Prediction of Joint Shear Strength of Concrete BeamColumn ... · PDF fileaverage value of...

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 1, No 3, 2010

© Copyright 2010 All rights reserved Integrated Publishing services Research article ISSN 0976 – 4399

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Prediction of Joint Shear Strength of Concrete BeamColumn Joints Reinforced Internally with FRP Reinforcements

Saravanan Jagadeesan 1 , Kumaran G 2 , 1 Assistant Professor, 2 Professor, Department of Civil and Structural Engineering, Annamalai University, Annamalai Nagar608002, Chidambaram, Tamil Nadu, India

[email protected]

ABSTRACT

This experimental study primarily focuses on the joint shear strength of full scale size exterior concrete beamcolumn joint reinforced internally with Glass Fibre Reinforced Polymer (GFRP) reinforcements under monotonically increasing load on beams keeping constant load on columns. Four series of joints and totally eighteen numbers of such specimens are cast and tested for different parametric conditions like beam longitudinal reinforcement ratio, concrete strength, column reinforcement ratio, joint aspect ratio and influence of the joint stirrups at the joint. Also finite element modelling and analysis of GFRP reinforced concrete beamcolumn joints are performed to simulate the behaviour of the beamcolumn joints under various parametric conditions. Based on this study, a modified design equation is proposed for predicting the joint shear strength of the GFRP reinforced beamcolumn specimens based on the experimental results and the review of the prevailing design equations.

Keywords: Nonmetallic Reinforcements, Concrete beamcolumn joints, Finite Element, Stirrups, Strength Reduction Factor.

1. Introduction

Non metallic reinforcements or Fibre reinforced polymer (FRP) reinforcements has rapidly emerged as an effective alternative to conventional steel reinforcement to overcome the problem of corrosion. Owing to its superior durability characteristics, the use of FRP reinforcement can extend the lifespan of concrete structures and reduce the need for maintenance or repair of concrete structures (ACI 440R96; Ehab, et al., 2010; Deiveegan, 2009 and Sivagamasundari, 2010). However, although FRPs are already adopted quite extensively in various sectors of the construction industry (e.g. strengthening and repair of existing structures), their use as internal reinforcement for concrete is limited only to specific structural elements and does not extend to the other parts of the structure. The reason for the limited use of FRPs as internal reinforcement can be partly attributed to the lack of commercially available curved or shaped reinforcing elements used for shear reinforcement for beamcolumn connections. But the studies related to the use of nonmetallic reinforcements for beamcolumn joints are not explored in detail. Therefore the present study discusses mainly on the joint shear strength of concrete beamcolumn joints reinforced internally with Glass Fibre Reinforced Polymer (GFRP) reinforcements. Based on this study suitable modified



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design expressions are derived and are compared with the conventionally reinforced beamcolumn joints for more rational concept. First part of this study covers the experimental investigation of GFRP/Steel reinforced concrete beamcolumn joints. Second part of this study is relates to the finite element modelling and analysis of GFRP/Steel reinforced concrete beamcolumn joints. Full scale finite element modelling is done similar to experimental set up. The static analysis is performed with the help of ANSYS software with different parametric conditions (Sivakumar, 2008). Finally, the results are summarised and compared with the experimental findings. Design equations are proposed and are validated with the existing theories.

2. Materials

2.1 Concrete

Normal Strength Concrete (NSC) of grades M 20, M 25 and M 30 are used to cast the concrete beamcolumn exterior joint. The mix proportions of the NSC are carried out as per Indian Standards (IS) and the average compressive strengths are obtained from laboratory tests (Sivagamasundari, 2010; Sivakumar, 2008; Sofi, 2006).

2.2 Reinforcements

The mechanical properties of all the types of GFRP reinforcements as per ASTMD 391684 Standards and steel specimens as per Indian standards are obtained from laboratory tests and the results are tabulated in Table1. The tensile strength of steel reinforcements (S) used in this study, conforming to Indian standards and having an average value of the yield strength of steel is considered for this study. GFRP reinforcements used in this study are manufactured by pultrusion process with the Eglass fibre volume approximately 60% and these fibres are reinforced with epoxy resins. Three different types of GFRP reinforcements (grooved, sand sprinkled & threaded) (ACI 440R96; Ehab, et al., 2010; Deiveegan, 2009; Sivagamasundari, 2010; Sivakumar, 2008 and Sofi, 2006) with different surface indentations and are designated as Fg, Fss and Ft. The diameters of the longitudinal and transverse reinforcements are 12 mm and 8 mm respectively. The tensile strength properties are ascertained as per standards shown in Table 1 and are validated by conducting the tensile tests at different testing agency (Central Institute for Plastic Engineering and Technology (CIPET), Chennai, Govt. of India and also from the laboratory tests. The compressive modulus of elasticity of GFRP reinforcing bars is smaller than its tensile modulus of elasticity (ACI 440R96; Ehab, et al., 2010; Deiveegan, 2009 and Sivagamasundari, 2010). It varies between 3647 GPa which is approximately 70% of the tensile modulus for GFRP reinforcements. Under compression GFRP reinforcements have shown a premature failures resulting from end brooming and internal fibre microbuckling. No standard test methods exist in composite literature. In this study, GFRP stirrups are manufactured by Vacuum Assisted Resin Transfer Moulding process, using glass fibres reinforced with epoxy resin (ACI 440R96; Ehab, et al., 2010; Deiveegan, 2009 and Sivagamasundari, 2010). Based on the experimental study, it is observed that the strength of GFRP bent bars/stirrups at the bend



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location (bend strength) is as low as 50 % of the strength parallel to the fibres. However, the stirrup strength in straight portion is comparable to the yield strength of conventional steel stirrups. In addition to stirrups, anchorage reinforcements near beamcolumn joints are important and are provided in two ways viz., i) providing bend in GFRP reinforcements (manufactured by Vacuum Assisted Resin Transfer Moulding process) and are designated as FF . ii) providing steel couplers at the junction between vertical and horizontal GFRP threaded reinforcements and are designated as FS. 3. Test Specimens

A typical beamcolumn joint specimen is shown in figure 1. Test specimens consist of four series and are designated as A, B, C & D. Totally eighteen specimens with identical dimensions, geometry and reinforcing arrangement are cast and the detailed descriptions of specimens are tabulated in Table 1. These specimens are applied with constant axial load on columns and static monotonically increasing load on beams with varying parametric conditions. The maximum beam length (Lb = 1050 mm) and column height (H = 2000 mm) are decided based on the experimental limitations. All the columns in the specimens are provided with 4 nos. of 12 mm diameters and beams are reinforced with 4 numbers of 12 mm diameter bars, 2 at top and 2 at bottom. The transverse reinforcements of column and beam for all the specimens are 8 mm diameter and spaced at 150mm centre to centre as shown in figures 2(a), 2(b) and 2(c).

P

H

aa

a a

b

b

bb

L

GFRP12 4Nos.

GFRP 8 150c/c bc

h c

GFRP 12 4Nos.

GFRP 8 150c/c

b b

h b

Figure 1: Typical beamcolumn joint specimen



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(a) (b) (c) Figure 2: (a) Skeleton of beamcolumn joint with steel reinforcement

(b) Skeleton of beamcolumn jointGFRP reinforcement with steel bent coupler at the joint

(c) Skeleton of beamcolumn jointGFRP reinforcement with FRP bent coupler at the joint

Table 1: Details of the test specimens

Specimen H mm

L mm

bb mm

bc mm

hb mm

hc mm

Beam tension reinft.

Column reinft.

Prov ision of

joint stirr ups

Cube streng th

MPa

Tens ile stre ngth MPa

BCJSM2A 2000 1000 125 150 150 150 212mm 412mm No 36.65 498 BCJSM3B 2000 1050 230 230 230 230 212mm 412mm No 46.23 498 BCJSM1C 2000 1000 150 150 200 200 212mm 412mm No 32.25 498 BCJSM3C 2000 1000 150 150 200 200 212mm 412mm No 44.15 498 BCJSM1D 2000 1000 150 150 200 200 212mm 412mm Yes 32.25 498 BCJSM3D 2000 1000 150 150 200 200 212mm 412mm Yes 44.15 498

BCJFgM2A 2000 1000 125 150 150 150 212mm 412mm No 36.65 525 BCJFssM2A 2000 1000 125 150 150 150 212mm 412mm No 36.65 690 BCJFgM3B 2000 1050 230 230 230 230 212mm 412mm No 46.23 525 BCJFssM3B 2000 1050 230 230 230 230 212mm 412mm No 46.23 690 BCJFtFSM1C 2000 1000 150 150 200 200 212mm 412mm No 32.25 580 BCJFtFFM1C 2000 1000 150 150 200 200 212mm 412mm No 32.25 580 BCJFtFSM3C 2000 1000 150 150 200 200 212mm 412mm No 44.15 580 BCJFtFFM3C 2000 1000 150 150 200 200 212mm 412mm No 44.15 580 BCJFtFSM1D 2000 1000 150 150 200 200 212mm 412mm Yes 32.25 580 BCJFtFFM1D 2000 1000 150 150 200 200 212mm 412mm Yes 32.25 580 BCJFtFSM3D 2000 1000 150 150 200 200 212mm 412mm Yes 44.15 580 BCJFtFFM3D 2000 1000 150 150 200 200 212mm 412mm Yes 44.15 580



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The designations of the specimens are as follows: BCJ ≡ BeamColumn Joint; S ≡ Steel Reinforcements; Fg ≡ GFRP Reinforcements with Grooved Surface; Fss ≡ GFRP Reinforcements with Sand Sprinkled Surface; FS ≡ Steel Coupler provided at the GFRP threaded reinforcement Joint; FF ≡ GFRP bends; M1, M2 & M3 ≡ Grades of concrete; A, B & C ≡ Different sizes of the BeamColumn Joint Specimens without joint stirrups; D ≡ BeamColumn Joint Specimen provided with stirrups at the Joint.

4. Test Set Up and Instrumentation

All the test specimens are instrumented to measure strains at the junctions using electrical strain gauges, demountable mechanical (demec) strain gauge, deflectometers and LVDTs (Linear Variable Displacements Transducer). All test specimens are provided with the special end supports which can provide equilibrium under the action of applied loads. The static loads are applied with the help of hydraulic jacks manually and are monitored by proving rings. Static constant axial load on column is applied prior to the application of load on beams (service load on column around 30% capacity of column) using hydraulic jack (capacity 200 tonnes). All specimens are pasted with internal and external surface strain gauges. A Data acquisition system is used with a sampling rate of 50 samples per second to record all LVDT and electrical strain gauge signals. All test specimens are applied with a seating load which is followed by monotonically increasing load on beams with an increment of 1 kN till the joint fails completely. The parameters considered in this study are tabulated in Table 1. The entire test set up is shown in figures 3 & 4. Demec pellets are pasted on the surface of the specimen at the joint interface to take the strain measurements and LVDTs are placed at the loading point and at the midpoint of the beam to measure the deflections as shown in figures 5 & 6 respectively. The results of the experimental study are depicted in the form of graphs (Figures 8) and are summarized in Table 2 & 3.



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P

H

L

Figure 3: Experimental set up Figure 4: Test set up with instrumentation

Figure 5: Typical specimen with demec pellets Figure 6: Positions of LVDT



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Table 2: Experimental data

Specimen beff mm

dc mm

db mm

Axial Load N in kN

Beam Load P in kN

Deflection at free end, mm

Moment M in kNm

Shear Strength V in kN

BCJSM2A 137.5 124 124 100 10.40 26.87 10.15 96.89 BCJSM3B 230 199 204 250 17.25 15.80 17.78 83.33 BCJSM1C 150 169 174 110 16.10 28.30 15.79 96.74 BCJSM3C 150 169 174 110 17.15 22.42 16.82 98.59 BCJSM1D 150 169 174 110 16.25 17.36 15.94 97.64 BCJSM3D 150 169 174 110 18.00 16.95 17.66 103.48

BCJFgM2A 137.5 124 124 100 8.90 45.73 8.00 73.40 BCJFssM2A 137.5 124 124 100 9.70 39.76 9.37 92.04 BCJFgM3B 230 199 204 250 14.25 18.45 14.89 69.15 BCJFssM3B 230 199 204 250 16.50 17.64 17.01 80.23 BCJFtFSM1C 150 169 174 110 11.65 63.46 11.43 69.21 BCJFtFFM1C 150 169 174 110 11.50 64.60 11.28 68.32 BCJFtFSM3C 150 169 174 110 12.55 50.48 12.31 71.58 BCJFtFFM3C 150 169 174 110 12.20 52.23 11.97 69.57 BCJFtFSM1D 150 169 174 110 11.75 61.32 11.53 69.80 BCJFtFFM1D 150 169 174 110 11.55 61.45 11.33 68.62 BCJFtFSM3D 150 169 174 110 13.20 51.27 12.95 75.28 BCJFtFFM3D 150 169 174 110 12.80 50.86 12.56 72.99

Table 3: Influencing parameters on joint shear strength

Specimen hb/hc bc/bb ρb ρc Stirrup Ratio Vj

Vj, predicted / Vj, actual

BCJSM2A 1.00 1.20 1.20 2.01 0.00 0.868 1.10 BCJSM3B 1.00 1.00 0.40 0.86 0.00 0.259 1.23 BCJSM1C 1.00 1.00 0.80 1.51 0.00 0.635 1.07 BCJSM3C 1.00 1.00 0.80 1.51 0.00 0.553 1.05 BCJSM1D 1.00 1.00 0.80 1.51 0.0034 0.641 1.06 BCJSM3D 1.00 1.00 0.80 1.51 0.0034 0.580 1.00

BCJFgM2A 1.00 1.20 1.20 2.01 0.00 0.657 0.98 BCJFssM2A 1.00 1.20 1.20 2.01 0.00 0.824 1.03 BCJFgM3B 1.00 1.00 0.40 0.86 0.00 0.215 1.00 BCJFssM3B 1.00 1.00 0.40 0.86 0.00 0.249 1.13 BCJFtFSM1C 1.00 1.00 0.80 1.51 0.00 0.454 0.98 BCJFtFFM1C 1.00 1.00 0.80 1.51 0.00 0.448 0.99 BCJFtFSM3C 1.00 1.00 0.80 1.51 0.00 0.401 0.99 BCJFtFFM3C 1.00 1.00 0.80 1.51 0.00 0.390 1.02 BCJFtFSM1D 1.00 1.00 0.80 1.51 0.0034 0.458 1.01 BCJFtFFM1D 1.00 1.00 0.80 1.51 0.0034 0.450 1.02 BCJFtFSM3D 1.00 1.00 0.80 1.51 0.0034 0.422 1.00 BCJFtFFM3D 1.00 1.00 0.80 1.51 0.0034 0.409 1.03



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5. Experimental Observations

The following observations are made during the experimental study. • From the experiment, it is seen that the joint shear failures are observed invariably in

all specimens as shown in figures 7(a) and 7(b). It is primarily due to the concrete in the joint that is likely to be cracked along both principal directions. None of the specimen failed due to anchorage failures. But because of experimental set up limitations, the anchorage failures are not possible to study.

(a) (b)

Figure 7: (a) Typical failure of control specimens; (b) Typical failure of GFRP specimens

• All specimens in each series show that the joint shear strength is increased with the increase of concrete grade, provision of additional joint stirrups at the joint zone and provision of additional anchorage reinforcements with and without steel couplers.



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(a)

(b)

(c)



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(d) Figure 8: Loaddeflection curves (a) Aseries; (b) Bseries; (c) C & D series for M1

grade & (d) C & D series for M3 grade

• From the loaddeflection curves, it is observed that all GFRP reinforced joints show higher deformations than the control specimens as shown in figure 8. This fact is primarily due to lower modulus of elasticity of GFRP reinforcements than steel reinforcements.

• It is also observed that for steel reinforced joints, the yielding of reinforcement leads to a larger increase in deflection with little change in load, whereas GFRP reinforced joints do not have definite yield point, and its stressstrain response shows linearelastic response up to joint failure and therefore deflection continues to increase with the increase in load, there by exhibiting some ductility despite the brittle nature of GFRP reinforcements.

• All tested joints reinforced with GFRP reinforcements are damaged at the beam column joint interface with excessive concrete cover spalling in proximity of the failure section. It is mainly due to larger deflection curvature where as conventionally reinforced specimens show a limited spalling of cover concrete. Hence a more pronounced spalling of concrete cover at a faster rate is followed by sudden failure that occurs in all GFRP reinforced joints.

• The experimental joint shear strength values are compared with theoretical values based on the equilibrium and stressstrain relationship for the constituent materials. The experimental values are 15 to 25% higher than the theoretical values.

• An examination of the loaddeflection curves reveals that the slope of the curves at the initial stages of loading is mild for GFRP reinforced joints where as for conventional specimens it is steeper and is primarily due to lower value of elastic modulus than the steel reinforcements.

• From experimental observations, it is seen that, the first cracks appeared approximately near the joint at the tensile face of the beamcolumn joint. When the load increases further small number of cracks appeared in conventional specimens and larger numbers for GFRP reinforced concrete joints especially in beams. Sand



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sprinkled GFRP reinforced beamcolumn joints show a better performance than the other type of GFRP reinforcements (grooved and threaded types) and is primarily due to better bond properties.

• Values of strains measured near the beamcolumn joint are generally in the range 0.0026 to 0.0035 as shown in figures 9 & 10. These data are helpful for designing purpose and are the average strains. The strains recorded from the strain gauges are pasted at the compression and tensile faces of the beam column joint. During tests some of the strain gauges proximity to the cracks lost the foils.

• Specimens of D series both for steel and GFRP reinforced joints show the increased joint shear strength due to the provision of additional joint shear stirrups. Similar studies for steel reinforced specimens were reported by Vollum and Newman (1999).

• For the specimens in series B, when the percentage of reinforcements is 0.8%, these specimens failed by rupture of GFRP reinforcements in tension leading to violent failure. It is primarily due to the ultimate tensile strains of the GFRP reinforcements that reach ultimate strain values before the beam reaches the pure bending and is shown in figure 8(b), and this failure is governed by brittle tension failures of GFRP reinforcements devoid of concrete crushing.

• It is also evident from the experimental study that in all the series of specimens when the percentage of reinforcements in beams is 0.4 to 1.2%, these joints failed by concrete crushing. But none of joints failed due to rupture of GFRP reinforcements in compression prior to concrete strain reaches ultimate. It is probably due to the fact that the ultimate compressive tensile strains of GFRP reinforcements are greater than the ultimate compressive strains of concrete.

• The softening branch of the applied load verses axial and lateral deformations, energy dissipated during the softening process, post peak behaviour of columns, ductility index ratio and the size effects in the softening region are however the quantification of this phenomenon and is beyond the scope.

6. Analytical Modelling

The finite element analysis is an assemblage of finite elements which are interconnected at a finite number of nodal points and the main objective is to simulate the behaviour of the beamcolumn joint under monotonically increasing load on beam keeping constant service load on columns. The present study, discrete modelling approach is used to model the behaviour of GFRP and Steel reinforced beamcolumn joints using ANSYS software (Sivakumar, 2008). In this approach, concrete column and beam elements are modelled by Solid65 elements while the reinforcement (steel/GFRP) is modelled by Link8 elements. The connectivity between concrete nodes shares the same node; hence perfect bond is assumed. The nonlinearity is derived from the nonlinear relationships in material models and the effect of geometric nonlinearity is not considered. Both standard and nonstandard elements can be refined with additional nodes. These refined elements are of interest for more accurate stress analysis.



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6.1 Finite Element Discretization, Loading and Boundary Conditions

An important step in finite element modelling is the selection of the meshing density. Therefore, in this finite element modelling study, a convergence study has been carried out to determine an appropriate mesh density. Based on this study, a suitable meshing density is arrived at using regular meshing type but not an adaptive type. All joints are modelled which dimensionally replicate the full scale joints as shown in figure9. Constant Loads on column are applied through the nodes of the column. The loads on beams are applied with increments. Simple boundary conditions are adopted i.e. both the ends are pinned. Since the ends of the column needs axial displacement and hence axial degrees of freedom is released and lateral displacement of column are restrained. Vertical line load is applied at an eccentric of 50mm from the edge of the beam along the depth of the beam section.

6.2 Nonlinear Analysis Procedure

This study uses NewtonRaphson equilibrium iterations for updating the model stiffness. NewtonRaphson equilibrium iterations provide convergence at the end of each load increment within tolerance limits. This approach assesses the outofbalance load vector, which is the difference between the restoring forces (the loads corresponding to the element stresses) and the applied loads prior to the application of load. Subsequently, the program carries out a linear solution, using the outofbalance loads, and checks for convergence. If convergence criteria are not satisfied, the outofbalance load vector is to be re evaluated, the stiffness matrix is to be updated, and thus a new solution is attained. This iterative procedure continues until the problem converges. In this study, convergence criteria are based on force and displacement, and the convergence tolerance limits are initially selected by the program. It is found that convergence of solutions for the models was difficult to achieve due to the nonlinear behaviour of reinforced concrete. Therefore, the convergence tolerance limits are increased to a maximum of 5 times the default tolerance limits (0.5% for force checking and 5% for displacement checking) in order to obtain convergence of the solutions.

For the nonlinear analysis, automatic time stepping is done in the program and it predicts that it controls load step sizes. Based on the previous solution history and the physics of the models, if the convergence behaviour is smooth, automatic time stepping will increase the load increment up to a selected maximum load step size. If the convergence behaviour is abrupt, automatic time stepping will bisect the load increment until it is equal to a selected minimum load step size. The maximum and minimum load step sizes are required for the automatic time stepping. These analyses are carried out with high end system configuration with an integrated environment for modelling and analysis (Deiveegan, 2009 and Sivagamasundari, 2010). The results are also compared with experimental observations.



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Figure 9: ANSYS finite element model with reinforcement and node numbers

7. Comparison of Test Results

The results of the finite element study are compared with experimental study and suitable recommendations are made. 1. The general behaviour of the finite element models represented by the loadstrain

plots show good agreement with the experimental data. However, the finite element models show higher loads than the experimental study both in linear and nonlinear ranges. This is attributed to higher stiffness of the finer finite element meshing strategy.

2. Discrete finite element model proves to be computationally simple and better representation of the actual behaviour of the beamcolumn joints under various parametric conditions.

3. The predicted joint shear strength values are well compared with the experimental values. The joint shear strength values obtained from the softwares are 5 to 10% higher than the experimental values. However, it is observed from the finite element analysis results gave stiffer initial behaviour than that of the experimental curves and is primarily due to seating load imperfections.

4. Also the finite element model observes stiffer loads; however stiffer loads cannot be overcome due to denser meshing for convergence. But in some cases, the finite element analysis is terminated owing to numerical instabilities and processing time.

5. For GFRP reinforced concrete joints, it is observed from the finite element analysis results shown lesser steep curves than that of the steel reinforced column and is primarily due to variations in the compression to the tensile modulus of elasticity of GFRP reinforcements.

The loaddeflection plots and the loadstrain plots for joints with different parametric conditions using ANSYS software is compared with the experimental observations and are depicted in the figure 10.



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(a) (b) Figure 10: Typical ANSYS results (a) Control specimens; (b) GFRP specimens

8. Existing Design Equations For Exterior BeamColumn Joints

The existing joint shear strength design equations obtained from the past studies on exterior beam column joint reinforced with steel reinforcements are utilized for calculating the joint shear strength of GFRP reinforced joints with suitable modification factors to account the variability in the experimental values and theoretical predictions.

8.1 ACIASCE and BS 81101985 Code

The ACIASCE Committee (1996) and EC8 (1995) recommend the following design equations for the shear strength of monotonically loaded joints.

(ACI – ACSE Committee 352) (1) (EC8 Ductility class DCL) (2)

where is the joint shear strength (N); hc is the section depth of the column (mm); fc is the concrete cylinder strength (MPa); beff is the average of the beam and column widths (mm) The BS 81101985 Code 4 recommended the following equation to design the beam column joints.

(3)



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The equation is subject to the constraint of 1.0 where is the value of modified for axial force effects; N is design axial compressive force; is the design shear force; M is the design bending moment; A is the area of concrete section and d is the effective depth.

(4) (5)

where is the design ultimate shear resistance(uncracked section); b is the section breadth; h is the overall depth; is the concrete characteristic compressive strength (0.24 ); is the centroidal compressive stress due to prestress force; is the design ultimate shear resistance(cracked section); is the prestressing steel stress after losses; is the characteristic strength of prestressing tendons; is the moment necessary to produce zero stress in the concrete at the extreme tension fibre of the section.

8.1.1 Sarsam and Phillips(1985)

The proposed equation for the design of monotonically loaded exterior beamcolumn connections and the design shear capacity of the joint is,

(6) where, is the shear force resisted by the concrete at the joint and is the design shear force resisted by the links is taken as:

(7) where is the total area of horizontal link reinforcement crossing the diagonal plane from corner to comer of the joint between the beam compression and tension reinforcement (mm

2 ); is the tensile strength of the link reinforcement (MPa).

8.1.2 Vollum (1999)

The following equation determines the total joint shear strength Vj as: (8)

where Vc is the joint shear strength without stirrups (N), Asje is the crosssectional area of the joint stirrups within the top five eighths of the beam depth below the main beam reinforcement (mm

2 ); is a coefficient 0.2 that depends on many factors including

column load, concrete strength, stirrup index, and joint aspect ratio; hc is the section depth of the column (mm); fc is the concrete cylinder strength (MPa); beff is the average of the beam and column widths (mm); fy is the yield strength of stirrups (MPa).

8.1.3 P.G.Bakir and H.M.Boduroglu (2002)

The proposed equation is based on the following parameters viz., influences of concrete cyliderial strength, column reinforcement ratio, beam longitudinal reinforcement ratio, column axial stress, stirrups at joint and joint aspect ratio and proposed a more realistic



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design equation than the previously suggested equations for predicting the joint shear strength of monotonically loaded exterior beamcolumn joints as follows.

(9)

where, β and are the factors for anchorage detailing of reinforcements, is the cross sectional area of tension reinforcements of the beam, and are the breadth and depth of the beam, is the breadth of the column, and is the height of the beam and column respectively, is the factor for the amount of stirrups provided at the joints, Asje is the crosssectional area of the joint stirrups.

The experimental test data are compared with the existing design equations and found that the equation proposed by P.G.Bakir and H.M.Boduroglu (2002) is closer and agree well with theoretical formulations. Hence the present study uses expressions proposed by the above author for the beamcolumn joints reinforced GFRP reinforcements with suitable modification factor.

9. Proposed Design Equations for GFRP Reinforced Exterior BeamColumn Joints

The parametric investigation of exterior beamcolumn joint behaviour is carried out based on the previous tests available in the literatures; tests carried out in the laboratory are presented in Table 2 and 3. Originally the joint shear strength of beamcolumn joints are determined by the strut and truss mechanisms as suggested first by Park and Paulay (1975). The joint shear is calculated using the following procedure:

(10) where P is the failure load (N); L is the distance from the point of application of the load to the face of the column (mm); is the cover (mm). The joint shear strength is calculated as below:

(11) where Vj is the joint shear force (N); Tb is the tensile force in the beam longitudinal reinforcement (N); Vcol is the shear force in the upper column (N). The normalised joint shear strength is determined as:

(12)

where beff is the average of the beam and the column width; fcu is the concrete cylinder strength; hc is the height of the column. The unit of is (MPa)

0.5 .

The results obtained from the experiment are compared with the previous test data available and plotted a graph between the normalised joint shear strength and several key variables like influences of concrete cylinder strength, column reinforcement ratio, beam longitudinal reinforcement ratio, joint aspect ratio, stirrups ratio at the joint and the column axial stress to determine the equation for GFRP reinforced specimens are shown in figure11 to 16.



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Figure 11:Influence of concrete cylinder strength

Figure 12: Influence of column reinforcement ratio

Figure 13: Influence of beam longitudinal reinforcement ratio



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Figure 14: Influence of joint aspect ratio

Figure 15: Influence of joint stirrups

Figure 16: Influence of column axial stress

From the above graphs, it is clear that the joint shear strength values are lower for the GFRP reinforced concrete joints for the same parametric conditions. Hence a capacity



323

reduction factor is introduced in the reference equation. Normalised joint shear strength values are found after the reduction factor is introduced for all the specimens. Then Vj,predicted and Vj,actual values are calculated and presented in the Table 3. The typical forces acting at the joint zone and the force transferred by the truss mechanisms are shown in figure17.

hb

hc

L+cc P

hc

bb bc

Mb

Mb

Mb

Vcol

Vcol

N

N+P

V

ft fc

Cu

Cu

Cu

hb

L P

hc

hc

bb bc

Mb

Mb

Mb

Vcol

Vcol

N

N+P

V

Strut

Tie

(a) (b)

Figure 17: (a) Forces acting at the joint and (b) Diagonal truss mechanism Therefore the final equation can be formulated as

(13) where is the capacity reduction factor which is taken as 0.7 to 0.8 for the GFRP reinforcements; is the cube compressive strength of concrete and ffrp is the strength of stirrups at the joint.

10. Conclusions

Based on this study it is concluded that the behavior of beamcolumn joints are more influenced by the change in geometry of beam and column, amount of column and beam reinforcements, detailing of reinforcement and strength of concrete.



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• It is observed that in all the test specimens (both steel and GFRP), though the crack pattern differs with each other, in most of the joints first crack developed near the beamcolumn interface.

• In the steel reinforced joints, the initial crack developed near the interface and in beams slightly away from the interface. Diagonal cracks are developed upon further loading after the joint reaches half of its maximum load carrying capacity. Diagonal cracks are widened with braches for further increments of load. Ultimately joint shear failure occurs at the joint interface when ultimate load is reached.

• In all GFRP reinforced joint specimens, the initial crack developed at the interface and in beams subsequently away from the interface. Further the crack develops with the increment of loading. Vertical cracks are developed upon further loading after the joint reaches half of its maximum load carrying capacity. Vertical cracks are widened with small number of braches for further increments of load. Ultimately joint shear failure occurs at the joint interface when ultimate load is reached.

• Loaddeflection curves reveal the same kind of variation for both the specimens reinforced with steel and GFRP. The comparisons of the analytical result with the experimental data provide the basic validation of the proposed simplified model for GFRP reinforced joints. The comparisons presented between the analytical and experimental results show that a bond between the concrete and GFRP reinforcement is good.

• The joint shear strength and load carrying capacity of the beam for the GFRP reinforced specimens is less than 10% compared to the control specimens except the specimen reinforced with GFRP sand sprinkled which is higher than the control specimen in both A and B series by 5%. The D series specimens have higher joint shear strength than C series because of the additional provision of shear reinforcement at the joint. But both C & D series have lower values of joint shear strength than the A & B specimens when compared to the control specimens and plausible reasons could be the aspect ratios of the joints.

• These factors are thoroughly analysed and incorporated with the available equations for predicting the joint shear strength of exterior beamcolumn joints reinforced with GFRP specimens. A strength reduction factor is introduced in the proposed equations to account the variation of elastic modulus and ductility.

• GFRP reinforced specimens show a reduced joint shear strength by 10 to 15% overall. The failure mode for all the specimens is joint shear failure. The failure occurred at the joint interface for all the GFRP reinforced specimens and the failure is brittle.

• From the loaddeflection curve it is found that higher deformability by 30 to 50% for the GFRP reinforced specimens than the control specimens. But for B series specimens these variations are between 10 to 15% because of the higher grade of concrete and larger section.

• Anchorage failure is not observed for any of the tests. The anchorages for main reinforcements are provided by bending GFRP reinforcements or by providing steel couplers at the ends of the GFRP reinforcements. Provision of such steel couplers does not influence much, infact it is primarily due to aspect ratio of the joint.



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Probably it increases the joint shear strength considerably for higher sizes. • Provision of additional joint stirrups at the joint increases the joint shear strength. • The experimental results are well correlated with the proposed design equation. The

ratio between the predicted and the experimental values of joint shear strength is found as 1.015 and the standard deviation is 0.115. The suggested equation estimates the joint shear strength as well and conservative.

• The joint shear strength increases considerably with the increase in beam percentage of reinforcements. If the beam reinforcement ratio is increased for GFRP reinforced specimens by 20 to 30% than the conventionally reinforced specimens, the joint shear strength also increases.

• Based on the analysis, it is proposed to introduce a strength reduction factor ( ) of 0.8 for grooved and sand sprinkled types of GFRP reinforcements and 0.7 for threaded type of GFRP reinforcements without stirrups at the joint and 0.78 for threaded type of GFRP reinforcements with stirrups at the joint.

References

1. ACI 440R96, “StateoftheArt Report on Fiber Reinforced Plastic (FRP) Reinforcement for Concrete Structures”, Reported by ACI Committee 440.

2. ACI committee 352, “Recommendations for design for beamcolumn joints in monolithic reinforced concrete structures”, Farmington Hills, Mich: American concrete Institution Report 35291

3. Bakir, P.G. and Boduroglu, H.M., “A new design equation for predicting the joint shear strength of monotonically exterior beamcolumn joints”, Journal of Engineering Structures, Vol.24, pp. 11051117, 2002.

4. BS 8110, Structural Use of Concrete: Part1: Code of practice for design and construction, London, British Standards Institution, 1985.

5. Deiveegan. A and Kumaran. G, “Reliability Analysis of Concrete Columns reinforced internally with Glass Fibre Reinforced Polymer Reinforcements”, The ICFAI University Journal of Structural Engineering, The ICFAI University Press, India, Vol.2 (2), pp. 4959, 2009.\

6. Ehab A. Ahmed, Ahmed K. ElSayed, Ehab ElSalakawy, and Brahim Benmokrane, “Bend Strength of FRP Stirrups: Comparison and Evaluation of Testing Methods”, Journal of composites for construction, Vol.14(1), pp. 310, 2010.

7. Eurocode 8: “Design provisions for earthquake resistance of structures”, London: BSI, 1995.

8. Mohammad Shamim & V.Kumar, “Behaviour of reinforced concrete beamcolumn joint”, Journal of Structural Engineering, Vol.26, No.3. pp. 207214, 1999.

http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=Ahmed,+Ehab+A.&possible1zone=author&maxdisp=25&smode=strresults&aqs=true

http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=El-Sayed,+Ahmed+K.&possible1zone=author&maxdisp=25&smode=strresults&aqs=true

http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=El-Salakawy,+Ehab&possible1zone=author&maxdisp=25&smode=strresults&aqs=true

http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=Benmokrane,+Brahim&possible1zone=author&maxdisp=25&smode=strresults&aqs=true



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9. Pantazopoulou S, Bonacci J., “Consideration of questions about beamcolumn joints”, ACI Structural Journal, Vol. 89(1), pp. 27–37, 1992.

10. Park R, Paulay T, “Reinforced concrete structures”, New York: John Wiley and Sons, 1975.

11. Sarsam K.F, Phillips ME, “The shear design of insitu reinforced beamcolumn joints subjected to monotonic loading”, Magazine of Concrete Research, Vol. 37(130), pp.16–28, 1985.

12. Sivagamasundari, R., “Analytical and experimental study of one way slabs reinforced with glass fibre polymer reinforcements”, Ph.D. Thesis, Department of Civil and Structural Engineering, Annamalai University, 2010

13. Sivakumar. M, “Analytical modelling of beamcolumn joints reinforced with GFRP rebars”, M.E. Thesis report, Department of Civil and Structural Engineering, Annamalai University,2008

14. Sofi , “Behaviour of exterior RC. Beamcolumn joint reinforced with GFRP rebars ”, M.E. Thesis report, Department of Civil and Structural Engineering, Annamalai University, 2006

15. Vollum RL and J.B Newman, The design of external, reinforced concrete beam column joints, Magazine of Concrete Research, pp.2127, 1999.

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