Prediction of Joint Shear Strength of Concrete Beam-Column ... · Non metallic reinforcements or Fibre reinforced polymer (FRP) reinforcements has rapidly emerged as an effective

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

305

Prediction of Joint Shear Strength of Concrete Beam-Column 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 Nagar-608002, Chidambaram, Tamil Nadu, India

[email protected]

doi:10.6088/ijcser.00202010024

ABSTRACT

This experimental study primarily focuses on the joint shear strength of full scale size

exterior concrete beam-column 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 beam-column joints are performed to simulate the behaviour

of the beam-column 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 beam-column specimens based on the experimental results and the review of

the prevailing design equations.

Keywords: Non-metallic Reinforcements, Concrete beam-column 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 440R-96; 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 beam-column connections. But the

studies related to the use of non-metallic reinforcements for beam-column joints are not

explored in detail. Therefore the present study discusses mainly on the joint shear

strength of concrete beam-column joints reinforced internally with Glass Fibre





306

Reinforced Polymer (GFRP) reinforcements. Based on this study suitable modified

design expressions are derived and are compared with the conventionally reinforced

beam-column joints for more rational concept. First part of this study covers the

experimental investigation of GFRP/Steel reinforced concrete beam-column joints.

Second part of this study is relates to the finite element modelling and analysis of

GFRP/Steel reinforced concrete beam-column 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 beam-column 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 ASTM-D

3916-84 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 E-glass

fibre volume approximately 60% and these fibres are reinforced with epoxy resins. Three

different types of GFRP reinforcements (grooved, sand sprinkled & threaded) (ACI

440R-96; 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 440R-96; Ehab, et

al., 2010; Deiveegan, 2009 and Sivagamasundari, 2010). It varies between 36-47 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 micro-buckling. 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 440R-96;

Ehab, et al., 2010; Deiveegan, 2009 and Sivagamasundari, 2010). Based on the





307

experimental study, it is observed that the strength of GFRP bent bars/stirrups at the bend

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 beam-column 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 beam-column 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

a-a

a a

b

b

b-b

L

GFRP12- 4Nos.

GFRP 8- 150c/c

bc

hc

GFRP 12- 4Nos.

GFRP 8- 150c/c

bb

hb

Figure 1: Typical beam-column joint specimen





308

(a) (b) (c)

Figure 2: (a) Skeleton of beam-column joint with steel reinforcement

(b) Skeleton of beam-column joint-GFRP reinforcement

with steel bent coupler at the joint

(c) Skeleton of beam-column joint-GFRP 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

BCJS-M2A 2000 1000 125 150 150 150 2-12mm 4-12mm No 36.65 498

BCJS-M3B 2000 1050 230 230 230 230 2-12mm 4-12mm No 46.23 498

BCJS-M1C 2000 1000 150 150 200 200 2-12mm 4-12mm No 32.25 498

BCJS-M3C 2000 1000 150 150 200 200 2-12mm 4-12mm No 44.15 498

BCJS-M1D 2000 1000 150 150 200 200 2-12mm 4-12mm Yes 32.25 498

BCJS-M3D 2000 1000 150 150 200 200 2-12mm 4-12mm Yes 44.15 498

BCJFg-M2A 2000 1000 125 150 150 150 2-12mm 4-12mm No 36.65 525

BCJFss-M2A 2000 1000 125 150 150 150 2-12mm 4-12mm No 36.65 690

BCJFg-M3B 2000 1050 230 230 230 230 2-12mm 4-12mm No 46.23 525

BCJFss-M3B 2000 1050 230 230 230 230 2-12mm 4-12mm No 46.23 690

BCJFtFS-M1C 2000 1000 150 150 200 200 2-12mm 4-12mm No 32.25 580

BCJFtFF-M1C 2000 1000 150 150 200 200 2-12mm 4-12mm No 32.25 580

BCJFtFS-M3C 2000 1000 150 150 200 200 2-12mm 4-12mm No 44.15 580

BCJFtFF-M3C 2000 1000 150 150 200 200 2-12mm 4-12mm No 44.15 580

BCJFtFS-M1D 2000 1000 150 150 200 200 2-12mm 4-12mm Yes 32.25 580

BCJFtFF-M1D 2000 1000 150 150 200 200 2-12mm 4-12mm Yes 32.25 580

BCJFtFS-M3D 2000 1000 150 150 200 200 2-12mm 4-12mm Yes 44.15 580

BCJFtFF-M3D 2000 1000 150 150 200 200 2-12mm 4-12mm Yes 44.15 580





309

The designations of the specimens are as follows:

BCJ Beam-Column 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 Beam-Column Joint

Specimens without joint stirrups; D Beam-Column 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.





310

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





311

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

BCJS-M2A 137.5 124 124 100 10.40 26.87 10.15 96.89

BCJS-M3B 230 199 204 250 17.25 15.80 17.78 83.33

BCJS-M1C 150 169 174 110 16.10 28.30 15.79 96.74

BCJS-M3C 150 169 174 110 17.15 22.42 16.82 98.59

BCJS-M1D 150 169 174 110 16.25 17.36 15.94 97.64

BCJS-M3D 150 169 174 110 18.00 16.95 17.66 103.48

BCJFg-M2A 137.5 124 124 100 8.90 45.73 8.00 73.40

BCJFss-M2A 137.5 124 124 100 9.70 39.76 9.37 92.04

BCJFg-M3B 230 199 204 250 14.25 18.45 14.89 69.15

BCJFss-M3B 230 199 204 250 16.50 17.64 17.01 80.23

BCJFtFS-M1C 150 169 174 110 11.65 63.46 11.43 69.21

BCJFtFF-M1C 150 169 174 110 11.50 64.60 11.28 68.32

BCJFtFS-M3C 150 169 174 110 12.55 50.48 12.31 71.58

BCJFtFF-M3C 150 169 174 110 12.20 52.23 11.97 69.57

BCJFtFS-M1D 150 169 174 110 11.75 61.32 11.53 69.80

BCJFtFF-M1D 150 169 174 110 11.55 61.45 11.33 68.62

BCJFtFS-M3D 150 169 174 110 13.20 51.27 12.95 75.28

BCJFtFF-M3D 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 BCJS-M2A 1.00 1.20 1.20 2.01 0.00 0.868 1.10

BCJS-M3B 1.00 1.00 0.40 0.86 0.00 0.259 1.23

BCJS-M1C 1.00 1.00 0.80 1.51 0.00 0.635 1.07

BCJS-M3C 1.00 1.00 0.80 1.51 0.00 0.553 1.05

BCJS-M1D 1.00 1.00 0.80 1.51 0.0034 0.641 1.06

BCJS-M3D 1.00 1.00 0.80 1.51 0.0034 0.580 1.00

BCJFg-M2A 1.00 1.20 1.20 2.01 0.00 0.657 0.98

BCJFss-M2A 1.00 1.20 1.20 2.01 0.00 0.824 1.03

BCJFg-M3B 1.00 1.00 0.40 0.86 0.00 0.215 1.00

BCJFss-M3B 1.00 1.00 0.40 0.86 0.00 0.249 1.13

BCJFtFS-M1C 1.00 1.00 0.80 1.51 0.00 0.454 0.98

BCJFtFF-M1C 1.00 1.00 0.80 1.51 0.00 0.448 0.99

BCJFtFS-M3C 1.00 1.00 0.80 1.51 0.00 0.401 0.99

BCJFtFF-M3C 1.00 1.00 0.80 1.51 0.00 0.390 1.02

BCJFtFS-M1D 1.00 1.00 0.80 1.51 0.0034 0.458 1.01

BCJFtFF-M1D 1.00 1.00 0.80 1.51 0.0034 0.450 1.02

BCJFtFS-M3D 1.00 1.00 0.80 1.51 0.0034 0.422 1.00

BCJFtFF-M3D 1.00 1.00 0.80 1.51 0.0034 0.409 1.03





312

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.





313

(a)

(b)

(c)





314

(d)

Figure 8: Load-deflection curves (a) A-series; (b) B-series; (c) C & D series for M1

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

From the load-deflection 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 stress-strain response shows linear-elastic

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 stress-strain relationship for the constituent materials.

The experimental values are 15 to 25% higher than the theoretical values.

An examination of the load-deflection 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 beam-column 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





315

sprinkled GFRP reinforced beam-column 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 beam-column 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 beam-column 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 beam-column joints using ANSYS

software (Sivakumar, 2008). In this approach, concrete column and beam elements are

modelled by Solid-65 elements while the reinforcement (steel/GFRP) is modelled by

Link-8 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.





316

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 Newton-Raphson equilibrium iterations for updating the model stiffness.

Newton-Raphson equilibrium iterations provide convergence at the end of each load

increment within tolerance limits. This approach assesses the out-of-balance 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 out-of-balance loads, and checks for

convergence. If convergence criteria are not satisfied, the out-of-balance 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.





317

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 load-strain

plots show good agreement with the experimental data. However, the finite element

models show higher loads than the experimental study both in linear and non-linear

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 beam-column 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 load-deflection plots and the load-strain plots for joints with different parametric

conditions using ANSYS software is compared with the experimental observations and

are depicted in the figure 10.





318

(a) (b)

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

8. Existing Design Equations For Exterior Beam-Column 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 ACI-ASCE and BS 8110-1985 Code

The ACI-ASCE 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 8110-1985 Code4 recommended the following equation to design the beam-

column joints.

(3)





319

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 beam-column

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 (mm2); 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 cross-sectional area of

the joint stirrups within the top five eighths of the beam depth below the main beam

reinforcement (mm2); 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





320

design equation than the previously suggested equations for predicting the joint shear

strength of monotonically loaded exterior beam-column 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 cross-sectional 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 beam-column joints reinforced GFRP reinforcements with

suitable modification factor.

9. Proposed Design Equations for GFRP Reinforced Exterior Beam-Column Joints

The parametric investigation of exterior beam-column 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 beam-column 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.





321

Figure 11:Influence of concrete cylinder strength

Figure 12: Influence of column reinforcement ratio

Figure 13: Influence of beam longitudinal reinforcement ratio





322

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 beam-column 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.





324

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

beam-column 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.

Load-deflection 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 beam-column 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 load-deflection 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.





325

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 440R-96, “State-of-the-Art Report on Fiber Reinforced Plastic (FRP)

Reinforcement for Concrete Structures”, Reported by ACI Committee 440.

2. ACI committee 352, “Recommendations for design for beam-column joints in

monolithic reinforced concrete structures”, Farmington Hills, Mich: American

concrete Institution Report 352-91

3. Bakir, P.G. and Boduroglu, H.M., “A new design equation for predicting the joint

shear strength of monotonically exterior beam-column joints”, Journal of Engineering

Structures, Vol.24, pp. 1105-1117, 2002.

4. BS 8110, Structural Use of Concrete: Part-1: 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. 49-59, 2009.\

6. Ehab A. Ahmed, Ahmed K. El-Sayed, Ehab El-Salakawy, and Brahim Benmokrane,

“Bend Strength of FRP Stirrups: Comparison and Evaluation of Testing Methods”,

Journal of composites for construction, Vol.14(1), pp. 3-10, 2010.

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

BSI, 1995.

8. Mohammad Shamim & V.Kumar, “Behaviour of reinforced concrete beam-column

joint”, Journal of Structural Engineering, Vol.26, No.3. pp. 207-214, 1999.

http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=Ahmed%2C+Ehab+A.&possible1zone=author&maxdisp=25&smode=strresults&aqs=true

http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=El-Sayed%2C+Ahmed+K.&possible1zone=author&maxdisp=25&smode=strresults&aqs=true

http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=El-Salakawy%2C+Ehab&possible1zone=author&maxdisp=25&smode=strresults&aqs=true

http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=ASCERL&possible1=Benmokrane%2C+Brahim&possible1zone=author&maxdisp=25&smode=strresults&aqs=true





326

9. Pantazopoulou S, Bonacci J., “Consideration of questions about beam-column 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 in-situ reinforced beam-column 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 beam-column joints reinforced with GFRP

rebars”, M.E. Thesis report, Department of Civil and Structural Engineering,

Annamalai University,2008

14. Sofi , “Behaviour of exterior RC. Beam-column 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.21-27, 1999.

Documents

Prediction of Joint Shear Strength of Concrete Beam-Column ... · Non metallic reinforcements or Fibre reinforced polymer (FRP) reinforcements has rapidly emerged as an effective