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ACI Structural Journal/January-February 2007 49
ACI Structural Journal, V. 104, No. 1, January-February 2007.
MS No. S-2006-035.R1 received February 6, 2006, and reviewed under Institute publi-
cation policies. Copyright © 2007, American Concrete Institute. All rights reserved,
incl uding the making of copies unless permission is obtained from the copyright proprietors.
Pertinent discussion including author’s closure, if any, will be published in the November-
December 2007 ACI Structural Journal if the discussion is received by July 1, 2007.
ACI STRUCTURAL JOURNAL TECHNICAL PAPER
This paper describes an innovative approach for strengthening
reinforced concrete slabs in shear with carbon fiber-reinforced
polymer (CFRP) laminates. A process analogous to stitching is
used to retrofit concrete slabs with fiber-reinforced polymer (FRP)
strands. The experimental study reported herein was carried out on
28 square, isotropic two-way slab specimens simulating conditions
in the vicinity of an interior square column in a continuous flat plate
structure. Parameters such as the concrete strength, flexural
capacity, and shear reinforcement arrangement were investigated, and
the applicability of existing CSA A23.3-04 and ACI 318-05 standard
specifications for punching shear resistance were examined.
Results from the tests show that marked increases in the punching
shear capacity and ductility (over 80 and 700%, respectively)
can be achieved with CFRP retrofitting of slabs.
Keywords: flat plate; punching shear; shear reinforcement; slab.
INTRODUCTION
The rehabilitation and strengthening of structural
members with composite materials, such as carbon, glass,
kevlar, and aramid fiber-reinforced polymers (FRPs), has
recently received great attention. Reduced material costs,
coupled with labor savings inherent with its lightweight and
comparatively simple installation, its high tensile strength,
low relaxation, and immunity to corrosion, have made FRP
an attractive alternative to traditional retrofitting techniques.
Field applications over the last years have shown excellent
performance and durability of FRP-retrofitted structures.1
Research into the application of externally bonded FRPs to
reinforce concrete slabs has concentrated on improving the
flexural capacity. There is also the potential for FRP laminates
to improve the shear capacity of reinforced concrete slabs.
Shear failures occur suddenly and without warning and can be
catastrophic, especially in seismic zones. The avoidance of
such a failure is of paramount importance; and the benefits
from strengthening existing slabs in shear, either for purposes
of improved capacity and structural modification or due to
deterioration and aging or mistakes in design, are great.
This paper reports on a series of tests conducted to assess the
ability of carbon fiber-reinforced polymer (CFRP) laminates to
increase the two-way shear capacity of existing reinforced
concrete slabs.2,3 In a pilot test series, three slab specimens
retrofitted with CFRP were tested in 2000 and compared with a
control specimen.2 Based on these results, a program was
initiated in which 28 square isotropic two-way slab specimens,
simply supported on all four sides, were subjected to a concentric
monotonically increasing load until failure.3 Twenty-four of
these slab specimens contained CFRP laminate shear
reinforcement. The slabs were designed to fail in shear prior to
flexure so that the shear strength contribution of the CFRP
laminates could be measured. Pilot tests on three slab
specimens reinforced in shear found substantial increases in
concentric punching shear capacity and ductility.2 This paper
confirms the potential of CFRP laminates to reinforce existing
concrete slabs in shear; expands on the influence of variables
such as the concrete strength, flexural capacity, and shear
reinforcement arrangement on punching shear behavior;
and investigates the applicability of existing CSA23.3-044
and ACI 318-055 standard specifications for punching
shear resistance.
RESEARCH SIGNIFICANCE
This research investigates an innovative idea for increasing
the two-way shear strength of concrete slabs with FRP. FRP
reinforcement is provided in holes that are perpendicular to the
plane of the slab in a manner that is equivalent to stitching the
slab. The configuration of the holes determines the efficiency
of the reinforcement in enhancing the performance of the
retrofitted slab. Although the procedure was tested for retrofit-
ting of existing slabs, the results are equally applicable to new
structures. With the exception of fire resistance, the procedure
proposed herein is considered to be technically superior, easier
to implement, and produces more durable structures than
traditional strengthening techniques.
THEORETICAL RESPONSE
Concentric punching shear capacity
without shear reinforcement
Punching shear failure is characterized by the slab fracturing
along planes that extend from the column-slab interface on the
compressed face of the slab through the depth of the slab in an
inclined direction away from the column. For square columns,
the punching shear failure takes the form of a frustum of a
pyramid (Fig. 1).
Most research on the shear strength of slabs has been
concerned with developing empirical formulas based on a
nominal shear stress resistance.6 Nominal shear stress is
obtained by dividing the shearing force by the area of an
assumed critical section a certain distance from the column
perimeter. The CSA and ACI standards4,5 assume the shear
failure plane to have an angle of inclination of 45 degrees
from the slab surface and propose the use of a critical section
perimeter half the effective slab thickness from the column
periphery (Fig. 2). The depth of the critical section is taken
as the effective slab thickness.
In the absence of an unbalanced moment, the shear stress
due to factored loads vf is calculated as
vf = Vf/(bod)(1)
Title no. 104-S06
Strengthening Concrete Slabs for Punching Shear with
Carbon Fiber-Reinforced Polymer Laminates
by Kyriakos Sissakis and Shamim A. Sheikh
ACI Structural Journal/January-February 200750
where Vf is the shear force due to factored loads, d is the
effective slab thickness for shear, and bo is the perimeter of
the shear critical section d/2 from the column periphery.
According to the ACI standard,5 the nominal shear strength
for a critical shear section d/2 from the column periphery is
computed from the smallest of Eq. (2) to (4)
(2)
(3)
(4)
vrvc0.167 1 2
βc
-----+
⎝⎠
⎛⎞
f′
c (MPa)==
24
βc
-----+
⎝⎠
⎛⎞
f′
cpsi()=
vrvc0.083 αsd
bo
---------2+
⎝⎠
⎛⎞
f′
cMPa()==
αsd
bo
---------2+
⎝⎠
⎛⎞
f′
cpsi()=
vrvc0.33 f′
cMPa()4f′
cpsi()== =
where βc is the ratio of the long to short side of the column,
αs is a modification factor for the support type (αs = 40 for
interior columns), and f′
c is the unconfined concrete
compressive strength. The CSA standards’4 formulation is
identical to the aforementioned with the exception of inflated
coefficients to compensate for stringent material reduction
factors originating from column design.7 The same applies
to Eq. (7) through (11) that follow. Equation (4) governs for
the specimens tested in this study. Thus, the concentric load
required to fail the slab specimens without shear reinforcement
in punching shear4,5 is
(5)
Concentric punching shear capacity
with shear reinforcement
The CSA and ACI standards4,5 permit the use of closed
stirrups or vertical shear studs as shear reinforcement that are
positioned prior to casting and are typically located along
perimeters that parallel the column periphery (Fig. 3).
Reinforcements of these types also contribute to shear
strength by confining the concrete and facilitating the
distribution of shearing stresses outwards toward the
uncracked concrete. It is proposed that CFRP laminates can
be applied to existing slabs within vertical holes drilled
through the depth of the slab around the column. The holes
can be arranged into a series of perimeters offset from the
column in a manner similar to shear stud reinforcement. In
new slabs, the FRP reinforcement can be provided in a
similar configuration before or after casting.
Concrete slabs reinforced with shear studs can fail in shear
outside or within the shear-reinforced zone. Failures can occur
within the reinforced zone when the cumulative strength of the
shear reinforcement and the concrete is less than the force
required to fail the slab in shear outside the reinforced zone or
when the shear reinforcement does not sufficiently distribute
shearing forces. To ensure adequate distribution of shearing
forces, Joint ACI-ASCE Committee 4218 and CSA Standard4
specify Eq. (6) through (8) to determine the spacing of shear
stud reinforcement.
so ≤ 0.40d(6)
(7)
Pv0.33bodf′
cMPa()4bodf′
cpsi()==
s0.75d for vf0.5 f′
cMPa() or 6 f′
cpsi()≤≤
Kyriakos Sissakis is a Structural Engineer with Halsall Associates Limited, Toronto,
Ontario, Canada. His research interests include complex structures, advanced digital
applications, and design innovations.
Shamim A. Sheikh, FACI, is a Professor of civil engineering at the University of
Toronto, Toronto. He is a member of ACI Committee 374, Performance-Based Seismic
Design of Concrete Buildings, and a member and former Chair of Joint ACI-ASCE
Committee 441, Reinforced Concrete Columns. In 1999, he received the ACI
Structural Research Award. His research interests include earthquake resistance of
concrete structures, confinement of concrete, use of fiber-reinforced polymer in
concrete structures, and expansive cement and its applications.
Fig. 2—Critical shear section perimeters for slabs with and
without shear reinforcement.
Fig. 3—Closed stirrup and stud shear reinforcement.
Fig. 1—Punching shear failure.
ACI Structural Journal/January-February 2007 51
s ≤ 0.50d for vf > 0.5 (8)
In Eq. (6) through (8), so is the distance between the column
periphery and the first concentric line of shear studs parallel to
the column periphery and s is the spacing between consecutive
perimeters of shear studs (Fig. 2). In addition, the ACI
document8 recommends that shear studs be positioned at the
column corners, in-line with the column face (Fig. 3), and that
the spacing of shear studs in the direction parallel to the
column face be less than 2d (Fig. 2). For this research
program, several shear-reinforcing arrangements were inves-
tigated. Excessive amounts of shear reinforcement were
applied to the slab specimens in an attempt to avoid failures
within the shear-reinforced zone. The CSA standard and ACI
document,4,8 however, both impose a limit on the cumulative
nominal shear stress resistance of concrete vc and the shear
reinforcement vs for a critical section d/2 from the column
periphery to guard against diagonal crushing of the concrete.
For headed shear stud reinforcement
(9)
The shear strength of concrete at a critical section varies
with distance from the column. The confinement induced by
the triaxial stress condition in the vicinity of the column
decreases with increasing distance from the column, causing
a loss in shear strength. In general, immediately adjacent to
the column, a triaxial compressive state exists and at some
greater distance the triaxial compressive state dissipates to a
uniaxial compressive state. The CSA and ACI standards4,5
specify a nominal shear strength at a distance d/2 from the
outermost perimeter of shear reinforcement
(10)
Assuming adequate confinement by the shear-reinforcement,
the ultimate concentric load required to fail the slab specimens
in punching shear is thus
(11)
where b is the perimeter of the critical section d/2 from the
outermost perimeter of shear reinforcement (Fig. 2 and 4).
Flexural capacity
The flexural capacity of square isotropic two-way slab,
simply supported on all four sides and subjected to a
concentric square load, can be estimated using Johansen’s
yield line theory,9
(12)
where L is the length of the supported slab, c is the loading
plate side length, and mr is the flexural capacity of the slab
per unit width given by
f′
cMPa() or 6 f′
cpsi()
vrvcvs0.67 f′
cMPa() or 8 f′
cpsi()≤+=
vrvc0.167 f′
cMPa()2f′
cpsi()== =
Pv0.167bd f ′
c0.67bodf′
cMPa()≤=
2bd f ′
c8bodf′
cpsi()≤=
PYmr8
Lc 1–⁄
-------------------
⎝⎠
⎛⎞
2π+=
(13)
where ρ, d, and fy are the flexural reinforcement ratio, depth,
and yield strength, respectively. Equation (12) corresponds
to a collapse mechanism where the slab yields and divides
into quartered circular fans radiating from the corners of a
square column. For the specimens in this study, L and c are
1.35 m (53 in.) and 200 mm (8 in.), respectively (Fig. 5).
EXPERIMENTAL PROGRAM
Test specimens
All of the slab specimens had the same external dimensions
and contained either 15 M (0.31 in.2 area) or 20 M (0.465 in.2
area) flexural reinforcement bars. The effective depth was
120 mm (4.75 in.) in both types of flexural reinforcement
(Fig. 5). The slabs were cast with normal density concrete in
four separate batches, resulting in four different concrete
strengths. Each batch consisted of several slab specimens
cast with one of the four patterns of 25 mm (1 in.) diameter
holes shown in Fig. 4. The holes were later used to reinforce
the slabs with CFRP laminates. One slab in each batch was
the control specimen and not reinforced in shear.
mrρd2fy10.59–ρfy
f′
c
-----
⎝⎠
⎛⎞
=
Fig. 4—Shear reinforcement arrangements and assumed
critical shear section perimeters of tested slab specimens
with three peripheral lines of shear reinforcement.
Fig. 5—Slab specimen B5 specifications, load, and supports.
ACI Structural Journal/January-February 200752
The flexural reinforcement was spaced equally in all the
specimens and did not interfere with the holes intended for the
CFRP laminates. The development of the flexural reinforcement
was attained mechanically by welding the ends of the reinforcing
bars to flat steel plates, which occupied the perimeter of the slab
specimens (Fig. 5). The number of peripheral lines of
shear reinforcement varied between three and six among
the slab specimens and the spacing between the consecutive
lines was 0.5d or 0.75d. The first perimeter was offset 0.25d
from the loading plate periphery for all the slab specimens.
Table 1 summarizes the slab specimen details and material
properties. The slab specimens with primed pattern labels
contained 15 M flexural reinforcement bars, while other slab
specimens contained 20 M bars. Those specimens with shear
reinforcement are labelled in accordance with their shear
reinforcement pattern, A, B, C, or D, with numerical
subscripts denoting the number of peripheral lines of shear
reinforcement. The amounts of CFRP laminate ACFRP used
in each concentric shear-reinforcing perimeter are presented
in width of CFRP laminate. For slab specimens A3′, A3, and
A5, the amount of CFRP laminate applied in each reinforced
perimeter varied and is listed in Table 1 starting from the
perimeter nearest the loading plate. PY and PV represent the
predicted applied loads required to fail the slab specimens in
flexural yield and shear, respectively. PY is derived from
Eq. (12) and PV is derived from Eq. (5) or (11). The critical
shear sections perimeters outside the shear-reinforced zone
b, specified by the CSA and ACI standards,4,5 are depicted
in the upper portion of Fig. 4.
A commercially available CFRP system was used. The
ultimate tensile strength and tensile modulus per unit width
of CFRP laminate was determined experimentally to be
97 kN/m (66.6 kips/ft) and 79.5 MN/m (5452 kips/ft),
respectively. The rupture strain was 1.30% and the specified
thickness of the CFRP laminate was 0.89 mm (0.035 in.).
The CFRP was applied to the slab specimens by cutting long
thin strands that could pass through the holes positioned in
the slab. The CFRP strands were soaked in epoxy and looped
continuously between pairs of holes several times, in a stitch-
like manner, until the desired amount of CFRP laminate
spanned the depth of the slab (Fig. 5 and 6). The continuous
loop of CFRP laminate formed a solid ring of reinforcement
that also confined the concrete. Shear reinforcement Pattern A
with odd numbers of peripheral lines of shear reinforcement
Table 1—Slab specimen variables and material properties
Specimen
Concrete Flexural reinforcement Shear reinforcement Calculated properties
fc
′, MPa (ksi) fY, MPa (ksi) fU, MPa (ksi) ρ, % b, mm (in.) s/dACFRP, mm (in.)/perimeter PY, kN PV, kN
Control 1 42.6 (6.18) 428 (62.1) 730 (105.9) 1.49 1280 (50.4) — — 643 (144.7) 331 (74.5)
A4′42.6 (6.18) 428 (62.1) 730 (105.9) 1.49 2234 (88.0) 0.50 814 (32.0) 643 (144.7) 304 (65.7)
Control 2 36.1 (5.23) 428 (62.1) 730 (105.9) 1.49 1280 (50.4) — — 631 (142.0) 305 (68.6)
A3′36.1 (5.23) 428 (62.1) 730 (105.9) 1.49 2234 (88.0) 0.75 506/1012/506 631 (142.0) 269 (60.5)
(19.9/39.8/19.9)
B3′
36.1 (5.23) 428 (62.1) 730 (105.9) 1.49
2356 (92.8) 0.75 748 (29.4)
631 (142.0)
284 (53.8)
B4′2356 (92.8) 0.50 748 (29.4) 284 (53.8)
C3′2960 (116.5) 0.75 924 (36.4) 356 (80.2)
C4′2960 (116.5) 0.50 924 (36.4) 356 (80.2)
D3′2960 (116.5) 0.75 924 (36.4) 356 (80.2)
D4′2960 (116.5) 0.50 924 (36.4) 356 (80.2)
Control 3 34.5 (5.00) 480 (69.6) 623 (90.3) 2.23 1280 (50.4) — — 966 (217.4) 298 (67.1)
A334.5 (5.00) 480 (69.6) 623 (90.3) 2.23 1894 (74.6) 0.50 462/924/462 966 (217.4) 223 (50.2)
(18.2/36.4/18.2)
A534.5 (5.00) 480 (69.6) 623 (90.3) 2.23 2573 (101.3) 0.50 858/858/660/1320/660 966 (217.4) 303 (68.1)
(33.8/33.8/26/52/26)
B3
34.5 (5.00) 480 (69.6) 623 (90.3) 2.23
2017 (79.4) 0.50 616 (24.3)
966 (217.4)
237 (53.4)
B52697 (106.1) 0.50 792 (31.2) 317 (71.4)
C32480 (97.6) 0.50 792 (31.2) 292 (65.7)
C53440 (135.4) 0.50 1188 (46.8) 405 (91.1)
D32480 (97.6) 0.50 792 (31.2) 292 (65.7)
D53440 (135.4) 0.50 792 (31.2) 405 (91.1)
Control 4 26.6 (3.86) 480 (69.6) 623 (90.3) 2.23 1280 (50.4) — — 902 (203.0) 261 (58.7)
A4
26.6 (3.86) 480 (69.6) 623 (90.3) 2.23
2234 (88.0) 0.50 638 (25.1)
902 (203.0)
231 (52.0)
A62912 (114.6) 0.50 924 (36.4) 301 (67.7)
B42356 (92.8) 0.50 660 (26.0) 244 (54.8)
B63035 (119.5) 0.50 924 (36.4) 314 (70.6)
C42960 (116.5) 0.50 924 (36.4) 306 (68.8)
C63920 (154.3) 0.50 1276 (50.2) 405 (91.2)
D42960 (116.5) 0.50 858 (33.8) 306 (68.8)
D63920 (154.3) 0.50 1254 (49.4) 405 (91.2)
ACI Structural Journal/January-February 2007 53
had the two adjacent outer rings of CFRP share a cast hole and
as such, the shared hole had twice the CFRP reinforcement
(Table 1). The voids that remained after the application of the
CFRP laminates were subsequently filled with epoxy.
Specimens in the pilot test series1 had shorter strands of
CFRP laminate that were passed through the cast holes once
and had their ends adhered to the top and bottom surfaces of
the slab. Large sheets of CFRP laminate were later installed
on the top and bottom surfaces to ensure anchorage to the
concrete (Fig. 7). The experiment found partial separation of
the CFRP laminates from the concrete surface during testing
and considerable increases in flexural stiffness and strength
due to the added CFRP laminates on the top and bottom
surfaces of the specimens. The newly proposed solid rings of
CFRP reinforcement minimized the dependence on bond
between the concrete and the FRP and avoided increases in
flexural strength and stiffness.
Test setup
The slabs were tested under a vertical monotonically
increasing concentric load distributed by means of a 200 mm
(8 in.) square by 100 mm (4 in.) thick loading plate. A
closed-loop servo-controlled stiff frame test machine (Fig. 8)
was used to apply the load in displacement control mode at a
rate of 0.01 mm/second (4 × 10–4 in./second). A universal
ball joint was attached to the loading plate to prevent
moments from being imposed onto the slab specimens.
The slabs were positioned horizontally and simply
supported on all four sides by rollers comprised of solid 44 mm
(1.75 in.) diameter steel rods. The rollers rested on a steel
podium placed directly onto the solid metal base of the test
machine. Two of the rollers were welded to the podium,
while the opposite two rollers were left free to rotate. The
rollers were positioned 75 mm (3 in.) within the edges of the
slab specimens. Metal plates 150 x 25 mm (6 x 1 in.) in
section, were loosely positioned in between the slab specimens
and rollers to distribute bearing forces.
To monitor the displacement of the slab specimens, six
linearly variable differential transducers (LVDTs) were
used—four to measure the displacements of the supporting
structure and two for the displacement of the loading plate.
The four LVDTs used to measure the displacement of the
supporting structure were positioned at the four corners of
the slab, directly above the supporting rollers (Fig. 8).
Local strains in the CFRP laminates and the flexural
reinforcement were measured with electrical resistance
strain gauges. Four strain gauges were applied with
cyanoacrylate adhesive to the lower two central reinforcing
bars that passed underneath the loading plate. Two of the
gauges were positioned at the middle of the reinforcing bars
and the other two were offset 200 mm (8 in.) from the middle
in opposing directions. Long-gauge strain gauges were
applied to every vertical stem of the CFRP laminate rings.
The gauges were adhered to epoxied segments on separate
CFRP strands (Fig. 9) that were later attached with epoxy to
the solid rings of CFRP reinforcement (Fig. 6). Two gauges
were adhered to each strand. The gauges were positioned
such that when the strands were applied to the CFRP rings;
the gauges were aligned with the center of the slab depth in
two adjacent holes. The epoxied segments were formed by
sandwiching a small amount of epoxy resin on the CFRP
strands between sheets of polyethylene. This made a smooth
surface on to which the gauges could be adhered. Several
layers of polyurethane and foam mounting tape were applied
to all the gauges to prevent moisture penetration and any
tangential pressures from being exerted on to the gauges.
EXPERIMENTAL RESULTS
The slabs were designed such that they would fail in shear.
With retrofitting, the shear capacity increased significantly
causing yield of flexural steel in some slabs. Stress in steel,
however, was significantly lower than rupture. Therefore,
each slab failed in shear as clearly demonstrated by the
failure modes observed during the tests. The results from the
tests on the slab specimens are presented in the following.
After the description of the failure patterns, responses of the
slab specimens are discussed to evaluate different CFRP
reinforcement patterns. Theoretical prediction of capacity
and the design aspects conclude this section of the paper.
Failure plane description
Figure 10 shows sketches of the shear fractures, portrayed
as dotted lines, on the compressed surface of failed slab
specimens. Figure 11 shows photographs of the cross
sections of selected slab specimens cut in half. The slab
specimens were cut such that those with CFRP laminate
Patterns A and C had the cut pass through the CFRP laminates
and in specimens with reinforcement Patterns B and D the cut
passed between the CFRP laminates. The fractures have been
Fig. 6—Slab specimen D4 before and after CFRP application.
Fig. 7—CFRP application of slab specimen in pilot studies.
Fig. 8—Test setup.
54 ACI Structural Journal/January-February 2007
highlighted with a black marker. No specimen experienced
tensile or compressive flexural failure before failing in shear.
The punching shear failures occurred outside, within or
prior to the shear-reinforced zones. In plan, the shear fractures
outside the shear-reinforced zone were typically circular in
shape. CFRP laminate Pattern A exhibited greater tendency
towards shear failures within the shear-reinforced zone than
CFRP laminate Patterns B and C. All and only the slab
specimens with CFRP laminate Pattern D failed in shear at
the perimeter of the loading plate. The specimens with larger
spacing of consecutive shear-reinforcing perimeters s were
more prone to shear failures within the shear-reinforced zone
than the specimens with smaller spacing and equivalent
potential critical section perimeters (that is, A3′ versus A4′,
B3′ versus B4′, C3′ versus C4′, and D3′ versus D4′).
In section, the shear fractures extended through the depth
of the slabs at an angle of inclination generally smaller than
45 degrees. Upon reaching the flexural reinforcement, the
failure planes continued horizontally toward the perimeter of
the slab between the layers of flexural reinforcement.
Varying degrees of shear and flexural cracking were
evident among the slab specimens. The specimens with
greater number of shear-reinforcing perimeters, larger
consecutive spacing of shear-reinforcing perimeters and
lower flexural reinforcement ratios exhibited greater degrees
of concrete cracking within the shear-reinforced zone. For
the specimens cut through the CFRP laminates, it was
observed that none of the laminates spanned shear fractures,
thus implying the specimens did not undergo progressive
shear failures within the shear-reinforced zone and that the
shear reinforcement and the concrete behaved cohesively.
Load-deformation response
Load-deformation curves for all the tested slab specimens
are given in Fig. 12. The slab deformation is taken as the
difference between the deflection at the loading plate and the
average deflection at the supports. The load has been
normalized with respect to bod to compare specimens
with different concrete strengths and corresponds to the
cumulative shear stress at a distance of d/2 from the loading
plate periphery. Table 2 shows the results from all the tests.
f′c
Fig. 9—CFRP strands with adhered strain gauges.
Fig. 10—Sketched slab specimen compressed surface
fractures relative shear reinforcement.
Fig. 11—Photographs of selected slab specimen cross sections.
Fig. 12—Slab specimen load-deformation curves.
ACI Structural Journal/January-February 2007 55
The strain energy absorbed U80 is taken as the area under the
load-deformation curve up to 80% of the ultimate load PTEST
beyond the peak. Figure 13 compares the load deformation
curves for slab Specimens A6, B6, C6, and D6, and their
respective control specimen. The load-displacement curve
for Specimen B5 is shown in Fig. 14 along with the load-
average strain curves for each peripheral line of shear
reinforcement and the flexural reinforcement. The CFRP
strains and flexural reinforcement strains remained less than
3000με and 6500με, respectively, for all the specimens.
The slab specimens with shear reinforcement demonstrated
increases in load carrying capacity and ductility of up to 82 and
768%, respectively, over that of their respective control
specimens and, in some cases, changed the mode of failure
from punching shear to flexural (refer to Ptest/Pcontrol, U80 /
(U80)control and Ptest/PY in Table 2). The increase in shear
strength and ductility was accompanied by an increase in
audible signs of distress. The formation of a complete shear
failure plane was often not instantaneous and formed
partially at various sections of the slab, expanding until
failure. This growth of the shear failure plane is identified by
the slab specimens without abrupt losses of load and/or
losses of load followed by plateaus (Fig. 12). As expected,
stiffness of the slab specimens with a larger amount of flexural
steel was higher than that of specimens with a lower amount
of flexural steel. The slab specimens reinforced in shear
showed no significant change in stiffness over that of their
respective control specimen (Fig. 13).
It can be observed from Fig. 12 and Table 2 that the load-
carrying capacity of the slab specimens increased with the
increase in the number of CFRP perimeters. The slab specimens
with shear-reinforcing Patterns A and D exhibited shear
capacity improvements that were approximately half as
much as those with shear-reinforcing Patterns B and C. The
specimens with larger shear-reinforcing perimeter spacing s
exhibited no appreciable loss in strength or ductility when
compared with the specimens with smaller shear-reinforcing
perimeter spacing and equivalent potential critical section
perimeters (A3′, and versus A4′, B3′ versus B4′, C3′ versus
C4′, and D3′ versus D4′). Another important observation that
can be made from Fig. 12 is related to the lack of significant
enhancement in deformability and ductility despite the
additional CFRP reinforcement in slab specimens of
Patterns A and D. Contrary to this behavior, for specimens of
shear-reinforcing Patterns B and C in which CFRP is distributed
more uniformly, an increase in the number of reinforcement
perimeters results in a substantial increase in ductility and
hence the energy dissipation capacity of the slabs. Greater
increases in ductility, capacity, and audible distress were
exhibited with greater numbers of shear-reinforcing perimeters
and a greater number of vertical elements of reinforcement
in each perimeter.
Failure characteristics
The concrete contribution to shear resistance vc within the
CFRP laminate reinforced zone can be approximated by
subtracting the nominal shear resistance of the CFRP laminate
shear reinforcement vCFRP from the total shear resistance vr.
vc = vr – vCFRP (14)
vr = P/bd (15)
vCFRP = (FCFRPcotθ)/bs (16)
where P is the instantaneous applied load, FCFRP is the total
tensile force in the CFRP laminates in-line with the assumed
shear critical section, b is the perimeter of the assumed critical
shear section, θ is the angle of inclination of the principle
compressive stresses from the slab surface, and s is the spacing
of the shear-reinforcing perimeters perpendicular from the
loading plate periphery. Figure 15 presents the responses of all
shear-reinforced perimeters of slab Specimens A6, B6, C6, and
D6 with respect to the applied load. The concrete shear
strength was derived from Eq. (14) through (16). Based on the
observed angles of inclination of the shear failure planes, a mean
angle of 31 degrees was used for θ. The CFRP laminate tensile
force was derived from direct strain measurements during
testing, such as shown in Fig. 14, the ACFRP given in Table 1, and
the experimentally determined CFRP laminate modulus.
Two general observations can be made. First, the concrete
shear strength varies with the distance from the loading plate
periphery. Perimeters near the plate exhibit higher concrete
shear strengths than perimeters further away from the plate.
Second, the shearing stresses are distributed differently
among the slab specimens. Slab Specimen A6 shows a
gradual increase in shear resistance for all the shear-reinforced
perimeters and a sudden loss in shear strength at failure. Slab
Specimens B6 and C6 also show a gradual increase in shear
resistance for all the reinforced perimeters. These specimens,
however, portray a gradual loss in shear strength prior to
failure. Slab Specimen D6 shows a gradual loss in shear
Fig. 13—Load-deformation curves for slab specimens A6,
B6, C6, D6, and Control 4.
Fig. 14—Load-deformation and stress curves for slab
Specimen B5.
ACI Structural Journal/January-February 200756
strength prior to failure only in the first three reinforced
perimeters and a complete loss in shear strength in the
innermost perimeter.
The slab specimens with CFRP laminate Patterns A and D
were prone to premature shear failures inside the shear-
reinforced zone. Pattern A mostly failed between the second
and third shear-reinforcing perimeters. Pattern D always
failed between the loading plate face and the first perimeter
of shear reinforcement. It is probable that the shear stresses
at the corners of the loading plate are considerably higher
than those at the face of the loading plate. This can be attributed
to the flexural curvature of the slab specimen conforming to
the rectangular loading plate. The corners of the loading
plate were observed to pierce the slab surface during testing
and it is likely that the concrete at these locations fractured
in shear initially. The lack of shear reinforcement in the
vicinity of the loading plate corners of Pattern A may have
allowed these fractures to propagate. Upon reaching the
shear reinforcement, the shear cracks have developed
considerably and could no longer be contained by the shear
reinforcement, permitting them to pass between the shear
reinforcing elements. This is reflected by the sudden loss in
vc values within the shear reinforced zone prior to failure.
The gradual dissolution of vc values in the first shear
Table 2—Slab specimen test results and ultimate analysis
Specimen
Test results Ultimate analysis
Failure
within shear
reinforcement
(Y/N)
U80,
kJ (ft-kip) PTEST,
kN (kip)
,
MPa (ksi)
,
MPa (ksi)
,
MPa (ksi)
,
MPa (ksi)
Control 1 4.0 (2.9) 575 (129) 0.57 (6.9) 0.57 (6.9) 0.41 (4.9) 0.41 (4.9) 0.90 1.74 1.25 — — —
Control 2 2.1 (1.5) 439 (99) 0.48 (5.7) 0.48 (5.7) 0.33 (4.0) 0.33 (4.0) 0.70 1.44 1.00 — — —
Control 3 1.8 (1.3) 476 (107) 0.53 (6.3) 0.53 (6.3) 0.31 (3.5) 0.31 (3.5) 0.49 1.60 0.89 — — —
Control 4 1.9 (1.4) 479 (108) 0.60 (7.3) 0.60 (7.3) 0.34 (3.9) 0.34 (3.9) 0.53 1.83 0.99 — — —
Average — 0.55 (6.5) — 0.35 (4.1) — 1.65 1.03 — — —
Standard deviation — 0.06 (0.7) — 0.04 (0.6) — 0.17 0.15 — — —
A3
′5.3 (3.9) 591 (133) 0.64 (7.7) 0.37 (4.4) 0.44 (5.3) 0.25 (3.1) 0.94 2.20 1.37 2.52 1.35 N
A4
′5.9 (4.4) 632 (142) 0.63 (7.6) 0.36 (4.3) 0.45 (5.4) 0.26 (3.1) 0.99 2.16 1.39 1.48 1.10 N
A34.0 (2.9) 646 (145) 0.72 (8.6) 0.48 (5.8) 0.42 (4.8) 0.27 (3.2) 0.67 2.90 1.44 2.22 1.36 Y
A44.6 (3.4) 595 (134) 0.75 (9.0) 0.43 (5.2) 0.42 (4.9) 0.23 (2.8) 0.66 2.58 1.24 2.42 1.24 Y
A56.4 (4.7) 671 (151) 0.74 (8.9) 0.37 (4.4) 0.43 (5.0) 0.21 (2.5) 0.69 2.22 1.10 3.56 1.41 N
A65.3 (3.9) 631 (142) 0.80 (9.6) 0.35 (4.2) 0.44 (5.1) 0.19 (2.3) 0.70 2.10 1.01 2.79 1.32 Y
Average — 0.39 (4.7) — 0.23 (2.8) — 2.36 1.26 — — —
Standard deviation — 0.05 (0.6) — 0.03 (0.4) — 0.31 0.17 — — —
B3
′6.4 (4.7) 659 (148) 0.71 (8.6) 0.39 (4.7) 0.49 (6.0) 0.27 (3.2) 1.05 2.32 1.52 3.05 1.50 Y
B4
′5.0 (3.7) 638 (144) 0.69 (8.3) 0.38 (4.5) 0.48 (5.8) 0.26 (3.1) 1.02 2.25 1.47 2.38 1.45 N
B35.5 (4.1) 744 (167) 0.82 (9.9) 0.52 (6.3) 0.48 (5.5) 0.29 (3.5) 0.77 3.13 1.66 3.06 1.56 N
B45.1 (3.8) 701 (158) 0.88 (10.6) 0.48 (5.8) 0.49 (5.7) 0.26 (3.1) 0.78 2.88 1.46 2.68 1.46 N
B510.5 (7.7) 791 (178) 0.88 (10.5) 0.42 (5.0) 0.51 (5.8) 0.23 (2.8) 0.82 2.49 1.30 5.83 1.66 N
B614.8 (11) 791 (178) 1.00 (11.9) 0.42 (5.1) 0.56 (6.5) 0.23 (2.7) 0.88 2.52 1.27 7.79 1.65 N
Average — 0.43 (5.2) — 0.26 (3.1) — 2.60 1.45 — — —
Standard deviation — 0.06 (0.7) — 0.02 (0.3) — 0.34 0.14 — — —
C3
′5.8 (4.3) 612 (138) 0.66 (8.0) 0.29 (3.4) 0.46 (5.5) 0.20 (2.4) 0.98 1.72 1.16 2.76 1.39 Y
C4
′7.3 (5.4) 673 (151) 0.73 (8.8) 0.32 (3.8) 0.51 (6.1) 0.22 (2.6) 1.08 1.89 1.28 3.48 1.53 N
C35.8 (4.3) 775 (174) 0.86 (10.3) 0.44 (5.3) 0.50 (5.7) 0.25 (3.0) 0.80 2.65 1.46 3.22 1.63 N
C47.6 (5.6) 781 (176) 0.99 (11.8) 0.43 (5.1) 0.55 (6.4) 0.23 (2.8) 0.87 2.55 1.34 4.00 1.63 N
C59.9 (7.3) 858 (193) 0.95 (11.4) 0.35 (4.2) 0.55 (6.3) 0.20 (2.4) 0.89 2.12 1.13 5.50 1.80 Y
C616.5 (12) 872 (196) 1.10 (13.2) 0.36 (4.3) 0.61 (7.1) 0.19 (2.3) 0.97 2.15 1.11 8.68 1.82 N
Average — 0.36 (4.4) — 0.21 (2.6) — 2.18 1.24 — — —
Standard deviation — 0.06 (0.7) — 0.02 (0.3) — 0.37 0.14 — — —
D3
′3.1 (2.3) 550 (124) 0.60 (7.2) 0.26 (3.1) 0.41 (5.0) 0.18 (2.1) 0.88 1.54 1.04 1.48 1.25 Y
D4
′5.5 (4.1) 605 (136) 0.66 (7.9) 0.28 (3.4) 0.45 (5.5) 0.20 (2.4) 0.97 1.70 1.15 2.62 1.38 Y
D34.1 (3.0) 616 (139) 0.68 (8.2) 0.35 (4.2) 0.40 (4.5) 0.20 (2.3) 0.64 2.11 1.16 2.28 1.29 Y
D44.1 (3.0) 634 (143) 0.80 (9.6) 0.35 (4.2) 0.45 (5.2) 0.19 (2.2) 0.70 2.07 1.09 2.16 1.32 Y
D54.4 (3.2) 617 (139) 0.68 (8.2) 0.25 (3.1) 0.40 (4.6) 0.14 (1.7) 0.64 1.52 0.81 2.44 1.30 Y
D65.9 (4.4) 639 (144) 0.81 (9.7) 0.26 (3.2) 0.45 (5.2) 0.14 (1.7) 0.71 1.58 0.81 3.11 1.33 Y
Average — 0.29 (3.5) — 0.17 (2.1) — 1.75 1.01 — — —
Standard deviation — 0.04 (0.5) — 0.03 (0.3) — 0.27 0.16 — — —
PTEST
bodf′
c
------------------ PTEST
bd f′
c
---------------- PTEST
bodf′
cϕo
⁄
----------------------------PTEST
bd f′
cϕo
⁄
--------------------------PTEST
PY
-------------PTEST
PV
-------------PTEST
PV′
-------------U80
U80
()
cont
-------------------- PTEST
Pcont
-------------
ACI Structural Journal/January-February 2007 57
reinforcing perimeter and the lack of apexes in the vc values
in the outer shear reinforcing perimeters for slab Specimen D6
imply that the shearing forces were not being adequately
transmitted to the outer perimeters of shear reinforcement,
resulting in the first perimeter being over-stressed and failure
of the specimen.
The slab specimens with CFRP Patterns B and C were less
likely to fail prematurely within the shear reinforced zone.
The lack of sudden strength loss and the presence of apexes
in the vc values for most of the reinforced perimeters imply
that the patterns offered sufficient resistance and confinement to
prevent the development of large shear cracks and effectively
distributed shearing forces to the uncracked concrete outside
the shear reinforced zone.
Evaluation of theoretical predictions
Table 2 contains the test results and ultimate load analysis
including those using the provisions of the CSA and ACI
standards.4,5 The experimental ultimate loads PTEST have
been normalized with respect to bod and bd to
make direct evaluation of Eq. (5) and (11). This corresponds
to the shear strength of concrete at a distance d/2 from the
loading plate periphery and from the outermost perimeter of
shear reinforcement, respectively. As stated previously,
excessive amounts of shear reinforcement were provided to
avoid failure of the reinforcement. Table 2 shows that the
CSA and ACI standards4,5 highly underestimated the punching
shear capacity of the specimens, in particular those specimens
reinforced in shear (refer to PTEST/PV). This is attributed to the
conservative prediction of concrete shear strength. The standards
did foresee the occurrence of most shear failures inside the
shear-reinforced zone.
The standards specify that the nominal shear stress resistance
of concrete be taken as 0.33 (4 ) and
0.167 (2 ) at a distance d/2 from the
column periphery and from the outermost perimeter of shear
reinforcement, respectively. The standards also impose a
limit of 0.67 (8 ) on the cumulative
shear stress resistance of concrete and the shear reinforcement at
a critical section d/2 from the column periphery. The vc values of
all of the control specimens and the shear reinforced specimens
outside the shear reinforced zone were much greater than
0.33 (4 ) and 0.167
(2 ), respectively, (see PTEST/bd√f′c). Most of the
shear reinforced slab specimens attained shear strengths
greater than 0.67 (8 ) at a distance d/2
from the loading plate periphery (refer to PTEST/(bod)).
All the slab specimens with CFRP laminate Pattern D and
slab Specimens A3, A4, A6, B3′, C3′, and C5 did not fail in
shear outside the shear reinforced zone. As discussed in
Failure characteristics, high shear stresses initiate failure at
the corners of the loading plate. This is confirmed by the
findings of Sherif and Dilger.10 Shear reinforcing Pattern A
did not have shear reinforcing at the loading plate corners as
recommended by the ACI standards5 and was incapable of
confining the shear fractures initiating from them. Pattern D
had shear reinforcement at the corners but was incapable of
transferring shear stresses sufficiently away from the loading
plate. Slab Specimens B3′ and C3′
had consecutive shear
reinforcing perimeters spaced at 0.75d. Equation (7) specifies
that for this spacing the shear stress shall not exceed
0.5 (6 ) at a critical section perimeter
d/2 from the column periphery. Both these specimens exceeded
this limitation (refer to PTEST/(bod)).
fc
′fc
′
fc
′ (MPa) fc
′ (psi)
fc
′ (MPa) fc
′ (psi)
fc
′ (MPa) fc
′ (psi)
fc
′ (MPa) fc
′ (psi) fc
′ (MPa)
fc
′ (psi)
fc
′ (MPa) fc
′ (psi) fc
′
fc
′ (MPa) fc
′ (psi)
fc
′
Design consideration
The conservative shear strength of concrete specified in
the CSA A23.3-04 and ACI 318-05 standards can be attributed
to the assumption that the shear to flexural capacity ratio is
almost unity. Shear strength is known to decrease as the
extent of flexural yielding in the slab increases. The decrease
in shear strength is attributed to the loss in membrane action
as a consequence of greater flexural yielding.11 Hognestad12
identified the influence of flexural yielding and introduced
the variable φo equal to the ratio of shear to flexural capacity.
A properly designed slab has a flexural strength less than the
shear strength. To simplify design procedures, the ACI and
CSA standards4,5 assume φo equal to unity, which is
conservative because a value less than unity has higher
nominal shear stress resistance, as is evident in the test
results presented herein.
Using the ultimate capacity and the specified4,5 critical
section area, Fig. 16 plots the nominal shear resistance of
concrete for the slab specimens with shear failures outside
the shear-reinforced zone (Table 2), with and without
Fig. 15—Concrete shear strength for critical sections in-line
with shear reinforcement.
Fig. 16—Shear strength of concrete outside shear-reinforced
zone.
58 ACI Structural Journal/January-February 2007
consideration of the flexural to shear capacity ratio. The
capacities have been normalized with respect to concrete
strength. The shear-to-flexural capacity ratio φo is taken as that
for the respective control specimen of each slab (Table 1). The
shear strength is referenced with respect to α, the ratio of
distance between the loading plate periphery and the critical
shear section to the effective slab thickness. Evident in Fig. 16
is that the shear strength of concrete is lower in specimens that
have larger φo values (those slab specimens with 15 M flexural
reinforcement bars) and that the CSA and ACI standards4,5
specified concrete shear strengths of 0.33
(4 ) and 0.167 (2 ) for the
control and shear-reinforced specimens, respectively, are
conservative. Also evident is that this disparity in shear
strength when compared with the CSA and ACI provisions
appears to be mitigated when concrete strength is normalized
with respect to φo. The shear strength of concrete is approxi-
mately 0.33 (4 ) at a distance α =
0.5 and diminishes asymptotically toward
0.167 (2 ) at a distance α > 3
(refer also to PTEST/bd in Table 2). The cumulative
nominal shear stress resistance at a distance d/2 from the
loading plate periphery does not exceed 0.67
(8 ) for any of the specimens (refer to PTEST/
bod in Table 2).
From the observed shear fractures (Fig. 10), it can be
concluded that the influence of the rectangular loading plate
to impart a rectangular shear stress distribution dissipates
with distance from the loading plate and that the failure
planes furthest away from the loading plate are of circular
shape. The lower portion of Fig. 4 depicts the proposed
critical shear perimeters that are circular at the corners. In
fc
′ (MPa)
fc
′ (psi) fc
′ (MPa) fc
′ (psi)
fc
′ (MPa)/φofc
′ (psi)/φo
fc
′ (MPa)/φofc
′ (psi)/φo
fc
′φ
o
⁄
fc
′ (MPa)/φo
fc
′ (psi)/φo
fc
′φ
o
⁄
this way, the proposed perimeters are near rectangular
immediately adjacent to the loading plate and become near
circular furthest away from the loading plate. Using both the
specified and the proposed critical perimeters, concrete
strength is determined by Eq. (14) through (16) for each
peripheral line of shear reinforcement for all specimens
except those of Pattern D (Fig. 17). Pattern D was not
included due to its failure to effectively distribute shear
stresses among the shear reinforcement. The fact that the
interior perimeters of shear reinforcement Pattern C are no
longer in line with the proposed peripheral lines (Fig. 4),
only the outermost perimeter is plotted. It is clear that the
scatter in the results using the specified critical shear
perimeters is considerably reduced with the use of the
proposed critical shear perimeters and that the results of
Fig. 16 that include φo are further substantiated.
In Table 2, column PTEST/PV′ has revised code predictions
based on the proposed critical shear sections defined in
Fig. 4 and concrete strengths normalized with respect to φo.
It is apparent that these predictions are much closer to actual
but still conservative. Because the CSA and ACI standards
specify concrete shear strength of 0.167
(2 ) irrespective of how far the shear reinforcement is
extended, the capacity will be underestimated in cases where
the shear reinforcement is appropriately distributed and
extends to a distance α < 5. Sherif and Dilger10 experienced
shear strength less than 0.2 (2.4 ) at α > 5
and recommend that shear reinforcement not be extended
beyond α = 4.5. The shear reinforcement was not extended
sufficiently in this investigation to evaluate this parameter.
CONCLUDING REMARKS
An innovative technique to retrofit concrete slabs for
enhancing their punching shear capacity was first suggested
by the authors in 2000.2 Further tests were completed and
reported in 2002.3 This extensive experimental work is
summarized in this paper. The approach involves reinforcing
the slab in the vicinity of a column with FRP laminates
through an elaborate pattern of vertical holes. Conceptually,
the slab is stitched with FRP fabric and the holes are filled
with epoxy. The experimental program consisted of 32 1.5 m
(4.9 ft) square and 150 mm (5.9 in.) deep slabs under
concentric load to validate the proposed technique. Results
from four specimens of the pilot series are not included
herein because anchorage of FRP laminates resulted in
increased flexural strength of the slabs in addition to the
enhanced shear capacity. Results from 28 specimens are
presented herein based on which the following conclusions
can be drawn:
1. The slab specimens retrofitted with CFRP laminate
shear reinforcement demonstrated a substantial increase in
shear strength, ductility, and energy dissipation capacity.
Shear strength increase of over 80% and enhancement of
ductility of over 700% were observed;
2. Greater increases in ductility, capacity, and audible distress
are exhibited with greater numbers of shear reinforcing
perimeters, particularly in shear-reinforcing patterns with
closer spacing of shear reinforcement along peripheral lines;
3. Within a group of slab specimens with equal potential
shear critical sections outside the shear-reinforced zone, larger
consecutive spacing of shear reinforcement did not have any
adverse effect on strength or ductility but caused greater
degrees of concrete cracking and increased the probability of
shear failures within the shear-reinforced zone;
fc
′ (MPa)
fc
′ (psi)
fc
′ (MPa) fc
′ (psi)
Fig. 17—Shear strength of concrete within shear reinforced
zone.
ACI Structural Journal/January-February 2007 59
4. Closer spacing of shear reinforcement resulted in
greater improvements in the behavior of slabs. Thus, shear-
reinforcing Patterns A and D (Fig. 4) exhibited comparatively
lower improvements in ductility and shear capacity. The
patterns were susceptible to premature shear failures within
the shear-reinforced zone. Patterns B and C exhibited
comparatively higher ductility and shear capacity
improvements. These patterns offered effective confinement to
prevent the development of shear failure within the shear-
reinforced zone;
5. The proposed critical shear section perimeters with
rounded corners in the manner depicted in Fig. 4 best
represent the behaviors of the shear reinforcement patterns
tested in this research program; and
6. The nominal shear stress resistance of concrete
varies with distance from the loading area and can be
taken as 0.33 (4 ) at α = 0.5,
decreasing asymptotically toward 0.167
(2 ) at α > 4, where φo is the shear to flexural
capacity ratio and α is the ratio of the distance between the
loading area periphery and the critical shear perimeter to the
effective slab thickness. All the slab specimens had cumulative
shear strength less than 0.67 (8 )
at α = 0.5.
ACKNOWLEDGMENTS
The research reported herein was funded by grants from the Natural
Sciences and Engineering Council of Canada (NSERC) and ISIS Canada, an
NSERC Network of Centres of Excellence. Technical and financial support
from R. J. Watson Inc. of East Amherst, N. Y., Fyfe Co. LLC of San Diego,
Calif., and Premier Corrosion Protection Services Inc. of Oakville,
Ontario, Canada, is gratefully acknowledged. The experimental work
was carried out at the Structures Laboratories of the University of
Toronto, Toronto, Ontario, Canada. Thanks are extended to O. Bayrak
for his help in the experimental program during his post-doctoral tenure
at the University of Toronto.
NOTATION
ACFRP = width of CFRP shear laminate on concentric line parallel to
loading area periphery
b= shear critical section perimeter d/2 from outermost peripheral
line of shear reinforcement
bo= perimeter of shear critical section d/2 from loading area periphery
c= rectangular loading plate width
d= effective slab thickness for shear
FCFRP = total tensile force in peripheral line of CFRP laminates
f′
c= concrete cylinder compressive strength
fU= ultimate strength of flexural reinforcement
fY= yield strength of flexural reinforcement
L= width of simply supported slab
mr= flexural capacity of slab per unit width
P= instantaneous applied load
Pcont = applied ultimate load during testing of respective control
specimen
PTest = applied ultimate load during testing
PV= CSA A23.3-04 and ACI 318-05 standards punching shear
capacity
PV
′=PV values based on fc′ normalized with respect to φo and
critical shear perimeters defined in Fig. 4(b)
PY= yield line theory flexural capacity
s= spacing between consecutive peripheral lines of shear
reinforcement parallel to loading area periphery
so= distance between loading area periphery and first peripheral
line of shear reinforcement
U80 = strain energy absorbed up to 80% of ultimate load, beyond
the peak
(U80)cont = strain energy absorbed up to 80% of ultimate load, beyond
peak of respective control specimen
Vf= shear force due to factored loads
vCFRP = nominal shear stress resistance of CFRP laminate shear
reinforcement
vc= nominal shear stress resistance of concrete
vf= nominal shear stress due to factored loads
vr=nominal shear stress resistance
α= ratio of distance between loading area periphery and critical
shear section to effective shear slab thickness
αs= support type modification factor
βc= ratio of long to short side of loading area periphery
φc= resistance factor for concrete
φo= calculated ratio of shear to flexural capacity, PV/PY
θ= angle of inclination of principle compressive stresses from
slab surface
ρ= percent flexural reinforcement
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the Punching Shear Resistance of Concrete Slabs,” Research Report,
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Canada, 2000, 86 pp.
3. Sissakis, K., “Strengthening of Concrete Slabs for Punching Shear
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Institute, Farmington Hills, Mich., 2005, 430 pp.
6. Criswell, M. E., and Hawkins, N. W., “Shear Strength of Slabs: Basic
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8. Joint ACI-ASCE Committee 421, “Shear Reinforcement for Slabs
(ACI 421.1R-99),” American Concrete Institute, Farmington Hills, Mich.,
1999, 15 pp.
9. Johansen, K. W., Yield Line Theory, Cement and Concrete Association,
London, 1962, 181 pp.
10. Sherif, A. G., and Dilger, W. H., “Critical Review of the CSA A23.3-94
Punching Shear Provisions for Interior Columns,” Canadian Journal of
Civil Engineering, V. 23, 1996, pp. 998-1011.
11. Hawkins, N. M., and Mitchell, D., “Progressive Collapse of Flat
Plate Structures,” ACI JOURNAL, Proceedings V. 76, No. 7, July 1979,
pp. 775-808.
12. Hognestad, E., “Shear Strength of Reinforced Concrete Column
Footings,” ACI JOURNAL, Proceedings V. 50, No. 11, Nov. 1953, pp. 189-208.
fc
′ (MPa)/φofc
′ (psi)/φofc
′ (MPa)/φo
fc
′ (psi)/φo
fc
′ (MPa)/φofc
′ (psi)/φo
