Carbon fiberreinforced polymer materials have become popular in the construction industry during the last decade for their ability to strengthen and retrofit concrete structures. The recent availability of highmodulus carbon fiberreinforced polymer strips (HMCFRP) has opened up the possibility of using this material in strengthening steel structures as well. The strips can be used in steel bridge girders and structures that are at risk of corrosioninduced crosssectional losses, structural deterioration from aging, or changes in function. In this study, a set of bending experiments was performed on three types of steel beams reinforced with HMCFRP. The results were used to enhance a nonlinear finite element model built with ABAQUS software. The accuracy of the mathematical models for HMCFRP, epoxy, and steel profiles was compared with the experimental results, and the ability of HMCFRP to continue carrying load from the steel beams during rupture and postrupture scenarios was observed using numerical analysis. Using these verified finite element models, a parametric analysis was performed on the HMCFRP failure modes and the quantity to be used with IPE profile steel beams. The maximum amount of HMCFRP needed for strengthening was determined, and an upper limit for its use was calculated to avoid any debonding failure of the fiber material.
Steel structural elements may require strengthening due to changes in functionality, increases in loadbearing capacity due to heavier traffic loads and corrosion occurring over time. The replacement of such elements and the installation of additional layer sections are typically proposed and applied in practice to solve these problems. However, these proposed solutions are problematic due to the increase in traffic delays they incur for bridge repairs and their cost inefficiencies [
The experiments found in the literature survey are limited and do not include a broad parametric study. Questions remain about whether there is an upper limit to the quantity of CFRP material that can be used in these scenarios, whether there is a relationship between an increase in loadcarrying capacity and the use of HMCFRP and whether CFRP debonding occurs at epoxy interfaces such as in concrete structures. The goal of this study was to answer these questions as they apply to BAcomposite IPE steel profiles strengthened with HMCFRP. Parametric studies were conducted using the nonlinear finite element method, and the developed finite element model was verified with three different experiments.
A twostep experiment was performed in this part of the study. In the first step, a steel Ibeam specimen was constructed and tested that matched the loadcarrying capacity of a concrete composite steel Ibeam. The concrete slab components were replaced by their steel counterparts and used for further studies, avoiding problems associated with manufacturing concrete parts and issues with numerical modeling during this parametric study on concrete composite Ibeams. The load deflection behavior from the bending experiment validating this assumption is shown in Figure
Comparison of beams with a reinforced concrete slab and a steel plate slab.
LoadMidspan deflection
Reinforced concrete composite Ibeam (in mm)
Reference beam with steel plate instead of RC slap (in mm)
Three identical steel composite beam plates were identically prepared and strengthened with HMCFRP to verify and test their nonlinear finite element model components. HMCFRP with dimensions of
The beam specimens had a length of 3,000 mm, and the distance between the supports was 2,900 mm. The distance between the loading point and the end of the HMCFRP material was 1,050 mm, the distance between loading points was 800 mm, and the load was applied using a 400 kN piston. A
Test setup and results for strengthened beams.
The load deflection figures for the three strengthened beams and the unstrengthened reference beam are shown in Figure
This section discusses the steps involved in nonlinear finite element modeling. Instead of costly lab experiments, nonlinear finite element models can be used to obtain approximate results with numerical experiments. However, the accuracy of the results may depend on the type of finite elements, material mathematical models, interface models and mesh densities used. The finite element model in this study was continuously improved until its results matched the actual experimental results.
ABAQUSExplicit software was used for the numerical analysis. Numerical difficulties arise when solving nonlinear problems in the implicit finite element method since the iterative approach which needs to achieve convergence to enforce equilibrium may fail in highly nonlinear problems. The nonlinearities in the material and geometries were accounted for in the analysis, and the nonlinear finite element model was derived by considering sensitive mesh dependency, using reduced integration in its formulation. This reduced computing time and minimized potential inaccuracies. The mechanical properties of the steel, epoxy, and HMCFRP used in the numerical model were experimentally measured and are provided in Table
Mechanical properties of the specimen.
HMCFRP  Steel (Ibeam)  Steel plate  Epoxy  

Ult. strength (MPa)  1200  Flange  Yield strength (MPa)  275  Yield strength (MPa)  255  G, modulus (GPa)  10720 
E. modulus (GPa)  440  E. modulus (GPa)  179  E. modulus (GPa)  210  E. modulus (GPa)  29770  
Width (mm)  50  Web  Yield strength (MPa)  265  Nom. stress (MPa)  25  
Thickness (mm)  1.4  E. modulus (GPa)  161  
Ult. long strain (mm/mm)  0.20.3%  Poisson’s ratio  0.3 
Finite element properties of the specimen.
Member  Finite element name in ABAQUS  Description  Material model  Depiction of behavior 

Steel Ibeam  S4R  Shell, 4noded, reduced integration  Elastoplastic 

 
Steel plate  C3D8R  Solid, 8noded, reduced integration  Elastoplastic 

 
Epoxy  COH3D8  Cohesive, 8noded  Tractionseparation 

 
HMCFRP  C3D8R  Solid, 8noded, reduced integration  Brittle cracking 


The steel components were modeled using mathematical models of an elastoplastic material (Table
It is very important to have accurate and robust models for the epoxy material named as a cohesive layer in the analysis because the epoxy provides the medium for stress transfer between the steel and HMCFRP. It was modeled as a solid 8node cohesive layer element and defined with a tractionseparation mathematical model because it creates only a very thin layer and has a separation failure mode (Table
Equations (
Epoxy layer which is modeled by employing cohesive elements is tied to the neighboring surfaces both on steel bottom flange and HMCFRP top surface. Thus, the degree of freedom at the intersecting nodes is same for epoxy, steel, and HMCFRP. Traction separation properties are assigned to epoxy material which is modeled as a film material with a thickness of 0.1 mm.
HMCFRP is defined by the Brittlecracking mathematical model because it is exposed to higher tensile stresses and will not yield after rupture. In this analysis, the material was modeled as linearelastic up to its maximum tensile stress capacity, beyond which it loses all loadcarrying capacity. It can be very hard to identify this postcracking phase experimentally because it occurs so quickly. This study modeled postcracking as the 1% strain level using the linear model (Table
The model developed for the experimental test beam using the modeling details provided above is depicted in Figure
Finite element model of experimental specimen.
The results obtained from the numerical model analyses were compared with the actual experimental results to validate the accuracy of the models. The comparisons of the beam’s behavior under loading are shown in Figure
Comparison of strengthened and reference beams during numerical analysis and experimental testing.
Experiment  FEM  % Difference  

Reference beam  Max load (kN)  83  84  1.2 
Max moment (kNm)  43.6  44.13  1.2  
Strengthened beam  Max load (kN)  115.4  121  4.85 
Max moment (kNm)  60.58  63.52  4.85 
Numerical verification of experimental results.
Comparison of numerical and experimental test results
The experimental results and numerical models for the unstrengthened beam show a difference of 1.2% in maximum loadcarrying capacity. This difference increased to 4.85% for strengthened beams. Both of these values are within acceptable ranges. The higher error of the strengthened beams can be explained by the complex behavior of the interface element. The difference between deflection points corresponding to the maximum loads is approximately 24% and could be explained as a consequence of the approximations used in the material models and ignoring geometric imperfections for the numerical model. Hence, the material is more inclined to display rigid behavior in the numerical model. Because the goal of this study was to determine the increase in loadcarrying capacity during the strengthening process, the difference in the deflection estimates can be considered negligible for parametric studies.
The most important result obtained from the numerical model is the rupture behavior of the HMCFRP and the initiation of the postrupture load bearing of the steel. Analysis of the figures shows a sudden drop in the specimen’s loadcarrying ability right after the peak point, which corresponds to the rupture of the HMCFRP. When this rupture occurs, the steel continues to carry load because it has undergone a strain hardening process. This experimentally observed behavior was also achieved using numerical analysis under similar conditions.
Upon further development and testing, the experimentally validated numerical models provided insight into the specific questions asked at the beginning of the study, including the maximum quantity of HMCFRP that can be used, failure modes, and the relationship between HMCFRP usage and loadcarrying capacity increases. A total of 149 models for numerical specimens were developed using various quantities of HMCFRP with 7 commonly used industrywide IPE profile sections of different lengths. Table
Numerical specimens in the parametric study.
Beam section  Beam length (mm)  Development length (mm)  HMCFRP length (mm)  Area_{HMCFRP}/Area_{Section} 

IPE 120  3000  900  2600  3.5–16.3 
IPE 160  3000  900  2600  3.5–17.5 
IPE 220  3000  900  2600  3.5–18.0 
6000  1800  5200  3.5–11.7  
IPE 270  3000  900  2600  3.5–11.8 
6000  1800  5200  3.5–22.4  
IPE 330  6000  900  5200  3.5–22.4 
IPE 400  6000  900  5200  3.5–14.1 
12000  1800  10400  1.7–7.10  
IPE 500  6000  900  5200  3.5–11.7 
12000  1800  10400  1.8–8.80 
Individual load deflection figures were created for all numerical specimens after the parametric study was completed. The results are discussed for an example in more detail, while the results for all beams are tabulated.
To illustrate the results, the load deflection figures obtained for an IPE 270 profile with different HMCFRP ratios are shown in Figure
Load deflection plots for IPE 270,
Relationship between HMCFRP ratio and load percentage increase.
To explain this behavior, one must analyze the stresses of all materials at midspan where the maximum stresses have been observed. Figure
Stress contour of each material at beam midspan.
Investigation of the stress contour maps for the beam strengthened with 11.8% HMCFRP shows that the steel did not yield around the boundary of the elastic region (a), while the epoxy and HMCFRP seemed to approach their respective maximum stress levels. The region following the ultimate capacity (b) shows the point where epoxy broke along with the associated decay in the stress of the HMCFRP. (b) was also the point at which the steel stresses started to increase. This behavior can also be explained by the debonding of the HMCFRP without having reached its maximum deformation. In other words, although the HMCFRP stress level did not achieve failure, the epoxy material reached its ultimate capacity.
The maximum HMCFRP quantities are listed for each numerical specimen in Table
Maximum HMCFRP ratio for each beam.
Section  Beam length (mm)  HMCFRP ratio (%)  Increase in 
Number of specimens 

IPE 120  3000  14  97  16 
IPE 160  3000  11  67  17 
IPE 220  3000  15  69  15 
6000  8  109  12  
IPE 270  3000  8.9  51  9 
6000  7.3  54  15  
IPE 330  6000  8.8  61  16 
IPE 400  6000  6.7  31  13 
12000  3.5  62  9  
IPE 500  6000  5.1  39  12 
12000  4.2  40  11 
The values in the table above show a declining trend in the maximum HMCFRP usage ratio as the beam section area increases. This is an expected outcome because there is a higher chance of interface element failure due to extra loading on the HMCFRP installation.
The loadcarrying capacity of steel beams can be increased up to approximately 100% by strengthening the beams with HMCFRP. The ability to increase loadcarrying capacity without increasing the structure’s dead weight is a significant improvement over previous strengthening techniques. This improvement also reduces deformations due to dead weight loading. The amount of HMCFRP used in such a scenario affects the behavior of the beam significantly. To achieve effective strengthening, HMCFRP must reach high stress levels close to rupture without debonding at the epoxy interface. It is important to prevent such cases from occurring. Although greater HMCFRP usage is expected to progressively increase the loadcarrying capacity, it has been shown that this is not generally the case. Instead, there is an upper limit to the quantity of HMCFRP that can be used. The most effective method of determining this upper limit is to develop a nonlinear finite element model of the beam type and analyze this model. This study discussed a methodology for developing such finite element models in detail. Using this methodology, steel beams can be repaired and strengthened when environmental effects such as corrosion and everincreasing load requirements necessitate the addition of material to a structure.