Torsional Improvement of RC Beams Using Various Strengthening Systems

Abstract

Many structural elements are subjected to a significant torsional moment that affects the structural design and may require strengthening. This paper presents different effective strengthening techniques to enhance the torsional capacity of reinforced concrete (RC) beams. An experimental and numerical investigation was undertaken to evaluate the efficacy of utilizing various strengthening systems. The experimental program included six full-scale RC beams with a cross-section dimension of (150 mm × 300 mm) and a length of 1500 mm, split into one beam without strengthening as a control beam, and six beams strengthened with various materials. The various strengthening materials were wrapped aluminum strips with anchorage bolts, wrapped stainless steel strips with anchorage bolts, wrapped glass fiber reinforcement polymer (GFRP), one layer of wrapped steel wire, and two layers of wrapped steel wire meshes along the beam. The results showed that the ultimate torque of the beam strengthened by wrapped aluminum strips and the beam strengthened by wrapped stainless steel strips was larger than the control beam by about 32% and 40%, respectively, because the strips acted as an external reinforcement. In addition to the strengthening systems, using aluminum strips and stainless steel strips is effective in raising the capacity to a similar degree despite the high cost of the stainless steel strips. The ultimate torque of the beams strengthened by GFRP, one-layered wrapped steel wire meshes, and two-layered wrapped steel wire meshes along the beam is larger than the control beam by about 62%, 118%, and 163%, respectively, in addition to the ultimate angle of twist, which was larger than the control beam by about 53%, 93%, and 126%, respectively. This showed that the strengthening using the two-layered wrapped steel wire meshes along the beam would be very significant in increasing the ultimate torque strength. Moreover, the strengthened beam by two-layered fully wrapped steel wire meshes along the beam developed the highest ductility factor compared to all strengthened beams; in contrast, the beam strengthened by GFRP had less ductility. To verify the outcomes of the experimental tests, a finite-element program, ABAQUS, was performed. Finally, an excellent agreement between the experimental and numerical results was obtained.

1. Introduction

Numerous structural components are exposed to a large torsional moment which impacts the structural design and might require strengthening. It may be necessary to strengthen reinforced concrete members with low-torsional shear capacity. There are some causes for this, such as inadequate transverse steel as a result of poor construction, a reduction in the effective rebar area due to corrosion, or greater loading as a result of an alteration in occupancy. Additionally, there are fewer overall safety criteria than before in the design codes currently in use. Thus, torsion is emerging as a widespread issue. RC members that are subjected to increasing torsion may abruptly fail. Steel plate bonding is one of the most often used reinforcing procedures that have been created, although it is frequently vulnerable to corrosion damage and fails in the strengthening system.

Analytical and finite element (FE) studies were performed to explore the behavior of RC beams strengthened with a fiber reinforcement polymer (FRP) composite subjected to torsional loading [1]. The comprehensive nonlinear FE investigation was conducted in conjunction with the analytical research utilizing the software program ABAQUS. To forecast the torsional behavior of the FRP-strengthened RC members considering the impact of FRP confinement, an improved analytical model was proposed. It was concluded that the ability of both methodologies to predict the behavior of FRP-strengthened RC beams under torsion was confirmed by a comparison of the FE and analytical predictions with the experimental data. The falling of the concrete cover was postponed by the exterior confinement presented by the FRP strengthening. Furthermore, the FRP strengthening improved the strength and stiffness.

The torsional behavior of RC beams strengthened with an externally bonded fiber-reinforced cementitious matrix (FRCM) composite has been studied using numerical simulation [2]. Results demonstrated that when failure is caused by the crushing of the concrete strut, the torsional strength increases with increasing concrete compressive strength. On the other hand, the torsional strength was not responsive to the compressive strength of the concrete when the failure was caused by fiber rupture. Additionally, the torsional strength improved as the fiber reinforcement ratio increased. The behavior of the RC beams strengthened with the CFRP laminate strips and ropes around the cross-section with epoxy and cement-based adhesives and the exposure to pure torque was experimentally investigated [3]. It was found that when employing epoxy adhesive for CFRP laminate and rope, the ultimate capacity of the beams for torsion increased greatly by almost 15.4% and 23.3%, respectively. In addition, the fracture torque was enhanced in comparison to the reference beams.

Experimental research has been done to determine the effectiveness of ultra-high-performance fiber-reinforced concrete (UHPFC) that strengthens RC beams in torsion [4]. It was established that, in comparison to strengthen beams with three and two sides, strengthened RC beams with four sides with a thin layer of UHPFC display improved torsional behavior and greater capacity. For RC beams without stirrups, the UHPFC could be employed as an efficient external torsional reinforcement. Experimentally, adding steel fibers to normal RC beams to increase the torsional strength has been investigated [5]. It was revealed that using steel fiber increased the torsional strength of RC beams positively exposed to pure torsion. When compared to the reference beam without steel fibers, the torsional strength of steel fiber beams was increased up to 47.27%.

A wide review of the torsional strengthening of RC beams employing externally bonded composites has been provided [6]. It was stated that completely wrapped FRP beams had the greatest gains in torsional strength. The increase in torsional strength was about 51%. Additionally, the torsional strength values predicted by the FE software were within 38% of the experimental values. The torsional behavior of RC beams externally strengthened by coir fiber sheets was experimentally studied [7]. It was found that for the U-shaped wrapping beam, the torsional strength was increased by 34.28% when compared to the reference unstrengthened beam, while for the two-sided wrapping beams, the torsional strength was increased by 24.18%. To evaluate the energy absorption of CFRP strengthened by two equal-span concrete beams under pure torque, an experimental program consisting of sixteen beams was carried out [8]. According to the experimental findings, all the beams wrapped with CFRP sheets had greater torsional energy absorption capacity than the control specimens.

High-strength concrete (HSC) beams strengthened with CFRP and having minimum torsional reinforcement were experimentally tested to examine the pure torsional behavior of the strengthened beams [9]. Results revealed improved behavior of CFRP-strengthened RC beams. Compared to the unstrengthened reference beam, the CFRP-strengthened beams displayed a 75% enhancement in torsional capacity. An experimental investigation has been performed to study the torsional behavior of RC flanged T-beams strengthened with GFRP [10]. Results revealed that all GFRP-strengthened beams have significantly improved torsional strength when compared to unstrengthened specimens.

Analytical research has been done on the torsional behavior of hollow cross-section-reinforced concrete elements strengthened by steel fibers (end hooked and corrugated) [11]. It was stated that utilizing steel fibers increased the initial and final cracking torque of RC structural elements under pure torsion. The perfect bond theoretical assumption between the steel bars and surrounding concrete is most likely the cause of the discrepancy between the theoretical and experimental results. Compared to end-hooked steel fibers, corrugated steel fibers have a lower torsional resistance. Furthermore, the torsional ductility of the concrete members under pure torsion was improved by the addition of steel fibers to the concrete mixture.

Experimental research has been done on the torsional strengthening of RC beams employing various configurations of near-surface-mounted FRP with epoxy resins and cement-based adhesives [12]. Results discovered that the epoxy adhesives significantly increased the maximum torsion capacities of the beams by 21.6% and 30.7%. However, when employing the cement-based adhesives for the four-face and three-face strengthening, the improvements were only 12.7% and 15.7%, respectively. Experimental and analytical research has been done on the torsional strengthening of CFRP externally strengthened solid and box-section RC beams [13]. Results have demonstrated that externally bonded CFRP is a practical method of torsional reinforcing RC box sections and solid beams for cracking and ultimate strength. Moreover, despite debonding at high loading levels, complete anchoring of the CFRP avoided the failure of the specimen.

Strengthening of RC beams using epoxy-bonded carbon FRP sheets and strips as external transverse reinforcement to study the torsional behavior has been experimentally studied [14]. It was reported that epoxy-bonded carbon FRP materials are a practicable strengthening method for beams subjected to torsion. In comparison to the failure of the control specimens, the failure of the wrapped beams with FRP strips was slightly delayed, and fibers initially prevented cracking. Experimentally, the torsional strengthening of solid and box-section RC beams using externally bonded CFRP has been thoroughly studied [15]. Experimental results showed that externally bonded CFRP is a practical method of torsional strengthening for RC box-section and solid beams. In comparison to the control unstrengthened specimens, cracking and ultimate strengths increased for CFRP-strengthened beams by up to 40% and 78%, respectively.

Experimental research has been done on the behavior of RC box beams reinforced with externally bonded CFRP sheets under combined bending moment, shear, and cyclic torque effects [16]. According to the experimental findings, externally bonded CFRP significantly improved the beams’ torsional and deformation capacities. Moreover, it was stated that CFRP strengthening decreases the ductility of the beams, thus extra care should be taken with the number of CFRP layers to prevent brittle failure. A detailed parametric investigation was done to study the effect of CFRP strengthening different shapes and techniques on the torsional capacity of RC beams [17]. It was revealed that instead of employing CFRP strips, continuous wrapping conditions are significantly more successful at improving torsion strength. Additionally, when employing strip wrapping, the effect of using CFRP double layers or increasing the CFRP strength on torsion strength was insignificant, but the CFRP continuous wrapping was significantly more dependable.

The torsional behavior of externally bonded FRP beams with a large web opening exposed to pure torsion has been investigated experimentally [18]. It was found that the best results come from strengthening the beam with an opening using a full 90° wrap around the chords and solid parts close to the opening region. Consequently, the torsional strength of the strengthened beam increased by 48% compared to the control beam with an opening and approached that of the reference solid beam without an opening.

RC beams reinforced with FRP were studied numerically under torsional failure using an FE computer program and then validated using experimental data from several earlier investigations [19]. It was concluded that completely wrapped beams with continuous FRP sheets exhibited torsional failure at higher levels very little torsional cracking and tensile rupture of the FRP laminate. The detected discrepancies between the experimental results and FE results showed that the assumption of complete interaction of steel rebar and CFRP with concrete is practicable. In an experimental study, the effects of torsion and bending on RC beams strengthened with different configurations of continuous spiral near surface mounted (NSM) steel wire rope has been studied [20]. It was determined that, regardless of the spiral NSM steel wire rope spacing, all beams reinforced by the wire rope demonstrated stronger torsional resistance than the control beam. Moreover, because the inclined steel wire ropes remained under stress until they failed, the spiral proposal is an efficient method.

During an extensive parametric study, several important elemental effects on the energy absorption of torsional RC beams reinforced with external FRP were investigated [21]. The findings demonstrate that the concrete compressive strength, FRP thickness, and vertical steel ratio were the most crucial factors influencing the RC beams torsional energy absorption. Continuous RC beams exposed to pure torsion strengthened with CFRP have been studied during experimental research [22]. The results showed that, compared to the reference unstrengthened specimens, the torsional resistance of all beams wrapped with CFRP has been improved by about 64%. Moreover, due to the presence of CFRP, which delays the first cracking, the failure of the CFRP-wrapped beams was delayed in contrast to the failure of the reference specimens.

Experimental research was done on the torsion behavior of hollow and solid sections of RC beams reinforced with steel fiber [23]. Results showed that when the proportion of steel fibers increased from 0% to 2.5%, the ultimate torsional capacities for solid and hollow sections increased by 98.2% and 178%, respectively. The number of cracks was higher in the hollow sections than in the solid ones. The ABAQUS program was used to study the behavior of rectangular RC beams strengthened with CFRP laminates under pure torsion [24]. It was found that, when compared to earlier experimental investigations, the ultimate torsional capacity of the finite element methods showed good agreement with the experimental data. Additionally, the difference in the FE capacity between the CFRP-strengthened beams and the unstrengthened reference beam was less than 11%.

Muhammad et al. [25] examined experimentally the flexural and shear behavior of RC beams strengthened with CFRP. The results showed that increasing CFRP does not always increase bearing capacity. Moreover, by combining CFRP flexural and shear in the right way, the structural performance can be improved. In addition to the bond properties at the concrete–CFRP interface are crucial, since the debonding of the CFRP strips frequently causes failure.

The purpose of this study is to determine experimentally and numerically the most effective system for strengthening RC beams under pure torsion. The torsional strengthening techniques suggested in this paper include (1) bonding-wrapped aluminum strip with anchorage bolts every 125 mm along the beam, (2) bonding-wrapped stainless steel strip with anchorage bolts every 125 mm along the beam, (3) bonding fully wrapped glass fiber reinforcement polymer (GFRP) along the beam, (4) bonding fully wrapped one-layer steel wire meshes along the beam, finally bonding fully wrapped two-layer steel wire meshes along the beam. To represent the nonlinear behavior of the tested beams, a numerical analysis of the finite element models was carried out using the ABAQUS [26] software.

2. Experimental Program

2.1. General Description

All the tested beams were constructed using ordinary Portland cement (OPC) 42.5 grade, which has a specific gravity of 3.10 g/cm³ and an. The experimental program included six full-scale RC beams with a cross-section of (150 mm × 300 mm) and a length of 1500 mm, divided into the control beam without strengthening and the other beams with different materials strengthening. All the tested beams have the same reinforcement details as illustrated in Figure 1. Each beam has four longitudinal reinforcement bars with a diameter of 16 mm with an experimental yield strength of 420 MPa. The beams have closed transverse reinforcement with a diameter of 12 mm every 167 mm with an experimental yield strength of 280 MPa. The corresponding reinforcement ratio for the longitudinal reinforcement and transverse reinforcement was ρ_sl = (A_sl/A_c) =1.78% and ρ_st = (A_st p_t/A_c s) = 1.05%, respectively, where A_sl is the total area of the longitudinal reinforcement bars, A_c is the concrete cross-section area, A_st is the area of one leg of transverse reinforcement, p_t is the perimeter of the one stirrup, and s is the center-to-center distance between the stirrups. To avoid locally crushing the concrete near the supports, the terminal portions of the beams were suitably over-shear reinforced. Four holes were made on both sides of all beams by placing pipes with a diameter of 1 inch inside the wooden box before beam casting. All the beams were cast with normal-strength concrete (NSC with a cylinder compressive strength of f_c’ = 30 MPa). Two steel arms were fixed and positioned opposite each other at the end parts of each beam with a length of 500 mm. The control beam B0-Control was without strengthening. The second beam (B1-AS) was strengthened by bonding-wrapped aluminum strips with anchorage bolts every 125 mm along the beam. The third beam (B2-SS) was strengthened by bonding-wrapped stainless steel strips with anchorage bolts every 125 mm along the beam. These types of previous strengthening are not susceptible to corrosion. Both aluminum strips and stainless steel strips have a width of 100 mm and a thickness of 2 mm. The fourth beam (B3-GFRP) was strengthened by bonding fully wrapped glass fiber reinforcement polymers (GFRP) along the beam. The fifth beam (B4-1SM) was strengthened by fully bonding one layer of steel wire meshes along the beam. The last beam (B5-2SM) was strengthened by fully bonding two layers of steel wire meshes along the beam.

Table 1. Program details for tested beams.

Beam No.	Terminology	Strengthening Strategy
B0	B0-Control	-
B1	B1-AS	Aluminum strips with anchored bolts every 125 mm
B2	B2-SS	Stainless steel strips with anchored bolts every 125 mm
B3	B3-GFRP	Fully wrapped glass fiber reinforcement polymer
B4	B4-1SM	Fully wrapped single layer of steel wire meshes
B5	B5-2SM	Fully wrapped dual layer of steel wire meshes

shows the program details of the tested beams.

2.2. Strengthening Techniques

2.2.1. Beams Strengthened with Aluminum and Stainless Steel Strips

The beam (B1-AS) was strengthened by bonding wrapped aluminum strips with anchorage bolts along the beam. The following was the strengthening procedure: (a) casting the NSC concrete and curing it with pure water for 28 days; (b) unscrewing the wooden box and turning over the beam; (c) roughing the RC beam surfaces using drilling equipment; (d) utilizing the drilling equipment to create a-holes with a depth of 80 mm where the aluminum strips were bonded; (d) using air pressure was used to remove all of the residual dust and small particles; (e) thoroughly combining Sika-Dur-31 [27] adhesive’s two components before casting into the holes and painting the sides of the RC beam where the wrapped aluminum strips were bonded every 125 mm along the beam, and the overlap splices of the aluminum strips were 200 mm; (f) using anchored bolts to connect the aluminum strips with the RC beam. The average experimental yielding stress for the aluminum strips was 262 MPa. Figure 2 shows the final prepared beam B1-AS. The strengthening process of the beam (B2-SS) is similar to the beam (B1-AS) but the strengthening has been done by wrapping stainless steel strips every 125 mm along the beam. Both aluminum strips and stainless steel strips have a width of 100 mm and a thickness of 2 mm. The average experimental yielding stress for the stainless steel strips was 448 MPa. Figure 3 shows the final prepared beam B2-SS. The used bolts have a diameter and length of 8 mm and 80 mm, respectively. The experimental maximum shear for used bolts was 105 kN.

2.2.2. Beams Strengthened with GFRP and Steel Wire Meshes

The preparation of the beams B3-GFRP, B4-1SM, and B5-2SM is the same as the previous beams B1-AS and B2-SS. The beam B3-GFRP was fully wrapped by a GFRP sheet along the beam and the GFRP sheet is covered with cement mortar. Figure 4 shows the location of the GFRP, as was the case with the preparation of the beam B4-1SM, but it was strengthened by fully bonding one layer of steel wire meshes around the perimeter of the beam and the steel wire meshes were covered with cement mortar. Figure 5 shows the location of fully wrapped steel wire meshes. The strengthening process of the beam (B5-2SM) was similar to the beam (B4-1SM) but the strengthening was done by fully wrapping two layers of steel wire meshes along the beam. Figure 6 illustrates the preparation process of the beam B4-1SM and Figure 7 illustrates the strengthening beams before testing.

3. Material Properties

The cement used in the concrete mix of the RC beams was Ordinary Portland cement CEM I N-42.5.

Table 2. Chemical compositions of the used cement.

Chemical composition %	SiO2	Al2O3	Fe2O3	CaO	SO3	K2O	Na2O	MgO
	19.39	4.13	4.70	55.66	3.9	0.28	0.31	1.70

shows the chemical compositions of the used cement. Fine aggregates were natural sand and crushed dolomite stone, which are coarse aggregates with a maximum size of 10 mm. The proportions of the NSC concrete mixture are illustrated in

Table 3. Concrete mix design (normal-strength concrete with f_c’ = 30 MPa).

Mix	Dry Weight, Kg/m3
Ordinary Portland cement	500
Sand	595
Dolomite (10 mm)	1105
Water	215 L/m3

. Three cylinders (φ 150 × 300 mm) were used for the beam’s concrete mix to explain the average stress–strain relationship after 28 days, as illustrated in Figure 8. The concrete cylinder compressive strength f_c’ was 30 MPa. The experimental tensile strength of the beam concrete mix was 2.10 MPa according to the splitting cylinder test [28]. The modulus of elasticity of the NSC was 31,600 MPa. The modulus of elasticity, tensile yield strength, and Poisson’s ratio of the longitudinal reinforcement bars were 200 GPa, 420 MPa, and 0.30, respectively, whereas the experimental yield strength of the transverse reinforcement bars was 280 MPa. Figure 9 shows the average stress–strain curves for the longitudinal reinforcement bars. Figure 10 and Figure 11 show the average stress–strain curve for three specimens of aluminum strips and stainless steel strips, respectively. According to the manufacturers’ report, the tensile strength and modulus of elasticity for Sika-Dur-31 were 30 MPa and 3600 MPa, respectively. The typical shape and the properties of steel wire meshes are illustrated in Figure 12 and

Table 4. Properties of steel wire meshes.

SW (mm)	LW (mm)	Thickness (mm)	Width (mm)	Weight (kg/m2)
16.7	20.60	0.60	0.60	0.58

. The ultimate strength of steel wire meshes was 350 MPa. The typical shape of GFRP is illustrated in Figure 13. The GFRP is made of eight bundles in primary warp directions of approximately 5 mm width and 0.55 mm thickness. The free space between the strands in both directions was about 10 mm, as illustrated in Figure 13.

Table 5. Mechanical properties of GFRP and steel wire meshes.

Properties	GFRP	Steel Wire Meshes
Young’s Modulus (E) MPa	70,000	200,000
Poisson’s Ratio (ν)	0.2	0.3
Rupture stress (MPa)	2000	280

shows the mechanical properties of GFRP and steel wire meshes according to the manufacturer. The surface density of GFRP was 486 gm/m².

Table 6. Cement mortar mix (kg/m³).

Cement	Sand	Silica Fume	Fly Ash	Superplasticizers	Water
800	1200	50	100	2.0	286

shows the mortar cement mix that covers the strengthened systems. The experimental compressive strength and tensile strength for cement mortar were 91 MPa and 5.90 MPa, respectively.

4. Test Setup and Instrumentation

The experimental setup is shown in Figure 14. All tested beams were tested under pure torsional loading up to the ultimate torque. The load was applied through a diagonally placed steel spreader beam on the ends of two steel arms that were fixed at the end of each tested beam. The length of the steel arm is equal to 500 mm. All tested beams were supported on two hinged supports, which allowed the two ends of the beam to rotate and prevent the movements, as illustrated in Figure 14. Proper care was taken to ensure that the loading lever arm was perpendicular to the longitudinal axis of the beam to prevent bending. Thus, the beams between the two supports were subjected to pure torsion. The steel spreader’ top surface was subjected to a point load by a hydraulic jack with a capacity of 150 kN. The measurements of the loads were monitored through a computer-driven data acquisition system. An inclinometer was used to measure the twist angle of the beam.

5. Results and Discussion

5.1. Research Limitations

The current study is limited to studying the behavior of RC beams constructed from normal-strength concrete (NSC with a cylinder compressive strength of f_c’ = 30 MPa) and subjected to pure torsional moments strengthened by aluminum strips with anchored bolts every 125 mm, stainless steel strips with anchored bolts every 125 mm, fully wrapped glass fiber reinforcement polymer, one layer of steel wire meshes, and two layers of steel wire meshes along the beam.

5.2. Cracking Patterns

Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20 illustrate the crack patterns of the beams that were tested until they failed. The cracking torque (T_cr), and the angle of twist at cracking (θcr) are illustrated in

Table 7. Experimental test results.

No.	Beam	Tcr (kN.m)	θcr (rad/m)	Tu (kN.m)	θu (rad/m)	θ85Tu (rad/m)	μ
1	B0-Control	4.41	0.0009	8.50	0.0015	0.0010	1.11
2	B1-AS	6.56	0.0011	11.20	0.0019	0.0013	1.18
3	B2-SS	6.78	0.0016	11.90	0.0028	0.0019	1.19
4	B3-GFRP	8.38	0.0018	13.80	0.0023	0.0021	1.17
5	B4-1SM	10.24	0.0021	18.50	0.0029	0.0026	1.22
6	B5-2SM	12.36	0.0026	22.40	0.0034	0.0032	1.23

. The control beam B0-Control exhibited a wider range of crack propagation and a faster rate of crack progression than the other beams because of the absence of any strengthening along the beam. According to elasticity theory, the cracks of a beam subjected to pure torsion occur on the large faces of a rectangular cross-section because these faces undergo the largest shear stresses. The crack behavior of beams B1-AS and B2-SS have the same manner but the cracking torque was delayed concerning the control specimen. At the torque of 5.56 and 6.78 kN.m, initial hairline cracks appeared for beams B1-AS and B2-SS, respectively, with a crack inclination of approximately 45 degrees to the longitudinal axis. The cracking torque of beams B1-AS and B2-SS are larger than the control beam B0-Control by about 49% and 54%, respectively. Later, with the increase in loading values, the cracks propagated and widened between the strips. After the beam reached its peak load, no debonding was noticed between the RC concrete beams surface and strengthening systems. In addition, the aluminum strip was ruptured whereas the stainless steel strip was not ruptured because the aluminum strip remained under stress until it failed.

Strengthened beams with wrapped GFRP and steel wire mesh sheets exhibited different failure modes, since the sheets inhibited the propagation of cracks. This is the reason that the warped sheets presented higher values of cracking torque moment concerning the other beams as illustrated in Table 7. The cracking torque of beams B3-GFRP, B4-1SM, and B5-2SM is larger than the control beam B0-Control by about 90%, 132%, and 180%, respectively. After the beams reached their peak load, no debonding was noticed at the interface of RC and strengthening systems but GFRP sheets tensile rupture at a location of the diagonal cracks.

5.3. Ultimate Strength

Figure 21 shows the torque versus the twist angle of the beams with various strengthening systems until failure. The ultimate torque (T_u) and ultimate angle of twist (θ_u) are illustrated in Table 7. The control beam (B0-Control) reached the maximum torque of (8.50 kN.m) with a maximum rotation of (0.0015 rad/m). All strengthened beams showed a clear increase in the ultimate torsional moment in comparison with the control beam. The ultimate torque of beams B1-AS and B2-SS are larger than the control beam B0-Control by about 32% and 40%, respectively. The results showed that the beams strengthened with strips of aluminum and stainless steel strips exhibited increased torsional strength and improved performance relative to the control specimen because the strips acted as a like external reinforcement. In addition to the strengthening systems, using aluminum strips and stainless steel strips is effective in raising the capacity to a similar degree despite the high cost of stainless steel strips, whereas the ultimate angle of twist for beams B1-AS and B2-SS is larger than the control beam B0-Control by about 27% and 87%, respectively.

The ultimate torque of beams B3-GFRP, B4-1SM, and B5-2SM are larger than the control beam B0-Control by about 62%, 118%, and 163%, respectively. The experimental results showed that the strengthening using wrapped two layers of steel wire meshes along the beam would be very significant in increasing the ultimate torque strength. The ultimate angle of twist for beams B3-GFRP, B4-1SM, and B5-2SM are larger than the control specimen B0-Control by about 53%, 93%, and 126%, respectively. The effect of the strengthening type on the ultimate torque is presented in Figure 22. Moreover, the results showed that the strengthening using stainless steel strips and aluminum strips was less effective than the previous strengthening methods, but this type is distinguished by its resistance to corrosion.

5.4. Ductility Coefficient

The ductility coefficient (μ) can be expressed as the ratio between the torsion angle at 0.85% of the failure torque and that at the first cracking in torsion of concrete, as illustrated in Table 7. This could be also expressed as the increase in the ability of the beam to sustain a larger twist angle without failing in a brittle manner. Furthermore, the ductility coefficient of the tested beams under pure torsion was improved by various strengthening systems. The ductility factor of beams B1-AS, B2-SS, B3-GFRP, B4-1SM, and B5-2SM is larger than the control specimen by about 6%, 7%, 5%, 10%, and 11%, respectively. From Table 7, it can be seen that the strengthened beam B5-2SM developed the highest ductility factor compared to all strengthened beams; in contrast, beam B3-GFRP has less ductility.

6. Numerical Investigation

RC beams strengthened with various materials strengthening and subjected to pure torsion are modeled numerically using finite element (FE) methods utilizing the ABAQUS software [24]. The FE simulation employs three-dimensional elements, including solid, surface shell, and truss. The models account for the materials’ elastic and plastic properties.

6.1. Modeling of Materials

6.1.1. Concrete

The damaged plasticity model is frequently used for systems that are subjected to pure torque because it can forecast how a process would behave up until failure. The concrete damaged-plasticity (CDP) model can be described as compression d_c and tension damaged d_t, respectively. The uniaxial compressive and tensile concrete models were derived from the experimental results.

Table 8. CDP model for NSC concrete (f_c’ = 30 MPa).

Young’s Modulus (E) MPa	31,600		Dilation angle	30
Poisson’s Ratio (ν)	0.2		Eccentricity	0.1
Compression yield stress	Compression inelastic strain	Compression damage parameter	fbo/fco	1.16
19.02250352	0	0	K	0.667
29.03305204	0.000534509	0.065027563	Viscosity parameter	0.005
37.2257384	0.001137974	0.103528939
41.44514768	0.001938179	0.15014224
36.80379747	0.002709555	0.217604589
25.72081575	0.004879537	0.417483032
14.82419128	0.007033935	0.64190036
5	0.008876666	0.8702447
Tension yield stress	Tension displacement	Tension damage parameter
3.5	0	0
1.167	0.024	0.887295826
0.4	0.08	0.89867822

and

Table 9. CDP model for mortar cement (f_c’ = 90 MPa).

Young’s Modulus (E) MPa	29,100		Dilation angle	35
Poisson’s Ratio ν	0.17		Eccentricity	0.1
Compression yield stress	Compression inelastic strain	Compression damage parameter	fbo/fco	1.16
27.956	0	0	K	0.667
37.2747	0.00033	0.00033	Viscosity parameter	0.005
46.5933	0.00065	0.00065
58.2787	0.00126	0.00126
63.817	0.00155	0.00155
68.8792	0.00184	0.00184
73.4652	0.00212	0.00212
77.5751	0.00241	0.00241
81.2089	0.0027	0.0027
84.3665	0.00299	0.00299
87.048	0.00328	0.00328
89.2534	0.00357	0.00357
90.9826	0.00386	0.00386
75.8333	0.00466	0.00466
60.6667	0.00547	0.00547
45.5	0.00627	0.00627
39.4333	0.00868	0.00868
33.3667	0.01109	0.01109
27.3	0.0135	0.0135
Tension yield stress	Tension displacement	Tension damage parameter
4.59406657	0	0
5.829956585	0.015766782	0.015766782
2	0.020701201	0.020701201

display the values of compression and tension damage of NSC (with f_c’ = 30 MPa) and mortar cement (with f_c’ = 90 MPa), respectively.

6.1.2. Geometric Modeling Technique

The solid three-dimensional eight-node bricks (C3D8R) were used to describe the NSC concrete and mortar cement in the FE study. The C3D8R had less integration and hourglass control. The main beam’s reinforcement bars are modeled using a bar truss element called T2D3. The beam reinforcement is supposed to provide the ideal elastic-plastic behavior, as illustrated in Figure 9. Stainless steel strips, aluminum strips, GFRP sheets, and steel wire meshes were defined as surface elements (S4R). The mechanical properties of GFRP sheets and steel wire meshes were taken from the manufactory. The stress–strain relationships for both stainless steel strips and aluminum strips are illustrated in Figure 10 and Figure 11, respectively. Since no debonding was observed during the experimental test, the interface between the concrete surface and both main beam reinforcement bars and the strengthening systems were modeled as a perfect bond. All of the elements in the FE model were purposefully given the same mesh size to guarantee that every pair of dissimilar materials shared a node to obtain accurate results. To choose an appropriate mesh with acceptable accuracy in terms of ultimate torque and ultimate angle of twist, three models with various mesh sizes fine, medium, and coarse of 15, 25, and 35 mm, respectively, were examined. The concrete medium volume meshes and beams reinforcement medium meshes are illustrated in Figure 23. The beams supports were hinged support and the loads were applied at the free end of the steel arm as illustrated in Figure 24 to simulate the experimental test setup. Figure 25, Figure 26, Figure 27 and Figure 28 show the FE strengthening of the tested beams. In this investigation, the total applied load is separated into many load increments. Convergence is provided after each load increase by Newton–Raphson equilibrium iterations within the permitted tolerances. During the various cracks that appeared in the concrete, the loads were applied gradually with lower load increments. Beam failure occurred when the convergence failed with small load increments.

7. Comparison of the Experimental and Finite Element Findings

It has been found that the medium mesh gives satisfactory results compared to the experimental results in the ultimate torque and ultimate angle of twist values, as shown in

Table 10. Comparison of the experimental and finite element findings.

Specimen	Ultimate Torque, kN.m				Ultimate Angle of Twist, rad/m
	FE			EXP./FE (Medium)	FE			EXP./FE (Medium)
	Fine	Medium	Coarse		Fine	Medium	Coarse
B0-Control	8.75	8.40	8.30	1.01	0.0019	0.0017	0.0015	0.88
B1-AS	10.50	10.10	9.90	1.11	0.0023	0.0020	0.0018	0.95
B2-SS	11.64	11.20	11.01	1.06	0.0026	0.0024	0.0022	1.17
B3-GFRP	14.21	13.70	13.50	1.01	0.0028	0.0026	0.0025	0.88
B4-1SM	18.23	17.60	17.30	1.05	0.0031	0.0028	0.0026	1.04
B5-2SM	22.66	21.90	21.50	1.02	0.0033	0.0031	.00290	1.10

. Moreover, it has an acceptable computational time compared to the other meshes. The range between 0.88 and 1.17 is the FE forecast for the experimental angle of twist ratio, as illustrated in Table 10. Compared to the experimental results, the torque–twist curves from the numerical simulations behave stiffer before the first crack, which is likely caused by a sizable scatter in the tensile strength of the concrete. The action of quasibrittle materials, such as concrete, depends greatly on the position of cracks created on the tensile side. It can be observed that the experimental results and the FE predictions are in good agreement throughout the entire loading range. The findings of the theoretical finite elements were somewhat smaller than the values from the experiments. These variations might be a result of the experiment’s human measurement errors. Moreover, a stiffer finite element model could result from assuming a perfect bond between the concrete surfaces and strengthening systems. Figure 29, Figure 30, Figure 31, Figure 32, Figure 33 and Figure 34 show the FE cracks of the examined beams, and by comparing it with the experimental failure patterns, it is clear that there is a great match. The ultimate torque angle of twist relations for the numerical model and the corresponding experimental result is shown in Figure 35, Figure 36, Figure 37, Figure 38, Figure 39 and Figure 40. It is noted that the FE model can track the torque–twist behavior with a difference of no more than 6% in the maximum torque and 17% in the twist. The experimental findings and the FE predictions can be seen to be in good agreement. The behavior of numerical models is consistent with the numerical models performed by [1].

8. Conclusions

To assess the effectiveness of using various torsional strengthening techniques for beams, six strengthened beams and one unstrengthened beam as a control were experimentally tested in this study up to failure. The following conclusions can be written as follows:

• The ultimate torque of the beams B1-AS and B2-SS are larger than the control beam B0-Control by about 32% and 40%, respectively, because the strips acted as an external reinforcement.
• The strengthening systems using aluminum strips and stainless steel strips are effective in raising the torsion capacity to a similar degree despite the high cost of the aluminum strips.
• The ultimate torque of the beams B3-GFRP, B4-1SM, and B5-2SM are larger than the control beam B0-Control by about 62%, 118%, and 163%, respectively, in addition to the ultimate angle of twist being larger than the control specimen B0-Control by about 53%, 93%, and 126%, respectively.
• The strengthened beam B5-2SM developed the highest ductility factor compared to all strengthened beams; in contrast, the beam B3-GFRP had less ductility.
• The cracking torque of beams B3-GFRP, B4-1SM, and B5-2SM are larger than the control beam B0-Control by about 90%, 132%, and 180%, respectively. After the beams reached their peak load, no debonding was noticed at the interface of the RC and strengthening systems, but the GFRP sheets tensile rupture at a location of the diagonal cracks.
• The range between 0.88 and 1.17 is the finite element forecast for the experimental ultimate torque ratio. The finite element analysis demonstrates a clear agreement with the test and provides additional insight into the effects of various strengthening procedures based on the results of the experimental investigation.

Future work: the torsional improvement of high-strength and ultra-high-strength RC beams with various strengthening systems.