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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
ausjs5070@gmail.com
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
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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
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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
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(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
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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.
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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
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
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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: 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
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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.
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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 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.
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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 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.
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(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)
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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 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
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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.
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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
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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.
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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
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.
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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 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
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9. Pantazopoulou S, Bonacci J., “Consideration of questions about beam-column joints”,
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