ACI STRUCTURAL JOURNAL

TECHNICAL PAPER

Title no. 110-S47

Behavior of Concrete Deep Beams Reinforced with
Internal Fiber-Reinforced Polymer—Experimental Study
by Matthias F. Andermatt and Adam S. Lubell
Concrete deep beams with small shear span-depth ratios (a/d) are
common elements in structures. To mitigate corrosion-induced
damage in concrete structures, members internally reinforced
with fiber-reinforced polymer (FRP) are increasingly specified.
However, very little experimental data exist for FRP-reinforced
concrete deep beams, as prior research has mainly focused on
slender beams having a/d greater than 2.5. This paper reports
on an experimental study designed to investigate the shear
behavior of concrete deep beams internally reinforced with FRP
and containing no distributed web reinforcement. Test results of
12 large-scale specimens that were loaded in a four-point bending
configuration are presented, where the primary variables included
the a/d, reinforcement ratio, member height, and concrete strength.
The results show that an arch mechanism was able to form in FRPreinforced concrete beams having a/d less than 2.1.
Keywords: cracks; deep beams; failure mechanisms; fiber-reinforced
polymer reinforcement; reinforced concrete; shear span-depth ratio (a/d);
shear strength; size effect.

INTRODUCTION
Steel-reinforced concrete structures have been built for
over a century and numerous research programs have been
conducted to understand the behavior of such structures.

Many steel-reinforced concrete structures, such as bridges,
parking garages, and marine structures, are exposed to
aggressive environments which, over time, can cause extensive damage and the need for costly rehabilitation due to
corrosion of the steel reinforcement. Fiber-reinforced polymers (FRPs), which are a composite material consisting
of fibers embedded in a resin, are an alternative type of
reinforcement that can be used instead of steel.1,2 Not only
is FRP noncorrosive but it is also nonmagnetic, making it
useful in many applications where corrosion and electromagnetic interference are problematic.1
The shear behavior of steel-reinforced concrete members
has been well-documented and many design procedures
have been developed.3 In general, concrete members can be
classified in two categories based on shear behavior: slender
and deep. Of particular interest in this paper is the shear
behavior of deep members containing no distributed web
reinforcement. It is generally accepted that deep members
have a shear span-depth ratio (a/d) less than 2.5.3-6 Five shear
force-transfer mechanisms have been identified in cracked
concrete members without transverse reinforcement.3 These
consist of shear stresses in the uncracked flexural compression region, aggregate interlock and residual tensile stresses
at diagonal cracks, dowel action of longitudinal reinforcement, and arch action through formation of direct compression struts. The shear capacity of reinforced concrete slender
members is governed by the breakdown of beam action with
failure once equilibrium of forces can no longer be satisfied at the inclined crack locations. In deep beams, a major
ACI Structural Journal/July-August 2013

reorientation of the internal forces can occur after cracking
such that forces tend to flow directly from the loading
points to the supports. This arch action involves the formation of compression struts to directly transmit the load to
the supports, while the longitudinal reinforcement acts as
a tie holding the base of the arch together. Unlike slender
members with no web reinforcement, deep members can

have substantial reserve capacity after diagonal cracking.
Considerable research has been conducted on the shear
behavior of slender (a/d > 2.5) FRP-reinforced concrete
members. The overall shear behavior of slender FRPreinforced members is similar to that of steel-reinforced
slender members, but the shear capacity of members
reinforced with glass FRP (GFRP) is lower than steelreinforced members having the same reinforcement ratio
due to the lower reinforcement stiffness of GFRP.7-9 While
numerous shear models have been proposed and incorporated into codes and design guidelines for concrete members
internally reinforced with FRP,1,2,10-12 no distinction is made
between analysis provisions for slender and deep members.
In contrast, design guidelines for steel-reinforced concrete
construction10,13-15 recognize that different analytical models
are required to evaluate the shear capacity of slender and
deep members. While the steel-reinforced concrete design
codes10,13-15 allow the use of strut-and-tie models to analyze
deep members, the FRP-reinforced design codes do not
allow the use of strut-and-tie modeling. For example,
CSA S806-0212 explicitly states that “analysis by strut and
tie models is not permitted.” The use of sectional models
in the analysis of FRP-reinforced concrete deep members
may result in uneconomical designs in instances where large
members are used,16 as is the case when steel-reinforced
deep beams are designed using sectional models.
Limited prior research on FRP-reinforced deep beams
containing no distributed web reinforcement has indicated
that arch action forms after inclined cracking in specimens
having an a/d less than 2.3.17,18 However, the 25 FRPreinforced specimens tested in these prior test programs
had small cross-sectional dimensions when compared to
the common sizes of beams encountered in industry practice. The effective depths d were less than 350 mm (13.8 in.)
with 11 specimens having d = 150 mm (5.9 in.). In addition,

only limited values for the a/d and longitudinal reinforcement
ratios ρ were used in the prior research. This paper presents
a large-scale experimental program that was undertaken to
ACI Structural Journal, V. 110, No. 4, July-August 2013.
MS No. S-2011-226.R2 received May 2, 2012, and reviewed under Institute
publication policies. Copyright © 2013, American Concrete Institute. All rights
reserved, including 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 May-June 2014 ACI Structural Journal if the discussion is received
by January 1, 2014.

585


ACI member Matthias F. Andermatt is a Bridge Engineer at AECOM, Edmonton,
AB, Canada. He received his BSc in civil engineering and his MSc in structural engineering from the University of Alberta, Edmonton, AB, Canada. His research interests
include large-scale testing of structural components and shear transfer in concrete.
ACI member Adam S. Lubell is a Project Engineer at Read Jones Christoffersen Ltd.,
Vancouver, BC, Canada, and an Associate Adjunct Professor of civil engineering at the
University of Alberta. He received his PhD from the University of Toronto, Toronto,
ON, Canada. He is Secretary of ACI Subcommittee 445A, Shear and Torsion-Strut and
Tie; and a member of ACI Committees 440, Fiber-Reinforced Polymer Reinforcement;
544, Fiber-Reinforced Concrete; and Joint ACI-ASCE Committee 445, Shear and
Torsion. His research interests include the design and rehabilitation of reinforced and
prestressed concrete structures, and the development of structural detailing guidelines
to allow the use of high-performance materials.

further study the behavior of concrete deep beams internally
reinforced with GFRP. The new test results presented in this
paper are used with the results from the prior research17,18 to

develop and validate a modeling technique for FRPreinforced deep beams in a companion paper.16
RESEARCH SIGNIFICANCE
The efficient use of FRP reinforcement in deep members
has been hindered due to a lack of knowledge on the behavior
of such members. Due in part to a lack of experimental data,
there are currently no separate design guidelines for slender
and deep FRP-reinforced concrete beams. Prior research has
mainly focused on the shear behavior of slender members
longitudinally reinforced with FRP and only testing at small
scales has been conducted on FRP-reinforced deep members.
This paper presents the results of an experimental investigation
of 12 large-scale concrete deep beams internally reinforced
with GFRP. The influences on shear capacity from the crosssection geometry, concrete strength, a/d, and reinforcement
ratio are discussed. The results are used in a companion
paper16 to validate modeling techniques for deep members.
EXPERIMENTAL INVESTIGATION
Twelve concrete deep beams internally reinforced with
GFRP were constructed and tested to failure in the I. F.
Morrison Structural Engineering Laboratory at the University of Alberta.19 The primary test variables included the
a/d, the reinforcement ratio ρ, the effective depth d, and the
concrete strength fc′. The objective of the test program was to

assess the design parameters that influence the strength and
behavior of FRP-reinforced concrete deep beams containing
no web reinforcement.
Specimen configurations
The as-built configuration of the specimens is given in
Table 1 and Fig. 1. The specimens were designed using
a preliminary version of the CSA-1 strut-and-tie model
described in the companion paper16 and elsewhere.19 The a/d

of the specimens were selected to cover a wide range of the
deep beam category at the ultimate and equivalent serviceability limit states and to fill gaps in the limited experimental data available on FRP-reinforced concrete deep
beams. Specimens were grouped into three series having
nominal heights h of 300, 600, and 1000 mm (11.8, 23.6,
and 39.4 in.). To determine the influence of h on the shear
capacity, a/d, ρ, and fc′ were held approximately constant,
while h and the bearing plate length Lb were varied. The
parameter Lb was scaled proportional to h. In all cases, the
bearing plate width was the same as the member width bw,
which was approximately 300 mm (11.8 in.) for all specimens. Member width is not considered to have an influence on the shear stress at failure.20,21 To study the effect of
concrete strength on the shear capacity, both normal- and
high-strength concretes were used.
The reinforcement in all specimens consisted of GFRP,
as this is the most commonly used FRP in the industry.
Furthermore, GFRP has a lower modulus of elasticity Efrp
than carbon FRP, leading to higher strain values for a given
reinforcement ratio and overall member configuration. High
reinforcement strains at the time of failure were desired to
better validate the analytical capacity models presented in
the companion paper16 for strain values significantly greater
than those generally used in the design of steel-reinforced
concrete deep beams. The behavior of deep beams is not
well-understood for the case of where high reinforcement
strains would occur. The reinforcement ratios were selected
such that the stress level in the FRP would not exceed
approximately 25% of the specified tensile strength fFRPu of
the GFRP bar under the equivalent serviceability limit state
loads.10 Note that ACI 440.1R-061 limits the service stress
level in the GFRP to 0.20fFRPu. The specimens with h =


Table 1—As-built specimen properties
Specimen

a/d

ρ, %

Height h,
mm

Effective depth d,
mm

Shear span a,
mm

Width bw,
mm

Overhang length, Plate length Lb,
mm*
mm
Age, days fc′, MPa

A1N

1.07

1.49


306

257

276

310

874

100

171

40.2

A2N

1.44

1.47

310

261

376

310


874

100

36

45.4

A3N

2.02

1.47

310

261

527

310

874

100

173

41.3


A4H

2.02

1.47

310

261

527

310

623

100

160

64.6

B1N

1.08

1.70

608


503

545

300

605

200

129

40.5

B2N

1.48

1.71

606

501

743

300

605


200

108

39.9

B3N

2.07

1.71

607

502

1040

300

605

200

105

41.2

B4N


1.48

2.13

606

496

736

300

814

200

111

40.7

B5H

1.48

2.12

607

497


736

300

614

200

96

66.4

B6H

2.06

1.70

610

505

1040

300

460

200


106

68.5

C1N

1.10

1.58

1003

889

974

301

826

330

104

51.6

C2N

1.49


1.56

1005

891

1329

304

821

330

97

50.7

*

Overhang length is measured from center of bearing plate to end of specimen/GFRP.
Notes: 1 mm = 0.0394 in.; 1 MPa = 145 psi.

586

ACI Structural Journal/July-August 2013


300 mm (11.8 in.) had one layer of reinforcement, while specimens with h = 600 and 1000 mm (23.6 and 39.4 in.) had three
layers of reinforcement. Overhangs were provided beyond the

supports in all specimens to allow for anchorage of the FRP
reinforcement.10 Side and bottom clear cover was 38 mm
(1.5 in.). Vertical bar clear spacing between layers was 38 mm
(1.5 in.). Refer to Fig. 1 for the reinforcement configuration.
Material properties
Commercially available GFRP bars in U.S. Customary
sizes of No. 6, No. 7, and No. 8 (19, 22, and 25 mm) were
used as the longitudinal reinforcement. The sand-coated
GFRP bars contained surface deformations produced from
wrapping groups of fibers diagonally in opposite directions to form a diamond-shaped pattern on top of the main
longitudinal core, as shown in Fig. 2. Tension coupon tests
conforming to CSA S806-0212 were performed on five
samples of each bar size to determine the failure stress fFRPu
and modulus of elasticity EFRP. The GFRP exhibited linear
elastic stress-strain responses to brittle failures. The crosssectional area of the different nominal bar sizes was determined by using volumetric measurements.19,22 The measured
properties of the GFRP bars are provided in Table 2.
Two types of concretes were obtained from a local
ready mix supplier: a normal-strength mixture and a highstrength mixture having nominal specified 28-day strengths
of 35 and 70 MPa (5075 and 10,150 psi), respectively. Both
mixtures had a maximum aggregate size of 14 mm (0.55 in.).
Four batches of concrete were required with three specimens cast from each batch. All specimens were moist-cured
for 7 days, after which they were removed from the formwork and stored in the laboratory until testing. Cylinders
with dimensions of 100 x 200 mm (3.9 x 7.9 in.) were cast
and cured under the same conditions as the specimens. The
age of each specimen and the average concrete strength from
three cylinders on the day of testing are given in Table 1.
Test setup and testing procedure
Specimens were tested in a 6600 kN (1484 kip) capacity
MTS testing frame with the test setup as shown in Fig. 1.
A stiff distributing beam was used to apply two equal point

loads on the top surface of the specimen. Each specimen was
supported on roller assemblies and knife edges that allowed
longitudinal motion and in-plane rotation. Both loading
points also contained rollers and knife edges. The specimens
were tested with all four roller assemblies free to rotate to
ensure no global restraint forces were introduced into the
test setup. One roller assembly was locked prior to failure
to provide stability and prevent dangerous movement at
failure. Bearing plates were 100 x 310 x 38 mm (3.9 x 12.2 x
1.5 in.) and 200 x 300 x 50 mm (7.9 x 11.8 x 2.0 in.) for the
h = 300 and 600 mm (11.8 and 23.6 in.) specimens, respectively. For specimens with h = 1000 mm (39.4 in.), top and
bottom plates were 330 x 330 x 38 mm (13 x 13 x 1.5 in.)
and 330 x 330 x 75 mm (13 x 13 x 3 in.), respectively. A
thin layer of plaster was used between the specimen and the
bearing plates to ensure uniform contact.
Five linear variable differential transformers (LVDTs)
were mounted along the bottom of the specimens to measure
vertical deflection at the supports, quarter-spans, and
midspan. All deflection data presented in this paper have
been corrected for the measured support settlements. Electrical resistance strain gauges were applied to the FRP bars to
measure the strain during the test. Between 12 and 30 strain
ACI Structural Journal/July-August 2013

Fig. 1—Test setup and specimen geometry.

Fig. 2—GFRP bars, No. 8 at top and two No. 7.
Table 2—Properties of GFRP bars
Reinforcing bar size
No. 6
(19 mm)


No. 7
(22 mm)

No. 8
(25 mm)

19 (0.75)

22 (0.87)

25 (0.98)

Cross-sectional area, mm (in. )

322 (0.50)

396 (0.61)

528 (0.82)

Failure stress fFRPu, MPa (ksi)

765 (111)

709 (103)

938 (136)

37.9 (5496)


41.1
(5960)

42.3 (6134)

72.0

64.8

64.1

Reinforcement property
Nominal diameter, mm (in.)*
2

Modulus of elasticity EFRP,
GPa (ksi)
Glass content, % vol.*

2

*

Provided by manufacturer.

gauges were applied to the bars at the center of the supports
and loading points, midspan, and at a uniform spacing in the
shear spans. The majority of the strain gauges were applied
on the bottom bars except at the location of the supports,

loading points, and midspan, where strain gauges were
applied on all layers. Additional information on instrumentation of the specimens is documented elsewhere.19
587


Table 3—Experimental results
Maximum midheight
diagonal crack width
(last load stage)

Ultimate load

Specimen

Inclined
cracking
load Pc, kN

A1N

Equivalent service load

Pc/Pmax

Failure
type*

Pmax,
kN


Dmax,
mm†

Average
midspan
strain, mε

Width,
mm

% of Pmax

Ps, kN

Ds,
mm

fFRPs/fFRPu, %

Crack width,
mm

312

0.38

FC

814


12.4

17,400

1.5

94

407

4.0

37

0.9

A2N

187

0.40

SC

471

11.3

8900


1.5

82

235

3.7

22

0.5

A3N

143

0.59

SC

243

10.9

6000

1.5

92


121

2.6

14

0.33

A4H

163

0.85

DT

192

9.5

4800

2.5

96

96

0.9


5

0.3

B1N

387

0.30

FC

1273

9.1

8400

1.25

76

637

3.5

25

0.9


B2N

287

0.36

SC

799

13.1

6900

3.0

92

400

4.6

16

0.8

B3N

237


0.55

SC

431

15.3

5200

2.75

84

215

2.7

14

0.33

B4N

412

0.50

SC


830

11.5

6200

4.0

98

415

3.4

21

0.5

B5H

387

0.36

S

1062

14.2


6900

4.0

91

531

5.1

21

1.25

B6H

212

0.56

DT

376

12.9

4500

7.0


96

188

1.3

4

0.3

C1N

613

0.27

SC

2269

15.9

9600

2.5

80

1135


6.1

22

1.5

C2N

413

0.31

S

1324

18.3

6800

4.5

88

662

6.7

15


1.5

*

DT is diagonal concrete tension failure; FC is flexural compression failure; SC is shear compression failure; S is compression strut failure.
†
Midspan deflection occurring at Pmax.
Notes: 1 mm = 0.0394 in.; 1 MPa = 145 psi.

The specimens were tested under displacement control
with a displacement rate of 0.1 to 0.25 mm/min (0.004 to
0.01 in./min) of machine stroke depending on the stiffness of
the specimen. Each specimen was loaded in five to 10 increments. After each increment, the deflection was held while
the crack patterns were photographed and the crack widths
were measured using a crack comparator gauge. Data
from the instrumentation were recorded continuously
until specimen failure. The duration of the tests ranged
between 3 and 6 hours depending on the specimen configuration and the number of load increments.
EXPERIMENTAL RESULTS AND DISCUSSION
All 12 specimens were loaded to failure in displacement
control, which allowed for the observation of both the preand post-peak behavior. The majority of the specimens failed
suddenly with a significant drop in load-carrying capacity. A
summary of the key experimental results for the specimens
is given in Table 3. The applied load P is the applied load
measured by the internal load cell in the testing frame plus
the self-weight of the loading apparatus. The self-weight of
the specimen is not included in P. The peak shear capacity is
taken as Pmax/2. For each specimen, the midspan deflection
Dmax corresponding to Pmax is given in Table 3.
The equivalent service load Ps was taken as 50% of the

peak load.19 The equivalent service load was calculated in
this study by assuming that the nominal resistance of the
specimen was equal to the peak load, a dead to live load ratio
of 3:1, and load and resistance factors as per current Canadian
design codes.15,19 Note that the actual service to peak load
ratio may vary in practice depending on the design code and
dead to live load ratio. To prevent creep rupture of the GFRP
reinforcement, design codes impose a limit on the allowable
sustained stress in the FRP.1,2,10,12 ACI 440.1R-061 requires
that the stress in the GFRP at the sustained service load be
kept below 0.20fFRPu, while CSA S6-0610 has a higher limit
of 0.25fFRPu at the serviceability limit state. The stress level
588

in the GFRP at the equivalent service load was between
0.04fFRPu and 0.37fFRPu, with only Specimen A1N exceeding
0.25fFRPu.
Failure mechanisms
Among the specimens, four types of failure mechanisms
were observed, as given in Table 3. Shear compression was
the most common failure mode, occurring in six specimens.
Shear compression failure was characterized by the crushing
of the concrete in the flexural compression zone at the tip of
the main diagonal crack. The main diagonal crack extended
from the inside edge of the support plate toward the inside
edge of the loading plate into the flexural compression zone.
At failure, the crack penetrated through the top of the specimen and an abrupt drop in load-carrying capacity occurred.
A typical shear compression failure is shown in Fig. 3(a).
Flexural compression failures occurred in Specimens A1N
and B1N—both having an a/d of 1.1. This type of failure

was characterized by the crushing of the concrete in the
flexural compression zone between the two loading plates,
as shown in Fig. 3(b). The main diagonal cracks in each
shear span propagated from the inside edge of the reaction
plates toward the inside edge of the loading plates. Near the
loading plates, the cracks became horizontal and eventually
joined. The region above the horizontal crack between the
loading plates then slowly deteriorated through crushing
of the concrete. At failure, there was also movement along
the main diagonal cracks; however, this sliding action along
the main diagonal cracks occurred after deterioration of the
compression zone.
Failure of the diagonal compression strut region
between the loading plates and the supports occurred in
Specimens B5H and C2N, as shown in Fig. 3(c). Failure of
the compression struts occurred in a brittle and noisy manner.
A drop of more than 60% in the load-carrying capacity of the
specimens occurred during this action.
ACI Structural Journal/July-August 2013


Fig. 3—Failure mechanisms: (a) shear compression failure in Specimen A2N; (b) flexural compression failure in Specimen A1N;
(c) failure of compression strut in Specimen B5H; and (d) diagonal concrete tension failure of Specimen B6H where vertical
crack formed from top surface.
A concrete diagonal tension failure or splitting failure
occurred in Specimens A4H and B6H—both of which had
fc′ ≈ 66 MPa (9570 psi). A major S-shaped diagonal crack
formed in each shear span from the inside edge of the reaction plate toward the inside edge of the loading plate. The
diagonal crack extended above the diagonal line between the
centerlines of the loading and support plates. As the crack

width increased, a vertical crack formed from the top surface
of the concrete in the shear span and intersected the diagonal crack, leading to an immediate drop in load-carrying
capacity. The concrete above the diagonal crack was forced
upward after the vertical crack formed, as shown in Fig. 3(d).
Load-deflection behavior
The relationship between the applied load P and the
midspan deflection ∆ is shown in Fig. 4, where the specimens
are grouped according to h. The failure of Specimen A1N
was gradual, with crushing occurring in the main flexural
compression zone. A2N and A3N exhibited a sudden drop
in load-carrying capacity after Pmax was attained, although
the load-carrying capacity of Specimen A2N remained
largely intact as deflection increased by approximately 1 mm
(0.039 in.). The load-carrying capacity of A4H showed little
ACI Structural Journal/July-August 2013

change at the peak load as the midspan deflection and inclined
crack widths grew larger. A gradual decrease in load-carrying
capacity occurred after the peak load was reached.
Specimen B1N reached a load of 1273 kN (286 kip), at
which point there was a 3% loss of load. The specimen
continued to gain load, but the behavior was characterized by
a reduced stiffness as crushing of the flexural compression
region initiated. At 1286 kN (289 kip), a sudden 8% drop in
load was recorded. As the flexural region continued to crush,
the load-carrying ability was slowly regained and reached
a new maximum of 1324 kN (298 kip). Extreme deterioration of the flexural compression zone was observed. For
subsequent discussions, the failure load of B1N was taken
as 1273 kN (286 kip), as the drop in load-carrying capacity
from this local peak and regain in strength is considered to be

an unreliable mechanism. Nevertheless, B1N demonstrated
that a large amount of member ductility can be provided by
the concrete response, even though the reinforcement has a
linear-elastic response. B2N and B3N experienced brittle
failures, while B4N experienced a more ductile failure with
a gradual decrease in load-carrying capacity after reaching
the peak load. The failure of B5H was extremely brittle,
with significant damage along the main inclined crack. The
589


Fig. 4—Experimental load-deflection behavior of specimens: (a) h = 300 mm; (b) h = 600 mm;
and (c) h = 1000 mm. (Note: 1 mm = 0.0394 in.; 1 MPa = 145 psi.)

Fig. 5—Crack diagrams after failure of specimens with h =
300 mm (11.8 in.). (Note: 1 MPa = 145 psi.)

Fig. 4(b), it is also apparent that the post-cracking stiffness
of the specimens is dependent on the reinforcement ratio.
Specimen B4N, which had a reinforcement ratio 24% larger
than B2N while all other variables remained constant, had a
stiffer loading response and a capacity that was 4% greater
than B2N. The post-cracking stiffness was not influenced by
h, while a/d and ρ were kept approximately constant. The
post-cracking stiffness of A1N, B1N, and C1N was similar,
as was the post-cracking stiffness of A2N, B2N, and C2N,
where the only difference between the specimens was h.
B4N and B5H, which were identical except for the
concrete strength, had a similar load-deflection response
up to approximately 90% of the B4N failure load. Similarly, B3N and B6H, which were also identical except for

the concrete strength, exhibited the same load-deflection
response. A similar result was observed between A3N and
A4H. Therefore, the concrete strength had no discernible
effect on the post-cracking stiffness of the specimens.

load-carrying capacity immediately dropped by approximately 80%. B6H also failed suddenly and the load-carrying
capacity dropped by approximately 60%.
Both specimens having h = 1000 mm (39.4 in.) failed
abruptly with a loss in load-carrying capacity of 30% and
60% in Specimens C1N and C2N, respectively. The postcracking stiffness of both specimens was approximately
linear to failure, indicating a shear type of failure rather than
a more gradual flexural compression failure.
All specimens exhibited a bilinear load-deflection
response. As seen in Fig. 4, the initial flexural stiffness
was the same for the specimens having the same h. After
cracks fully developed, the load-deflection response was
linear to failure for most specimens. As the a/d increased,
the post-cracking stiffness of the specimens decreased. From

Crack patterns and widths
The crack diagrams showing the condition of the specimens after failure are given in Fig. 5 through 7 for specimens
having h = 300, 600, and 1000 mm (11.8, 23.6, and 39.4 in.),
respectively. Crushing and spalling of concrete is indicated
by shading. The crack patterns in all of the specimens indicated the formation of an arch mechanism. Inclined cracks
developed, joining the supports and loading points, which
disrupted the internal force flow from beam action to arch
action, similar to documented behavior in steel-reinforced
deep beams.6
For all specimens, the first cracks appeared at the bottom
near midspan as flexural cracks. The flexural cracking load

for each specimen was determined from where the bilinear
load-deflection curve began to deviate from the initial linear

590

ACI Structural Journal/July-August 2013


Fig. 7—Crack diagrams after failure of specimens with h =
1000 mm (39.4 in.). (Note: 1 MPa = 145 psi.)

Fig. 6—Crack diagrams after failure of specimens with h =
600 mm (23.6 in.). (Note: 1 MPa = 145 psi.)
segment. Flexural cracking occurred between 14 and 35%
of Pmax. The flexural cracks in the constant-moment region
rapidly propagated to approximately 80% of h in all specimens. Subsequently, additional flexural cracks formed
progressively closer to the supports in the shear spans. These
cracks almost immediately became inclined (diagonal)
cracks and grew toward the loading plates. The inclined
cracking load Pc reported in Table 3 corresponds to the
load at which the first inclined crack was visually observed
during pauses in loading. Most of the specimens had diagonal cracks at the equivalent service-load condition.
The Pc/Pmax ratios reported in Table 3 serve as a measure
of the reserve load capacity after the formation of the first
inclined crack. Specimens with larger a/d had a smaller
reserve capacity after diagonal cracking when compared to
specimens with smaller a/d. Increasing h caused a decrease in
the Pc/Pmax ratio. The inclined cracking shear stress, normalized by bw d fc′, decreased as either the a/d or h increased,
while fc′ and ρ were approximately constant, as shown in
Fig. 8. In all instances, the low Pc/Pmax ratio or high reserve

capacity was indicative of the formation of arch action after
inclined cracking occurred.
The maximum crack widths for the specimens at the
equivalent service load varied between 0.3 and 1.5 mm
(0.012 and 0.059 in.). The crack widths given in Table 3 are
the maximum crack widths measured at the load interval that
was closest to the equivalent service load. Only half of the
specimens met the ACI 440.1R-061 crack width criterion for
structures not subjected to aggressive environments, where
the maximum allowable crack width is 0.7 mm (0.028 in.).
ACI Structural Journal/July-August 2013

Fig. 8—Influence of a/d and h on normalized inclined
cracking shear stress. (Note: 1 MPa = 145 psi.)
Specimens that satisfied the ACI 440.1R-061 crack width
requirement typically had larger a/d, larger ρ, or smaller h.
Prior to reaching Pmax, all specimens had at least one main
inclined crack in both shear spans. The main inclined crack
would extend from the inside edge of the reaction plate
toward the loading plate. In most of the specimens, the crack
trajectory was toward the inside edge of the loading plate
and the crack would become increasingly horizontal near
the flexural compression zone. Smaller secondary inclined
cracks were observed parallel to the main inclined crack
close to the support region in the majority of the specimens. These cracks would often initiate near the centroid
of the reinforcement above the support plate and expand
diagonally away in both the up and down directions. In
most instances, the secondary cracks would disappear near
the midheight of the specimen and the main diagonal crack
would be wider at midheight than near the centroid of the

reinforcement. In Specimens A1N, A2N, B1N, and C1N, a
second diagonal crack formed parallel to the main diagonal
crack and extended from the support to the loading point.
The formation of the multiple inclined cracks indicated that
reorientation of internal forces was occurring.
Crack widths measured at the last loading stage prior
to Pmax (Table 3) ranged from 1.25 to 7.0 mm (0.049 to
0.28 in.) and were even wider at failure. The cracks were
large enough in some cases to easily see through the full
specimen width, indicating the complete breakdown of the
aggregate interlock shear-transfer mechanism. The predominant force-transfer mechanism consisted of arch action.
The main inclined crack in the right shear span (Fig. 9)
of A4H initiated as a flexural crack approximately 200 mm
(8 in.) to the inside of the right support. The flexural crack
591


Fig. 9—Right shear span of Specimen A4H at conclusion
of test.
extended above the diagonal line between the centerlines
of the loading and support plate. The crack then grew more
horizontal and extended toward the loading plate. Near
the bottom of this crack, at approximately one-third of the
specimen height, a new crack formed that extended toward
the inside edge of the reaction plate, which completed the
formation of the critical crack. Once the crack had formed,
very little additional load could be carried before failure.
Large deflections resulted and the inclined crack width
became increasingly larger. The specimen continued to
hold load past the peak load with the maximum crack

width growing to approximately 10 mm (0.39 in.). Splitting
cracks formed along the reinforcement after the load reached
Pmax (Fig. 9). The splitting cracks resulted from the visible
downward movement of the center section of the specimen
(dowel action) and the clockwise rotation of the right end,
which produced a prying action as the diagonal crack width
increased (refer to Fig. 9). The large crack opening indicated
that arch action formed as aggregate interlock was no longer
possible. However, the arch action was insufficient to support
additional load due to the curvilinear nature of the crack,
which prevented the efficient transfer of load to the support.
Specimen B6H had a cracking behavior that was similar
to Specimen A4H. The main inclined crack in the left shear
span initiated as a flexural crack at the bottom of the specimen near the middle of the shear span that rapidly extended
above the diagonal line from the centerline of the support
and loading plates. Subsequently, an inclined crack extended
from the existing inclined crack at a dimension of approximately h/3 from the soffit toward the inside edge of the reaction plate forming the critical crack. The aggregate interlock
ceased to exist once the crack grew in width and the load had
to be transmitted mainly by arch action. Because the crack
was curved and extended above the diagonal line between
the support and the loading point, the load had to be transferred in compression around the curve, which produced an
outward thrust. The lack of top reinforcement and distributed web reinforcement limited the load-carrying ability of
the curved strut and a tensile splitting crack formed at the top
of the shear span, as shown in Fig. 3(d) and 6, which resulted
in an immediate drop in load-carrying capacity.
Influence of fc′
The load-carrying capacity of Specimen B5H was higher
than that of comparable Specimen B4N, which differed
only by fc′. B5H had a concrete strength 63% greater than
B4N and achieved a 28% larger peak load. While a higher

concrete strength is expected to enable a specimen to carry
additional load when compared to an identical specimen
592

Fig. 10—Typical reinforcement strain distribution along
bottom layer of reinforcement as load increased. (Note:
1 mm = 0.0394 in.; 1 kN = 0.2248 kip; 1 MPa = 145 psi.)
with lower-strength concrete, this was not the case for the
other companion specimens differing only by fc′. A4H had a
concrete strength 56% greater than A3N, but the peak load
was only 79% of the A3N peak load. Similarly, B6H had a
concrete strength 66% greater than B3N, but the peak load
was only 87% of Specimen B3N. These discrepancies can be
explained by the nature of the crack patterns, which prevented
the specimens from achieving an efficient arch mechanism,
as discussed previously. Additional research is required to
determine if the reduced capacity of A4H and B6H is related
to the low stiffness of the reinforcement combined with the
brittle nature of the high-strength concrete and at what a/d
the transition from deep beam behavior to sectional shear
behavior occurs.
Reinforcement strains
The strain distribution in the bottom reinforcement layer of
Specimen B1N as the load increased is shown in Fig. 10 and
is typical of all specimens.19 For all specimens, there was
minimal change in the GFRP reinforcement strains until the
formation of the first flexural crack. The strain readings of the
bottom bar increased rapidly in the vicinity of the first crack,
usually in the constant-moment region. As additional cracks
formed closer to the supports, the measured strains in the

GFRP reinforcement also increased closer to the supports. In
the uncracked regions, strain readings showed minimal strain
changes in the GFRP. As loading progressed, the reinforcement strains became similar over the entire region between
the supports. Localized strain increases were noted where the
strain gauge locations coincided with cracks. In the majority
of the specimens, the strain in the GFRP over the center of
the support was significantly lower than the strain reading at
midspan. With the exception of A4H, no strain increase was
registered in the GFRP past the supports with the first strain
gauge typically located 100 to 200 mm (3.9 to 7.9 in.) past
the edge of the support. In A4H, the reinforcement strain
at the right support location was approximately the same
as at the midspan once Pmax was reached. The increase in
ACI Structural Journal/July-August 2013


reinforcement strain in the right end region corresponds to
the visual observation of splitting cracks at the level of the
reinforcement. In specimens containing multiple reinforcement layers, a strain gradient between the lower, middle, and
upper reinforcement layers was present. The midspan strains
in the middle bars and upper bars were, on average, 23 and
28% less than the strain in the bottom bars at midspan.
The reinforcement strain distribution is an indicator of
whether and to what extent a tied-arch mechanism formed
in the specimens. In a fully developed tied-arch mechanism,
the strain level in the reinforcement is expected to be approximately uniform from support to support. In all specimens,
the strain distribution between the supports at peak load was
approximately constant, indicating that a tied-arch mechanism had developed. Based on the strain gradient noted
previously, the bottom layer of GFRP anchored a greater
amount of force than the upper layers. Generally, in simplified analysis of a tied arch such as the ACI 318-0813 strutand-tie modeling provisions, it is assumed that all the layers

of reinforcement carry the same tensile stress. However, this
is only true when all reinforcement has yielded (that is, steel
reinforcement), which is not the case with the fully elastic
FRP reinforcement.
INFLUENCES ON SHEAR CAPACITY
Shear capacity trends are discussed in terms of the a/d, h,
ρ, and fc′, which were the main variables in the test program.
To facilitate these comparisons, the peak shear stress was
normalized by fc′, as shown in Eq. (1)
ν=


Pmax
(1)
2bw dfc′

a /d and reinforcement ratio
Figure 11(a) shows that as the a/d decreased, there was a
significant increase in the normalized shear capacity regardless of h, ρ, or fc′. This is similar to the documented trend
for steel-reinforced concrete deep beams.5,6 Increasing the
reinforcement ratio by 24% resulted in a 3% increase in the
normalized shear capacity of B4N compared to B2N.
Concrete strength
Increasing the concrete strength by 63% while maintaining
ρ = 2.13% resulted in a 22% decrease in the normalized shear
capacity (top curve in Fig. 11(b)). As the concrete strength
of the specimens increased, the normalized shear capacity
decreased regardless of the a/d, ρ, or h, as shown in Fig. 11(b).
For specimens with a/d = 2.0 and 2.1, increasing fc′ by approximately 64% resulted in a 50% decrease in the normalized
shear capacity. The decrease was due to the cracking mechanism that occurred in the specimen with the higher fc′.

Overall height
Specimens having different heights were tested to determine if there was a size effect on the shear-carrying capacity
of GFRP-reinforced deep beams. The dimensions of the
loading and support plates in the direction of the span Lb
were scaled in proportion to h to eliminate the bearing plate
as an independent variable.23 Figure 11(c) shows the influence of h on the normalized shear stress at failure ν, where
the specimens have been grouped by similar a/d and ρ. For
the three a/d—1.1, 1.5, and 2.1—ν decreased as the specimen
height increased, except for Specimen A2N. The effect was
ACI Structural Journal/July-August 2013

Fig. 11—Influence on normalized shear capacity from: (a)
a/d; (b) concrete strength; and (c) member height. (Note:
1 mm = 0.0394 in.; 1 MPa = 145 psi.)

most pronounced for the specimens having an a/d of 1.1. In
addition, the specimen height had minimal influence on the
normalized shear capacity for a/d = 1.5 and 2.1 when h was
less than 600 mm (23.6 in.). However, this observed trend
could be due in part to the small differences in ρ between
the 300 and 600 mm (11.8 and 23.6 in.) deep beams. The
reinforcement ratio of the h = 300, 600, and 1000 mm (11.8,
23.6, and 39.4 in.) specimens was 1.5%, 1.7%, and 1.6%,
respectively. An increase in ρ is known to produce a higher
shear capacity in deep beams when other design parameters
are kept constant.5,17
Figure 12 shows the relationship between the a/d, the
midspan strain in the bottom layer of reinforcement at Pmax,
593



ACKNOWLEDGMENTS

Funding for this project was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), Alberta Ingenuity, and
the University of Alberta. The authors also acknowledge the donation of
materials from BP Composites and Lehigh Inland Concrete.

REFERENCES

Fig. 12—Midspan strain in bottom layer of reinforcement at
peak load. (Note: 1 MPa = 145 psi.)
and the normalized shear capacity for specimens having
fc′ ≈ 40 MPa (5800 psi) and ρ ≈ 1.7%. Lower a/d values
resulted in higher midspan strain in the reinforcement and
higher normalized shear capacities when compared to larger
a/d values.
CONCLUSIONS
The following conclusions are drawn from the laboratory
testing of 12 GFRP-reinforced concrete deep beam specimens containing no distributed web reinforcement:
1. With the exception of two specimens, failure of the
specimens was brittle. The majority of the specimens failed
by shear compression after the formation of a major diagonal
shear crack extending from the inside edge of the support
plate toward the loading plate.
2. The failure mode was observed to be ductile in
Specimen B1N. After initial crushing of the flexural region,
the specimen continued to resist increasingly more load
while undergoing substantial deformation, demonstrating
the overall member ductility that can be attained from a
member reinforced with a linear elastic material.

3. An arch mechanism formed in all specimens. This
was confirmed by the crack orientations, crack widths, and
measured strains in the longitudinal reinforcement. Significant reserve capacity was available after the formation of
the main diagonal cracks, indicating internal redistribution
of forces and the formation of an arch mechanism. Prior to
failure, the measured crack widths were typically between
1.25 and 7.0 mm (0.05 and 0.28 in.).
4. The reserve capacity after inclined cracking decreased
as the a/d increased, indicating that the arch mechanism
became less efficient at higher a/d.
5. The post-cracking stiffness of the FRP-reinforced
deep beam specimens increased as the a/d decreased or
ρ increased. The specimen height and fc′ had a negligible
effect on the post-cracking stiffness of the FRP-reinforced
concrete specimens.
6. The normalized shear strength of the specimens
increased as the a/d decreased and ρ increased, while all
other variables were held constant.
7. A size effect in shear capacity was observed for specimens having a/d = 1.1, where increased h resulted in reduced
normalized shear stress at the peak load. Specimens having
a/d = 1.5 and 2.1 had no significant size effect in shear for h
less than 600 mm (23.6 in.). However, a detailed relationship
for size effect could not be established due to some variations in other specimen parameters.
594

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ACI Structural Journal/July-August 2013


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