate ductility in case of reinforcement other than 420 MPa.

Al-Haddad [3,4] examined the influence of Saudi rebar’s HSSR on the ductility of beam elements. It was established that the ACI-318 provisions limiting the maximum longitudinal reinforcement ratio do not provide enough ductility for seismic and conventional constructions. Mast et al. [5] presented a simplified technique for flexural design of HSSR beams. Flexural members were created utilizing the simplified design procedure based on the conventional Grade 420 MPa. The predicted techniques closely match the measured behavior reported by previous researchers. Sumpter et al. [6] studied the behavior of concrete beams reinforced by HSSR as shear reinforcement. Test results revealed that using HSSR increases the shear capacity and reduction in shear crack width. Zhou et al. [7] predicted an empirical formula to measure the deformability of RC beams. The proposed empirical formula provides flexibility of using HSSR in RC beams, adding rebars in compression or confinement to enhance the deformability. Youcef and Chemrouk [8] recorded a reduction in ductility with HSSR. To recover the desired ductility, it was recommended to use proper compression rebars. Harries et al. [9] studied the flexural crack widths of RC beams with HSSR. The obtained crack widths were found below the limit provisions by ACI. Soltani et al. [10] studied the crack widths in concrete under service load and discovered that they were within accepted limitations and could be anticipated using ACI. According to Shahrooz et al. [11], the strain limitations for HSSR must be altered in order to obtain the curvature ductility implied by the existing usage of Grade 414 reinforcing steel. Furthermore, stresses in steel at service load levels must be reduced to 60% of their YS.

Giduquio et al. [12] investigated the behavior of RC beams reinforced with two different types of HSSR (Grade 100 A1035 and SD685). The obtained results illustrate that design provisions of the ACI can be used to estimate the strength of RC beams reinforced with either types of HSSR. Charif et al. [13] formulated that the beam ductility decreased by the increase in the steel yield stress and violated the condition of tension-control imposed in the design stage. Aldabagh et al. [14] showed that compression rebars have little to no effect on the concrete compression failure of HSSR RC beams. Furthermore, they demonstrated that fiber RC outperforms compression steel in enhancing the bending characteristics of such beams. Duy and Jack [15] evaluated the performance of RC beams with HSSR under reversed cyclic lateral loads modeling earthquake impacts. The results show that strain in longitudinal bars with higher TS/YS ratio obtained more ductility dispersion than beams with lower TS/YS. Xianhua et al. [16] compared the estimated values for RC beams’ ultimate bearing capacities based on various national codes. They showed that the formulas used to calculate the flexural strength of beams reinforced with steel of Grades 400 or 500 MPa can also be used to calculate the flexural strength of beams reinforced with steel of Grades 600 MPa. Lim and Lee [17] used RC beams using HSSR to assess the application of the ACI rules for the design of flexural members. The results demonstrate that the nominal flexural strength of members may be calculated using the nominal strength equation described in the ACI.

There are many sources of deformed rebar in the Middle East, all of whom follow ASTM A 615M [18] requirements. The steel bars are produced with YS greater than or equal to 420 MPa, and ultimate strength greater than or equal to 620 MPa. Also, the TS/YS ratio is greater than or equal 1.25. In the last few years, HSSR has been commercially available in the Middle East. However, the limited applications of HSSR owe to a lack of strength-matching concrete and associated design principles. As a result, there is a significant danger that a beam meant to break in a ductile mode would instead fracture in a brittle mode. The need for clarification of the impact of increased rebar YS on beam behavior must be investigated to fill the gap due to limited research.

The purpose of the present work is to illustrate the effect of HSSR on the flexural behavior of RC beams reinforced with three types of steel with different stress–strain characteristics (i.e., TS/YS ratio). The investigation is performed numerically by using ABAQUS software and verified with Giduquio et al. [12] experimental results. Furthermore, a parametric study is carried out to illustrate the influence of TS/YS ratio on beam behavior with different collapse mechanism (compressive, balance, and tensile).

2 Overview of experimental program

A brief description of the experimental test performed by Giduquio et al. [12] to verify the numerical solution proposed in this study is presented in this section. Three RC beam tested specimens designed by Giduquio et al. [12] to satisfy tension-controlled collapse mechanism were chosen to validate numerical analysis. The details of experimental data of these specimens are illustrated in Tables 1 and 2 and Figures 1–3.

Table 1

Summarized material prosperities of steel [12]

Bar type	Bar size	Minimum ε _sh (%)	Minimum ε _su (%)	ε _y	Minimum f _y (MPa)	Minimum f _u (MPa)
ASTM A706 (GRADE 420)	No. 3 to No. 6	NA	14	0.24%	414	550
	No. 7 to No. 11		12
	No. 14 and No. 18		10
SD685	All sizes	1.4	10	0.38%	690	>1.25 f _y
A1035	No. 3 to No. 11	NA	7	0.67%	690	1,035
A1035	No. 14 and No. 18	NA	6	0.67%	690	1,035

Table 2

Design parameters of specimens [12]

Specimen		Specified material properties
Group	Label	f _c, MPa	Bar type	f _y, MPa	Top/bottom bars
Control	C1 and C2	28	Grade 420	414	Two No. 5
Control	C1 and C2	28	Grade 420	414	Four No. 9
I-Group	I-S1 and I-S2	28	SD685	690	Two No. 4
	I-S1 and I-S2	28	SD685	690	Three No. 8
	I-A1 and I-A2	28	A1035	690	Two No. 4
	I-A1 and I-A2	28	A1035	690	Three No. 8
II-Group	II-S1 and II-S2	35	SD685	690	Two No. 5
	II-S1 and II-S2	35	SD685	690	Three No. 8
	II-A1 and II-A2	42	A1035	690	Two No. 8
	II-A1 and II-A2	42	A1035	690	Three No. 8

Figure 1

Stress–strain relationship of steel reinforcement [12]: (a) Grade 420, (b) SD685, and (c) A1035.

Figure 2

Specimens’ dimensions and reinforcement layout [12]. (a) Specimen cross section. (b) Specimen longitudinal section.

Figure 3

Specimens test setup [12].

3 Numerical FE modeling

Numerical simulation is carried out in this work utilizing the FE-code ABAQUS software [19]. The concrete’s inelastic behavior is described using the concrete damaged plasticity (CDP) model, which serves as the basis for Abaqus’ concrete plastic damage model. It is based on the formulations of Lee and Fenves [20] and Lubliner et al. [21] which provide a general facility for modeling concrete. Damage calculation may be based on a predetermined standard or on the law of damage variables. The CDP technique by Lee and Fenves [20] and Lubliner et al. [21] modifies the formulation to generate closed-form expressions of the damage variables in terms of the pertinent strains. This method can take into account any concrete constitutive law, whether it is based on specific experiments or empirical formulations like those frequently advised by design standards. The CEB-FIB 2010 [22] proposed model formula was adopted in this study to represent the concrete uniaxial stress–strain relationship. Table 3 lists the CDP parameters that were used in the FE model.

Table 3

CDP parameters

Parameter	Value	Description [19]
ψ	56	Dilation angle
ε	0.1	Eccentricity
Fb₀/Fc₀	1.16	The ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress
K	0.667	K _c, the ratio of the second stress invariant on the tensile meridian
μ	0.0001	Viscosity parameter

The behavior of the tension softening component following cracking is outlined in this work, utilizing Hordijk’s [23] exponential model of tension softening. Reinforcing steel material behavior is characterized depending on the experimental data by Giduquio et al. [12] as elastic and inelastic stress–strain correlations with effects of strain hardening.

3.1 Modeling of geometry

As illustrated in Figures 2 and 3, Giduquio et al. [12] proposed a simply supported RC beam with dimensions of 4,600 mm span, 460 mm section height, and 300 mm section width. The concrete steel plates utilized the (C3D8R) in the FE model, whereas the rebar used the (T3D2) 3D truss linear element, assumed fully embedded in the concrete. Several analytical attempts were made to find the optimum mesh for the numerical model that was chosen, and it was based on matching the load–displacement curve with the experimental verification problem and obtaining the required load. A 50 mm mesh size with aspect ratio of 1 is used in this study as shown in Figure 4.

Figure 4

Finite element meshed model.

3.2 Support boundary condition and loads

The RC beam is prevented from moving in the Y direction on one side, and both the X and Y directions on the other, with a uniform force applied to the two plates as shown in Figure 5.

Figure 5

Support boundary conditions and load.

4 Numerical parametric study

The monotonic flexural behavior of RC beam specimens is calculated using 24 simply supported RC beams numerical models in this work. The dimensions of these specimens were (300 mm × 460 mm × 4,100 mm) as illustrated in Figures 2 and 3. Three types of steel with different stress–strain characteristics (i.e., TS/YS ratio) as illustrated in Table 1 and different collapse mechanisms (compressive, balance, and tensile) used as variables are used in this investigations. The collapse mechanism of RC beams is represented by applying load till crushing occurs. The numerical load, deflection, mode of failure, failure concrete strain, and bottom steel strain at failure are recorded. The collapsed conditions are calculated according to ACI-318M-19 [2], the tension-controlled ( ρ _max ≤ 0.75, ρ _b and ρ _min), balanced ( ρ = ρ _b), and compression-controlled ( ρ > 0.75 and ρ _b) i.e., ρ = 1.2 and ρ _b. The change in steel reinforcement ratio ( ρ ) was proportionate to the rise in rebar YS. The shear reinforcement for all modeled beam specimens are Ø 10@125 mm Grade 420 as illustrated in Figure 2.

The 24 numerical specimens are divided into 7 groups. First group focuses on the validation of our numerical model with experimental results [12]. While groups 2, 3, and 4 investigate the behavior of singly reinforced beams with different YSs. Also, groups 5, 6, and 7 are focused to investigate the effect of compression reinforcement ratio ρ ¯ / ρ to longitudinal reinforcement on the behavior. The details of groups and beam specimens are mentioned in Table 4.

Table 4

Numerical parametric study

Group no.	Specimen ID	Bar type	Specified reinforcements				Collapsed condition	Remarks
Group no.	Specimen ID	Bar type	Top bars	Bottom bars	ρ	ρ ¯ ρ	Collapsed condition	Remarks
1	B1C2	Grade 420	Two No. 5	Four No. 9	ρ _max	0.155	Tension-controlled	Validation
	B2S2	SD685	Two No. 4	Three No. 8	ρ _max	0.155	Tension-controlled	Validation
	B3A2	A1035	Two No. 4	Three No. 8	ρ _max	0.155	Tension-controlled	Validation
2	B4G	Grade 420	N/A	Six No. 9	1.2 ρ _b	0	Compression-controlled
	B5G	Grade 420	N/A	Five No. 9	ρ _b	0	Balanced
	B6G	Grade 420	N/A	Four No. 9	ρ _max	0	Tension-controlled
	B7G	Grade 420	N/A	Two No. 5	ρ _min.	0	Tension-controlled
3	B8S	SD685	N/A	Four No. 8	1.2 ρ _b	0	Compression-controlled
	B9S	SD685	N/A	Three No. 8	ρ _b	0	Balanced
	B10S	SD685	N/A	Two No. 8	ρ _max	0	Tension-controlled
	B11S	SD685	N/A	Two No. 4	ρ _min	0	Tension-controlled
4	B12 A	A1035	N/A	Four No. 8	1.2 ρ _b	0	Compression-controlled
	B13 A	A1035	N/A	Three No. 8	ρ _b	0	Balanced
	B14 A	A1035	N/A	Two No. 8	ρ _max	0	Tension-controlled
	B15 A	A1035	N/A	Two No. 4	ρ _min	0	Tension-controlled
5	B16G	Grade 420	Three No. 5	Four No. 9	ρ _max	0.25
	B17G	Grade 420	Two No. 9	Four No. 9	ρ _max	0.5
	B18G	Grade 420	Three No. 9	Four No. 9	ρ _max	0.75
6	B19S	SD685	Three No. 4	Two No. 8	ρ _max	0.25
	B20S	SD685	Five No. 4	Two No. 8	ρ _max	0.5
	B21S	SD685	Seven No.4	Two No. 8	ρ _max	0.75
7	B22 A	A1035	Three No. 4	Two No. 8	ρ _max	0.25
	B23 A	A1035	Five No. 4	Two No. 8	ρ _max	0.5
	B24 A	A1035	Seven No. 4	Two No. 8	ρ _max	0.75

5 Numerical results and discussions

5.1 Validation of numerical results

The load against mid span–displacement curves from the FE analysis of experimental specimens [12] in group 1 are presented in Table 5 and Figures 6–8. On the graphs, it appears that the level of ultimate and yield load, in addition to a significant loss of stiffness owing to flexural collapse after exceeding ultimate displacement, are all correctly replicated. The degree of error between FE and the experimental test that is illustrated in Table 5 ranges from 5 to 10%. In other words, the FE analysis adequately validates the flexural behavior of the experimental test with three types of steel with different stress–strain (TS/YS) ratio.

Table 5

Numerical results of experimental specimens

Specimen ID	Reinforcement grade	Experimental ultimate load (kN)	Numerical ultimate load (kN)	Error of load %	Experimental ultimate deflection (mm)	Numerical ultimate deflection (mm)	Error of deflection %
B1C1	Grade 420	473.6	506.7	7+	68.1	64.7	−5
B2S1	SD685	454.2	499.5	10+	73.7	67	−9
B3A1	A1035	520.6	565.9	9+	68.3	61.5	−10

Figure 6

Numerical and experimental load–displacement curve of specimen B1C1.

Figure 7

Numerical and experimental load–displacement curve of specimen B2S2.

Figure 8

Numerical and experimental load–displacement curve of specimen B3A1.

On the other hand, the experimental test result curves is less stiff than FE models results. Micro-cracks that decrease the stiffness of the RC element may induce higher stiffness in FE models. Although FE models do not include them, they are known to exist in real-world concrete [24]. Furthermore, certain unknown environmental conditions might have affected the rigidity of the experimental specimen. Figures 9–11 show damage occurrences at collapse level for both numerical and experimental tests in terms of concrete plastic strain (CPS). It is verified that the FE model accurately depicts the experimental damage distribution in the test members. The numerical results of all specimens are presented in Table 6.

Figure 9

Damage (CPS) for specimen B1C1.

Figure 10

Damage (CPS) for specimen B2S1.

Figure 11

Damage (CPS) for specimen B3A1.

Table 6

Numerical results

Group no.	Specimen ID	Bar type	Specified reinforcements			Ultimate load (kN)	Ultimate displacement (mm)	Failure concrete strain (CPS) (mm/mm)	Bottom steel strain at failure (mm/mm)	Yield strain ε _y (%)
Group no.	Specimen ID	Bar type	Top bars	Bottom bars	ρ	Ultimate load (kN)	Ultimate displacement (mm)	Failure concrete strain (CPS) (mm/mm)	Bottom steel strain at failure (mm/mm)	Yield strain ε _y (%)
1	B1C1	G 420	2#5	4#9	ρ _max	506.7	64.7	0.0226	0.0062	>ε _{y = 0.0024}
	B2S1	SD685	2#4	3#8	ρ _max	499.5	67.0	0.0261	0.0051	>ε _{y = 0.0038}
	B3A1	A1035	2#4	3#8	ρ _max	565.9	61.5	0.0199	0.0041	<ε _{y = 0.0067}
2	B4G	G 420	N/A	6#9	1.2 ρ _b	492.3	18.4	0.0045	0.0012	<ε _{y = 0.0024}
	B5G	G 420	N/A	5#9	ρ _b	482.6	22.2	0.0049	0.0021	<ε _{y = 0.0024}
	B6G	G 420	N/A	4#9	ρ _max	435.9	72.9	0.0260	0.0083	>ε _{y = 0.0024}
	B7G	G 420	N/A	2#5	ρ _min	384.6	79.0	0.0251	0.0135	>ε _{y = 0.0024}
3	B8S	SD685	N/A	4#8	1.2 ρ _b	500.5	28.5	0.0054	0.0031	<ε _{y = 0.0038}
	B9S	SD685	N/A	3#8	ρ _b	419.8	25.5	0.0053	0.0036	<ε _{y = 0.0038}
	B10S	SD685	N/A	2#8	ρ _max	389.9	65.1	0.0209	0.0069	>ε _{y = 0.0038}
	B11S	SD685	N/A	2#4	ρ _min	304.9	47.1	0.0077	0.0072	>ε _{y = 0.0038}
4	B12A	A1035	N/A	4#8	1.2 ρ _b	451.4	46.2	0.0132	0.0029	<ε _{y = 0.0067}
	B13A	A1035	N/A	3#8	ρ _b	409.2	35.5	0.0081	0.0028	<ε _{y = 0.0067}
	B14A	A1035	N/A	2#8	ρ _max	386.5	45.5	0.0093	0.0072	>ε _{y = 0.0067}
	B15A	A1035	N/A	2#4	ρ _min	341.0	56.3	0.0128	0.0096	>ε _{y = 0.0067}
5	B16G	G 420	3#5	4#9	ρ _max	574.4	33.0	0.0085	0.0067	>ε _{y = 0.0024}
	B17G	G 420	2#9	4#9	ρ _max	615.1	25.3	0.0045	0.0038
	B18G	G 420	3#9	4#9	ρ _max	656.4	25.1	0.0051	0.0043
6	B19S	SD685	3#4	3#8	ρ _max	533.3	38.9	0.0063	0.0031	<ε _{y = 0.0038}
	B20S	SD685	5#4	3#8	ρ _max	508.7	30.7	0.0046	0.0034
	B21S	SD685	7#4	3#8	ρ _max	553.8	27.5	0.0053	0.0035
7	B22A	A1035	3#4	3#8	ρ _max	584.5	73.1	0.0204	0.0061	<ε _{y = 0.0067}
	B23A	A1035	5#4	3#8	ρ _max	604.6	41.6	0.0064	0.0042
	B24A	A1035	7#4	3#8	ρ _max	363.8	35.2	0.0055	0.0042

5.2 Load and displacement

Figures 12–17 show the load against mid span–displacement curves from the FE analysis of all specimens in groups 2–7. For single reinforced specimens in groups 2, 3, and 4 as illustrated in Figures 12–14 and the results in Table 6.

Figure 12

Load–displacement curve of Group 2.

Figure 13

Load–displacement curve of Group 3.

Figure 14

Load–displacement curve of Group 4.

Figure 15

Load–displacement curve of Group 5.

Figure 16

Load–displacement curve of Group 6.

Figure 17

Load–displacement curve of Group 7.

Specimens with ρ _max and ρ _min for different stress–strain characteristic (i.e., TS/YS ratio) present ductile behavior as it can be seen in the plateau after yield of bottom reinforcement up to failure. While specimens with 1.2 ρ _b and ρ _b have higher load carrying capacity and less ultimate displacement, as shown in Figures 18 and 19. For specimens with compression reinforcement in groups 5, 6, and 7 as illustrated in Figures 15–17 and the results in Table 6, specimens with ρ ¯ ρ ratio equal 0.25 for different HSSR has greater ductility and a higher ultimate displacement. Also, the load carrying capacity of these specimens was less compared with specimens having a ratio ρ ¯ ρ of 0.5 and 0.75 as shown in Figures 20 and 21. As a consequence, it is possible to deduce that as the compression reinforcement ratio increases, the beam becomes brittle. Furthermore, when the yield stress of reinforcement increases, the stress and strain of flexural reinforcement decrease, while the stress and strain of concrete in the compression zone increase, resulting in brittle failure.

Figure 18

Load capacity for specimens with single reinforcement.

Figure 19

Ultimate displacement for specimens with single reinforcement.

Figure 20

Load capacity for specimens with double reinforcement.

Figure 21

Ultimate displacement for specimens with double reinforcement.

5.3 Failure concrete strain and flexural (bottom) steel strain at failure

As shown in Table 6, the FE findings of failure concrete strain at extreme fiber in the compression zone at mid span demonstrate that the concrete strain is greater than 0.003 for all beam specimens. This finding agrees with the provisions of ACI-318-19 [2]. The strain of flexural rebar at failure for single reinforced specimens in groups 2, 3, and 4 is less than the yield strain for higher reinforcement ratios (1.2 ρ _b and ρ _b) and greater than the yield strain for lower reinforcement ratios ( ρ _max and ρ _min). As a result, it can be concluded that as the tensile reinforcement ratio increases, so does the concrete compressive stress and strain at the compression zone, resulting in brittle behavior of the beam. While the strain for lower reinforcements increases as the tensile reinforcement ratio decreases, the beam becomes ductile. The strain of flexural rebars at failure for specimens with compression reinforcement in Group 5 (reinforcement Grade 420 MPa) is greater than yield strain.

While specimens in Groups 6 and 7 (reinforcement Grade SD685 and A1035, respectively) is less than yield strain. As a result, it can be concluded that as the TS/YS ratio decreases, so does the tensile stress and strain increase of flexural rebar, resulting in more ductile behavior of the beam.

5.4 Visualization of damage (CPS)

From Figures 22–24 for specimens in Groups 2, 3, and 4, it can be seen that at the stage of final collapse, CPS for specimens with higher reinforcement ratios (1.2 ρ _b and ρ _b) localizes to the compression zone, resulting in a brittle failure mode because strain in flexural reinforcement is smaller than yield strain for various TS/YS ratios. CPS localizes in both tension and compression zones for specimens with lower reinforcement ratios ( ρ _max and ρ _min), leading to a ductile failure mode because flexural reinforcement strain is larger than yield strain for varied TS/YS ratios.

Figure 22

Damage (plastic strain) for Group 2.

Figure 23

Damage (plastic strain) for Group 3.

Figure 24

Damage (plastic strain) for Group 4.

As shown in Figures 25–27 for specimens in Groups 5–7, higher CPS can be seen in tension zone. Because compression reinforcement increases the capacity, the destruction process in the area of tensile zone will be more visible for varied TS/YS ratios. Also, even after the concrete failed, these bars were able to withstand a certain amount of load, preventing the members from completely failing [26,27].

Figure 25

Damage (plastic strain) for Group 5.

Figure 26

Damage (plastic strain) for Group 6.

Figure 27

Damage (plastic strain) for Group 7.

5.5 Effect of varied TS/YS ratios on the behavior of beam specimens

For specimens reinforced with 1.2 ρ _b and ρ _b, the dominate mode of failure is compression for the three types of reinforcement with a higher ultimate displacement for reinforcement types SD685 and A1035 as shown in Figures 28 and 29. Even if there is no yield, a large strain in flexural reinforcement can be created [25], (Table 6).

$Figure 28 Load–displacement curve for specimens with 1.2 ρ \rho b.$

Figure 28

Load–displacement curve for specimens with 1.2 ρ _b.

$Figure 29 Load–displacement curve for specimens with ρ \rho b.$

Figure 29

Load–displacement curve for specimens with ρ _b.

For specimens reinforced with ρ _max and ρ _min, the dominate mode of failure is tension for the three types of reinforcement with a higher ultimate displacement for Grade 420 rebar compared with SD685 and A1035 rebars as shown in Figures 30 and 31. The beam ductility decreased with HSSR, this is in agreement with previous findings by Youcef and Chemrouk [8] and Charif et al. [13].

Figure 30

Load–displacement curve for specimens with ρ _max.

Figure 31

Load–displacement curve for specimens with ρ _min.

Figures 32–34 illustrate that the use of compression reinforcement with different percentages increases flexural strength (load carrying capacity) for the three types of reinforcement.

Figure 32

Load–displacement curve for specimens with ρ _top /ρ _bot = 0.25.

Figure 33

Load–displacement curve for specimens with ρ _top /ρ _bot = 0.5.

Figure 34

Load–displacement curve for specimens with ρ _top /ρ _bot = 0.75.

6 Conclusion

An effort has been made in the current work to illustrate the effect of HSSR on the flexural behavior of RC beams reinforced with three types of steel with different stress–strain characteristics (i.e., TS/YS ratios). This investigation was performed numerically using ABAQUS software. The following are the important concluding remarks for this work:

(1) The FE analysis adequately validates the flexural behavior of the experimental test [10] with three types of HSSR including different stress–strain (TS/YS) ratios.

(2) The ductile failure behavior of single reinforced specimens with ρ _max and ρ _min for varied TS/YS ratios and designed according to current standards ACI-318M-19 is demonstrated (i.e., tension-controlled). Furthermore, specimens with 1.2 ρ _b and ρ _b show brittle failure behavior (i.e., compression-controlled). Because of this, the current standard applies even when HSSR bars are used in flexural members. Previous findings by Lim and Lee [17] agree with this result.

(3) The use of compression reinforcement increases load capacity and decreases the displacement.

(4) Brittle failure of beams occurs as the yield stress of compression reinforcement increases.

(5) The FE findings of failure concrete strain at extreme fiber in the compression zone at mid span show that the concrete strain is more than 0.003 for all beam specimens. This conclusion agrees with the provisions of ACI-318-19.

(6) Similar to the behavior seen for beams with varying stress–strain (TS/YS) ratios, as the tensile reinforcement ratio increases, so does the concrete compressive stress and strain at the compression zone, resulting in brittle failure of the beam.

(7) It may be deduced that when the TS/YS ratio reduces, the tensile stress and strain of flexural rebar increases, resulting in the beam becoming more ductile. Previous findings by Youcef and Chemrouk [8], Charif et al. [13], and Duy and Jack [15] support this.

(8) Extending the technique given to model the complex RC framework performance with HSSR under cyclic stress can create models that are suitable for modeling this complex behavior.

Conflict of interest: Authors state no conflict of interest.

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Received: 2022-03-22

Revised: 2022-07-05

Accepted: 2022-08-01

Published Online: 2022-12-02

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2022-0365

Keywords for this article

high-strength rebar; flexural behavior; ABAQUS; FE; reinforced concrete beam

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