ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Title no. 93-S52

Performance of High-Strength Concrete Corbels

by Stephen J. Foster, Rex E. Powell, and Hani S. Selim

In this study, 30 high-strength concrete corbels were tested to friction model used in ACI 318-89 has been calibrated for
destruction. Variables considered in the investigation are shear only relatively low-strength concretes. The experimental
span-to-depth ratio, concrete strength (45 to 105 MPa [6500 to results presented in this paper are compared with two design
15,200 psi), and the provision of secondary reinforcement. The models: 1) the ACI 318-1989 model and 2) the plastic truss
investigation examines corbel behavior in the context of the
model of Rogowsky and MacGregor.5 The plastic truss model
previous parameters and compares the experimental results with
the ACI 318-89 design method and the plastic truss model of was chosen from available truss models because its design is
Rogowsky and MacGregor. Particular attention is given to deter- simple, yet it utilizes rigorous plasticity theory.
mining the concrete efficiency factor for members failing in
compression, and the results are compared with the efficiency RESEARCH SIGNIFICANCE
model proposed by Warwick and Foster. The results of the investiga- While a considerable amount of research has been
tion show that good load predictions can be obtained using the performed on corbels in general, very little exists in conjunc-
plastic truss model when combined with the Warwick and Foster tion with high-strength concrete, and, in particular, on
efficiency factor. It is concluded that the design method given in ACI compression failures. This paper examines the behavior of
318-89 is not appropriate for corbels fabricated using high- high-strength concrete (HSC) corbels with emphasis on
strength concrete.
failure through crushing of the compression strut. Previous
research6-8 has shown that the main variables affecting the
Keywords: brackets; corbels; high-strength concretes; shear properties;
efficiency of the compression strut are concrete strength,
structural design; trusses.
shear span-to-effective depth ratio, and the provision of
secondary reinforcement. Each of these variables is studied
INTRODUCTION in the experimental program.
Reinforced concrete corbels and nibs are commonly used
to transfer loads from beams to columns and are similar in DESIGN MODELS
behavior to half-joints used to transfer shear forces in bridges. Plastic truss model
With the growing use of high-strength concrete (HSC), The plastic truss model shown in Fig. 1 consists of
particularly in high-rise structures and long-span bridges, compression struts in uniaxial compression with a uniform
there is a need for experimental data on the performance of distribution of stress across the strut of fc* and a tension tie.
corbels, nibs, and half-joints. This model is chosen due to its simplicity of form and
Yong et al.1,2 conducted a study of 14 reinforced and two rigorous structure. In this model, only two failure modes are
unreinforced HSC corbels. The study concentrated on the possible: failure by crushing of the concrete in the compres-
tension (beam-shear) mode of failure, with only one of the sion strut and failure by yielding of the tension tie. It is also
reinforced specimens reported to have failed prior to notable that in this model bearing failure is simply an exten-
yielding of the primary reinforcement. Where failure sion of the compression failure mode, where crushing occurs
occurred after yielding of the primary reinforcement, they in the concrete strut immediately below the bearing pad.
observed that the behavior of the HSC corbels was similar to Secondary failures, such as anchorage and end splitting
that of normal-strength concrete corbels. Provided that the failure, are accommodated by sensible detailing. Fig. 2
corbels remained under-reinforced, the extent of cracking compares the theoretical compression strut for the plastic
was not affected by concrete strength and the crack patterns truss model with the compression stress contours obtained
were not affected by the amount of primary reinforcement. A for a corbel analyzed using the nonlinear finite element
comparison of the test data with ACI 318-893 and the Hagberg program RECAP developed by Foster.6 It can be seen that
truss model4 was undertaken. Yong et al. concluded that the the plastic truss model compares well with the stress trajec-
Hagberg model provided better accuracy and considered the tories at ultimate given by the FE model.
ACI 318 limit of 5.5 MPa (800 psi) on the shear stress at the
interface to be overly conservative. In this paper, 30 HSC
corbels are tested, predominantly failing in compression. ACI Structural Journal, V. 93, No. 5, September-October 1996.
Received Feb. 27,1995, and reviewed under Institute publication policies. Copy-
Design methods currently available include empirical right © 1996, American Concrete Institute. All rights reserved, including the making of
design, design based on stress analysis, design based on the copies unless permission is obtained from the copyright proprietors. Pertinent discussion
will be published in the July-August 1997 ACI Structural Journal if received by
shear friction model, and strut-and-tie modeling. The shear March 1, 1997.

ACI Structural Journal/September-October 1996 555

ACI Member Stephen J. Foster is a lecturer in the Department of Structural Engi-
neering at the University of New South Wales, Sydney, Australia. He received his PhD
from the University of New South Wales in 1993 and has over 12 years’ experience as
a structural engineer in practice and teaching. His research interests include the
design of deep beams and nonflexural members, nonlinear finite element analysis of
reinforced concrete, and the structural use of high-strength concretes.

Rex E. Powell is a structural engineer with Morrison Whitten and Nicey. He is a grad-
uate of the Victoria University of Technology, Victoria, Australia, and received a Mas-
ter of Engineering Science degree from the University of New South Wales.

Hani S. Selim is a graduate of Alexandria University, Egypt, and received a Master of

Engineering Science degree from the University of New South Wales. His research
interests include the commercial use of high-strength concretes in the precast industry,
precast and prestressed components for commercial and civil structures, and the
design of concrete facades.

Fig. 2—Comparison between plastic truss model and stress

contours obtained from FE analysis for Corbel PG1.

is distributed over a distance of 2/3d. These detailing recom-

mendations are maintained in the plastic truss model; however,
no additional advantage is sought for the tension failure mode
from the additional horizontal reinforcement provided.
Several relationships for concrete efficiency have been
proposed. The first documented is that of Nielsen et al.,7 and is
Fig. 1—Plastic truss model for reinforced concrete corbels.5
ν = 0.8 – fc′/200 (4)

In the simplest form of the plastic truss model (shown in Eq. (4) was calibrated for shallow beams failing in shear
Fig. 1), the ultimate capacity of the section in tension is for a limited range of conventional-strength concretes. In the
same publication, however, Nielsen et al.7 used the relation-
w ship for the design of deep beams and corbels without veri-
V u = A st f sy ---- (1) fication. This relationship has been picked up in the
Ω
literature10 and has been adopted by AS 360011 for use
and in compression is (without restriction) in the design of nonflexural members.
Rogowsky and MacGregor5 suggest that the strength of
V u = f c∗ bw (2) the compression strut is reduced by an uneven stress distri-
bution acting within the strut. They proposed that an effi-
where Ast is the area of main tension reinforcement, fsy is the ciency factor of 0.85 be used for corbels with 0.15 ≤ a/d ≤ 1.
yield strength of the tension reinforcement, w is the effective Schlaich and Schäfer12 observed that the shape of the
width of the bearing plate (which may be less than the phys- concrete strut is bowed, and that this produces transverse
ical width), Ω is the effective anchorage depth (Ω = d – tensile forces acting across the compression strut. These
2 2
d – 2aw – w ), b is the width of the corbel, and fc* is the forces can lead to a premature diagonal splitting failure if
effective strength of the concrete compression strut given by sufficient secondary reinforcement is not provided. Foster6
added that the shape of the strut is not constant but varies
f c∗ = νf c ′ (3) from an exaggerated bowed shape at low loads to a shape
approximating that used in Rogowsky and MacGregor’s5
fc′ is the characteristic cylinder strength of the concrete in model near ultimate.
uniaxial compression, and ν is an efficiency factor. The Warwick and Foster8 investigated the influence of shear
corbel’s capacity is taken as the lower of Eq. (1) and (2). span-to-effective depth ratio (a/d), concrete strength, and the
Secondary reinforcement is required in corbels to guard presence of secondary reinforcement on concrete efficiency.
against diagonal splitting and interface shear. Mattock9 noted They found that the a/d ratio and concrete strength were the
that diagonal splitting failure was not observed, provided that most important parameters affecting concrete efficiency, and
an area of secondary reinforcement is provided that has a proposed the following relationship on the condition that a
force capacity of one-half that of the main reinforcement and minimum amount of secondary reinforcement is provided

556 ACI Structural Journal/September-October 1996

 Fig. 3—Details of test specimens.

fc ′ with 0.2 fc′ > 5.5 MPa (800 psi), where b is the width of the
a 2
ν = 1.25 – --------- – 0.72 --- + 0.18 ⎛ ---⎞ ≤ 0.85… for a ⁄ d < 2
a
⎝ d⎠ corbel and fc′ is the uniaxial compression strength of
500 d
concrete. It is not clear to the authors why the limit on
concrete strength was imposed on the design—presumably
fc ′ because of the relatively low strength of the corbels tested in
- … for a ⁄ d ≥ 2
ν = 0.53 – -------- (5)
500 1983. However, this limit requires review if the full advan-
tage of HSC is to be available to the designer. In the analysis
Other efficiency models have been proposed and detailed of the test data that follows, comparisons are made with and
by Rogowsky and MacGregor10 and Foster and Gilbert.13 without this limit.

ACI model EXPERIMENTAL PROGRAM

Recommendations for the design of corbels were first Test specimens
introduced into the ACI Building Code in 1971, with two
The testing program was designed to investigate the influ-
design methods given. The first was based on the empirical
ence of concrete strength (45 to 105 MPa [6500 to 15,200
relationships of Kriz and Raths14 for corbels with a/d ≤ 1.0,
psi]), shear span-to-effective depth ratio (0.3 to 1.0), and the
and the second was based on the shear friction theory for
influence of secondary reinforcement on the behavior of
corbels with a/d ≤.0.5. In 1983, the design rules for corbels
HSC corbels. All specimens were wet-cured until the desired
given by ACI 318 were completely revised. The empirical
strength was attained. The day prior to testing, the specimens
relationships of Kriz and Raths were omitted and the recom-
were allowed to dry and were painted.
mendations of Mattock9 were added. For a shear failure, the
shear strength of a corbel is given by Dimensions and reinforcing details are given in Fig. 3 and
Table 1. Three types of reinforcing steel were used: hot-
Vu = Avf fsyμ (6) rolled deformed bars (Y-grade), hard-drawn wire (W-grade),
and mild steel round bars (R-grade). The measured yield
where Avf is the area of shear friction reinforcement, fsy is the strengths for the reinforcing steels for each specimen are given
yield strength of the reinforcement, and μ is the coefficient in Table 1.
of friction (taken as 1.4 for monolithic construction). For In Test Series SA and SB, the main reinforcement was
tension failure, a simple flexural model was added with bent through 180 deg and welded (at the center of the
column) into a continuous loop. Tensile tests on the welded
V u = A st f sy jd
----- (7) bars were undertaken to ascertain the effect of the welds on
a the strength properties of the bar. It was shown that the welds
had no detrimental effect on the strength or modulus of
where Ast is the area of main tension reinforcement, a is the elasticity of the reinforcement. Anchorage was then
shear span, and jd is the lever arm. The ultimate strength is provided by tying Y12 bars to the corners of each bend. For
taken as the lesser value of Eq. (6) and (7). Series SC, straight bars were used with anchorage provided
The code also places a limit on the shear capacity of by welding Y24 crossbars to the underside of each bar. For
all the corbels prefixed “P,” the main longitudinal bars were
Vu > 0.2fc′ bd (8) threaded and mechanical anchors used to avoid any possibility

ACI Structural Journal/September-October 1996 557

Table 1—Details and dimensions of test specimens
Dimensions Main reinforcement Secondary reinforcement
Corbel fc′, MPa a, mm c, mm d, mm w, mm Width, mm A fsy, MPa B fsy, MPa
SA1 87 250 400 740 100 150 6Y20 430 12W6 420
SA2 87 250 400 740 100 150 6Y20 430 12W6 420
SA3 92 250 400 740 100 150 2Y20 430 Nil —
SA4 92 250 400 740 100 150 6Y20 430 Nil —
SB1 56 250 400 740 150 150 4Y20 430 12W6 420
SB2 56 250 400 740 150 150 4Y20 430 12W6 420
SC1-1 90 300 425 600 125 125 6Y20 430 12W6 420
SC1-2 90 300 425 600 125 125 6Y20 430 Nil —
SC1-3 90 300 425 600 125 125 6Y12 430 12W6 420
SC1-4 90 330 425 600 125 125 6Y12 430 Nil —
SC2-1 62 300 425 600 125 125 6Y20 430 12W6 420
SC2-2 62 300 425 600 125 125 6Y20 430 Nil —
SC2-3 62 300 425 600 125 125 6Y12 430 12W6 420
SC2-4 62 300 425 600 125 125 6Y12 430 Nil —
SD1 95 300 425 600 100 125 6Y20 430 12W6 420
SD2 65 300 425 600 125 125 6Y20 430 12W6 420
PA1 53 300 400 500 100 150 6Y20 450 Nil —
PA2 53 300 400 500 100 150 6Y20 450 10R10 360
PB1 105 300 400 500 100 150 6Y28 495 Nil —
PB2 105 300 400 500 100 150 6Y28 495 10R10 360
PC1 53 150 300 500 100 150 6Y12 420 Nil —
PC2 53 150 300 500 100 150 6Y12 420 10R10 360
PD1 71 200 300 500 100 150 3Y28 450 Nil —
PD2 71 200 300 500 100 150 3Y28 450 10R10 360
PE1 71 450 550 450 100 150 3Y36 480 Nil —
PE2 71 450 550 450 100 150 3Y36 480 10R10 360
PF1 105 150 300 500 100 150 6Y12 420 Nil —
PF2 105 150 300 500 100 150 6Y12 420 10R10 360
PG1 45 300 450 500 100 150 6Y20 415 8W6 490
PG2 94 300 450 500 100 150 6Y20 415 8W6 490
Note: 1 MPa = 145 psi; 1 mm = 0.039 in.

of anchorage failure. In all cases, the horizontal reinforcement (for Groups SA, SC, SD, PB, PD-PF, and PG2) contained a
in the corbels passed inside the vertical column bars. Series SD mix of silica fume and powdered superplasticizer. Where
corbels had the same dimensions and reinforcement layout required, additional superplasticizer was added at the site to
as Series SC but with mechanical anchorages similar to achieve the desired workability. Characteristic concrete
Series P corbels. strengths were obtained from 300 x 150-mm-diameter
For Specimens SA2 and SB2, additional confinement cylinders for Groups SB, PA, PC, and PG1, and 200 x
reinforcement was provided in each corbel along the lines of 100-mm-diameter cylinders for the HSC specimens. Details
the predicted compression struts. The aim of this experiment of the mix proportions for Specimens SC are given in Selim.15,16
was to indicate if there was any strength advantage in more
tightly confining the compression strut. No significant gain Instrumentation
in strength was achieved and this reinforcement layout was Each corbel was instrumented to record strains in the
not used in any further tests. middle layer of the main tension reinforcement and the
One of the main aims of the experimental program was to deflection at the tip of the corbel. For all but Series PD and
look at the behavior of HSC corbels failing in compression. PE corbels, strains were measured using a demec strain gage
To determine the efficiency factor required by the plastic over a gage length of 250 mm. Three or four gage lengths
truss model, it is necessary to know the width of the were used for each specimen, depending on the shear span-
compression strut. This was obtained by using stiff bearing to-effective depth ratio (a/d). Steel pins 40-mm long and 6 mm
plates and insuring that any bearing reinforcement used did in diameter were welded onto the tension tie reinforcement.
not lie outside the line of the bearing plate. Thus, provided that Demec targets were then glued to the pins and strains were
failure is in a compression mode (discussed below), the effec- measured. A sample section of reinforcement was fabricated
tive bearing width w, given in Eq. (2), equals the plate width. with two welded lugs and tested in tension to evaluate the
effects of welding on the strength properties of the bar. No
Materials detrimental effects were recorded either on the yield point or
All concrete was supplied by a local ready-mix supplier ductility of the bar. Details of strain gage, locations, and
and had a maximum aggregate size of 10 mm. All HSC mixes target connection are given in Fig. 4. For Series PD and PE

558 ACI Structural Journal/September-October 1996

 Table 2—Test results
Experimental
Failure efficiency
Specimen a/d fc′, MPa load, kN factor* Failure mode†
SA1 0.34 87 1200 0.92 Bearing
SA2 0.34 87 1300 1.00 Bearing
SA3 0.34 92 860 — Tension
SA4 0.34 92 1500 1.09 Compression
SB1 0.34 56 1000 0.79 Bearing
SB2 0.34 56 1200 0.95 Diagonal splitting
SC1-1 0.50 90 720 — Anchorage
SC1-2 0.50 90 950 0.68 Diagonal splitting
SC1-3 0.50 90 700 — Tension
Fig. 4—Location of strain gages and LVDTs and details of SC1-4 0.55 90 470 — Tension
target connections.
SC2-1 0.50 62 980 1.01 Compression
SC2-2 0.50 62 700 0.72 Diagonal splitting
corbels, strains were measured using electronic strain gages
SC2-3 0.50 62 580 — Tension
located directly beneath each load plate.
SC2-4 0.50 62 490 — Diagonal splitting
Displacements were measured using LVDTs that were
connected to each corbel tip and at the center of each column SD1 0.50 95 1000 0.84 Compression
(see Fig. 4). The relative tip deflection was taken as the SD2 0.50 65 1000 0.98 Compression
displacement of the central LVDT minus one-half the sum of PA1 0.6 53 550 0.69 Diagonal splitting
the displacements at the tip. Zero errors caused by crushing PA2 0.6 53 800 1.01 Diagonal splitting
of the thin plaster layer beneath the load plate have been taken PB1 0.6 105 1180 0.75 Diagonal splitting
into account. PB2 0.6 105 1150 0.73 Compression
Vertical loading was applied to each specimen using either PC1 0.3 53 650 0.82 Diagonal splitting
one or two hydraulic jacks, with each jack having a capacity PC2 0.3 53 1040 1.31 Compression
of 2000 kN. The load was recorded using an electronic load PD1 0.4 71 540 0.51 Premature failure
cell connected to a signal carrier.
PD2 0.4 71 960 0.9 Compression
PE1 1.0 71 680 0.64 Diagonal splitting
RESULTS
Failure loads and failure modes recorded for each spec- PE2 1.0 71 710 0.67 Compression
imen are given in Table 2. Load-versus-strain measurements PF1 0.3 105 750 — Tension
for the main reinforcement for specimens failing in tension PF2 0.3 105 1050 — Tension
are typified by the data recorded for Corbel SC1-4, shown in PG1 0.6 45 674 1.0 Compression
Fig. 5(a). Fig. 5(b) shows the load-versus-strain results for PG2 0.6 94 1050 0.74 Compression
Corbel PG2, typical of specimens failing in compression. *
Based on plastic truss model proposed by Rogowsky and MacGregor5 for corbels
Similarly, load-versus-deflection diagrams for Corbels SC1-4 failing in compression.
†
and PG2 are given in Fig. 6(a) and (b), respectively. Failure mode based on definitions given in text.
Note: 1 MPa = 145 psi; 1 kN = 0.225 kips; 1 mm = 0.039 in.
Cracks observed in the corbels can be categorized as either
1) flexural cracks occurring in the flexural tension region, or
2) strut cracks occurring diagonally from the loading region
to the corbel column interface. Flexural cracks at the corbel- secondary reinforcement generally contained finer and more
column interface were usually the first to form and occurred irregular cracks. Strut cracks usually followed a path from
at approximately 15 to 30 percent of the ultimate load. The the load plate (commonly from the inside edge) to a point
depth that the flexural cracks had penetrated into the spec- in the column—inside from the corbel-column junction.
imen at failure varied between 25 and 65 percent of the total Strut cracks were often initiated by existing primary or
depth of the corbel. The load at which first cracking occurred secondary flexural cracks.
appeared to be influenced by both the a/d ratio and the Three different primary modes of failure are defined in
concrete strength. Corbels with high a/d ratios and low this study:
concrete strengths cracked earlier than their counterparts. • Compression—failure by crushing of the concrete
This was as expected, as the shear span controls the cracking forming one of the compression struts.
moment causing cracking, and both concrete strength and • Diagonal splitting—failure caused by significant
corbel depth are important factors in determining the resis- opening of the diagonal crack(s) before crushing of the
tance to cracking. The presence of secondary reinforcement concrete in the compression struts.
or the amount of main steel did not appear to influence the • Tension—failure of the corbel by any mode after the
load at first cracking. main tension reinforcement has yielded.
In the majority of the specimens, strut cracks formed at All three primary failure modes were witnessed in this
between 35 and 55 percent of the failure load. For corbels study. Two specimens also failed by secondary modes. Spec-
failing in compression, the formation of new strut cracks and imen SC1-1 failed in anchorage after welds between the
the widening and extension of existing cracks continued main reinforcement and the anchorage bar failed. Specimen
until failure. The load at which strut cracks were first PD1 failed by splitting through the section, possibly due a
observed did not appear to be significantly influenced by any weakness caused by the relatively large reinforcing bars and
of the variables tested. However, specimens containing a lack of confinement in the out-of-plane direction.

ACI Structural Journal/September-October 1996 559

 Fig. 5—Load-versus-strain results for: (a) Corbel SC1-4; (b) Corbel PG2.

Fig. 6—Load-versus-deflection results for: (a) Corbel SC1-4; (b) Corbel PG2.

Figure 7 illustrates typical crack patterns for the three specimen gave a high efficiency factor when analyzed using
observed modes of failure. Detailed results for individual the plastic truss model. Cracks observed from a compression
corbels are given in Selim et al.15 and Powell and Foster.17 failure were finer, more numerous, and more evenly distrib-
uted across the specimen than for specimens that failed by
ANALYSIS OF RESULTS diagonal splitting. As expected, the most ductile failures
All corbels without any secondary reinforcement failed by observed were tension failures.
diagonal splitting. This failure mode is brittle and occurs The load-versus-strain relationship for specimens that
with little warning. Specimens failing in this manner typically failed by either diagonal splitting or compression comprise
displayed a well-defined diagonal crack that formed between two phases. Phase I is the precracking state where the tension
the inside edge of the loading plate and the column-corbel forces are carried by the concrete section. In this stage,
junction. Corbels containing secondary reinforcement strains measured in the main tension reinforcement were
generally failed in the more ductile compression mode. The small and irregular. In Phase II, the cracking phase, strains
exception was Specimen PA2, which failed by diagonal increased in a linear fashion until failure. Specimens that
splitting; note, however, that later analysis shows that this failed in tension exhibited a third phase that occurs on yielding

560 ACI Structural Journal/September-October 1996

 Fig. 7—Typical crack patterns.

of the primary tension reinforcement. Phase III is shown by Table 3 and Fig. 8 indicate that the plastic truss model is a
a plateau in the load-versus-strain graph [see Fig. 6(a)]. good tool for designing corbels of high-strength concrete
Phases II and III are consistent with the plastic truss theory. when combined with the efficiency factor relationship
The ultimate load predicted by the plastic truss model, proposed by Warwick and Foster. The mean predicted to
with efficiency factors given by Warwick and Foster,8 Nielsen experimental failure load for specimens containing
et al.,7 and ACI 318-893 (with and without the limitation on secondary reinforcement and failing in compression using
fc′) are given in Table 3. The results for specimens this model is 0.86, with a standard deviation of 0.10.
containing secondary reinforcement and failing in compres- The plastic truss model for corbels failing in tension gives
sion are compared in Fig. 8 for each of the design models.
good results for the specimens with no secondary reinforce-
A comparison between the ACI 318-89 provisions and the
ment, but generally underestimates the capacity of the
experimental results shows that when the limits on concrete
strength are included, the ACI method is grossly conserva- section when horizontal stirrups are added. The plastic truss
tive. When the limit on concrete strength is removed, the model used does not consider the effect of the secondary
results are grossly nonconservative. reinforcement in increasing the tension capacity of the spec-
Results predicted by plastic truss theory in combination imen, although a more complex model could. The difficulty
with the Nielsen et al.7 efficiency relationship underesti- in adopting a more advanced model is in guaranteeing that
mated the experimental results to an extent similar to the all the secondary reinforcement is at yield at failure. In the
ACI procedure. Nielsen’s effective strength relationship authors’ opinion, it is the role of the secondary reinforcement
(fc*) is a second order polynomial in fc′ and has a maximum to guard against interface shear and diagonal splitting fail-
value of 32 MPa when fc′ = 80 MPa. Actual values of effec- ures and to improve the performance of the compression
tive concrete strength of up to 79 MPa (Specimen PB1) were strut by reducing transverse strains. Strains in the secondary
recorded in this study. reinforcement should not be assumed to be at yield at failure.

ACI Structural Journal/September-October 1996 561

Table 3—Experimental versus predicted failure loads
Plastic truss model* ACI 318-89
Warwick et al. Nielsen et al. With limit on fc′, Without limit on
Specimen Failure load, kN ν Vu, kN ν Vu , kN kN fc′, kN
Compression failures
SA1 1200 0.85 1110 0.37 480 610 1310
SA2 1300 0.85 1110 0.37 480 610 1310
SA4 1500 0.84 1160 0.33 450 1140 1140
SB1 1000 0.85 1070 0.52 660 610 940
SB2 1200 0.85 1070 0.52 660 610 940
SC1-2 950 0.76 1060 0.35 630 410 1110
SC2-1 980 0.81 790 0.49 570 410 1350
SC2-2 700 0.81 790 0.49 570 410 1150
SD1 1000 0.75 880 0.33 390 410 1330
SD2 1000 0.81 770 0.48 460 410 980
PA1 550 0.78 620 0.54 510 410 800
PA2 800 0.78 620 0.54 510 410 800
PB1 1180 0.67 1060 0.28 600 410 1580
PB2 1150 0.67 1060 0.28 600 410 1580
PC1 650 0.85 680 0.54 510 410 800
PC2 1040 0.85 680 0.54 510 410 800
PD2 960 0.85 900 0.45 590 410 1070
Fig. PE1
8—<fgc><fgc>Comparison
680 between predicted
0.57 610 and 0.45 580 370 890
experimental
PE2 failure loads
710 for corbels
0.57 with secondary
610 rein- 0.45 580 370 890
forcement
PG1 and failing in
670 compression
0.79 540 0.78 660 400 680
PG2 1050 0.69 980 0.33 610 410 1220
Tension failures
SA3 860 0.84 620 0.33 470* 380 380
SC1-3 700 0.76 590 0.35 590 410 560
SC1-4 470 0.73 550 0.35 550 410 400
SC2-3 580 0.81 600 0.49 570* 410 550
SC2-4 490 0.78 550 0.49 550 410 400
PF1 750 0.84 680 0.28 590* 400 400
PF2 1050 0.84 680 0.28 590* 400 800
*
Theoretical compression failure.

For corbels failing in compression, the efficiency factor 3. Providing secondary reinforcement reduces crack
is a measure of the performance of the compression strut. widths, improves ductility, and for beams failing in compres-
The detrimental effect of transverse strains on the ultimate sion may change the failure mode from diagonal splitting to
capacity of concrete in compression is well documented.18 compression strut crushing. A minimum quantity of hori-
The effect of providing horizontal reinforcement is to zontal stirrups similar to that for normal-strength concrete
increase the effectiveness of the compressive strut. The should be used in corbels fabricated with HSC.
provision of secondary reinforcement generally improved 4. The ACI 318-89 design method is not recommended for
the compressive strength of the corbels. For specimens with use with corbels designed with high and very high-strength
low a/d (such as Series SA), the transverse strains are small concretes.
and the variation in measured ultimate strengths is within the 5. The plastic truss model provides a good tool for
normal range of experimental scatter for the testing of designing HSC corbels and is best used in conjunction with
concrete structures. the efficiency factor proposed by Warwick and Foster.

CONCLUSIONS ACKNOWLEDGMENTS
In this investigation, 30 corbels were prepared and tested This research was funded through Faculty Research Grants from the
under vertical loading. The main test variables were concrete Faculty of Engineering at the University of New South Wales. The authors
strength (45 to 105 MPa [6500-15,200 psi]), shear span-to- are grateful for this assistance. The contributions of Warwick Faulkner and
Derek Graham to the experimental program are gratefully acknowledged.
depth ratio, and the provision of secondary reinforcement.
The following conclusions can be drawn based on the test results:
1. The first cracks are flexural cracks propagating from the REFERENCES
1. Yong, Y. K.; Douglas, H.; McCloskey, H.; and Nawy, E. G., “Rein-
corbel-column intersection, and the flexural cracking load forced Corbels of High-Strength Concrete,” High-Strength Concrete, SP
decreases with an increase in the shear span-to-depth ratio. 87, American Concrete Institute, Detroit, 1985, pp. 197-212.
2. Corbels fabricated from HSC behaved similarly to those 2. Yong, Y. K., and Balagura, P., “Behavior of Reinforced High-Strength
made of normal-strength concrete. Concrete Corbels,” Journal of Structural Engineering, ASCE, V. 120, No.

562 ACI Structural Journal/September-October 1996

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