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THE FINITE ELEMENT ANALYSIS OF RC JOINTS STRENGTHENED WITH EXTERNAL FRP COMPOSITES

M. Kazem Sharbatdar1, Mostafa Fakharifar2

1Assistant Professor, Faculty of Civil Engineering, Semnan University, Semnan, Iran 2M.Sc Student, Faculty of Civil Engineering, Semnan University, Semnan, Iran

ABSTRACT Externally bonded fiber-reinforced-polymer (FRP) sheets have been successfully used for strengthening of damaged or deficient reinforced concrete members. Despite of a lot of research conducted and tests on application of these new sheets during the last decade, further research is still required to consolidate recent developments and expand the scope of application of FRPs for structural applications. Nonlinear finite element analysis combined with laboratory testing constitutes an efficient approach for pursuing this objective. The objective of this paper is exploring and illustrating the contribution of a refined three-dimensional (3D) constitutive FE model for investigating the nonlinear response of concrete joint, reinforced with steel rebars and strengthened with external FRP sheets. The analyses were carried out by using finite element software having different capacities. Different parameters such as application of FRP sheets with different patterns, different loading conditions and different strengthened areas have been considered to show the results. Several results regarding increasing ultimate values in the strengthened model in comparison with the reference specimen, ductility of the strengthened model, and evaluation of ductile against non-ductile joint have been presented in this paper. Keywords: FE model, nonlinear analysis, RC joint members, FRP sheets, strengthening 1. INTRODUCTION Existing reinforced concrete (RC) structures that were designed according to pre-1970’s codes often have inadequate reinforcement detailing, which not only results in deficient lateral load resistance, but also in insufficient energy dissipation, rapid strength deterioration and improper hinging mechanisms during earthquakes, leading to excessive drifts and ultimately to structural collapse. Non-ductile detailing is generally manifested through deficient joint shear resistance, deficient column shear capacity, deficient column’s main reinforcement lap splices, deficient anchorage of beam positive reinforcement at the beam-column joint, and deficient beam shear resistance. In particular, recent earthquakes have demonstrated that RC beam-column joints that have been constructed based on pre-1970’s design codes may initiate and cause total collapse of structures. For instance, Figure 1-a [1] shows a RC structure that collapsed during the 1999 Kocaeli Earthquake in Turkey

388 / The Finite Element Analysis of RC Joints…. –––––––––––––––––––––

in which joints failures appear to be the major contributor to such collapse, while Figure 1-b shows a close-up of a non-ductile failure of a beam-column joint during the same earthquake. Beam-column joint deficiencies combined with the weak column/strong beam glitch contradict failure hierarchy of the design capacity concept. A failure in the beam is usually less critical than that in the column, and the latter is less critical than a failure in the joint. Hinging in the joint, being at the point of intersection of the beam and column, allows excessive rotations both in the beam and column in conjunction with a loss of load carrying capacity of the column. Such dangerous failure mechanism is unacceptable and must be prevented in design.

(a) (b)

Figure 1. Damages to moment resisting frames during the Kocaeli 1999 earthquake: (a) joint induced structural collapse; (b) beam-column joint failure [1]

There is a perceived void in the current literature for studies that focus on the behavior of reinforced concrete beam–column joints under cyclic loading. In fact, most reported research in the literature is mainly on cyclic behavior of connections [3] in newly designed steel structures and also concrete connections retrofitted by traditional rehabilitation techniques [2]. Moreover; most of the recent researches involved in finite element modeling of RC connections; are concerned with exterior beam-column joints. This study intends to investigate the effect of various combinations of FRP wrapping patterns on the performance of interior reinforced concrete beam–column joints, i.e. ductility, under combined axial and lateral cyclic loads. A three-dimensional finite element analysis model of FRP wrapped beam–column joints, which exhibit material and geometric nonlinearities that are due to large displacements, confinement effect, and concrete nonlinear behavior, are developed. The FEA model is validated through leveraging an experimental study on a FRP-wrapped beam–column joint. 2. EXPERIMENTAL TEST ON INTERIOR RC BEAM-COLUMN JOINTS There are abundant experimental tests regarding RC beam-column joints, and most

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of them have been carried out on exterior beam-column joints. In addition; limited researches have been investigated on finite element modeling of interior beam-column joints. A. Mukherjee et al [5] have performed a fully detailed, comprehensive experimental test on interior RC beam-column joints strengthened with FRP laminates. The test scheme and specimen which have been investigated in the test are firstly introduced. Eventually, the FE model calibrated regarding the experimental study is presented and results are analyzed. 2.1. Specimens Details Two different types of RC joints have been cast for experimental verification [5]. One set of joints has adequate steel reinforcements with proper detailing of reinforcements at the critical sections (Figure 2). In the other set of specimens the beam reinforcements have deficient bond lengths at the junctions with the columns (Figure 3). When the beam was transversely loaded the first set was characterized by a long plastic zone (ductile) while the second set failed in reinforcement pull out and exhibited sudden failure (non-ductile).

Figure 2. Specimen with ductile joint reinforcement [5]

Figure 3. Specimen with non-ductile joint reinforcement [5]

The specimens in Figures (2) and (3) were strengthened using carbon and glass FRP materials. Prior to the application of the FRP, the concrete substrate was

Column

Beam


smoothed by grinding. Figures (4) and (5) present schematic arrangement for two typical systems; L-overlays and precured carbon plates which were utilized respectively, in the aforementioned experiment. In Type A; GFRP/CFRP sheets have been applied in L shape to upgrade the joints. These sheets have been applied in several layers. FRP has been applied on the top and bottom surface of concrete surfaces, so the fibers were along the axes of the members (Figure 4a). Then, FRP wraps were provided over the inner layers (Figure 4b), the direction of fibers in wraps was perpendicular to the axis of the members. Figure 5a shows glass fiber sheets (80mm wide and 250mm long) on either side of the joint. Only one layer is provided on one side. Two layers of FRP have been provided on the other side to evaluate its efficacy.

Figure 4. Type a strengthening system-use of composite overlays [5]

Figure 5. Type B strengthening system-use of precured carbon plate [5]

Both the column and the beam are then wrapped by unidirectional glass fibers with 100mm lap length. Same conFigure uration is repeated using carbon fiber sheet using 1 and 2 layers of overlays and single wrap with 100mm overlap. Both adequate and deficient joints were reinforced using this conFigure uration. Furthermore, procured carbon plate (25mm wide and 1.2mm thick) have been used in the beams in Type B to improve bending stiffness. To achieve a good bond between the plate and the concrete, a groove (25mm wide and 25mm deep) has been created inside the joint. The plates have been inserted into the joint as shown in Figure 5, and then the groove has been filled by injecting epoxy resin, and the


plates have been inserted in the groove as shown in step 1 of Figure 5. The beams and columns have then been wrapped using a single wrap of carbon sheet. 2.2. Test Program The experimental setup which has been utilized by A. Mukherjee et al [5] is shown in Figure 6. The column was fixed at its ends on a loading frame. It was subjected to a constant axial load of 100KN which is 50% of ultimate load carrying capacity of the column. Cyclic load was applied using a hydraulic actuator with load cycle based on increasing displacement control. Three cycles were repeated at each level of displacement. Vertical deflection of the tip of the beam was recorded directly by the linear variable displacement transducer (LVDT). The compressive strength of concrete used in this experiment has been 30N/mm2 and also properties of other material used are shown in Table (1). The same values have also been used for FE modeling of aforementioned specimens. Totally, 12 specimens at two categories of ductile and non-ductile reinforcement, including as-built and strengthened specimens with different patterns have been tested in this experimental research by [5].

Figure 6. Experimental setup [5]

The elaborate test matrixes for adequate and deficient specimens which have been investigated through this experiment are presented in Tables (2) and (3) respectively.

Table 1: Properties of materials [5]

Material Effective thickness

(mm)

Ultimate strength (MPa)

Tensile modulus

(GPa)

Ultimate strain

Glass-G (fiber) 0.36 2250 70 0.0239 Carbon-C (fiber) 0.11 3500 230 0.0117 Carbon plate-CP

(composite) 1.2 2800 165 0.017

Mild steel longitudinal reinforcement 6 mm dia 275 198 0.045

Mild steel transverse reinforcement 3 mm dia 555.13 193 0.043


Table 2: Test matrix for ductile specimen [5]

S. no Specimen name Details

1 D-1 - 2 G1L-D Type A with single L of GFRP at top and bottom 3 G2L-D Type A with two L of GFRP at top and bottom 4 C1L-D Type A with single L of CFRP at top and bottom 5 C2L-D Type A with two L of CFRP at top and bottom 6 CP1-D Type B with CFRP plate at top and bottom

Table 3: Test matrix for non-ductile specimen [5]

S. no Specimen name Details

1 ND-1 - 2 G1L-ND Type A with single L of GFRP at top and bottom

3 G2L-ND Type A with two L of GFRP at top and bottom

4 C1L-ND Type A with single L of CFRP at top and bottom

5 C2L-ND Type A with two L of CFRP at top and bottom 6 CP1-ND Type B with CFRP plate at top and bottom

3. FINITE ELEMENT MODELING OF INTERIOR RC BEAM-COLUMN JOINTS All specimens which have been investigated in the experimental study conducted by Mukherjee [5] are modeled in this section by using non-linear finite element ANSYS ver 11. 3.1. Material Models The constitutive relationships employed to describe the mechanical behavior of materials as well as the interaction between steel bars and concrete are basically those proposed in CEB-FIP Model Code 1990 [4], with some slight modifications. In compression, the behavior of the concrete is that proposed by the same code and, in tension, a linear elastic behavior is assumed up to the strength of concrete in tension (fct). For the sake of comparison, a second model that indirectly incorporates the tension-stiffening effect [6] is also implemented. In such a model, the progressive loss of rigidity after cracking is quantified indirectly through an adaptation of the tension behavior introducing a softening branch, which is calibrated using the α and εm parameters. Both the curves are illustrated in Figure 7. The aforementioned parameters are usually set at 0.5≤α≤0.7 and εm= 0.0020. In this case, fracture mechanics could be used to establish these values, based on energy criteria [8]. The perfect plasticity model of the behavior of the longitudinal reinforcement bars and also the interaction between reinforcement bars and concrete are shown in


Figures (8) and (9), respectively. The parameters shown in Figure 9 depend on the bond conditions and confinement of concrete, as established in CEB-FIP Model Code 1990 [4].

Figure 7. Stress-strain relationship for concrete [6]

Figure 8. Stress-strain relationship for steel [6]

Figure 9. Bond stress-slip relationship [4]

Solid 65, Solid46 and Link8 are the element used in ANSYS to develop these FE models. The Solid65 and Link8 elements were used to model the concrete and reinforcement, and also layered solid elements, Solid46, were used to model the FRP composites. 3.2. Bond Model The correct simulation of the bond between concrete and reinforcement bars plays


a significant role in the proper modeling of beam-column connections. When the bond forces tend to zero it is apparent that the majority of the shear force will be transferred across the joint core by a diagonal compression strut mechanism and hence severe diagonal tension cracking is less likely if bond deterioration occurs at an early stage of loading [9]. A complex interaction between flexural response of the adjacent beam element and the joint shear transfer mechanism occurs also due to the stress penetration into the panel zone from the beam bars, combined with a fixed-end rotation in the beam due to progressive bond degradation and pull out mechanism. The discrete bond model implemented in ANSYS consists of a one-dimensional (1D) finite element with a realistic bond-slip relationship as shown in Figure 10. Additional information on the discrete bond model can be found in [7].

Figure 10. Bond-slip relationship for deformed bars [7]

For plain round bars with a diameter of 12 mm, the total bond strength was approximately m fτ τ+ = 1 MPa ( mτ = mechanical bond; fτ = frictional bond) for a slip of 1s = 0.03 mm [10]. During cycling, the bond degradation valid for deformed bars is principally due to the shear failure of concrete between the ribs of the bar. In the case of smooth bars, it is reasonable to assume that friction is the only source of bond mechanism at the steel-concrete interface and that it is scarcely influenced by the cycling. 3.3. Analytical Modeling of Specimens Two different finite element models for each of the specimen in two different categories of ductile and non-ductile were analyzed. Albeit, neither of the experimental specimen had been investigated for monotonic loading, but in order to acquire the ductility and load-displacement curves for specimens; all the FE models in this analyses went under monotonic loading for non-linear analysis. A relatively fine discretization was employed for monotonic loading as Figure 11a. On the other hand, for saving computation time, cyclic analyses were carried out using a relatively coarse discretization shown in Figure 11b. The FE model of steel bars is shown in Figure 11c.


(a) (b) (c) Figure 11. Finite Element model of Ductile specimen: a) fine 3D FE mesh used for monotonic loading; b) coarse 3D FE mesh used for cyclic loading; c) steel bars FE

model The experimental control specimen of ductile category (D-1) was firstly modeled and then went under both monotonic and cyclic loading to asses and validate the accuracy of FE model. Figure 12 compares the applied force versus free tip of the beam drift curves for monotonic loading of the fine and coarse models with the envelope curve from the cyclic experiments for ductile specimen. It can be seen that the numerical results agree reasonably well with the experimental results. The coarse model, however, slightly overestimated the peak resistance and exhibited slightly more brittle response. For both models the failure mode was diagonal shear failure of the joint. This point confirms the accuracy of FE model; therefore FE model is extended to acquire further results.

Figure 12. Comparison of the model response for the coarse and fine meshes with

experimental results for ductile specimen Non-linear finite element analyses for the entire models including ductile and non-ductile; has been implemented by utilization of the two different patterns of strengthening Type A & B. The usage of two different types of strengthening which has been performed for both ductile and non-ductile FE models is illustrated in Figure 13.


(a) (b)

Figure 13. Finite element model of strengthened joint: a) Strengthening Type A; b) Strengthening Type B

3.4. Results for FE Models with Ductile Joint Reinforcement The displacement levels of the first few cycles do not generate any nonlinear deformation in the model. The onset of stiffness degradation is identified by simultaneous appearance of tension cracks at the root of the cantilever beam. The analyses show that at this point the steel started to yield and it was not capable of taking any further load. The additional load from this point was carried out by the FRP. At this point, linearity of the ascending and the descending paths is lost. This phenomenon is yield point. The post yield behavior is signified by monotonic degradation of stiffness. Ability of the structure to survive an earthquake depends to a large extent, on its ability to dissipate the input energy. Forms of energy dissipation include kinetic energy, viscous damping and hysteretic damping, etc. An estimate of the hysteretic damping can be found by the area enclosed in the load–displacement hysteresis loops. Yield points for ductile specimen are provided in Table (4). Columns 2 & 3 of Table (4) summarize the percentage increase in the yield load. The CP1-D exhibited the highest increase in the yield load followed by the C2L-D, G2L-D, C1L-D and G1L-D specimens. It may be noted that the forces at the tensile face of the beam are shared by the steel and FRP in proportion of their relative stiffnesses. The stiffness of carbon is considerably higher than that of glass. Therefore, for the same tip load, the tensile force in steel is lower in the carbon reinforced FE model than in the glass reinforced models. As a result, the steel in the carbon reinforced models yield at higher tip loads. The CP1-D models are anchored at the joint through a groove. Therefore, they exhibit higher stiffness than other sheet models. The models with two-layer reinforcement had higher yield loads than the models with one layer reinforcements. Due to FRP reinforcements the displacement at yield increased to a much lesser extent than the load (Comparison of column 2 (or 3) with 4 (or 5), Table 4). Another interesting point is that the glass reinforced models had much higher displacement at yield than the carbon reinforced models. This is due to the higher stiffness of carbon than glass. There is satisfactory agreement between FE model and experimental test results. The initial stiffness and the ultimate displacements are also summarized in Table (5). It is worthwhile to mention that almost all the values of increase and promotion for

Procured carbon plate elements

1

X

Y

Z

DEC 9 200819:42:33

ELEMENTS

F


FE models are higher in comparison with experimental results. This is due to the reduction of degrees of freedom in analytical finite element model in comparison with the real specimen. FE models are inherently stiffer than real specimens. Figure 14 reveals the ratio of ductility for strengthened specimen versus control specimen. Apparently ductility for all strengthened FE ductile models has increased between 25 to 78%. The joint shear crack, which ultimately caused the model to fail, was similar to the shear cracks observed in the experiments.

Table 4: Yield points of ductile specimens Yield load Deflection at yield load % increase % increase Specimen

experiment FE model experiment FE model

Control-D - - - - G1L-D 21.32 23.48 -10.00 -9.25 G2L-D 48.42 51.12 58.95 61.25 C2L-D 57.89 59.60 -3.16 -3.62 CP1-D 116.18 112.10 161.84 158.31

Table 5: Ultimate points in ductile specimens

Initial stiffness Ultimate deflection % increase % increase Specimen

experiment FE model experiment FE model Control-D - - - -

G1L-D 17.14 18.25 14.65 15.22 G2L-D 75.00 73.28 29.21 31.25 C2L-D 140.94 138.25 42.83 44.21 CP1-D 41.37 45.95 20.63 19.75

Unfortunately, a direct comparison of the sequence of cracking (flexural to shear) was not possible since monotonic loading of the test specimens was not performed. The finite element model for monotonic loading (fine mesh) was also used to investigate: 1) the influence of the bond strength (Figure 15a) and 2) the influence of the normal column force (Figure 15b). Figure 15 shows the influence of the ultimate bond strength ( m fτ τ+ ) on the response of the joint. It can be seen that with higher bond strength the resistance is higher and the failure more brittle. Figure 15b shows the influence of the axial column force on the applied force versus free tip of beam drift curve. It can be seen that with higher compressive force the joint shear (thus overall subassembly) resistance increases. The time that analyses finished and elements turned to fail, pondering through strain distribution in the control model revealed that the beam has failed at the joint through the formation of a hinge. The hinge has formed between the two shear links of the beam. It seems concrete has spalled in such a fashion that two semicircular surfaces have been created. The FRP reinforced models, on the other


hand, did not have the semicircular failure planes. The failure planes were approximately vertical. It could be concluded that the difference in the failure mode is due to the presence of the FRP wraps.

Figure 14. Ductility for Strengthened ductile models

(a) (b)

Figure 15. Comparison of numerical and experimental results for monotonic loading: a) effect of variation of bond strength; b) effect of variation of axial load

3.5. Results for FE Models with Non-Ductile Joint Reinforcement Non-linear analyses show that to some extent the extracted results from non-ductile FE models are close to ductile FE model. However due to the presence of continuous steel bars in the joint area, ductile model have a higher load bearing capacity, stiffness and energy dissipation capability. In Tables (6) & (7) the yield and ultimate points for non-ductile models are given. The G2L-ND exhibited the highest increase in the yield load followed by the C2L-ND, CP1-ND and C1L-ND. The models with two-layer reinforcement had higher yield loads than the models with one layer. Due to FRP usage the displacement at yield increased to a much lesser extent than the load (Comparison of column 2 (or 3) with 4 (or 5), Table 6).


Table 6: Yield points of non-ductile specimens Yield load Deflection at yield load % increase % increase Specimen

experiment FE model experiment FE model Control-ND - - - -

G2L-ND 103.75 42.56 15.24 16.32 C1L-ND 12.60 13.25 -18.29 -19.23 C2L-ND 79.36 36.45 4.27 5.34 CP1-ND 68.36 -45.25 78.05 81.21

Table 7: Ultimate points in non-ductile specimens

Initial stiffness Ultimate deflection % increase % increase Specimen

experiment FE model experiment FE model Control-ND - - - -

G1L-ND 41.46 42.56 20.45 22.36 G2L-ND 9.52 13.25 55.11 58.12 C2L-ND 32.49 36.45 41.37 39.96 CP1-ND -41.17 -45.25 16.08 17.91

The load-displacement envelopes for ductile and non-ductile FE models are plotted in Figures (16-17). The envelopes let us compare the relative performance of the models. All the FRP reinforced models have higher peak loads than the control model. For ductile joints the CP1 model has the highest peak load followed by the C2L, G2L and G1L. For non-ductile joints the G2L-ND model has the largest envelope area followed by the C2L-ND, CP1-ND and C1L-ND. Comparing these Figures reveal the superior performance of ductile joints.

Figure 16. Load-Deflection envelope for

ductile models Figure 17. Load-Deflection envelope for

non-ductile model s Ductility promotion for non-ductile joints is approximately between 16 to 51% (Figure 18).


Figure 18. Ductility for Strengthened non-ductile models

4. CONCLUSION With application of FE models (validated based on experiment) for two different types of RC joints including ductile and non-ductile reinforcement details the promotional effect of both glass and carbon composite has been investigated. These two composites could be efficiently used for seismic retrofitting of RC joints regardless of reinforcement details. Obviously due to presence of continuous steel bars in the joint area for ductile joints, they exhibit a more superior, ductile behavior rather than non-ductile joints. The main cause of superior performance of the FRP reinforced joints is the continuous confinement provided by the FRP wraps which impede the creation of hinge through the spalling of concrete. FE models confirm the advantage of carbon reinforcements over glass reinforcement in case of ductile joints. But for non-ductile joints, glass reinforcing is preferable. Utilization of FRP sheets have a promotional efficiency regarding to yield load, performance and initial stiffness of joints. Commonly CFRP strengthened joints reveal stiffer behavior than GFRP strengthened joints regardless of reinforcing details. REFRENCES 1. Saatcioglu M., and Ghobarah A., ‘The August 17, 1999, Kocaeli Earthquake –

Damage to Structures’, Canadian Journal of Civil Engineering 28(4), 2001, 715-737.

2. Alcocer S, Jirsa Jo. Strength of reinforced concrete frame connections rehabilitated by jacketing. Struct J, ACI 1993;90(3):249-61.

3. Anderson JC, Duan J, Xiao Y, Maranian P. Cyclic testing of moment connections Upgraded with weld overlays. J Struct Eng ASCE 2002;128(4):509-16.

4. Comite´ Euro-International du Be´ton CEB-FIP Model Code 1990: Final draft, CEB Bulletin D’Information, 1990. p. 203-5.

5. Mukherjee Abhijit, Joshi Mangesh. FRPC reinforced concrete beam-column joints under cyclic excitation. J Composite Structures 2004; 70: 187-99.

6. Figure ueiras Ja. Ultimate load analysis of anisotropic and reinforced concrete plates and shells, PhD thesis. Swansea, University College of Swansea, 1983.

7. Ozbolt, J., Lettow, S. and KOZAR, I., 2002. Discrete Bond Element for 3D


Finite Element Analysis of Reinforced Concrete Structures. 8. Ranjbaran A. Dena: finite element program for the non-linear stress analysis of

two-dimensional, metallic and reinforced concrete, structures. Comput Struct 1994;51(2):191-211.

9. Lettow, S. Ein Verbundelement für nichtlineare Finite Elemente Analysen - Anwendung auf Übergreifungsstöße. Dissertation, Institut für Werkstoffe, Universität Stuttgart, 2006.

10. Fabrocino G. and Cosenza E., 2002. Experimental behaviour of smooth bars anchorages in existing RC Buildings. 2002 “Concrete struct in the 21st Century”: w-463.

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