ACI CODE VERIFICATION FOR FRP EXTERNALLY REINFORCED SLABS
Usama Ebead
Department of Civil Engineering, University of Sherbrooke
2500 boulevard de l’Université, Quebec, Canada, J1K 2R1
Hesham Marzouk
Department of Civil Engineering, Memorial University of Newfoundland
300 Prince Philip Dr., St. John’s, Newfoundland, Canada, A1B 3X5
ABSTRACT
An ACI code verification of FRP externally reinforced two-way slabs is introduced. An implementation
of the ACI-318 [1] and the ACI-440 F [2] is presented for the purpose of verification against
experimental results. In the experimental work, two different types of FRP materials were evaluated;
namely carbon FRP (CFRP) strips and glass FRP (GFRP) laminates. The externally reinforced or
strengthened slabs had steel reinforcement ratios of 0.35% and 0.5%. Results show that the flexural
capacity of two-way slabs can be increased to an average of 35.5% over that of the reference
(unstrengthened) specimen. An increase of the initial stiffness is achieved; however, an apparent
decrease in the overall ductility is evident. In addition, an average decrease in the values of the energy
absorption of about 30% is observed. The estimated ultimate load capacity using the ACI code is in an
accepted level of agreement with the experimental results.
Keywords: concrete; FRP; external reinforcement, strengthening; reinforcement; two-way slabs.
INTRODUCTION
FRP materials have been used for strengthening reinforced concrete beams, columns and one-way
slabs. The flexural capacity of concrete beams can be increased by bonding FRP sheets, strips or
laminates to the tension side [3,4,5]. In addition, the shear strength of concrete beam can be increased by
gluing FRP laminates to the concrete web at locations of high shear stresses [6,7]. The ease of handling
FRP materials provides the means to the extension of their applications for strengthening other structural
elements. A few research works has been conducted on FRP strengthening of reinforced concrete slabs
especially two-way slabs. Some research works dealt with the strengthening of one-way slabs using FRP
materials in which slabs were treated in a very similar way to beams [8,9]. Using FRP materials to
enhance two-way slabs in flexure is very desirable from the applicability point of view due to the ease of
handling and installing FRP materials. FRP materials are not subject to either corrosion or rust on the
long term. A drawback of using FRP materials for flexural strengthening is the potential for brittle
failure that results in a decrease of the overall ductility.
In the following sections, a summary of an experimental program on two-way slabs strengthened
using FRP is presented. Following that summary, ACI code verification is presented with a comparison
between the experimental and the code implementation results.
SUMMARY OF EXPERIMENTAL PROGRAM
Materials
The concrete mix was designed for an average target cylinder compressive strength of 35 MPa after
28 days. The mix proportion of 1.0 m3 is 1160 kg of gravel, 690 kg of sand, 350 kg of Portland cement
and 175 litres of water. The actual cylinder compressive strengths ranged from 29 to 38 MPa as shown
in Table 1. The steel reinforcement bars were CSA grade 400 deformed bars. The actual yield strength
of the steel reinforcement ranged from 435 to 450 MPa. Two different diameters were used, namely 10
and 20mm for the slab and column, respectively.
Unidirectional GFRP laminates and CFRP strips were used for strengthening. The Sika CarboDur
was used for the CFRP strips and the glass fibre fabric, SikaWrap Hex 100G, was used for the GFRP
laminates. The thickness of one layer of the GFRP laminates and CFRP strips was 1.0 mm and 1.2 mm,
respectively. Two different types of two-component adhesive epoxy resins were used for each type of
the FRPs as per the manufacturer’s specifications. Sikadur 30 and Sikadur Hex 300 epoxy resins were
used for the CFRP strips and the GFRP laminates, respectively. The properties of FRP materials and the
epoxy resins provided by the manufacturers are listed in Tables 2 and 3, respectively.
Table 1: Compressive strength of concrete
Specimen Title
Ref-0.35%
Ref-0.5%
GFRP-F-0.35%
GFRP-F-0.5%
CFRP-F-0.35%
CFRP-F-0.5%
Cylinder
compressive
strength, MPa
30.0
35.0
29.0
38.0
35.0
34.0
Strengthening material
Reinforcement
ratio
Preload,
kN
GFRP laminates
GFRP laminates
CFRP strips
CFRP strips
0.35%
0.5%
0.35%
0.5%
0.35%
0.35%
125
165
125
165
Table 2: Properties of one layer of the FRP materials
FRP
Thickness
, mm
Tensile
strength, MPa
E,
GPa
CFRP strips*
GRFP laminates**
1.2
1.0
2800
600
170
26.1
Elongation
at break ,
%
>1.7
2.24
Weight
,
g/m2
2240
913
Fibre
content
68%
50-80%
Fibre
density
g/cm3
1.5
2.54
* Sika CarboDur ** Sika Wrap
Table 3: Properties of the epoxy adhesive
Property
Tensile strength, Mpa
Elongation at break, %
Elastic modulus, Gpa
Epoxy for strips*
24.8
1.00
4.5
Epoxy for laminates**
72.4
4.8
3.1
*Sikadur 30 **Sikadur Hex 300
Test slabs
The tested specimens were square with 1900-mm side length and 150-mm thicknesses. The test
specimens were simply supported along the four edges with corners free to lift and were loaded through
the column stub. A layout of the tested slabs is shown in Fig. 1 that shows also reinforcement details of
the tested specimens.
Two unstrengthened specimens were used as reference specimens, namely, Ref-0.35% and Ref-0.5%
of reinforcement ratios of 0.35 and 0.5%, respectively. Specimens CFRP-F-0.35% and CFRP-F-0.5%
had steel reinforcement ratios of 0.35 and 0.5%, respectively, and were strengthened using CFRP strips.
Similarly, specimens GFRP-F-0.35% and GFRP-F-0.5% had reinforcement ratios 0.35 and 0.5%,
respectively and were strengthened using GFRP laminates.
A minimum concrete cover of 25 mm was maintained for all specimens at compression and tension
sides. Column stubs were square of 250-mm side dimension and were located at the slab center. The
column stubs were extended on the compression side to a distance 850-mm from the concrete surface to
allow for the application of the load.
Fig. 1: Details of a typical test specimen
Test set up and instrumentation
The specimens were tested using a large reaction steel frame. A 10-ton capacity crane was used to
lift and install the specimens vertically inside the frame. Rubber pieces were placed between the back
surface of the tested slabs and the supporting edges of the frame. A hydraulic actuator facing the
specimen was used to apply a uniform load through the column stub. A load cell was used to measure
the load using four calibrated electrical resistance strain gages fixed to the inner cylinder of the load cell.
The actuator had a maximum load capacity of 700 kN and a maximum stroke of 150 mm.
Linear Variable Displacement Transformers (LVDT’s) were built in the front actuator to measure the
deflection of slabs. The loads were applied using displacement control to avoid the uncontrolled failure
at the maximum loads. The displacement rate for the actuator was 0.25 mm/min. A displacement
function of the ramp type was applied through computerized function generator. Eight-mm length
electrical resistance strain gages having a resistance of 120 ± 0.3% and a gage factor equal to 2.070 ±
0.5% were used to measure the steel reinforcement strains at locations shown in Fig. 1.
The LVDT’s and the electrical strain gages were connected through a master panel to a data
acquisition system. The analog electrical signals of loads, deflections and steel strains were converted
through the data acquisition system to digital signals and were stored in digital computer files.
Load application and testing procedure
The unstrengthened reference specimens; Ref-0.35% and Ref-0.5% were loaded through the column
stub until failure to estimate the ultimate load carrying capacity. The ultimate load carrying capacity of
the reference specimens was 250 and 330 kN, respectively. Fifty percent of the ultimate load carrying
capacity of the reference specimens was used as an initial loading for the specimens prior to
strengthening. Hence, the specimens with reinforcement ratios of 0.35 and 0.5% to be strengthened were
loaded prior to strengthening with initial loads of 125 and 165 kN as initial loading. Fifty percent of the
load represents a level of load on a building in field where strengthening may be required. The applied
loads were completely released to represent a state of shoring two-way slabs in the field prior to
strengthening. Afterwards, the specimens were removed from the loading frame for strengthening
according to the strengthening procedure detailed below. After one week of curing, the specimens were
relocated at the loading frame and were subjected to the load until failure.
Strengthening procedure
The concrete surface to be strengthened was roughened carefully using a vibrating hammer to
improve the bond characteristics between concrete and CFRP strips and GFRP laminates. Dust and fine
materials caused from the roughening process were removed carefully from the concrete surfaces. In
addition, for CFRP strips, a special solvent was used to remove all grease, waxes, foreign particles and
other bond inhibiting materials from the bonded surface as specified by the manufacturer. The two-part
epoxy resin was applied on the concrete surfaces and the strengthening materials. Afterwards, the FRP
strengthening materials were bonded to the concrete surface according to the type of strengthening.
The strengthening material was located at the tension side of the slab and was extended to a location
50 mm before the support. Two 300-mm width layers of GFRP laminates were bonded to the slab
surface in both directions of specimens GFRP-F-0.35% and GFRP-F-0.5%. Specimens CFRP-F-0.35%
and CFRP-F-0.5% were strengthened using three adjacent CFRP strips 100-mm width each so that the
strengthened width is 300 mm. Additional transverse layers of CFRP strips were bonded at the end of
the FRP materials to improve the end anchorage of the FRP strips or laminates with concrete surface.
The anchorage layers were 100 mm wide and 500 mm long. Fig. 2 shows the strengthening details of the
specimens.
Additional FRP strips layer
One layer of FRP
strips at the tension
side
Two layers of FRP
laminates at the
tension side
Fibres direction
GFRP-F-0.5%
GFRP-F-0.35%
Fibres direction
CFRP-F-0.5%
CFRP-F-0.35%
Fibres direction
Fibres direction
Fig. 2: The strengthening details of the specimens
TEST RESULTS AND DISCUSSION
Deformational properties and load capacity
The load-deflection relationship was recorded using the data acquisition system. The slope of the
load-deflection curve was higher than that of the corresponding reference specimens. Moreover, the
average deflection at the ultimate load of the specimens was about 0.61 that of the corresponding
reference specimens. In general, the strengthened specimens experienced smaller deformation compared
to the corresponding reference specimens due to the effect of the FRP materials on the overall behaviour
of the slabs. Fig.3 shows the load deflection relationship for the tested specimens.
The ultimate load carrying capacity will be referred to as the load capacity. The strengthened
specimens showed higher load capacity than that of the corresponding reference specimens. Specimens
CFRP-F-0.35% and GFRP-F-0.35% showed an increase of 44.4 and 38%, respectively in the load
capacity over that of the reference specimen, Ref-0.35%. Moreover, Specimens CFRP-F-0.5% and
GFRP-F-0.5% showed an increase of 36.4 and 25.8 %, respectively in the load capacity over that of the
reference specimen, Ref-0.5%. The load capacity of the corresponding reference specimens was
influenced by the reinforcement ratio that is in accordance with earlier research work [10]. The load
capacity of specimen Ref-0.5% was 1.32 times that of specimen Ref-0.35%.
The stiffness of a slab at any loading point is the slope of the load-deflection curve at that point. The
initial stiffness, K, was evaluated numerically as the slope of the load-deflection curve within the first 5-
mm deflection. This is an approximation made to avoid the misleading initial readings when there is a
relaxation of the load actuator. The strengthened specimens showed higher initial stiffness over that of
the reference specimens. The average initial stiffness of Specimens CFRP-F-0.35% and GFRP-F-0.35%
was about 2.37 times that of the reference specimen, Ref-0.35%. Moreover, the average initial stiffness
of Specimens CFRP-F-0.5% and GFRP-F-0.5% was about 1.99 times that of the reference specimen,
Ref-0.5%.
The energy absorption is the area under the load-deflection curve for a tested specimen. This area
was evaluated numerically based on the available values of load and the corresponding values of
deflection. At the maximum load, it was clearly noticed that the strengthening technique contributed to a
decrease in the energy absorption of the strengthened specimens. An average decrease in the values of
the energy absorption of about 30% for the strengthened specimens was observed.
Values of deflection at the cracking load, cr, the ultimate load, Pu, the Deflection at the ultimate load,
u, the initial stiffness, K, and energy absorption,  for each slab are summarized in Table. 4.
Fig. 3: Load deflection relationship of the tested slabs
Table 4: Ultimate capacities and deflection characterestics of the tested slabs
Title
Ref-0.35%
Ref-0.5%
CFRP-F-0.35%
GFRP-F-0.35%
CFRP-F-0.5%
GFRP-F-0.5%
Deflection at
cracking load,
cr,
mm
7.00
6.25
7.25
7.69
6.03
6.35
Ultimate
load,
Pu,
KN
250
330
361
345
450
415
Deflection at
ultimate load,
u,
mm
42.01
35.57
18.08
27.72
21.03
26.71
Energy
Absorption’
,
kN.mm
9346
9445
7821
4597
6686
7475
Stiffness,
K,
kN/mm
8.42
12.54
15.54
24.42
26.76
23.15
Failure characteristics
Reference specimens, Ref-0.35% and Ref-0.5%, failure mode was classified as flexural-ductile.
Flexural reinforcement yielded and the two specimens showed relatively large deflection values before
reaching the ultimate load.
Fig. 4 shows a typical flexural failure mode of GFRP and CFRP strengthened specimens after
failure. It is evident that the FRP materials contributed to an increase of the capacity until the bond
between the FRP material and concrete failed. De-bonding cracks appeared at a late stage of loading that
resulted in a separation of the strengthening materials. These cracks were located along the edges of the
strengthening material length. This indicates that end anchorage severed to a certain extent preventing a
premature bond failure at the cut-off end of FRP materials. Followed the appearance of these cracks, the
specimens failed due to accelerated concrete flexural failure after the FRP de-bonded from the slabs
without rupture of the FRP material.
(a) GFRP strengthened specimen
(b) CFRP strengthened specimen
Fig. 4: Typical layout of GFRP and CFRP strengthened specimens at failure
ACI CODE EVALUATION
A simplified method for the code evaluation of the load carrying capacity for two-way slab strengthened
with steel plates and bolts was introduced [11]. This method is based on the analysis of two-way slabs
recommended by Rankin and Long [12]. This approach is based on the following formula:
 S

Pflex  8 M b 
 0.172  .
(1)
l

c


Equation (1) is based on the virtual work done by the action of the yield lines. The value of M b in
Equation (1) is the radial moment capacity of the slabs. For the original concrete specimens, the ACI
318-1995 is used to evaluate M b . For the strengthened FRP specimens, the ACI 318-1995 is used to
evaluate M b . The same equation can be used for the analysis of two-way slab strengthened with FRP
using approximated evaluations of some of the parameters of Equation (1). The contribution of the
strengthening materials is taken into account when evaluating the radial moment capacity, M b .
M b  M b1  M b 2 ,
(2)
where M b1 is the unstrengthened capacity of the slab. According to ACI 318-1995, M b1 is evaluated
according to the following Equation:


  ,
2
,
,
,
(3)
M b1  bd    f y 1  0.59
f
   f yd d  d ,
y
,
fc








where M b 2 is the contribution of the strengthening material and is evaluated according to the following
equation assuming full bonds between FRP and concrete,
a w

(4)
M b 2  E FRP t FRP  FRP  h   FRP .
2 l

Equation (4) is based on the FRP section analysis as recommended by ACI 440 F Repair and
w
Rehabilitation guidelines [2]. The term FRP is introduced for the two-way slab equation to take into
l
account the ratio between the width of the strengthening material and the slab width, l. The factor  is
the strengthening efficiency factor and is taken as 0.75 for two-way slabs as recommended by Ebead
[13].
The strain in FRP strips layer can be evaluated as:
h
h 
 FRP    1  cu   s
(5)
d
d 
The distance of the neutral axis from the top of slab a can be calculated as follows:
d
(6)
a  0.8
 cu
 cu   y
The test results indicated for CFRP strips, it could be assumed that at failure concrete reached the
ultimate strain and the steel reached the yield strain. However, for the specimen strengthened with
GFRP, the concrete strain reached the ultimate value and the steel strain at failure reached four times the
yield strain. Once the FRP strain and the location of neutral axis are determined, the strengthened
moment contribution to the slab can be evaluated from Equation 4.
For the evaluation of the total load capacity, Equation 1 is used and replacing the value of c by the FRP
width, wFRP , Hence in the case of FRP strengthening,
 S

(7)
Ptheo  8 M b 
 0.172 
 l  wFRP

The implementation of the prescribed analytical method showed a good agreement with the
experimental results as shown in Table 5.
Table 7: Comparison with code evaluation
Specimen
Pexp Ptheo Ptheo /Pexp
CFRP–F–0.35% 361 332
0.92
GFRP–F–0.35% 345 323
0.94
CFRP–F–0.5%
450 420
0.93
GFRP–F–0.5%
415 411
0.99
CONCLUSION
Strengthened two-way slabs using GFRP laminates and CFRP strips showed an average gain in the
load capacity of about 40 and 31%, respectively over that of the reference specimens. In addition, the
strengthened specimens showed a stiffer behaviour than that of the reference specimens. An ACI code
verification of FRP externally reinforced two-way slabs is introduced. An implementation of the ACI318 and the ACI-440 F is presented for the purpose of verification against experimental results. The
recommended theoretical analysis used for FRP strengthening of two-way slabs showed a good
agreement with experimental test results.
NOMENCLATURE
a = distance from the top of slab to the neutral axis, mm
c = side length of the square column, mm
cequ= equivalent side length due to strengthening, mm
d= distance from the compression face to the center of the tension reinforcement, mm
d`= distance from the compression face to the center of the compression reinforcement, mm
Ec = the modulus of elasticity of concrete, MPa
EFRP = the modulus of elasticity of FRP materials, MPa
fc`= Compressive strength of concrete, MPa
fy = yield stress of the slab reinforcement, MPa
h = Overall slab thickness, mm
K = the initial stiffness of specimen, kN/mm
l = side length of the square slab, mm
lp = length of the strengthening steel plates, mm
Mb = radial moment of resistance of the strengthened section, N.mm/mm
Mb1 = radial moment of resistance of the unstrengthened section, N.mm/mm
Pcr = first crack load of a slab before strengthening, kN
Pflex = flexural load carrying capacity, kN
Pu = ultimate load of a specimen, kN
tFRP = total thickness of FRP material, mm
wFRP = the width of FRP materials, mm
cr = the deflection at a slab center at the first crack load, mm
u = the deflection at a slab center at the ultimate load, mm
 = the energy absorption of a specimen, kN/mm
tension reinforcement ratio of the slab
 compression reinforcement ratio of the slab
 = Effective strengthening width coefficient
 FRP  the strain in FRP material
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