- Open Access
On the FE Modeling of FRP-Retrofitted Beam–Column Subassemblies
© The Author(s) 2013
Received: 13 February 2013
Accepted: 23 July 2013
Published: 20 May 2014
The use of fiber reinforced polymer (FRP) composites in strengthening reinforced concrete beam–column subassemblies has been scrutinised both experimentally and numerically in recent years. While a multitude of numerical models are available, and many match the experimental results reasonably well, there are not many studies that have looked at the efficiency of different finite elements in a comparative way in order to clearly identify the best practice when it comes to modelling FRP for strengthening. The present study aims at investigating this within the context of FRP retrofitted reinforced concrete beam–column subassemblies. Two programs are used side by side; ANSYS and VecTor2. Results of the finite element modeling using these two programs are compared with a recent experimental study. Different failure and yield criteria along with different element types are implemented and a useful technique, which can reduce the number of elements considerably, is successfully employed for modeling planar structures subjected to in-plane loading in ANSYS. Comparison of the results shows that there is good agreement between ANSYS and VecTor2 results in monotonic loading. However, unlike VecTor2 program, implicit version of ANSYS program is not able to properly model the cyclic behavior of the modeled subassemblies. The paper will be useful to those who wish to study FRP strengthening applications numerically as it provides an insight into the choice of the elements and the methods of modeling to achieve desired accuracy and numerical stability, a matter not so clearly explored in the past in any of the published literature.
The use of fibre reinforced polymer (FRP) composites in strengthening, reinforced concrete structures has risen considerably in recent years. Combining the strength of the fibers with the stability of the polymer resin, FRP offer ease of application lowered labour cost and extra durability. Researches originally and practicing engineers with about 10 years lag, have used FRP to strengthen different reinforced concrete members such as beams, columns and slabs. Extensive experimental studies have shown that externally bonded FRP can significantly increase the stiffness and load carrying capacity of the retrofitted structures. However, there have been reports of reduction in ductility associated with brittle behaviour due to bond failure and FRP rupture.
Experimental database for reinforced concrete structures retrofitted or strengthened using FRP sheets or fabric is extensive. In the context of beam–column subassembly, numerous studies have been carried out (El-Amoury 2004; Ghobarah and El-Amoury 2005; Karayannis and Sirkelis 2008; Pantelides et al. 2008; Alhaddad et al. 2012). In this area, different issues such as joint shear strengthening; increasing member stiffness and plastic hinge relocation have been investigated. Along with experimental studies, many researches have utilised finite element models to predict the behaviour of FRP strengthened beam–column subassemblies (Parvin and Granata 2000; Wong and Vecchio 2003; Mahini and Ronagh 2009; Alhaddad et al. 2012; Shrestha et al. 2013). Variety of finite element programs are currently available for the purpose of numerical study of FRP strengthened reinforced concrete structures. These programs can be divided into two categories: general-purpose commercial and purpose-made specialised programs. Amongst the commercial programs, ANSYS (2012) has been very popular Although commercial general-purpose programs such as ANSYS offer great flexibility and extensive element library, they suffer from many shortcomings when it comes to modelling specific features of certain type of structures like reinforced concrete structures (solid element is the only available element for modelling concrete, lack of appropriate material softening model for concrete, tension stiffening is based on simple model rather than fracture energy based models, lack of appropriate hysteretic rules for concrete material and rebar to concrete bond, absence of special modelling features needed in modelling concrete structures such as tension and compression softening, rebar dowel action and rebar buckling). In order to overcome these shortcomings, supplementary subroutine for special elements or material can be added to these programs by users. Examples of these subroutines can be found in the literature (Králik 2009). On the other hand, as a specialised program, VecTor2 (Wong and Vecchio 2003) is a powerful tool especially developed for nonlinear analysis of membrane concrete structures especially those with shear–critical behaviour (Vecchio and Bucci 1999).
This paper presents different modelling options available in ANSYS for modelling FRP retrofitted beam–column subassemblies. Various failure and yield criteria along with different element types will be investigated. Moreover, special features of the program VecTor2 (a specially developed software for analysis of reinforced concrete membrane structures) in modelling beam–column subassemblies is also discussed. Comparison will be made between the results of these program and the test results reported by Mahini (2005). This study aims to provide useful information in the context of FE modelling of FRP retrofitted reinforced concrete structures.
2 Test Data
FRP configuration and concrete compressive strength (Mahini 2005).
No. of ply
l f (mm)
t f (mm)
f u (MPa)
Two cycles are applied at each ductility ratio level from equal to 1, going up to 2, 3, 4 etc., where Δ is the beam-tip displacement and μ is the displacement ductility ratio. In this study, however, for the numerical analysis, only one cycle is applied at each ductility level. A displacement–control loading starting with the ductility ratio of one and ending with the ductility ratio of four is used.
3 ANSYS Analytical Procedure
ANSYS program has been used by many researchers for FE modeling of reinforced concrete structures. With regards to FRP strengthened reinforced concrete structures, Kachlakev et al. (2001) used ANSYS to examine the structural behavior of beams and bridges strengthened with FRP laminates. In their numerical modeling, SOLID65, LINK8 and SOLID46 elements were used to model concrete, bars and FRP laminates, respectively. Alhaddad et al. (2012) presented a detailed procedure for nonlinear finite-element analysis of FRP and textile reinforced mortar (TRM) upgraded reinforced concrete beam–column exterior joints using ANSYS. In their numerical modelling, they used similar elements to those used in Kachlakev et al. (2001). The FE results were compared with the test results through load–displacement behavior, ultimate loads, and crack pattern. Comparison of FE results with the experimentally observed response indicated that the proposed nonlinear FE model can accurately predict the behavior and response of tested RC beam–column joints. Parvin and Granata (2000) investigated the application of FRP laminates to exterior beam–column joints in order to increase their moment capacity using numerical analysis performed by ANSYS. In their study again SOLID65, LINK8 and SOLID46 elements were used to simulate the concrete, rebar and the FRP laminates, respectively. Mahini and Ronagh (2011) investigated the effectiveness of FRP strengthening in relocating the plastic hinge away from the face of the column in beam–column joints.
A quick literature review on finite element analysis of reinforced concrete structures strengthened by FRP laminates shows that the majority of researchers have used SOLID65, LINK8 and SOLID46 to model concrete, rebar and FRP. There are some exceptions though; Hawileh et al. (2012) recently used the ANSYS program to simulate reinforced concrete beams externally strengthened with short-length CFRP plates. SOLID65 and LINK8 elements were used to model concrete and rebar. On the other hand, instead of using SOILD46 to model the FRP laminates, they used SHELL99 element with orthotropic material properties. Mirmiran et al. (2000) developed a nonlinear finite element model for the analysis of FRP confined concrete. SOLID65 was used to model concrete while the FRP sheets were modelled by tension-only SHELL41 elements. Their model showed the same type of stress concentration around the edges of square sections as observed in the experiments. Furthermore, they concluded that the cyclic analysis of FRP-confined concrete confirmed capability of the model to effectively predict the cyclic response of FRP-confined concrete. There has not been any study that explores the suitability of the elements in a comparative way; and therefore, this is the target the current study is aiming for.
- f t :
Ultimate uniaxial tensile strength
- f c :
Ultimate uniaxial compressive strength
- f cb :
Ultimate biaxial compressive strength
- f 1 :
Confined triaxial compressive strength (compressive meridian)
- f 2 :
Confined triaxial compressive strength (tensile meridian)
While the full five input parameters are needed to define the failure surface (as well as an ambient hydrostatic stress state on which parameters f 1 and f 2 are based), ANSYS can build the failure surface with a minimum of two constants that are the uniaxial tensile and compressive strengths. For the rest of the parameters, ANSYS uses default values taken from the William et al. (1974) study.
With regards to the concrete tension model, one of the shortcomings of ANSYS is that it does not use the concept of fracture energy which is widely used in the analytical models for concrete cracking. In ANSYS, cracking is defined by a single material property which is the tensile strength of concrete. To consider tension stiffening, stress relaxation has to be considered after cracking. Figure 4b shows the model employed in ANSYS to consider tension stiffening. A constant T c is used to control the stiffening model which acts as a multiplier for the stress relaxation.
Shear behavior of SOLID65 element in ANSYS is controlled by two shear transfer coefficient for open and closed cracks. These coefficients represent conditions at the crack allowing for the possibility of shear sliding across the crack face. The value of these shear transfer coefficient ranges between zero and one, with zero representing a smooth crack (complete loss of shear transfer) and one (no loss of shear transfer).
3.2 Steel Rebar
There are two options to model the reinforcement bars in ANSYS; smeared and discrete. When the smeared option is used, reinforcement is defined as a part of SOLID65 concrete element. Up to three directions could be used to define the smeared bars. Figure 3 shows the arrangement of reinforcing bars in the element. The smeared rebar is capable of tension and compression, but not shear. In each direction, smeared bars behave similar to a uniaxial material. The second option for modeling the reinforcing bars is to model them as a discrete element which is attached to the concrete elements. If discrete reinforcements are to be modeled, use of LINK and COMBIN elements in ANSYS is suggested; amongst which 2-node uniaxial tension–compression LINK8 element is the most common. As previously mentioned, Von-Mises yield criterion is generally used for metals such as steel. Steel can be modeled as a bilinear or a multi-linear material. For cyclic analysis, generally one of the more common Kinematic hardening laws is used for the rebar. In the current study, bilinear Kinematic material behavior is used for bars. Longitudinal bars of beams and columns are modeled using discrete LINK8 element, but the shear bars (stirrup) are modeled using smeared reinforcement. Because no bond slip was reported in the Mahini’s (2005) experimental study in the current research bond elements are not modeled.
3.3 Fiber Reinforced Polymer (FRP)
As was explained in the previous sections, SOLID46 with anisotropic material properties has been used to model FRP laminates (Parvin and Granata 2000; Kachlakev et al. 2001; Mahini 2005). Tension-only membrane SELL41 and elastic SHELL99 have also been used for this purpose (Mirmiran et al. 2000; Hawileh et al. 2012). One possibility to better model FRP in ANSYS which is not tried previously by researchers (although used for modeling reinforcing bars in concrete, (Hunley and Harik 2012)) is to use its reinforced shells and solids elements. These elements constitute a base element that can be reinforced with additional elements. In the case of FRP, the saturant can be used as the base element while fibers are added as reinforcing elements. Figure 6 shows the saturant and the fibers as different element. Reinforcing elements can be defined as discrete or smeared, and they can act as tension-only, compression only or tension and compression elements. In fact, for FRP, the tension-only fibers are used. Element SHELL181 can be used as the base element for FRP composite material. Then, it can be reinforced using REINF265 smeared element. Each layer of reinforcement behaves as a unidirectional material. All layers including the base element perform like a parallel system. Perfect bond is assumed amongst the layers. Each layer can have its own thickness (defined as fiber area and space), orientation and local axis coordinate system. This option seems to be most appropriate for modeling FRP sheets in ANSYS. Fibers are embedded inside the base saturant and can have different directions without affecting each other. Even though the fibers are modeled as tension-only elements, the saturant which represents the base element can be modeled as an elastic element with isotropic properties.
In this study, two options will be considered to model FRP; tension-only membrane SHELL41 element and membrane-only option of SHELL181 reinforced with REINF265.
3.4 Geometry and Meshing
Using this method for the finite element analysis considerably reduces the number of elements. Usually in experimental studies, planar loading is applied on specimens. Therefore, the method that is proposed here can be used for any analytical study. Using this method, considerable time is saved, and the designer can use a finer mesh for the planar structure. The attention can thus be shifted from analysing a complex system towards parametric studies on this simpler form and processing of the results.
4 VecTor2 Analytical Procedure
The second nonlinear finite element software explored in this study is VecTor2, a two dimensional nonlinear finite element analysis program for reinforced concrete structures developed at the University of Toronto. VecTor2 is based on the Modified Compression Field Theory (MCFT) by Vecchio and Collins (1986) and the Distributed Stress Field Model (DSFM) by Vecchio (2000). VecTor2 is capable of modeling two-dimensional reinforced concrete membrane structures under monotonic, cyclic and reversed cyclic loading conditions. The element library of the program is limited. However, the element library covers many of the required elements for reinforced concrete structures. More importantly, it uses state-of-the-art material models for concrete, reinforcing and prestressing steel.
The MCFT is based on a smeared, rotating crack model for reinforced concrete, in which cracked concrete is represented as an orthotropic material with a unique constitutive relation. VecTor2 is a nonlinear finite element program that utilizes an incremental total load and iterative secant stiffness algorithm to produce an efficient and robust nonlinear solution. Additional information on VecTor2 program is given in “VecTor2 & FormWorks User’s Manual” by Wong (2002). Furthermore, the details of the constitutive models and their implementation into VecTor2 software have been described by Vecchio (2000).
VecTor2 program have been used in many studies. Vecchio and others undertook an analytical study on classic beam tests (Vecchio and Shim 2004), using VecTor2. They concluded that in a finite element simulation of the test beams, three dimensional stress effects were significant. They signified importance of the out-of-plane reinforcement in the accurate estimation of load–deformation behaviour of the test beams. Sagbas et al. (2011) have used the VecTor2 program to model beam–column subassemblies subjected to cyclic loading. They proposed general guidelines for effective finite element modelling of beam–column subassemblies. Bohl and Adebar (2011) used VecTor2 program to investigate the plastic hinge length in high-rise concrete shear walls. They reported that there is generally very good agreement between the predicted and observed curvature distributions. In the context of FRP repaired and strengthened structures, Vecchio and Bucci (1999) used VecTor2 program for the analysis of repaired reinforced concrete structures. They concluded that it is possible to implement modifications to nonlinear finite element procedures that will enable analysis of repaired, retrofitted or sequentially constructed concrete structures. Wong and Vecchio (2003) investigated modelling of reinforced concrete members with externally bonded FRP composites behaviour and especially bond between concrete and FRP materials using VecTor2 program. They showed that the implementation of link and contact elements, along with linear elastic and elastic–plastic bond laws produces accurate predictions of member response.
VecTor2 uses three node constant strain triangular elements with six degrees of freedom and four-node plane stress rectangular elements with eight degrees of freedom to model concrete with distributed reinforcement. Plain as well as reinforced concrete with smeared reinforcement can be modeled using these elements. In VecTor2 program, various constitutive and behavioral models are available for concrete. The concrete model in VecTor2 accounts for the reduction of compressive strength and stiffness due to transverse cracking and tensile straining. Concrete tension stiffening, crack shear slip, concrete tension splitting, concrete confinement and concrete dilatation can be considered in the analysis. Description of these effects is out of scope of this paper and details of all these options are available in VecTor2 user’s manual (Wong and Vecchio 2003).
Palermo and Vecchio (2003) model with cyclic decay is assigned to concrete in order to model the hysteretic behavior of beam–column subassemblies in this study. Figure 9 shows the Palermo hysteretic behavior in tension and compression. Sagbas (2007) applied this model in the cyclic analysis of beam–column subassemblies.
4.2 Steel Rebar
Reinforcement can be modeled using either a smeared or a discrete representation. If bond-slip of reinforcement is to be considered, the use of discrete truss elements is unavoidable. On the other hand, when the longitudinal or transverse bars are sufficiently well distributed, smeared reinforcement is appropriate. Smeared reinforcement can be defined based on rebar percentage and rebar direction. The smeared reinforcement layer behaves as a unidirectional (in the specified direction) material. In order to model the discrete reinforcement, two-node truss bar element with four degrees of freedom is used.
Dowel action as well as reinforcement buckling can be considered in the analytical model using VecTor2. In this study, transverse rebar (stirrups) are modeled based on smeared option, and all longitudinal reinforcement are modeled using truss elements. Although bond slip between concrete and rebar is modeled using link element, perfect bond has been assumed for this element. This means that no slip is considered between the bar truss elements and the concrete elements.
4.3 Fiber Reinforced Polymer (FRP)
Currently VecTor2 program does not have a specific element for modeling FRP materials. However, FRP fabric or sheets can be modeled using either smeared tension-only reinforcement layer or discrete tension-only truss elements. If the bond between FRP fabric and concrete is to be considered, only discrete truss elements can be used. FRP material is essentially elastic; i.e. prior to reaching the ultimate strength the material stress–strain relationship is linear and after that the material fails in a brittle manner. As the FRP material remains elastic, no special consideration needs to be given to the cyclic behavior. Essentially, loading and reloading follow the same path.
4.4 Geometry and Meshing
Longitudinal bars of the beam and the column are modelled using discrete truss element. Even though the link elements are defined between the nodes attached to the rectangular concrete element and the truss element, perfect bond is used in this study. Mild steel properties are used to model the two steel plates on the top and bottom of the column.
Summary of ANSYS and VecTor2 features in modelling RC structures.
Membrane (3 and 4 node)
Tension only smeared rebar layer
External FRP sheet layer
Link (2 node)
Interface (4 node)
Basic linear for convergence purposes
Based on fracture energy and variety of models
Concrete hysteretic rules
Linear w/no plastic offset
Linear w/plastic offset
Nonlinear w/plastic offset
Rebar hysteretic rules
Bauschinger effect (seckin)
Rebar dowel action
5 Comparison of the Results
In this section, using ANSYS and VecTor2 programs, the five specimens shown in Table 1 are analyzed. Three specimens are subjected to monotonic loading, while the other two are cyclically loaded. Displacement–control type loading is used in both programs. The maximum applied displacement is 80 mm for all specimens that are subjected to monotonic loading, and for those that are subjected to cyclic loading, four cycles are considered. First cycle starts with the yield displacement and in the following cycles, the displacement is two, three and four times the yield displacement.
Figure 12 shows that the results of Drucker–Prager and Von-Mises yield criteria are almost identical. As expected assuming elastic behavior for concrete results in stiffer behavior. The model which is based on William-Warnke fails in properly predicting the specimen behavior, as it does not allow the concrete to take any load after crushing. Once one of the concrete solid elements fails, its stiffness drops to zero and as result the stiffness of the structure reduces. This type of failure would not normally occur in concrete structures as concrete experiences softening after reaching its peak stress. For other considered options, the crushing option is turned off in ANSYS.
Comparison of finite element and test results for monolithically loaded specimens.
Results in Fig. 14 show that the agreement between VecTor2 and ANSYS results is reasonably good. Furthermore, SHELL41 and reinforced SHELL181 result in almost similar results for the force–displacement curve. For the retrofitted specimens, finite element results overestimate the load capacity of the both retrofitted specimens. According to Mahini’s (2005) declaration, for RSM1 specimen and at the peak load, concrete crushing occurred at the face of the column, which was followed by the rupture of FRP. It was observed that the specimen exhibited a brittle failure mode constituting of concrete crushing, FRP buckling and debonding. In both specimens, concrete cover of the compression zone started to spall off at the peak load stage. In this study concrete spalling and FRP to concrete surface debonding were not modeled. Therefore, as expected the finite element results obtained from VecTor2 and ANSYS do not show any softening. VecTor2 results show small softening at the end of loading. However, this softening is a result of material softening not concrete spalling. There are several researchers that have modeled bond slip between FRP and concrete. Recently, Biscaia et al. (2013) have presented a load–displacement behavior model for bond-slip between FRP and concrete. Hawileh et al. (2012) utilized interface cohesion element for modeling debonding of FRP plates using ANSYS program. They concluded that the developed finite element models are capable of accurately predicting and capturing capacity the debonding failure mode of RC beams strengthened with FRP plates. Kim and Vecchio (2008) used a two-node link element in VecTor2 program for modeling FRP-retrofitted portal frame. Due to lack of adequate information, debonding between FRP and concrete was not modeled in this study. As shown in Fig. 14, VecTor2 exhibits a stiffer post-yield behavior in comparison with ANSYS. Furthermore, material softening which is considered in the VecTor2 model does not have a significant impact on the structural results.
The main failure indicators such as the ultimate strain of steel, concrete and CFRP sheets were not properly reported in the experimental program by Mahini. Therefore, in this research, values corresponding to 80 mm beam tip displacement are used as maximum load state. Table 3 shows that both programs well predict the load and displacement of the specimens at crack state. Although the yield load is well predicted, the yield displacement is underestimated by both programs. It is worth mentioning that in Mahini’s experimental program, the mechanical properties of FRP sheets were not directly obtained in the laboratory and instead the information provided by the supplier was used. Mahini has reported some fibers rupture during test of retrofitted specimens. This was not observed in the finite element analysis. One likely reason could be that the supplier’s ultimate stress for fibers does not represent the true average value. Furthermore, because of the inherent uncertainty in mechanical properties of material, the properties of tested material could be different from those used in the specimens. Therefore, in this study, the accuracy of results is limited by the accuracy of the available data.
Maximum stress in FRP sheet (MPa).
According to Table 4, when reinforced SHELL181 element is used, and in comparison with SHELL41 element option, lower stresses are resulted. This is partly is to the fact that in this case the saturant is modeled in addition to the fibers. A part of the applied load is taken by the saturant (modeled by SHELL181 element) which is used as a base for fibers (modeled by REINF265 element). Accepting the ultimate strength of 3900 MPa for FRP, the resulted stresses show that the FRP material remains elastic. As previously discussed, the available mechanical properties of CFRP sheets were provided by the supplier and Mahini did not test the FRP sheets in the laboratory. If the true average mechanical properties of CFRP sheets were available, the finite element models would have been able to capture the progressive failure of the tested specimens.
Comparison of finite element and test results for cyclically loaded specimens.
Maximum load (kN)
Dissipated energy (kN mm)
VecTor2 is basically a special program developed for the analysis of reinforced concrete structures and hysteretic response is well addressed in this software. Although, ANSYS is capable of doing cyclic analysis, it does not have the appropriate rules for unloading and reloading of the reinforced concrete structures. To overcome this problem in ANSYS, special user-defined subroutines may be linked up in order to enhance its element library and material models.
For planar reinforced concrete structures subjected to in-plane loading, it is possible to model one row of solid elements in ANSYS. Accordingly, the rebar steel and the thickness of the FRP sheets are scaled down. This technique considerably reduces the number of elements and more attention could be paid to refining the mesh size.
As it does not consider the material softening properly, William-Warnke failure criteria in ANSYS cannot suitably predict the behavior of reinforced concrete structures. The crushed elements are removed from the model and that could lead to premature failure which is not consistent with the real behavior of reinforced concrete structures. Drucker–Prager yield criterion can be used as a proper yield criterion for concrete material.
In ANSYS, element SHELL41 and reinforced SHELL181 element (reinforced with REINF265 element) with tension-only and membrane options can model the FRP sheets properly. On the other hand, smeared tension-only layer of FRP sheet or rebar could be used for modeling FRP in VecTor2 program.
There is good agreement between ANSYS and VecTor2 results in monotonic loading. Finite element results can well predict crack and yield state displacements and forces. However, due to uncertainties in material properties such as post yield stiffness of steel rebar and FRP rupture strain, there is disparity between the finite element results and those of experimental results for post yield behavior.
Although ANSYS programs can predict the load capacity in cyclic loading, it is unable to properly model the pinching effect in cyclic loading of reinforced concrete structures properly. On the other hand, VecTor2 can well simulate the cyclic behavior of the modeled structures and consequently provide accurate estimation of dissipated energy during cyclic loading.
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