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 reinforc
Trang 1Title no 110-S47
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.
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
FRP-reinforced 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
exten-sive damage and the need for costly rehabilitation due to
corrosion of the steel reinforcement Fiber-reinforced
poly-mers (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
electro-magnetic 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
compres-sion region, aggregate interlock and residual tensile stresses
at diagonal cracks, dowel action of longitudinal
reinforce-ment, and arch action through formation of direct
compres-sion 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
satis-fied at the inclined crack locations In deep beams, a major
Behavior of Concrete Deep Beams Reinforced with
Internal Fiber-Reinforced Polymer—Experimental Study
by Matthias F Andermatt and Adam S Lubell
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 forma-tion 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 FRP-reinforced members is similar to that of steel-FRP-reinforced slender members, but the shear capacity of members reinforced with glass FRP (GFRP) is lower than steel-reinforced members having the same reinforcement ratio due to the lower reinforcement stiffness of GFRP.7-9 While numerous shear models have been proposed and incorpo-rated 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 FRP-reinforced specimens tested in these prior test programs had small cross-sectional dimensions when compared to the common sizes of beams encountered in industry
prac-tice 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 r were used in the prior research This paper presents
a large-scale experimental program that was undertaken to
Trang 2ACI 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
engi-neering 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
FRP-reinforced 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
cross-section 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
Univer-sity of Alberta.19 The primary test variables included the
a /d, the reinforcement ratio r, the effective depth d, and the
concrete strength f c′ 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 service-ability limit states and to fill gaps in the limited experi-mental 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, r, and f c′ were held approximately constant,
while h and the bearing plate length L b were varied The
parameter L b was scaled proportional to h In all cases, the bearing plate width was the same as the member width b w, which was approximately 300 mm (11.8 in.) for all speci-mens Member width is not considered to have an influ-ence 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 E frp
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 f FRPu 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 0.20f FRPu The specimens with h =
Table 1—As-built specimen properties
Specimen a /d r, % Height h, mm Effective depth d, mm Shear span a, mm Width bmm w, Overhang length, mm * Plate length L b,
mm Age, days f c′, MPa
* Overhang length is measured from center of bearing plate to end of specimen/GFRP
Notes: 1 mm = 0.0394 in.; 1 MPa = 145 psi.
Trang 3300 mm (11.8 in.) had one layer of reinforcement, while
spec-imens 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
direc-tions 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 f FRPu
and modulus of elasticity E FRP The GFRP exhibited linear
elastic stress-strain responses to brittle failures The
cross-sectional area of the different nominal bar sizes was
deter-mined 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
high-strength mixture having nominal specified 28-day high-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
speci-mens cast from each batch All specispeci-mens were moist-cured
for 7 days, after which they were removed from the
form-work 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,
respec-tively 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
Elec-trical resistance strain gauges were applied to the FRP bars to
measure the strain during the test Between 12 and 30 strain
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 instrumen-tation of the specimens is documented elsewhere.19
Fig 1—Test setup and specimen geometry.
Table 2—Properties of GFRP bars
Reinforcement property
Reinforcing bar size
No 6 (19 mm)
No 7 (22 mm)
No 8 (25 mm) Nominal diameter, mm (in.) * 19 (0.75) 22 (0.87) 25 (0.98) Cross-sectional area, mm 2 (in 2 ) 322 (0.50) 396 (0.61) 528 (0.82)
Failure stress f FRPu, MPa (ksi) 765 (111) 709 (103) 938 (136)
Modulus of elasticity E FRP,
* Provided by manufacturer.
Fig 2—GFRP bars, No 8 at top and two No 7
Trang 4The 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
incre-ments 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
configu-ration 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 pre-
and 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 P max/2 For each specimen, the midspan deflection
Dmax corresponding to P max is given in Table 3
The equivalent service load P s 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 0.20f FRPu, while CSA S6-0610 has a higher limit
of 0.25f FRPu at the serviceability limit state The stress level
in the GFRP at the equivalent service load was between
0.04f FRPu and 0.37f FRPu, with only Specimen A1N exceeding
0.25f FRPu
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 spec-imen 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
Table 3—Experimental results
Specimen
Inclined
cracking
load P c, kN P c /P max
Ultimate load
Maximum midheight diagonal crack width (last load stage) Equivalent service load
Failure type * P max,
kN Dmax,
mm †
Average midspan strain, me Width, mm % of P max P s, kN Ds,
mm f FRPs /f FRPu, % Crack width, mm
* 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 P max
Notes: 1 mm = 0.0394 in.; 1 MPa = 145 psi.
Trang 5A concrete diagonal tension failure or splitting failure
occurred in Specimens A4H and B6H—both of which had
f c′ ≈ 66 MPa (9570 psi) A major S-shaped diagonal crack
formed in each shear span from the inside edge of the
reac-tion 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
diag-onal 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 D 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 P max 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
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 deterio-ration 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
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.
Trang 6load-carrying capacity immediately dropped by
approxi-mately 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
post-cracking 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
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 r 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 Simi-larly, 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
Crack patterns and widths
The crack diagrams showing the condition of the speci-mens after failure are given in Fig 5 through 7 for specispeci-mens
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 indi-cated 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
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.)
Trang 7segment Flexural cracking occurred between 14 and 35%
of P max The flexural cracks in the constant-moment region
rapidly propagated to approximately 80% of h in all
speci-mens 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 P c 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
diag-onal cracks at the equivalent service-load condition
The P c /P max 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 P c /P max ratio The inclined cracking shear stress,
normal-ized by b d f w c′, decreased as either the a/d or h increased,
while f c′ and r were approximately constant, as shown in
Fig 8 In all instances, the low P c /P max 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.)
Specimens that satisfied the ACI 440.1R-061 crack width
requirement typically had larger a/d, larger r, or smaller h Prior to reaching P max, 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 speci-mens 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 P max (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 predomi-nant 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
Fig 6—Crack diagrams after failure of specimens with h =
600 mm (23.6 in.) (Note: 1 MPa = 145 psi.)
Fig 7—Crack diagrams after failure of specimens with h =
1000 mm (39.4 in.) (Note: 1 MPa = 145 psi.)
Fig 8—Influence of a/d and h on normalized inclined
cracking shear stress (Note: 1 MPa = 145 psi.)
Trang 8extended 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
P max (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
spec-imen 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
approxi-mately h/3 from the soffit toward the inside edge of the
reac-tion 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
trans-ferred in compression around the curve, which produced an
outward thrust The lack of top reinforcement and
distrib-uted 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 f c′
The load-carrying capacity of Specimen B5H was higher
than that of comparable Specimen B4N, which differed
only by f c′ 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
with lower-strength concrete, this was not the case for the
other companion specimens differing only by f c′ 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 reinforce-ment 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 P max was reached The increase in
Fig 9—Right shear span of Specimen A4H at conclusion
of test.
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.)
Trang 9reinforcement strain in the right end region corresponds to
the visual observation of splitting cracks at the level of the
reinforcement In specimens containing multiple
reinforce-ment 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
approx-imately 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
mecha-nism 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
simpli-fied analysis of a tied arch such as the ACI 318-0813
strut-and-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,
r, and f c′, which were the main variables in the test program
To facilitate these comparisons, the peak shear stress was
normalized by f c′, as shown in Eq (1)
2 w max c
P
b df
ν =
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
regard-less of h, r, or f c′ 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
r = 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, r, or h, as shown in Fig 11(b)
For specimens with a/d = 2.0 and 2.1, increasing f c′ by
approx-imately 64% resulted in a 50% decrease in the normalized
shear capacity The decrease was due to the cracking
mecha-nism that occurred in the specimen with the higher f c′
Overall height
Specimens having different heights were tested to
deter-mine 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 L b
were scaled in proportion to h to eliminate the bearing plate
as an independent variable.23 Figure 11(c) shows the
influ-ence of h on the normalized shear stress at failure ν, where
the specimens have been grouped by similar a/d and r 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
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 r 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 r 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 P max,
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.)
Trang 10and the normalized shear capacity for specimens having
f c ′ ≈ 40 MPa (5800 psi) and r ≈ 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
speci-mens 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
Signifi-cant 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
r increased The specimen height and f c′ 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 r increased, while all
other variables were held constant
7 A size effect in shear capacity was observed for
speci-mens 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
varia-tions in other specimen parameters
ACKNOWLEDGMENTS
Funding for this project was provided by the Natural Sciences and Engi-neering 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.
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Fig 12—Midspan strain in bottom layer of reinforcement at
peak load (Note: 1 MPa = 145 psi.)