Keywords

1 Introduction

Beam–column joint regions in reinforced concrete structural systems are one of the most critical parts, especially under seismic actions where shear demands are very high due to lateral inertia forces, resulting in brittle failures. Hence, the behavior of the joint region directly affects the capacity of the overall structure. Brittle shear failures occur usually with the effects of inadequate design detailing, lack of transverse reinforcement, and low compressive strength concrete.

Many of the heavily damaged or collapsed structures were designed for gravity loads only, with no regard to any significant lateral forces. Furthermore, concrete strength and reinforcement ratios were often below the minimum values specified by the respective design codes. Thus, the lateral load resistance of these structures was naturally very low even to resist small earthquakes.

Several strengthening techniques have been developed in the past, including RC and steel jacketing. Fiber-reinforced polymers are new materials used in the strengthening using externally bonded reinforcement in the critical regions of RC elements.

FRP materials, which are available today in the form of strips or in-place resin-impregnated sheets, are being used to strengthen a variety of RC elements, including beams, slabs, columns, and shear walls, to enhance the flexural, shear, and axial capacities of the elements. FRP materials offer advantages over other conventional methods such as steel and concrete for retrofitting.

The advantages are ease of installation, immunity to corrosion, high stiffness-to-weight ratio, and the ability to control the material’s behavior by selecting the proper orientation of the fibers. Even though the cost of CFRP is higher than conventional construction materials, all of these features make the CFRP sheet suitable for infrastructure applications and increase the shear and flexural capacities and ductility of structures including the BCJ of the unstrengthened specimens.

CFRP is a term used to describe a fiber-reinforced composite material that uses carbon fiber as the primary structural component. The binding polymer is usually epoxy. A method of wrapping and bonding FRP sheets along the sides of the beam, column, and surrounding its joints externally with epoxy as a binder to transfer stress between fibers provides high bond strength. The possible strengthening application methods are diagonal wrapping, L-shaped wrapping, longitudinal wrapping, and complete wrapping.

The numerical model analyzes different types of BCJ deficiencies and retrofitting methods. This is more cost and time effective than doing an experimental study. Design guidelines for retrofitting with CFRP wrap in BCJ are compiled using the developed simulation model.

1.1 Objectives and Scope

In this research, the main objective is to develop the simulation tool for validating the experimental results via the nonlinear finite element modeling approach and do a parametric analysis for retrofitting system.

The scope of the project is that to verify the potential of the FE model, the experimental database and parametric analysis will be done for the CFRP thickness.

2 Literature Review

Beam–column joint is one of the most critical parts in reinforced concrete structures under seismic actions. BCJ is subjected to high lateral inertia forces during seismic actions. It is still an unanswered question that how BCJ behaves under shear.

2.1 Experimental Study

Kaya et al. [3] investigated some BCJ behaviors for shear failure. A survey was conducted on existing buildings that were designed during the 1950s to 1990s to find the deficiencies of Turkish design during seismic actions. Plain reinforcement, low-quality concrete, insufficient transverse reinforcement, short beam anchorages, and lack of lap splices in the column were the deficiencies which were contributed to the shear failure of BCJ. TR-1 control specimen as shown in Fig. 1 was designed and detailed according to the Turkish Earthquake Code 1975, and it was experimentally tested through the test setup as shown in Fig. 2 by applying reversed cyclic lateral load (Fig. 3) at the top of the column with the constant axial load applied vertically from the top of the column.

Fig. 1
An image of T R-1 specimen includes the value of column (300 by 300) and beam (300 by 500).

TR-1 control specimen

Fig. 2
A diagram depicts the test setup for the experimental study. The labels are as follows, beam, column, strong floor, reaction wall, axial load, lateral load.

Test setup for the experimental study

Fig. 3
A graph represents the experimental study of lateral cyclic loading pattern along with the displacement in millimeters. The drift ratio is noted in percentage.

Lateral cyclic loading pattern in the experimental setup

The displacement-controlled loading was applied from the top of the column laterally with a dynamic actuator mounted on a steel reaction wall. Three cycles of the same amplitude in every story drift were repeated before displacement amplitude increased. The specimen was tested in a setup where the beam was placed parallel to the strong floor and attached by a rigid steel link element at its free end, simulating roller support. The column was placed in a vertical position and supported by a universal pin at the bottom end.

The constant axial load was applied vertically from the top of the column by the hydraulic ram. The amount of the constant axial force applied was 40% of the axial load capacity of the column. A steel frame was constructed surrounding the test setup to prevent any possible out-of-plane deformations, where the rollers mounted on both sides of the frame touched the specimen and forced it to move in the direction of loading.

The cylinder strength of the TR-1 control specimen was 15.3 MPa. The yield strength of the steel bars was 280 MPa. The beam and column moment capacities were 98.6 and 122.4 kNm, respectively. Deficiencies were introduced in TR-1 step by step to find the most critical and deficient BCJ specimen. Eventually, TR-5 shown in Fig. 4 was found as the most deficient BCJ with insufficient transverse reinforcement, short beam anchorages, and lack of lap splices in the column.

Fig. 4
An image of T R-5 specimen includes dimensions and values of the specimen.

TR-5 specimen

A total of 11 strain gauges were mounted on the reinforcing steel bars to gather the strain values during the experiment. Displacement at the tip of the column, the shear deformation in the BCJ region, and the curvature readings on the beam and columns near the maximum moment regions were monitored and measured by the linear variable displacement transducers (LVDTs). All data taken from strain gauges, LVDTs, and load cells were recorded by an electronic data acquisition system.

2.2 FRP Retrofitting

Fiber-reinforced polymers are new materials used in the strengthening using externally bonded reinforcement in the critical regions of RC elements. The FRP materials, which are available today in the form of strips or place resin-impregnated sheets, are being used to strengthen a variety of RC elements like beams, slabs, columns, and shear walls, to enhance the flexural, shear, and axial capacities [3]. FRP materials offer advantages over other conventional materials such as steel and concrete jacketing for retrofitting. They are ease of installation, immunity to corrosion, high stiffness-to-weight ratio, and the ability to control the material’s behavior by selecting the proper orientation of the fibers. CFRP is a highly engineered material suitable for infrastructure applications and increasing the shear and flexural capacities and ductility of BCJ subassemblies. In Parvin and Wu [5] study on the ply angle effect, it was found that the wrap ply angle stacking sequence of −45°/ +45°/−45°/+45° appeared to offer superior resistance for brittle shear failure when subjected to constant axial and cyclic lateral load. In the second part of the experimental study by Kaya et al. [3], three new strengthened specimens were used to determine the proper CFRP wrapping configuration for strengthening. The first one was strengthened with CFRP while considering the crack patterns, damage, and failure mechanisms that occurred in the TR-5 control specimen. For the next two identical specimens, the strengthening technique was modified step by step by observing the test results, damage, and failure patterns of the previous tests. Finally, an effective strengthening method was obtained for deficient BCJs.

The CFRP wrap was placed perpendicular to the crack propagation direction to give resistance against the tension as shown in Fig. 5. The same application was done in the opposite direction. Hence, X-shaped CFRP orientation was created.

Fig. 5
An image represents the carbon fiber-reinforced polymer wrap. The labels are as follows, joint panel, C F R P sheet, possible crack orientation.

CFRP wrap

3 Numerical Modeling

The optimum strengthening configuration for the CFRP shear retrofitting system was explored along with the following methodology. First, the parameters that should be included in the FE model were identified through the experimental database [3] and literature review. The properties of steel bars used in the experimental BCJ specimens are listed in Table 1. The properties of CFRP are listed in Table 2.

Table 1 Properties of steel bars
Table 2 Properties of CFRP

Then the unstrengthened specimen TR-1 was modeled in 2D using MIDAS FEA. After modeling of TR-1 control specimen in MIDAS FEA, the obtained results were verified with the experimental database. At first, the failure load and the failure mode did not match with the experimental results.

Filets were introduced in the corner regions to avoid local stress concentrations. After trials, the expected failure load and the failure mode were achieved. Similarly, TR-2 and TR-3 were modeled incorporating the deficiencies of insufficient transverse reinforcement and strong beam–weak column configurations, respectively. The cross section of the beam and column in the BCJ, cylinder strength, column reinforcement arrangement, and beam reinforcement arrangement are given in Table 3 to facilitate comparisons in configuration. TR-4 with short beam anchorages and TR-5 the most critical and deficient specimen with lap splices in the column need incorporating bond properties in the FE analysis which is currently being simulated.

Table 3 Properties of test specimens

Next, the suitable element for CFRP wrap was explored. After passing these stages, strengthened specimens were modeled in 2D by using the plate element for CFRP. The diagonal wrap was applied in the BCJ region of the TR-2 specimen in both directions. After obtaining the results from FE analysis, they were compared with the unstrengthened TR-2 specimen. Failure loads and displacements were obtained from load–displacement curves. Beam longitudinal reinforcement yielding loads were identified by analyzing the reinforcement stresses. Concrete stresses were studied to ensure that the BCJ failed in shear before the beam or column was able to reach their ultimate flexural strength for the unstrengthened specimens.

4 Numerical Simulation

A commercially available software package MIDAS FEA was used to perform nonlinear modeling of the CFRP retrofitting system (Analysis and Algorithm Manual, MIDAS FEA). The software facilitates the use of the total strain crack model classified under the smeared crack model to simulate concrete shear behavior. Two crack models are available: the fixed crack model and the rotating crack model. As will be discussed later, the validation process showed that the latter considerably underestimates the failure loads.

The rotating crack model was used throughout the modeling procedure. Thorenfeldt stress–strain relationship and linear–exponential softening curve were selected as concrete compression and tension models, respectively. The concrete fracture energy (Gf) was calculated using Eq. (1). The crack bandwidth (h) was taken as the square root of the mesh dimensions as recommended in the (Analysis and Algorithm Manual, MIDAS FEA).

$$G_{{\text{f}}} = {43}.{2} + {1}.{13} \times f_{{{\text{cu}}}}$$
(1)

The element size was selected, that it should be between 2–3 times the maximum aggregate size (ag), and assuming ag = 10 mm. Concrete was modeled using four-node, 25 mm square isotropic plane-stress elements as shown in Fig. 6. A sensitivity check for the FE parameters was done. For example, the mesh size was changed and checked with the results obtained.

Fig. 6
A graph depicts the 2D finite element mesh with four different nodes. The value of the isotropic plane is mentioned as 25 millimeters.

2D finite element mesh

The steel bearing plates (load and support bearings of 100 × 105 mm) were modeled to be triangular shape using triangular plane-stress elements to avoid stress singularities. All the reinforcement bars were modeled as embedded 1D elements defined by two-node line sections, and the von Mises yield criterion was used with a yield stress of 280 MPa. The perfect bond assumption can be used successfully to predict the behavior of CFRP strengthened RC structures when bond failure between the two components is not the governing failure mode. The CFRP wrap was modeled as 2D isotropic plate elements.

The two stages of analysis were adopted: the first stage was used to apply the constant axial load vertically from the top of the column, and the second stage was used to apply the load with 1 kN load increments. Two approaches of displacement-based and force-based loading were applied. The Newton–Rapshon method was used for iterations with an energy norm of 0.001 and a maximum number of iterations of 200 as the convergence criterion specified in Kurukulasuriya et al. [4].

5 Numerical Modeling

Obtaining reliable results through any FE modeling is a challenge because the entire modeling is influenced by the implemented material models, meshing, convergence criterion, etc. Hence to validate the FE model, some specimens were selected from the experimental study of Kaya et al. [3] which comprised of unstrengthened and strengthened beam–column joints.

The selected specimens are; control specimen TR-1, specimen TR-2 with Insufficient Transverse Reinforcements (ITR), and TR-3 with ITR and strong beam–weak column configuration. All were designed and detailed according to the Turkish Earthquake Code 1975. The specimens were applied with a force-based load of 75 kN and a displacement-based load of 30 mm in both directions.

Using numerous trials on material models, meshing, iteration method, type of loading, convergence criterion, etc., and considering appropriate recommendations found in the experimental study by Kaya et al. [3], a fairly reasonable validation was achieved. The smeared crack approach implemented in modeling provided the crack distribution as an output under the 2D element stresses. Figures 7, 8, and 9 show that those crack distributions were in a reasonable agreement with the experimental observations for BCJs.

Fig. 7
A graph depicts the formation of crack in T R-1 specimen as an output under the 2D element stresses.

Crack formation in TR-1

Fig. 8
A graph depicts the crack formation in T R-2 specimen as an output under the 2D element stresses.

Crack formation in TR-2

Fig. 9
A graph depicts the crack formation in T R-3 specimen as an output under the 2D element stresses.

Crack formation in TR-3

After that, all the above three specimens were subjected to reversed cyclic lateral loading by defining the construction stages for each displacement in both directions. The axial load was defined in the first construction stage with one increment and maintained constant throughout the FE analysis. Three cycles of the same amplitude were repeated before displacement amplitude increased. Depending on the behavior of the specimen, approximately 30 reversed cycles were applied throughout the test. The reversed cyclic lateral load was tried with two different compression models. They are the proposed compression model for loading–unloading (Carreira et al., cited in Aslani et al. [2]) shown in Fig. 10 and the Thorenfeldt curve which is inbuilt in MIDAS FEA.

Fig. 10
A graph depicts the compression model for loading and unloading along with the values mentioned. A curve forms a dip, then increases upward is noted in the graph.

Compression model for loading–unloading (Carreira et al., cited in Aslani et al. [2])

Figures 11, 12, and 13 show the hysteresis loops of the three specimens TR-1, TR-2, and TR-3 subjected to the reversed cyclic lateral loading with two compression models. The ultimate failure load was approximately similar to the experimental values, but even with the application of cyclic loading, the displacement at the failure load had a significant variation with the experimental data. The crack closure mechanism is governed by the crack closure stress which is the stress at which the crack is supposed to be completely closed. Once the crack is closed completely, the stiffness of the concrete is not affected by accumulated damage in tension. The crack closure mechanism had not been considered in the FE analysis while applying reversed cyclic lateral loading to the unstrengthened specimens. Next, the most deficient specimen TR-2 was selected for the strengthening applications with CFRP. The BCJ of the TR-2 specimen was strengthened with the diagonal wrap of thickness 0.176 mm. This orientation scheme was associated with the cracks observed in the TR-2 specimen that was caused due to the lack of transverse reinforcement in the BCJ region.

Fig. 11
A graph depicts the hysteresis loops for T R-1 under cyclic loading. It includes four curves: 1. New compression model, 2. T R-1 with force based, 3. Thorenfeldt, 4. T R-1 with disp based.

Hysteresis loops for TR-1 under cyclic loading

Fig. 12
A graph depicts the hysteresis loops for T R-2 under cyclic loading. It includes four curves: 1. New compression model, 2. Thorenfoldt, 3. T R-2 with force, 4. T R-2 disp based.

Hysteresis loops for TR-2 under cyclic loading

Fig. 13
A graph depicts the hysteresis loops for T R-3 under cyclic loading. It includes four curves: 1. New compression model, 2. Thorenfeldt, 3. T R-3 with force, 4. T R-3 disp based.

Hysteresis loops for TR-3 under cyclic loading

First, the CFRP was modeled as a single element with four nodes. There were not enough nodes to transfer the stresses from BCJ to the CFRP plate. Hence, the element size was reduced to 25 mm, and the CFRP plate was modeled as multi-element with many nodes. But still, there were connectivity issues since the nodes of BCJ were not connected to CFRP nodes. As solution, two surfaces were created with the same dimension of CFRP plate, one above the other. BCJ surface and one the CFRP surface were fused and the fused shape meshed with the concrete property. Then the other CFRP surface meshed exactly above that with CFRP property. This procedure eliminated the connectivity issue between BCJ and CFRP.

As a result, there was a significant increment in shear enhancement with the introduction of the CFRP plate into the FEM of TR-2. Figure 14 shows the finite element mesh of the CFRP plate element on the BCJ region of the TR-2 specimen in both directions. The formation of the crack on the BCJ region with CFRP plate in both directions under monotonic loading is illustrated in Fig. 15. Figure 16 shows the load–displacement curves for TR-2 with the application of CFRP diagonal wrap in both directions and without the application of CFRP under the reversed cyclic lateral loading.

Fig. 14
A graph represents a finite element mesh of the C F R P plate element on B C G region.

FE mesh of the CFRP plate element on the BCJ

Fig. 15
A graph depicts the formation of crack on the B C G region with C F P R plate in both directions.

Formation of crack on the BCJ

Fig. 16
A graph represents the load-displacement curves for T R-2 under reversed cyclic lateral loading. The curves, x shaped T R-2 cyclic and T R-2 cyclic forms from the negative axis to positive.

Load–displacement curves for TR-2 with the application of CFRP in both directions under reversed cyclic lateral loading

After that, CFRP thickness was analyzed through the simulation tool developed for the most vulnerable BCJ TR-2 specimen in the FE analysis. The effects of changing the thickness of the CFRP element were analyzed from 0.704 to 3 mm. Figure 17 shows the variation of the failure load with different thicknesses of X CFRP applied on the BCJ.

Fig. 17
A graph depicts the variation of failure load along with the C F R P thickness. It includes x shaped C F R P and beam numerical flexure. A vertical line named optimal thickness lies 2.3,0.

Variation of failure load with different thicknesses of X CFRP

6 Results

Table 4 summarizes the results for TR-1, TR-2, and TR-3 obtained from FEM in monotonic loading and the results stated in the experimental database. The compressive strength of the concrete used in each specimen and maximum loads obtained in both push and pull monotonic loading are listed below. All results are matched with maximum loading obtained experimentally in both push and pull directions.

Table 4 Experimental verification

Table 5 summarizes the results for TR-1, TR-2, and TR-3 obtained from FEM which is modeled incorporating the inbuilt Thorenfeldt compression curve and new compression model curve (Carreira et al., cited in Aslani et al. [2]) to improve the ductility of the specimen.

Table 5 Failure load of specimens under reversed cyclic lateral loading

Table 6 summarizes the results of strengthened TR-2 with CFRP plate element in one direction and both directions for displacement-based cyclic loading.

Table 6 Failure load of the strengthened specimen under reversed cyclic lateral loading

7 Discussion

The FE software has been able to capture the sensitivity of various beam–column joint configurations, both strengthened and unstrengthened specimens. It has also captured the effect of the difference in thickness of CFRP plate elements. All the strengthened beam–column joints have shown significant joint shear enhancement. The validation revealed that the FEM estimates the maximum loadings acceptably but overestimates the stiffness of the beam–column joint in monotonic loading and consequently the displacement obtained is less than the experimental displacement values. Although cyclic loading was expected to deteriorate the stiffness of the beam–column joint, it did not improve the ductility significantly. Hence, material modeling has to be done to incorporate the loading and unloading curve in the compression model and the pinching effect. The material model has to be programmed in FORTRAN in MIDAS FEA.

The orientation of the joint shear cracks observed in the control specimens depended on the width-to-height ratio of the joint panel cross section. Cracks were propagated diagonally from one corner to the other corner of the joint. From this observation, CFRP fibers were oriented diagonally to prevent the formation of shear cracks in the joint core in the strengthening process. TR-2 was selected for parametric analysis since it is the weakest beam–column Joint in the validated one which has the same size of the beam and column which was retrofitted in the experimental database.

8 Conclusion

The nonlinear FE modeling is promising in predicting the behavior of the beam–column joint for TR-1, TR-2, and TR-3 specimens. The FE model responded well enough for the lack of shear reinforcements and strong beam–weak column configuration as well. Predicted failure loads of the TR-1, TR-2, and TR-3 by the FE model are complying with the experimental failure loads. The projected cracks by the FE model in BCJ are similar to the crack patterns in the experimental database.

The shear strength of the joint is enhanced with the introduction of the CFRP element which is modeled as a plate element. Failure load increases in strengthened TR-2 with the increase of CFRP thickness. It increases with decreasing gradient. Applying CFRP in both directions (X-shaped CFRP) enhanced the shear strength of the BCJ more, instead of applying CFRP in one direction. The optimum thickness of CFRP was found as 2.1 mm, where the beam started to fail in flexure.

The study could be extended in validating TR-4 and TR-5 by introducing short beam anchorages and lap splices in column reinforcement bars. The bond element should be introduced between concrete and reinforcement elements for anchorages. The bond element should be introduced between reinforcement elements for lap splices in the column. The method to include this bond element into the FE model should be studied.

To improve the ductility of the FE model under reversed cyclic lateral loading, the material should be modeled in FORTRAN incorporating loading and unloading curve in both compression and tension models. Hence, the study on the techniques for modeling material in FORTRAN language should be done to achieve the failure displacement of the specimens.

In this study effect of unidirectional fiber, orientation is not taken into account. However, it may influence the optimum CFRP slope. Hence, the material properties of the CFRP element should be refined by considering the unidirectional fibers.