Experimental and Numerical analysis for ultra-high performance concrete beams strengthened with CFRP sheet

In recent years, the application of carbon fiber reinforced polymer (CFRP) for strengthening ultra-high-performance concrete (UHPC) has gained significant attention due to UHPC’s superior mechanical properties and dense matrix, which enhance the bond performance with CFRP. Finite element (FE) analysis has become a critical tool for understanding and predicting the structural behavior of CFRP-strengthened UHPC elements. For instance, (Abbas et al. 2020) developed a 3D nonlinear FE model to simulate the flexural performance of CFRP-strengthened UHPC beams and found good agreement with experimental results, highlighting the accuracy of FE simulations in capturing failure modes and load-displacement responses. Similarly, (He et al. 2019) conducted a numerical investigation using ABAQUS and demonstrated that the interfacial bond between CFRP and UHPC plays a crucial role in controlling debonding failure, emphasizing the need for accurate bond-slip modeling. (Moreover, Ma et al. 2021) introduced a cohesive zone model to simulate the interface behavior between CFRP and UHPC, which effectively predicted delamination patterns under shear loading. These studies underline the effectiveness of FE modeling in optimizing CFRP retrofit strategies and contribute to a better understanding of the structural behavior of UHPC composites. However, further research is still needed to calibrate interface models and validate them across different strengthening configurations and load scenarios.

Furthermore, most past studies either focus on flexural strengthening or small-scale bond tests, with insufficient attention to shear-critical regions and the role of CFRP in shear retrofitting of UHPC members. To address this gap, our study proposes FE models and an experimental program involving full-scale UHPC beams retrofitted with externally bonded CFRP sheets, aiming to assess their shear performance. The novelty lies in both the scale of testing and the targeted behavior (shear).

“(Dewi et al. 2024) conducted experimental tests on hollow circular RC columns strengthened with CFRP strips and validated a finite element (fiber element) model which closely matched the experimental strain results across reinforcement and CFRP layers. This confirms the reliability of FE modeling for predicting behavior of CFRP-strengthened concrete elements.”

“In (Maulana et al. 2025), finite element analysis was used to simulate CFRP-strengthened beam-column joints, showing that extending CFRP sheets to twice the beam height significantly improves seismic and shear resistance. Another study (CEE, 2025) performed numerical FE modeling on composite-strip-strengthened concrete beams, validating the reliability of the FE approach for predicting structural improvements comparable to CFRP strengthening.”

This paper contains a description of reinforced concrete beams that were strengthened using the CFRP sheets technique by experimental methods employing FE models. To compare the experimental results, the simulation was conducted in ABAQUS 6.14 under monotonic two-point loading. The Concrete Damaged Plasticity model was applied to simulate the irregular behavior of concrete, and its properties were derived from the results of experimental tests. The model contained both unimproved and strengthened CFRP beams to understand shear behaviour and check the success of strengthening the beams. Major aspects of bar interaction were described to make sure the simulation was accurate. The objective of the developed model was to imitate the ways failures and cracks spread in the material during the tests.

All specimens had beams of the same geometry and concrete grade, resulting in equal compressive strength in all cases (Concrete mix information and details are listed in Table 1. The choices for shear reinforcement in the beams differed a lot. In the control specimen, known as RC-C Beam, there was a tiny internal reinforcement to resist shear, with only two shear links added close to the supports and without external CFRP treatment.

Different types of CFRP reinforcement were used on the other beams to find out which was best. This specimen, RC-CFRP-U-90-100 Beam, included U-shaped CFRP strips joined with epoxy and arranged perpendicular (90 degrees) to the beam axis from the beam’s center support to the load point. These strips were spaced 150 mm apart center-to-center. A similar beam, the RC-CFRP-U-45-100, used the same width and spacing of CFRP strips but oriented at a 45-degree angle, offering a different shear reinforcement configuration. Another design, the RC-CFRP-2SIDE-600 Beam, employed wide (600 mm) epoxy-bonded CFRP strips applied to both sides of the beam, again extending from the center point of the support to the load point. The RC-CFRP-U-90-600 Beam followed a similar pattern but with U-shaped strips at a 90-degree angle on each side. Lastly, the RC-CFRP-FULL FACE Beam utilized full-face epoxy-bonded CFRP strips, also 600 mm wide, covering the entire side surfaces between the support and load center to maximize shear strengthening.

All beams were uniformly dimensioned at 200 mm width, 400 mm depth, and 2050 mm length as illustrated in Figure 1. The testing setup involved simply supported specimens subjected to four bending points, with supports placed 125 mm from the beam ends, according to ASTM C1609 or general practices in shear and flexural testing of concrete. The loading was load-controlled and monotonically applied at a constant rate of two kN/min. Reinforcement included three 16 mm diameter deformed steel bars at the bottom and two at the top, maintaining a longitudinal steel ratio of 1.67% in both layers. This flexural reinforcement was intentionally designed to prevent flexural failure, allowing the study to focus solely on the shear resistance provided by the CFRP strengthening. The effective depth was measured at 367 mm, with a concrete cover of 25 mm, ensuring consistent protection for the steel bars.

Figure 1:

Dimension and reinforcement details of specimens (all dimensions in mm)

In this study, CFRP was employed in various shear strengthening arrangements, as outlined in Table 2. The first beam, serving as a control specimen, was tested without CFRP reinforcement, as shown in Figure 2. The CFRP strips employed for shear strengthening were 100 mm wide and spaced at 150 mm center-to-center. The length of each strip corresponded to the full depth of the beam (400 mm) and was adjusted accordingly when applied at angles other than 90°, to account for the increased length resulting from the inclination.

In one configuration, the strips were oriented at 90 degrees, as illustrated in Figure 3, while in another, they were placed at a 45-degree angle, as shown in Figure 4. For the two-sided strengthening scheme, wider CFRP strips measuring 600 mm in width were bonded to both sides of the beam, as shown in Figure 5. The U-shaped configuration featured 600 mm-wide CFRP strips attached to the tension face at the bottom and to both side faces, as seen in Figure 6. Similarly, a closed-shaped arrangement involved wrapping CFRP strips around all faces of the beam, as illustrated in Figure 7. CFRP sheets were installed along the shear span, starting from the points of support to the locations where the loads were applied on both sides

Figure 2:

(RC-C) control specimen (all dimensions in mm)

Figure 3:

(RC-CFRP-U-90-100) (all dimensions in mm)

Figure 4:

(RC-CFRP-U-45-100) (all dimensions in mm)

Figure 5:

(RC-CFRP-2side-90-600) (all dimensions in mm)

Figure 6:

(RC-CFRP-U-90-600) (all dimensions in mm)

Figure 7:

(RC-CFRP-Full Face) (all dimensions in mm)

The major parts of the reinforced concrete beams are the concrete, steel reinforcement inside, and CFRP sheets added for shear strength. Each part of the analysis should capture the actual behaviour of the materials in monotonic stressed RC beams strengthened with CFRP. Material models available in the ABAQUS library reflect how every physical component behaves.

4.1.

Material Modelling

4.1.1.

Steel Reinforcement

You can use ABAQUS to include reinforcement using smeared reinforcement in the concrete mass, explicit truss or beam elements together with an embedded region constraint, or predefined layers of rebar. Rebar sets the reinforcement for membrane, shell and surface elements in terms of uniaxial reinforcement. The user must set up one or more options for reinforcing the behavior. For every layer, they should choose a label for the rebar layer, set the cross-sectional area per layer, and determine how far apart the rebars are arranged in the mentioned direction. This comes from their study (Malm, R., & Ansell, A. 2009). This part of the report will only cover embedded region modelling, which was used for reinforcement modelling in the study. To use the truss method, you just need to enter the area of the reinforcement bars. Another popular tactic for structures is to use beam element modelling, which recognizes the dowel effect and slightly makes the structure stronger. On the other hand, using this approach is not suggested since defining a large amount of input parameters takes a lot of computing power (Eriksson, D., & Gasch, T. 2011), (Hibbitt, Karlsson & Sorensen, Inc. 2014), and (Malm, R. 2009). (Hibbitt, H., Karlsson, B., & Sorensen, P. 2011) Writers state that bond slip is not included in the implementation of embedded region modelling. Still, the stiffening effect of concrete, according to (Malm, R. 2009), includes some of these aspects.

4.1.2.

Concrete

Smeared cracking and concrete damaged plasticity (CDP) are the two techniques available in ABAQUS for describing the actions of concrete. The smeared cracking model deals with beams, trusses, solids, and shells. This type of inquiry does not pay attention to each minuscule crack in the system. The CDP was introduced by applying the yield function from the paper written by (Lubliner, J., Oliver, J., Oller, S., & Onate, E. 1989). Here, linear elasticity gives a true account of how materials act under compression as well as tension. Tensile cracking and compression fractures are the two ways the model may fail. The CDP model is very popular as it accurately depicts the actions of concrete. For calculations involving non-straight forces in concrete, it is especially effective because it gives a thorough account of the material’s behaviour (especially in reinforced concrete members affected by shear) (Tyau, J. S. 2009).

Principle of concrete damaged plasticity formulation

Two important things define the damaged plasticity model: decreasing properties under compression and tension. Changing the initial stiffness of the member permits the element’s elastic stiffness to decrease when it goes into plasticization.

(1) dt=dtε˜t,pι,θ,fi; 0≤dt≤1 {d_t} = {d_t}\left( {{{\tilde \varepsilon }_t},{p_\iota },\theta ,{f_i}} \right);\;\;\;0 \le {d_t} \le 1 (2) dc=dcε˜c,pι,θ,fi; 0≤dc≤1 {d_c} = {d_c}\left( {{{\tilde \varepsilon }_c},{p_\iota },\theta ,{f_i}} \right);\;\;\;0 \le {d_c} \le 1

Where:

• The subscripts t and c refer to tension and compression, respectively.

• ε˜t,pι {\tilde \varepsilon _t},{p_\iota } , and ε˜c,pι {\tilde \varepsilon _c},{p_\iota } , These are the equivalent plastic strains.

• θ is the temperature.

• f_i - (i = 1,2,3,4,...) are other predefined field variables (Hibbitt, H., Karlsson, B., & Sorensen, P. 2011).

The numbers for “damage parameters” go from zero for undamaged and unchanged material to one for destroyed material. You can find the effects of the plasticity default in Figure (8). As you see in Figure (8), the curve shows the stress versus strain for tension and compression. A dotted line shows the shape of the curve. The purple line represents the shape of cyclic loading that happens when the element is in severe damage, and it experiences tension past its tensile strength limit. Reveal that communities often use colour to form their identities. Yet only part of the material is damaged in cracking, and this can be denoted by the amount of time dt. You can determine the elastic behavior after unloading by multiplying the original modulus by (1 – d_t). Parameter wc shows the percentage of change in stress due to strain, and the compression modulus is given by (1 − d_t + w_c d_t) (Colavita, M. M., Serabyn, E., Millan-Gabet, R., Koresko, C. D., Akeson, R. L., Booth, A. J., Mennesson, B. P., Ragland, S. D., Appleby, E. C., & Berkey, B. C. 2009).

You should also notice that when a crack appears, compression stiffness does not change, so w_c is still constant at one. If the stiffness brought by complete destruction and compression does not change with tension, the parameter (w_c) will equal zero. The attributes lost in the bashing part are shown by the d_c variable, while w_t represents the initial status in tension.

Figure 8:

Uniaxial load cycle (tension-compression-tension) ABAQUS 6.14

Concrete Plasticity Parameters

The adjustments given can be implemented to calculate the flow potential yield surface, first introduced by five important factors that need to be established to achieve this. Having tested many different materials, specialists could better determine the values of these parameters. However, all the default settings in ABAQUS were applied (Lubliner, J., Oliver, J., Oller, S., & Onate, E. 1989) and (Lee, J., & Fenves, G. L. 1998).

The five parameters that need to be defined are:

∈: When approaching the asymptote, Drucker-Prager function uses the rate ∈ to describe the curve. If eccentricity goes towards zero, the plastic stream moves towards a straight line. In the next steps of computation, the eccentricity was assumed to be 0.1. It allows a mild curvature in the potential flow and about the same dilation angle across a variety of confining pressure values, as is demonstrated in (9).

Figure 9:

Flow potentials in the p-q plane CAE (Hibbitt, H., Karlsson, B., & Sorensen, P. 2011)

Integer “∈bo/∈co” Parameter: That is the initial unidirectional compressive strength compared to the equiaxial compressive strength ratio. It is vital to determine the yield function. Figure (10) illustrates that we have used 1.16 as the initial constant, the default patient default risk.

Figure 10:

Yield surface in plane stress (Yu, J., Chen, S., Li, L., & Wang, H. 2011)

μ: stands for the parameter related to viscosity. It must be addressed when the problem arises due to decreasing stiffness of plastic and elastic materials. It’s easier for flat-plate models to converge for the μ value of 0.000375, thus this value gives the best results. If the parameter of viscosity equals zero, the material turns plastic, and divergence happens directly after the crack forms. The solution stretches out if μ is large in comparison to the time increment step. Generally, making the viscosity parameter small will improve the solution without affecting the outcome. The paper says that μ should be set to 15 percent of the time increment step (Lee, J., & Fenves, G. L. 1998).

Ѱ: dilation angle is the descriptor of the rate of change between volume and shear strain, found in the p – q plane at high confining pressure where p = − 1/3 (2σ₁+ σ₃) and q=√3/2s¯:s q = \sqrt{} \left( {3/2} \right)\left( {\bar s:s} \right) indicate hydrostatic pressure stress and Misses equivalent effective stress respectively and σ₁ σ₃ stand for the highest and lowest principal stresses in a triaxle test. Virtually all the published data used dilation angles for concrete that vary between 12° and 37° (Hibbitt, H., Karlsson, B., & Sorensen, P. 2011) and (Ennochsson, O., Lundqvist, J., Täljsten, B., Rusinowski, P., & Olofsson, T. 2007).

K_c: means the ratio between the second stress invariant on T.M. and C.M., and it is a ratio used to describe the yield surface in a deviatoric plane depicted in Figure (11), and it should always be within the range 0.5 ≤ K_c ≤ 1.0.

Figure 11:

(a) Drucker-Prager Yield Criteria in the Deviatoric Plane for Different K_c (Hibbitt, H., Karlsson, B., & Sorensen, P. 2011) and (b) Yield Surface in 3D for K_c =1 (Pankaj, P. & Donaldson, C. 2013)

Concrete Tensile Behaviour

ABAQUS standard supports three different methods to define the way post-cracking tension reduces. The methods are to specify strain, crack opening (displacement), or fracture energy, as shown in Figure (12). Plain concrete’s sensitivity to fine mesh can be seen by the strong influence of tensile stress and strain on the strength criterion. The predicted results keep varying as the mesh is refined. As a result, more mesh points make the cracks narrow, but there are fewer new fractures. Hence, you shouldn’t rely on the strain technique for components without reinforcing, as the structure often collapses spots. Yield stress-cracking strain data represent the process of softening data. Calculating cracking strain means taking the overall strain and then subtracting out the strain the undamaged material would experience. Mathematically, it may be expressed as ε˜tck=εt−ε˜elot \tilde \varepsilon _t^{ck} = {\varepsilon _t} - {\tilde \varepsilon}_{el}^{ot} where ε˜elot=σt/Ecm \tilde \varepsilon _{el}^{ot} = {\sigma _t}/{E_{cm}} . This relationship is illustrated in Figure (12) (a).

Figure 12:

(a) post-failure tensile behaviour:(a) stress-strain approach;(b) fracture (Hillerborg, A., Modéer, M., & Petersson, P.-E. 1976)

Alternatively, fracture energy and stress displacement can collectively be used to describe the tensile behaviour of concrete as they relate to cracking. They both use a cracking criterion devised by (Hillerborg, A., Modéer, M., & Petersson, P.-E. 1976), which eases the disadvantage of the older method caused by mesh dependence. The stiffness of concrete, which is a brittle behaviour, is shown by a tensile stress-displacement

The strategy depends on the concepts of brittle crack theory. G_f stands for concrete fracture energy and is the energy used to create a crack with a given area. Basically, fracture energy means the energy that results from the area under the tensile load curve and displacement for fracture.

Tension Stiffening Model

As the fractured concrete meets the steel, the tensile load it takes is normal to the crack, creating the rigidity strengthening of the concrete. To reach this, the stress component in the concrete is gradually released on the plane that goes across the crack. In the current analysis, three ways of representing the models using strength conditions were chosen: linear, bilinear, and exponential curves. Figure (13) represents the results from the research that was performed (Hsu, H.-M., & Wang, W.-P., 2001). (Bažant, Z. P., & Oh, B. H., 1983) worked with Oh to produce the bilinear curve.

(3) σt=ftεcrεt0.4εt>εcr \sigma_t = f_t\left( {{{\varepsilon_{\rm{cr}}} \over {\varepsilon_{\rm{t}}}}} \right)0.4\varepsilon_t > \varepsilon_{cr}

Figure 13:

Uniaxial tensile stress-strain behavior of concrete (Hsu, H.-M., & Wang, W.-P. 2001)

Concrete Compressive Behaviour

Concrete exhibits linear elastic behavior up to about 30–40% of its ultimate compressive strength. Beyond this range, microcracking initiates, and the material behavior becomes nonlinear. Therefore, the presence of cracks in the primary structure indicates that the concrete has exceeded its elastic limit and entered the nonlinear phase, which affects its load-carrying capacity. This behavior is well documented by (Neville 2011), who explains the transition from elastic to nonlinear behavior in concrete under compression. Additionally, (Mander, Priestley, and Park 1988) provide a theoretical stress-strain model for confined concrete that captures this nonlinear response. ABAQUS states that the level of hardening and strain softening is linked to the compressive stress and the elastic strain, so their connection is shown by the equation

(4) ε˜c in=εc−ε0cel \tilde \varepsilon c\;in = \varepsilon c - \varepsilon 0c{\rm{el}}

Where:

• ɛ0cel = σ_c / E_cm and E_cm It is the initial modulus of elasticity.

The model was proposed by (British Standards Institution. 2004). Eurocode 2 brings together several rules and recommendations on how concrete in Europe should be built. The modelling methods and the design details in this case are discussed with finite element analysis.

(5) σcfcm=kn−n21+k−2n {{\sigma_c} \over {f_{cm}}} = {{{\rm{kn}} - {{\rm{n}}^2}} \over {1 + \left( {{\rm{k}} - 2} \right){\rm{n}}}} (6) n=εcεc1 n = {{\varepsilon_{\rm{c}}} \over {\varepsilon_{\rm{c}1}}} (7) k=1.05Ecm×εc1fcm k = 1.05{E_{cm}} \times {{\left| {{\varepsilon _{c1}}} \right|} \over {{f_{cm}}}}

You should remember that the terms in equation (5) are correct only if 0 < |ɛ_c1| < |ɛ_cu1|. The nominal ultimate strain is represented by ɛ_cu1, and its value is about 0.0035. At the highest point of tension, strain is ɛ_c1 as shown in Table 3. The word fcm is used to show compressive strength.

Table 3:

Strength classes for concrete															Analytical relations / Explanation
fck (MPa)	12	16	20	25	30	35	40	45	50	55	60	70	80	90
fck,cube (MPa)	15	20	25	30	37	45	50	55	60	67	75	85	95	105
fcm (MPa)	20	24	28	33	38	43	48	53	58	63	68	78	88	98	fcm ​ = fck ​+ 8 (MPa)
fctm (MPa)	1,6	1,9	2,2	2,6	2,9	3,2	3,5	3,8	4,1	4,2	4,4	4,6	4,8	5,0	fctm=0,3×fck23≤C5060fctm=2,12.ln1+fcm10>C5060 \matrix{{{f_{ctm}} = 0,3 \times f_{ck}^{\left( {{\raise0.7ex\hbox{$2$} \!\mathord{\left/{\vphantom {2 3}}\right.}\!\lower0.7ex\hbox{$3$}}} \right)} \le {{C50} \over {60}}} \cr {{f_{ctm}} = 2,12.\ln \left( {1 + \left( {{{{f_{cm}}} \over {10}}} \right)} \right) > {{C50} \over {60}}} \cr }
fctk,0,05 (MPa)	1,1	1,3	1,5	1,8	2,0	2,2	2,5	2,7	2,9	3,0	3,1	3,2	3,4	3,5	fctk,0,05​ = 0,7 × fctm​ 5% fractile
fctk,0,95 (MPa)	2,0	2,5	2,9	3,3	3,8	4,2	4,6	4,9	5,3	5,5	5,7	6,0	6,3	6,6	fctk,0,95 ​ = 1,3 × fctm​ 95% fractile
Ecm (GPa)	27	29	30	31	33	34	35	36	37	38	39	41	42	44	Ecm=22fcm100.3 {E_{cm}} = 22{\left[ {{{{f_{cm}}} \over {10}}} \right]^{0.3}}
εc1 (%0)	1,8	1,9	2,0	2,1	2,2	2,25	2,3	2,4	2,45	2,5	2,6	2,7	2,8	2,8	εc1%0=0,7fcm0,31<2,8 {\varepsilon _{c1}}\left( {\% 0} \right) = 0,7f_{cm}^{0,31} < 2,8
εcu1 (%0)	3,5									3,2	3,0	2,8	2,8	2,8	f or fck≥50MPaεc1%0=2,8+2798−fcm1004 \matrix{ {f\;or\;{f_{ck}} \ge 50MPa} \cr {{\varepsilon _{c1}}\left( {\% 0} \right) = 2,8 + 27{{\left[ {{{98 - {f_{cm}}} \over {100}}} \right]}^4}} \cr }

4.1.3.

Carbon Fiber Reinforced Polymer (CFRP Sheet)

The CFRP composite plate model was treated as an orthotropic material. It behaves in a straight fashion until it can’t handle more stress. The equation below explains the connection between stress and strain in CFRP.

(8) σ1σ2σ3τ12τ13τ23=D1111D1122D1133000Sym.D2222D1212000D3333000D121200D13130D2323ε11ε22ε33γ12γ13γ23. \left\{ {\matrix{ {{\sigma _1}} \cr {{\sigma _2}} \cr {{\sigma _3}} \cr {{\tau _{12}}} \cr {{\tau _{13}}} \cr {{\tau _{23}}} \cr } } \right\} = \left[ {\matrix{ {{D_{1111}}} & {{D_{1122}}} & {{D_{1133}}} & 0 & 0 & 0 \cr {{\rm{Sym}}{\rm{.}}} & {{D_{2222}}} & {{D_{1212}}} & 0 & 0 & 0 \cr {} & {} & {{D_{3333}}} & 0 & 0 & 0 \cr {} & {} & {} & {{D_{1212}}} & 0 & 0 \cr {} & {} & {} & {} & {{D_{1313}}} & 0 \cr {} & {} & {} & {} & {} & {{D_{2323}}} \cr } } \right]\left\{ {\matrix{ {{\varepsilon _{11}}} \cr {{\varepsilon _{22}}} \cr {{\varepsilon _{33}}} \cr {{\gamma _{12}}} \cr {{\gamma _{13}}} \cr {{\gamma _{23}}} \cr } } \right\}. (9) D1111=E11−v23v32γ {D_{1111}} = {E_1}\left( {1 - {v_{23}}{v_{32}}} \right)\gamma (10) D2222=E21−v13v31γ {D_{2222}} = {E_2}\left( {1 - {v_{13}}{v_{31}}} \right)\gamma (11) D3333=E31−v12v21γ {D_{3333}} = {E_3}\left( {1 - {v_{12}}{v_{21}}} \right)\gamma (12) D1122=E1v21−v31v23γ=E2v12−v32v13γ {D_{1122}} = {E_1}\left( {{v_{21}} - {v_{31}}{v_{23}}} \right)\gamma = {E_2}\left( {{v_{12}} - {v_{32}}{v_{13}}} \right)\gamma (13) D1133=E1v31−v21v32γ=E3v13−v12v23γ {D_{1133}} = {E_1}\left( {{v_{31}} - {v_{21}}{v_{32}}} \right)\gamma = {E_3}\left( {{v_{13}} - {v_{12}}{v_{23}}} \right)\gamma (14) D2233=E2v32−v12v31/γ=E3v23−v21v13γ {D_{2233}} = {E_2}\left( {{v_{32}} - {v_{12}}{v_{31}}} \right)/\gamma = {E_3}\left( {{v_{23}} - {v_{21}}{v_{13}}} \right)\gamma (15) D1212=G12,D1313=G13,D2323=G23 {D_{1212}} = {G_{12}},{D_{1313}} = {G_{13}},{D_{2323}} = {G_{23}} (16) γ=11−v12v21−v23v32−v31v13−2v21v32v13 \gamma = {1 \over {1 - {v_{12}}{v_{21}} - {v_{23}}{v_{32}} - {v_{31}}{v_{13}} - 2{v_{21}}{v_{32}}{v_{13}}}}

Where:

• D₁₁₁₁ to D₂₃₂₃ - Component of the reduced stiffness matrix.

• E₁ to E₃ - Young’s (elastic) modulus in the main material direction 1; 2 and 3.

• G₁₂, G₁₃ a G₂₃ - Shear modulus in the 1–2 plane, 1-3 a 2-3.

• ν₁₂ - Poisson’s ratio (strain in direction 2 due to stress in direction 1).

• ν₂₁- Poisson’s ratio (strain in direction 1 due to stress in direction 2).

• ν₁₃ - Poisson’s ratio (strain in direction 3 due to stress in direction 1).

• ν₃₁ - Poisson’s ratio (strain in direction 1 due to stress in direction 3).

• ν₂₃ - Poisson’s ratio (strain in direction 3 due to stress in direction 2).

• ν₃₂ - Poisson’s ratio (strain in direction 2 due to stress in direction 3).

The values of all the variables are presented in Table 4.

Table 4:

Property	Value [MPa]	Notes
E1	230,000	Longitudinal modulus (fiber direction)
E2	16,000	Transverse modulus (in-plane, epoxy dominated)
E3	16,000	Transverse modulus (through-thickness)
G12	6,894	In-plane shear modulus
G13	6,894	Shear modulus (fiber–thickness plane)
G23	4,137	Shear modulus (transverse plane)
ν12	0.30	Poisson’s ratio (longitudinal transverse)
ν13	0.25	Poisson’s ratio (longitudinal–through-thickness)
ν23	0.25	Poisson’s ratio (transverse–through-thickness)

4.2.

Main Meshing Elements

ABAQUS was used to make the simulation model. Two kinds of elements (solid and truss) are used to define various geometric forms. The model in figure (14) includes a mesh.

Figure 14:

Mesh for Abaqus model

4.2.1.

Solid Element

The design of the concrete part and loading, and B.C pleats were determined in the ABAQUS simulation of the solid part. It took advantage of a 3D element that consists of eight nodes and is linearly reduced. Customarily, quadratic loads placed on slaves in Q4D8R would be applied to the grid; however, with C3D8R we are permitted to use linear brick elements in contact to make concrete parts. Shear locking problems were reduced by adopting the segmented layout instead of the completely merged layout, which looks like Figure (15). It has much in common with actual structure because this method calls for four integration points, adding no shear stress. Integration lines on both sides meet at right angles and the mesh is small.

Figure 15:

Linear brick elements undergo pure bending (reduced integration) (Daud, R., Cunningham, L., & Wang, Y. 2015)

4.2.2.

Truss Element

The linear three-dimensional model in ABAQUS/Standard (called T3D2) with a two-node truss element and three freedom’s degrees at each node was used to determine the special reinforcing rods in the beam. Figure (16) illustrates that truss pieces are inserted into the 3-D continuum elements acting like a host for the structure. In this analysis, areas called embedded areas represented steel and CFRP. Entering just the cross-sectional area of the bars into a truss element is the best way to reinforce the design. Another popular approach includes beam element modeling that includes the role of dowels and boosts the ability of a structure to hold heavy loads. Even so, it has to be used since it requires setting numerous input values.

Figure 16:

Element AB is Embedded in (3-D) Continuum Element; Node A is Constrained to edge (1-4), and Node B is constrained to face (2-6-7-3) (Daud, R., Cunningham, L., & Wang, Y. 2015)

4.3.

Boundary Conditions

Getting the boundary conditions right was an important element in the finite element modelling done with ABAQUS. It was assumed that the beam’s left side was gently supported, and the right side was free of support, fixed only in the Y direction. So that the model would resemble real conditions, two rectangular support plates (25 × 25 × 200 mm) were placed below both ends. The tie constraint linked the support plates together with the concrete. Support configuration and the boundary conditions are illustrated in Figure (17).

Figure 17:

Boundary Conditions for Beam Model in ABAQUS

4.4.

Loads

A monotonic load was applied to the beam in ABAQUS by running the Static General procedure. Loading forced the steel beam by applying pressure on the top of rectangular plates positioned at two spots along the beam’s top surface. Every loading plate measured 25 × 25 × 200 mm, according to the setup used for the experiment. A 25 mm wide assessment of concrete was used to mimic the line load in the real test. The tie constraint was applied to join the load plates to the concrete, so that the pressure is spread smoothly without sliding. As presented in Figure (18), the pressure loads were applied to the model according to a particular setup.

Figure 18:

Specification of Loading Line as Pressure on Beams in ABAQUS

ABAQUS’s Static General procedure was used to carry out the nonlinear finite element analysis. It employed the Modified Newton-Raphson method, which means the stiffness matrix got updated at each iteration to make the convergence faster in cases where the response is nonlinear. The increments in the algorithm were automatically set using the parameters given below: Initial increment size: 0.1

• Minimum increment size: 1e-5

• Maximum increment size: 1.0

As a result, the engineering model was able to show the beam specimens correctly as their cracks spread and they no longer behaved linearly.

The model of the numerical specimen was made in the general finite element software package called ABAQUS 6.13. Tables 5 and 6 show the concrete’s compressive strength, tensile strength, and a few other parameters in detail. The settings given in ABAQUS were kept for these parameters. Table 7 gathers the information used to describe concrete plasticity.

An 8-node brick element (C3D8R) was selected in ABAQUS to show the concrete part, and a 2-node truss element (T3D2) was used the steel bars. To make sure the concrete and steel are joined, the steel was woven through the concrete.

Inclusion This paper included a detailed study of how UHPC beams reinforced by CFRP behave under shear, considering different ways in which the materials are arranged and located in the beams. Through experimental and numerical studies, we discovered important results about the effectiveness of CFRP reinforcement that can now inform structural design codes. Whenever closed-shaped CFRPs were used in beams, they showed a much higher strain capacity than U-shaped configurations, where CFRP came loose at the interface and reduced the beam’s shear capacity greatly. In comparison, the closed configuration of CFRP resulted in much better closure and high shear resistance.

Predictions relying on codes tended to overstate the shear contribution of CFRP, mainly when the section formed a U-shaped bracket. The main reason for the discrepancy is the short bond length between CFRP and UHPC surface, affected by the concrete tensile strength, which is not considered enough by the current models, leading to less accurate shear predictions for UHPC beams. The results prove that making changes to current design standards is necessary to support CFRP-strengthened UHPC beams in practice. Most of the present codes were developed using typical concrete data, making them suitable for few UHPC usage cases.

Additional analysis and research on the bond mechanisms within FRP and UHP concrete are needed to increase how reliable and efficient such reinforcement is. This research highlights the role of correctly characterizing CFRP when used in U-shaped reinforcement, as debonding can make performance unstable. Adjusting design techniques to look at bond length, tension in concrete and CFRP bolts will result in better predictions for shear capacities and failure types in UHPC concrete supported by CFRP. Stronger and more reliable use of CFRP in concrete building will be made safer with increased research.

In this thesis, new FEA and analytical models were established to examine the response of the FRP/uhpc concrete connections. The results of FEA and the analytical proposed models show how these models can be used to predict the behaviour of the FRP/concrete joint reasonable accuracy. Based on tests carried on the experimental model, the finite element tests and analytical several conclusions can be drawn based on the models

Predictions of the shear response and failure patterns of were performed by means of 3D finite element models. the uhpc beams enhanced in shear reinforced with CFRP strips. The common reaction of the FE models depicts reasonable correspondence of the predictions with the test results (experimental). Overall, the finite element models are stiffer responding than the experimentally loaded ones. samples. This was attributed to the loss of the bond between the longitudinal steel reinforcement. This is due to the concrete in the actual case that is not modelled in the finite element models that are simulated in this. study. In addition, the inability to mathematically model concrete discrete cracks in a simulated fashion makes the FEA models stiffer than the real physical models. Shear failure mechanisms of the RC beams are highly complicated particularly in retrofitted samples FRP reinforced concrete with. Summing up, it could be stated that the developed in the current research 3D cracking FE models can serve as an extra tool to examine the shear mechanism and how different factors affect the shear behaviour of LWRC beams that are retrofitted with CFRP reinforcement. As one can conclude, the FE modelling of the RSS system with the assistance of the TS50 amplifier was carried out with satisfactory accuracy. The philosophy will come in handy with CFRP reinforcing in general.