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

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

Civil and Environmental Engineering
Volume 22 (2026): Issue 2 (June 2026)
By:  and    
Open Access
|Jun 2026
Figures & tables

Figures & Tables

Figure 1:

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

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)

Figure 8:

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

Figure 9:

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

Figure 10:

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

Figure 11:

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

Figure 12:

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

Figure 13:

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

Figure 14:

Mesh for Abaqus model

Figure 15:

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

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)

Figure 17:

Boundary Conditions for Beam Model in ABAQUS

Figure 18:

Specification of Loading Line as Pressure on Beams in ABAQUS

Figure 19:

Validation of (RC) sample

Figure 20:

Validation of (RC-CFRP-U-90-100) sample

Figure 21:

Validation of (RC-CFRP-U-45-100) sample

Figure 22:

Validation of (RC-CFRP-2SIDE-90-600) sample

Figure 23:

Validation of (RC-CFRP-U-90-600) sample

Figure 24:

Validation of (RC-CFRP-FULL-FACE) sample

Figure 25:

Von Mises stress distribution and failure pattern of RC-CFRP-FULL-FACE beam model

Figure 26:

Thickness of CFRP compares for the (RC-CFRP-U-90-100) sample

Figure 27:

The thickness of CFRP compared for the (CFRP-U-45-100) sample

Figure 28:

The thickness of CFRP compared for the (RC-CFRP-2SIDE-90-600) sample

Figure 29:

The thickness of CFRP compared for the (CFRP-U-90-600) sample

Figure 30:

The thickness of CFRP compared for the (RC-CFRP-FULL-FACE) sample

Figure 31:

Load deflection charts for the samples with CFRP spacing parameter

Figure 32:

Load deflection charts for the (RC-U-90-100) specimen with CFRP spacing (200 mm)

Figure 33:

Load deflection charts for the (RC-U-45-100) specimen with CFRP spacing (200 mm)

Figure 34:

Load deflection charts for the (RC-U-90-100) specimen with CFRP spacing (150 mm)

Figure 35:

Load deflection charts for the (RC-U-45-100) specimen with CFRP spacing (150 mm)

Concrete Tensile Strength Data Used in Numerical Model (Yield stress versus tensile strain values for concrete)

Yield Stress [MPa]Inelastic Strain [με]
8.000.00005
6.000.00012
4.000.00022
2.000.00040
1.000.00060
0.500.00080
0.200.00100

Mechanical Properties of CFRP Sheet Used in Numerical Analysis (Elastic constants and stiffness matrix components of CFRP)

DataValue
D1111233,289.0
D11224,111.30
D222217,235.46
D11333,029.38
D22334,237.36
D333317,202.34
D12126,894.00
D13136,894.00
D23234,137.00

Concrete Compressive Strength Data Used in Numerical Model (Yield stress versus inelastic strain values for concrete under compression)

Yield Stress [MPa]Inelastic strain [με]
72.630.000604
88.930.000768
92.690.000809
98.350.000878
108.140.001015
124.940.001425
127.000.001642
125.240.001806
121.360.001970
116.040.002135
108.740.002299
95.000.0026001
80.000.002910
65.000.003200
50.000.003500
35.000.003790
20.000.004200
10.000.004580
0.000.005000

CFRP-Reinforcement Configurations and Strengthening

SampleCFRP strengthening type at each sideCfrp orientation [degrees]
RC-CWithout/
RC-U-90-100U- shape,100 mm width,150mm spacing c/c90°
RC-U-45-100U- shape,100 mm width,150mm spacing c/c45°
RC-2side-90-6002-sided-shape,600 mm width90°
RC-U-90-600U- shape,600 mm width90°
RC-Full-FaceFull Face90°

Strength and deformation characteristics of concrete (British Standards Institution, 2004)

Strength classes for concreteAnalytical relations / Explanation
fck (MPa)1216202530354045505560708090
fck,cube (MPa)15202530374550556067758595105
fcm (MPa)2024283338434853586368788898fcm ​ = fck ​+ 8 (MPa)
fctm (MPa)1,61,92,22,62,93,23,53,84,14,24,44,64,85,0 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)1,11,31,51,82,02,22,52,72,93,03,13,23,43,5fctk,0,05​ = 0,7 × fctm​ 5% fractile
fctk,0,95 (MPa)2,02,52,93,33,84,24,64,95,35,55,76,06,36,6fctk,0,95 ​ = 1,3 × fctm​ 95% fractile
Ecm (GPa)2729303133343536373839414244 Ecm=22fcm100.3 {E_{cm}} = 22{\left[ {{{{f_{cm}}} \over {10}}} \right]^{0.3}}
εc1 (%0)1,81,92,02,12,22,252,32,42,452,52,62,72,82,8 εc1%0=0,7fcm0,31<2,8 {\varepsilon _{c1}}\left( {\% 0} \right) = 0,7f_{cm}^{0,31} < 2,8
εcu1 (%0)3,53,23,02,82,82,8 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 }

Input Parameters for Concrete Plasticity Model in ABAQUS (Material properties and plasticity parameters for concrete)

DataValue
Poisson ratio0.2
Dilation angle (degree)36
Eccentricity0.1
ϵbo/ϵc3.0
kc0.667
Viscosity parameter0.0001

Mechanical properties of CFRP sheet (Sika Wrap®-300C) used in Abaqus modelling

PropertyValue [MPa]Notes
E1230,000Longitudinal modulus (fiber direction)
E216,000Transverse modulus (in-plane, epoxy dominated)
E316,000Transverse modulus (through-thickness)
G126,894In-plane shear modulus
G136,894Shear modulus (fiber–thickness plane)
G234,137Shear modulus (transverse plane)
ν120.30Poisson’s ratio (longitudinal transverse)
ν130.25Poisson’s ratio (longitudinal–through-thickness)
ν230.25Poisson’s ratio (transverse–through-thickness)

Observed versus estimated shear contributions of CFRP in the strengthened specimens

SpecimensCFRP Contribution Determined by the Subtraction approach: [kN]CFRP Contribution According to ACI 440.2R-17: [kN]CFRP Contribution According to CNR-DT-215-2018: [kN]CFRP Contribution According to TR-55 (CS, 2013): [kN]
RC-U-90-10070.11073.13257.23463.593
RC-U-45-10080.615103.69857.23489.934
RC-2side-90-60080.900109.69885.85195.390
RC-U-90-60095.090109.69885.85195.390
RC-Full-Face99.120109.69885.85195.390

Summary for the thickness of the beam parameter

Name of beamThickness 0.167mmThickness 0.334mmLoad increase rate [%]
Load [kN]Deflection [mm]Load [kN]Deflection [mm]
RC-CFRP-U-90-100459.9016.54512.2418.3411.38
RC-CFRP-U-45-100483.2417.05543.6519.0112.46

Concrete mixes

Mixes all in [kg/m3]Fine sandcementWaterSuperplastizerSilica FumeFly AshCompressive strength [MPa] 28 days
107097018433.4107192.6126.97
DOI: https://doi.org/10.2478/cee-2026-0024 | Journal eISSN: 2199-6512 | Journal ISSN: 1336-5835
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Language: English
Page range: 558 - 584
Submitted on: Jul 2, 2025
Accepted on: Aug 14, 2025
Published on: Jun 19, 2026
Published by: University of Žilina
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Strengthening by CFRP Sheet,
Shear strengthening of ultra-high-performance concrete,
Finite element methodology of Ultra ultra-high-performance concrete
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Business and economics,
Political economics,
Economic theory, systems and structures,
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Industries,
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© 2026 Ali Khalid Ahmed, Mustafa Hameed Al-Allaf, published by University of Žilina
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 22 (2026): Issue 2 (June 2026)
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