Shear strength of RC deep beams

G. Appa Rao* & K. Kunal

*University of Stuttgart, 70569 Stuttgart, Germany
Indian Institute of Technology Madras, Chennai-600 036, India
R. Eligehausen
University of Stuttgart, 70569 Stuttgart, Germany.

ABSTRACT: This paper reports on some experimental investigations on the shear behaviour of reinforced
concrete (RC) deep beams without and with shear (web) reinforcement. Twelve large scale deep beams made
of 60 MPa concrete were tested. Three different beams of depth 250mm, 500mm and 750 mm were tested to
understand size effect. The behaviour of deep beams including load-deflection curves, web strains and crack
width, shear ductility and reserve strength has been investigated. The beams tested under three-point loading
failed in shear and failure modes were influenced by the beam depth and amount of shear reinforcement. The
shear strength was found to decrease with increase of beam size and large size beams exhibited brittle failure,
which was attributed to size effect. Sufficient shear reinforcement in beams turned brittle failure in to ductile.
The load-deflection curves are regular in small size beams with heavy shear reinforcement. The web strains
and the width of shear cracks increase at failure with web reinforcement. With increased quantity of shear re-
inforcement, more confinement is offered to sustain greater web strains and crack widths. Shear ductility (=
capability of withstanding severe cracking and deformation) decreases in deep beams and increases in highly
shear-reinforced deep beams. Significant reserve strength beyond diagonal cracking was observed in deep
beams. As a matter of fact, this reserve strength was to two times larger in small-size beams, compared to
large-size beams.

1 INTRODUCTION interact with shear stresses to form complicated

stress field in the web. Because of short horizontal
The shear behaviour of deep beams is very complex distance between top and bottom load points i.e.
and there is still no agreement on the role of size ef- small a/d ratios, the effect of such stresses result in
fect in shear due to lack of information. Deep beams arch action unique in deep beams. Because of these
are classified as nonflexural members, in which complexities, study of deep beams has become a
plane sections do not remain plane in bending. special interest. Over the years various models have
Therefore, the principles of stress analysis devel- been proposed by many researchers and extensive
oped for slender beams are neither applicable nor test campaigns have been carried out.
adequate to determine the strength of deep beams.
An important characteristic of deep beams is their
high shear strength. The greater shear strength of 2 REVIEW OF LITERATURE
deep beams is due to internal arch action, which
transfers the load directly to a support through con- Several research efforts have been made to under-
crete struts. The reinforcement acts as a tie and, stand the shear strength of deep beams and size ef-
hence RC beams are analogous to steel trusses. Deep fect. Due to complex behaviour of deep beams lim-
beams are also classified as disturbed regions, which ited information has been reported over the years
are characterized by nonlinear strain distribution. and further evidence is needed on the role of the
Elastic solutions of deep beams provide good de- many parameters involved, as demonstrated by some
scription of their behaviour before cracking. How- recent studies. The study on deep beams has been an
ever, after cracking major redistribution of strains interesting topic by varying the parameters. How-
and stresses takes place and the beam strength must ever, some studies have been reported on the inves-
be predicted by nonlinear analysis. For a simple tigations on the behaviour of deep beams in shear
deep beam with concentrated load on top, the top recently. As for the definition of deep beams, ACI
load and bottom reactions create large compressive 318 defines deep beams as those loaded on one face
stresses at a right angle to beam axis. These stresses and supported on other face and the shear span-to-
depth ratio is less than or equal to two. Due to their tensile splitting and diagonal crushing of concrete
geometric proportions deep beams fail in shear. A due to compression. Russo et al. (2005) proposed an
disturbance in internal stresses is caused by shear ac- explicit expression that considers the shear strength
tion with compression in one direction and tension based on strut and tie mechanism due to diagonal
in the perpendicular direction. This leads to an concrete strut and longitudinal reinforcement as well
abrupt shear failure of beam as the beam depth in- as vertical stirrups and horizontal web reinforce-
creases (Yang and Chung, 2003). The development ment. Bakir et al. (2004) recommended the strut and
of crack pattern is much faster than small size deep tie model for the design of short and deep beams.
beams and then leading to sudden failure (Bakir and The model consists of three separate mechanisms;
Boduroglu, 2004). direct strut mechanism, truss mechanism which
Several modifications have been incorporated in takes in to account the horizontal shear reinforce-
the shear design of deep beams in the codes of prac- ment and truss mechanism, which takes in to ac-
tice. ACI 318-2005 and IS 456-2000 consider the count of the stirrups.
contribution of concrete, percentage longitudinal and Several fracture mechanics models have been
transverse reinforcement, shear span-to-depth ratio proposed in order to characterize the failure of con-
for estimating the shear strength of deep beams, crete (Hillerborg and co-workers (1976), Bazant and
while BS 8110 does not specify any guidelines for Oh (1984), Jenq and Shah (1989). Each one of these
design of deep beams. However, it explicitly says models introduces some material fracture properties
that for design of deep beams specialist literature regardless of the structural geometry and size. Con-
should be referred. Unlike in ACI 318 and IS 456, crete structures exhibit size effect, which has been
BS 8110 considers size effect in shear design of RC explained as a consequence of the randomness of ma-
beam. However, the maximum depth is limited to terial strength. In large structures it is more likely to
400mm. Therefore, in order to understand the shear encounter a material point of smaller strength. Bazant
design of deep beams and to evaluate size effect se- proposed that whenever the failure does not occur at
rious research efforts are needed. the initiation of cracking, size effect should properly
Failure in deep beams is generally due to crush- be explained by energy release caused by macro-
ing of concrete in either reduced region of compres- crack growth, and that the randomness of strength
sion zone at the tip of inclined cracks or by fracture plays a meager role. Nevertheless, size effect in con-
of concrete along the crack. In deep beams with crete structures ought to be explained by a non-linear
shear span-to-depth ratio 2.5, there seems to be some form of fracture mechanics that takes in to account
reserve strength in the post-cracking region, result- the localization of damage in to a fracture process
ing in relatively less brittle in nature (Khaldoun, zone (FPZ) of a non negligible size. Bazant’s size ef-
2000, Lin and Lee, 2003). Therefore, to estimate the fect law (Bazant and Oh, 1984) is based on the duc-
reserve strength and ductility of deep beams in tile-brittle transition of the failure mode of geometri-
shear, the influence of various parameters need to be cally similar fracture specimens. For most practical
investigated. This paper presents some experimental cases, Bazant’s size effect law can be described by
observations on behaviour and size effect in RC the following equation
beams with different shear reinforcements. 1
B f0
Ashour and Morley (1996) carried out an upper = B f 0 (1 + β ) (1)
−
σN = 2
bound mechanism analysis on continuous reinforced 1+
d
concrete deep beams. The effect of horizontal and d0
vertical web reinforcement on the load carrying ca-
pacity is mainly influenced by the shear span-to- Where β = d/d0, B and d0 are empirical constants to
effective depth ratio. In deep beams, the horizontal be obtained by fitting equation to the experimental
shear reinforcement is effective than the vertical values from different sizes of specimens.
shear reinforcement. Ashour (2000) reported analy- Smith and Vantsiotis (1982) tested 52 RC deep
sis of shear mechanism in simply supported RC deep beams under two point loading to study the effect of
beams. Concrete and steel reinforcement are mod- shear span-to-depth (a/d) ratio and vertical and hori-
eled as rigid perfectly plastic materials. The failure zontal web reinforcement on ultimate shear strength
modes were idealized as assemblage of rigid blocks and crack width. The web reinforcement produces
separated by failure zones of displacement disconti- no effect on formation of inclined cracks but affects
nuity. The shear strength of deep beams is derived as the ultimate shear strength. The addition of vertical
a function of location of the instantaneous center of web reinforcement improves the ultimate shear
relative rotation of moving blocks. strength, but addition of horizontal web reinforce-
Tang and Tan (2004) proposed an approach to ment has negligible influence on ultimate shear
account for the effect of transverse stresses to the strength. Iguro et al. (1984) carried out some ex-
load carrying capacity of concrete in the diagonal perimental studies on uniformly loaded reinforced
strut based on strut-and tie concept. This involves an concrete beams of depth varying between 100 to
interaction between two modes of failure; diagonal
3000 mm without shear reinforcement, in order to of the critical diagonal crack. This theory has been
study size effect on shear strength of beams. As the applied to evaluate the shear strength of RC slender
effective depth increases the shear strength gradually beams subject to shear and flexure. According to
decreases. Collins and Kuchma (1999) reported that this, the reason for shear failure is the loss of shear
for large, lightly reinforced concrete beams, reduc- force of the main tension reinforcement, which oc-
tion in shear stress at failure was related more di- curs due to horizontal splitting of concrete cover
rectly to the maximum spacing between the layers of along the main reinforcement. Lubell et al. (2004)
longitudinal bars rather than overall depth of the used the specific situation of Bahen Center beams
member. It has been observed that high strength (University of Toronto) to investigate the possibility
concrete (HSC) beams exhibit strong size effect in of shear failure of large size thick deep beams. The
shear. Accordingly, some modifications to ACI conclusions by earlier researchers that the shear
shear design provisions are recommended. Karim strength of wide beams is directly proportional to the
(1999) proposed an alternative shear strength predic- width of the beam are found to be correct. Accord-
tion equation, at both ultimate and cracking stage, ingly, modifications have been suggested to ACI
for an RC member without web reinforcement. From code for shear design of large wide beams.
350 beam test results collected from the existing lit- Khaldoun et al. (2004) reported the experimental re-
erature of RC beams in shear covering a wide range sults on shear behaviour of 11 beams made of 65
of beam properties and test methods, a technique of MPa concrete, reinforced with transverse and longi-
dimensional analysis, interpolation function, and tudinal reinforcement. Performance of specimens
multiple regression analysis was carried out, for both based on cracking pattern, crack widths at estimated
normal strength concrete (NSC) and HSC members. service load, and on post cracking reserve strength
An interpolation function was used to account for have been evaluated. A significant reduction in
the difference in behaviour between arch action of crack width was observed with increase in amount
short beam and beam action of long beams. of longitudinal reinforcement. The quantity of longi-
Raghu et al. (2000) conducted a comprehensive tudinal reinforcement provided in the beams can
experimental and technical investigation to asses the demonstrate what should be limit of minimum trans-
concrete component of shear resistance in beams verse reinforcement. The shear strength equations in
made of HSC. The experimental program consists of current ACI, CSA, and AASHTO LRFD specifica-
testing of 24 beams, with and without shear rein- tions are conservative. Russo et al. (2005) proposed
forcement, to determine the contribution of concrete an explicit formula that considers the shear strength
to shear strength. The data from the experimental provided by the strut–and-tie mechanism due to di-
observations and literature were compared with agonal concrete and the longitudinal main rein-
shear provisions in codes of practice. When extrapo- forcement as well as the vertical stirrups and hori-
lated the current provisions for shear resistance of zontal web reinforcement.
HSC, the safety margins for structural designs are The objective of the study is to understand size
reduced. Angelakos et al. (2001) reported on tests of effect in RC deep beams in shear with and without
21 large RC beams in shear. It has been revealed web reinforcement and also to evaluate the shear
that concrete strength is the most important parame- ductility of RC deep beams failing in shear. The
ter influencing shear stress at failure and the longi- scope of this study is limited to RC deep beams with
tudinal reinforcement has only negligible effect. The shear span-to-depth ratio 1.5, concrete compressive
shear stress at failure decreases substantially as strength of 60 MPa, with longitudinal reinforcement
member size increases and as the longitudinal rein- of 2.0% and comparison of existing code values with
forcement ratio decreases. Aguilar et al. (2002) stud- the experimental values.
ied RC deep beams. The experimental results have
been compared with the shear design procedures laid
down in ACI 318-99. Yang et al. (2003) tested 3 RESEARCH SIGNIFICANCE
twenty one beam specimens to investigate the shear
characteristics with various variables such as con- The design of deep beams is rather complex, since
crete strength, shear span-to-depth ratio, and beam the very behaviour of these structural members is
depth. It has been found that decrease in shear span- complex and is still not totally clarified. Due to
to-depth ratio and increase in beam depth at a shear geometric proportions, the behaviour of RC deep
span-to-depth ratio resulting in more brittle failure beams is governed mainly by shear strength. The
with wide diagonal cracks and high energy release shear strength of deep beams seems to be signifi-
rate related to size effect. Also, HSC deep beams cantly greater than that of the slender beams due to
exhibited more remarkable size effects with brittle redistribution of internal stresses. Several parameters
behavior. affect the strength of RC beams in shear, which in-
Zararis (2003) reported that the shear failure of clude shear span-to-depth ratio, concrete strength,
RC deep beams is due to crushing of concrete in anchorage of reinforcement into the supports, size
compression zone with restricted depth above the tip effect, amount and arrangement of tensile and web
reinforcement. The disturbance of internal stresses concrete in to the beam moulds to avoid sand pock-
due to heavy concentrated loads causes reduction of ets. Needle vibrators were used to compact the con-
load carrying capacity of deep beams and fosters an crete in beam specimens. After 24hours, the beams
abrupt shear failure as the depth increases. Thus, it is were removed from the moulds and cured for 28
necessary to investigate the shear behavior of deep days. The curing was done using gunny bags cov-
beams with different sizes. The design codes are de- ered around the beams and water was sprinkled in
veloped from experimental test results using low every 3 hrs intervals to avoid evaporation of mois-
strength concrete and on RC beams without shear re- ture from the beam surfaces. After curing all the
inforcement and with depth less than 350mm. beams were white washed and square grids were
drawn on the beam surface in order to visualize the
crack pattern and to make crack-width measure-
4 EXPERIMENTAL PROGRAMME ments easier.
4.1 Materials
Concrete used for this program was designed to 4.3 Reinforcement and beam dimensions
achieve compressive strength of 60MPa for all the
Two variables are considered in this study; beam
beams. Mix proportions of the concrete used for
depth and web or shear reinforcement. All the beams
achieving the required strength were 1: 1.5:2.9 using
were rectangular in cross section with a width of
Portland Pozzolana Cement (PPC). Table 1 shows
150mm. The shear span-to-depth (a/d) ratio was 1.5.
the constituent materials used for the concrete. The
The beams are grouped in to four series. These se-
water cement ratio used was 0.32. Along with each
ries are designated as HSCB-0, HSCB-0.4, HSCB-
set of RC deep beams, six companion plain concrete
0.6 and HSCB-0.8. “HSCB” indicates “High
cubes of size 150x150x150mm were cast and tested
Strength Concrete Beam” and the number following
to find the characteristic compressive strength of
HSCB indicates the shear reinforcement index (SRI)
concrete. The coarse aggregate was 20mm maxi-
which is the measure of amount of shear reinforce-
mum size aggregate with specific gravity 2.70 and
ment provided in the beam. Each series consists of
fineness modulus of 6.93. Sand was naturally ob-
three beams of depth 250, 500 and 750 mm desig-
tained with specific gravity of 2.73 and fineness
nated by S, M and L respectively to indicate small,
modulus of 2.84. Potable water was used for mixing
medium and large size beams. The flexural rein-
of concrete and curing purpose. The steel reinforce-
forcement has been adopted after evaluating the
ment consists of high strength deformed bars for
flexural strength of beams and comparing with the
longitudinal flexural reinforcement in all the beams.
shear strength so that the failure could be initiated
The steel ratio of the flexural reinforcement was 2.0
by shear failure only. Sufficient reinforcement was
% in all beams. The properties of reinforcement are
provided near the support including for shear and
shown in Table 2.
anchorage length. All the flexural reinforcement
bars were bent up vertically at the supports to
Table 1. Constituent materials used for concrete. achieve adequate end anchorage. The clear cover of
the flexural reinforcement was kept as 25 mm in all
Mix Cement Sand Aggregate w/c the beams. 6mm diameter mild steel bars were used
kg/m3 kg/m3 kg/m3 Ratio
as top corner steel for hanging the shear reinforce-
M60 474 710 1373 0.32
ment. The stirrups were made from mild steel bars
of 6, 5 and 4mm diameter depending on the beam
Table 2. Mechanical properties of reinforcement. size according to the code provisions for minimum
S No. φ fy εY E σut
shear reinforcement and minimum spacing of shear
(mm) (MPa) (×10-3) (103, MPa) MPa
reinforcement in beams.
The reinforcement arrangement in typical RC
1. 4 400 2.0 200 480
beams is shown in Figure 1. For the first series of
2. 5 479 2.4 200 521
beams designated as HSCB-0, no web reinforcement
3. 6 425 2.1 200 600
was provided. However, in order to maintain the
4. 16 607 2.8 217 657
longitudinal bars in their position stirrups are pro-
5. 20 543 3.2 199 663
vided one each at the ends and at the center of the
beam. This series of beams was tested in order to
understand the shear behaviour of deep beams with-
4.2 Casting of test beams
out shear reinforcement for comparison with those
Well seasoned wooden beam moulds were fabri- with shear reinforcement. The subsequent series of
cated for casting beams of 250, 500 and 750mm beams were designated as HSCB-0.4, HSCB-0.6 and
depth and 150mm width. Superplasticizer was used HSCB-0.8 with different stirrup spacing to achieve
to produce flowable concrete in order to pour the the required SRI. The spacing of shear reinforce-
ment was varied in the beam specimens in order to
achieve the required shear reinforcement index. All Ends of all beams were extended by 150 mm from
the beams were reinforced with the same steel ratio the line of action of support reaction. Bearing plates
for the flexural reinforcement. The stirrups were of dimensions 100x150x20 mm were provided at the
provided with an end hook of 1350. Details of all the supports and below the point loading. All the beams
shear reinforcements are given in Table 3. The yield were tested using 1000kN capacity displacement
strength of longitudinal reinforcement is 521 MPa. controlled actuators. LVDT was attached at the mid
span to measure the deflection of beams under the
Table 3. Details of test specimens point loading. At each displacement increment, the
load applied on the beam, mid span deflection,
Beam Pt
Designation
D b l
%
fyv SRI maximum crack width and diagonal strain in con-
HSCB-S0.0 250 150 930 2 0.0 crete were measured.
HSCB-M0.0 500 150 1680 2 0.0
HSCB-L0.0 750 150 2430 2 0.0
HSCB-S0.4 250 150 930 2 400 0.40 5 DISCUSSION OF RESULTS
HSCB-M0.4 500 150 1680 2 479 0.40
HSCB-L0.4 750 150 2430 2 479 0.40 5.1 Modes of Failure
HSCB-S0.6 250 150 930 2 479 0.60
HSCB-M0.6 500 150 1680 2 425 0.60 All the beams tested under three-point loading failed
HSCB-L0.6 750 150 2430 2 425 0.60 in perfect diagonal shear. Typical crack pattern and
HSCB-S0.8 250 150 930 2 479 0.80 modes of failure are shown in Figure 3. In all the
HSCB-M0.8 500 150 1680 2 425 0.80
HSCB-L0.8 750 150 2430 2 425 0.80 beams, cracks started as flexural cracks, but no
cracks were observed up to 20% of the ultimate
A shear reinforcement index (SRI) is defined to load. The first vertical flexural crack was formed in
represent the shear reinforcement, which is given by the region of maximum bending moment within a
load range of 20–30% of ultimate load. In the range
of load between 40-70% of the ultimate load a major
SRI = R. fyv (2) diagonal tension crack formed at the middle of shear
span. With further increase in the applied load, new
Asv inclined cracks appeared within the shear span, their
Where R =
b.sv orientation being the same as that of the previously-
formed major inclined cracks. Eventually, beam
failure occurred due to crushing of concrete in either
reduced region of compression zone at the tip of in-
clined crack or by the fracture of the concrete along
the inclined crack.

Figure 1. Typical reinforcement in RC Beam.

4.4 Experimental setup and testing of beams

Twelve simply supported RC deep beams were
tested up to failure under three-point loading. Each Figure 3. Crack pattern for beams with SRI 0.4.
beam was loaded with a central concentrated load
and supported on two simply supported ends as
shown in Figure 2. The modes of beam failure were influenced by the
depth of beam and the amount of shear reinforce-
ment. It has been observed that for all smaller size
beams i.e. HSCB-S0.0, HSCB-S0.4, HSCB-S0.6 and
HSCB-S0.8 and also in medium size beams HSCB-
M0.0 and HSCB-M0.4 having relatively smaller
amount of shear reinforcement failed by fracture of
concrete along the tension diagonal. However, in
few medium size beams such as HSCB-M0.6 and
HSCB-M0.8, and also in all large size beams HSCB-
Figure 2. Beam specimen and experimental set up. L0.0, HSCB-L0.4, HSCB-L0.6 and HSCB-L0.8, the
failure was shear-compression type of failure. The than that of beams of depth 500mm and 250 mm. In
failure due to crushing of concrete resulted in brittle different sizes of beams, the maximum deflections
failure. In all the beam failures, the inclined cracking have been observed with SRI 0.8 followed by the
pattern reveals a tied-arch action, with tension rein- beams with SRI 0.6, 0.4 and 0.0. The post-peak re-
forcement acting as a tie rod and portion of beam be- sponse seems to be more gradual showing increase
tween the inclined cracks as struts. The cracking pat- of ductility of the beams with increase in percentage
tern was found to be more uniform as the amount of shear reinforcement or SRI. The failure of small size
shear reinforcement increases and also as the beam beams seems to be gradual indicating sufficient duc-
depth increases, keeping shear span-to-depth (a/d) tility before failure. This showed that being a shear
ratio constant. The deterioration of concrete and failure, deep beams exhibit reasonable ductility rep-
cracking were symmetric just before failure. How- resented by relatively larger deflections at failure
ever, at the stage of failure cracking propagated rap- and post peak response, with increase in shear rein-
idly at only one end of the beam due to diagonal forcement.
cracking. As the depth of the beam increases, the
failure mode changes from diagonal tension to di- 600 HS CB-L0.0 HS CB-M0.0 HS CB-S 0.0

agonal tension-compression type. The deeper the 500

beam, the steeper the inclination of the diagonal
400
crack. In all the large size beams, crushing of con-

Load (kN)
crete in compression at the tip of the diagonal crack 300

has been observed. As the shear reinforcement in- 200

creases, more inclined cracks formed with small 100
spacing in between the cracks. At failure only a ma-
jor crack was widened. 0
0.00 2.00 4.00 6.00 8.00 10.00
Deflection (mm)

5.2 Diagonal cracking and ultimate shear strength Figure 4. Load-deflection curves with SRI 0.0.
The diagonal-cracking strength is defined as the
strength at which the first fully developed major di- At a given loading, the strain in large size beams
agonal tension crack appears in the shear span. The seems to be more. However, the large size beams
diagonal tension cracking strength was observed to fail at lower stains. Also, it has been observed that as
be considerably less than the ultimate strength. the amount of web reinforcement increases the strain
Many mechanisms may be responsible for such be- in concrete also increases. This was mainly because,
haviour. However, the major phenomenon is attrib- with increase in amount of web reinforcement, the
uted to the arch action. Deep RC beams exhibited load is shared by the shear reinforcement, allowing
significantly enhanced shear resistance after first di- concrete to sustain more cracking strain. At any
agonal cracking as a result of strong strut action of given load, the diagonal tensile strains in large-size
concrete in compression. The difference between the beams are larger than in small-size beams, but the
ultimate shear strength and diagonal cracking strains at the onset of failure are smaller in the for-
strength can be considered as reserve strength. The mer case. Furthermore, the larger the shear rein-
reserve strength was analyzed from the experimental forcement, the larger the diagonal strains, mainly
observations in beams of varying sizes. Defining Vu because of the increasing share of the shear that is
and Vcr as the ultimate and diagonal cracking resisted by the reinforcement. As a result, concrete
strength of RC beams, a ratio of Vu/Vcr has been can absorb more distributed cracking.
evaluated to represent the reserve strength in terms
of measured cracking strength. The ratio Vu/Vcr in
all deep beams lies in the range between 2.0 to 1.08. 5.4 Shear ductility
The highest value has been observed in small size
beams. As the beam depth increases beams exhibited Though deep-beam failure is considered brittle in
brittle failure. design provisions, under certain circumstances deep
beams exhibit a reasonable ductility. To understand
ductility of beams failing in shear, shear ductility is
5.3 Load-deflection curves and diagonal strains defined as the ratio of Ac/Au, where Au is the area
under the load deflection curve up to ultimate load
Figure 4 shows the load–deflection curves of beams and Ac is the area under the load deflection curve for
with SRI 0.0. Similarly, the load-deflection curves in a beam up to its complete collapse. With certain
beams with SRI 0.0 to 0.8 respectively with different limitations shear ductility can measure the ductility
beam sizes have been drawn. It has been observed of RC beams failing in shear. It has been observed
that beams of 750 mm depth have higher deflections that shear ductility increases linearly as the SRI in-
at ultimate load and their failure is relatively brittle creases. However, this increase is prominent after
SRI of 0.4. Further, as SRI increases beyond 0.6, the REFERENCES
shear ductility has been found to increase signifi-
cantly. Also, it has been observed that large size Aguilar, G. Matamoros, A. Ramirz, J. and Wight, J. 2001. Ex-
beams exhibited brittle failure than those of small perimental evaluation of design procedures for shear
strength of deep RC beams. ACI StrJl 99(4): 539-548.
and medium size beams, in which the failure seems Anngelakos, D. Bentz, D. and Collins, M. 2001. Effect of con-
to be ductile. crete strength and minimum stirrups on shear strength of
large members. ACI StrJl 98(3): 290-300.
Ashour, A. and Morley, C. 1996. Effectiveness factor of con-
5.5 Comparison of code provisions crete in continuous deep beams. Jl St Eng 122(2): 169-178.
Ashour, A. 2000. Shear capacity of reinforced concrete deep
The ratio of experimental shear strength and those beams. Jl of StrEngg 126(9): 1045–1052.
evaluated using ACI 318, IS 456 and BS 8110, Bakir P. Boduroglu, H. 2005. Mechanical behaviour and non-
Vu/VACI and Vu/VBS are compared in all the tested linear analysis of short beams using softened truss and di-
rect strut and tie models. Eng Str 27: 639–651.
beams. It has been noticed that the shear strength Bazant, Z.P. and Oh, B.H. 1983.Crack band theory for fracture
provisions are more conservative for deep beams ac- of concrete. Mat and Strs, 16(93):155-177.
cording to IS 456 and ACI 318 than those of Collins, M. and Kuchma, D. 1999. How safe are our large,
BS8110 for small and medium size beams, while lightly reinforced concrete beams, slabs, and footings?. ACI
BS8110 code provisions are more conservative for Str Jl,.96(4): 482-490.
large size beams of depth greater than 750mm. Hillerborg, A. Modeer, M. and Petersson, P.E. 1976. Analysis
of crack formation and crack growth in concrete by means
However, code provisions by IS 456 give the most of fracture mechanics and finite elements. Cem Con Res
conservative ultimate shear strength of deep RC 6(6): 773-782.
beams. Further, it is worth mentioning that only BS Iguro, M. Shioya, T. Nojir, I.Y. and Akiyama, H. 1984. Ex-
8110 considers the size effect in shear strength of perimental studies on shear strength of large reinforced
RC beams. The design of RC deep beams consider- concrete beams under uniformly distributed loads. JSCE
Proc, 1(345): 137-154.
ing size effect given by BS 8110 seems to be appro- Jenq, Y. and Shah, S.P. 1985. Two parameter fracture model
priate for shear design of RC deep beams. for concrete. Jl. of Eng Mech 111(10): 1227-1240.
Karim, R. 1999. Shear strength prediction for concrete mebers.
Jl of Str Eng 125(3): 301–308.
6 CONCLUSIONS Khaldoun, R. and Khaled, A. 2004. Minimum transverse rein-
forcement in 65 MPa concrete beams. ACI StrJl 101(6):
872-878.
1. The modes of failure in reinforced concrete deep Kotsovos, M. 1990. Strength and behaviour of deep beams, in
beam are influenced by the beam size and the ’Reinforced Concrete Deep Beams’ by F. K. Kong, Van
percentage of shear reinforcement. However, as Nostrand Reinhold Publications, New York.
the depth of beam and amount of web reinforce- Lubell, A. Sherwood, T. Bentz, E. and Collins, M. 2004. Safe
ment increase the failure seems to be due to shear design of large, wide beams. Conc Intl, Jan, 67-77.
Mau, S.T. and Hsu, Thomas, T. Shear strength prediction for
shear-compression failure. deep beams with web reinforcement. ACI Jl 96: 513-523.
2. Deep beams exhibit significant reserve strength Raghu, P. and Priyan, M. 2000. Experimental study on shear
in shear measured as the ratio of Vu/Vcr. After a strength of high strength concrete beams. ACI StrJl, 97(4):
564-571.
fully developed diagonal crack, small beams ex- Russo, G. Venir, R. and Pauletta, M. 2005. Reinforced con-
hibit high reserve strength than large beams. crete deep beams – shear strength model and design for-
3. Increase in shear reinforcement increases the ul- mula. ACI Str Jl 102(3): 429-437.
timate shear strength of RC beams. However, in Smith, K. and Vantsiotis, A. 1982. Shear strength of deep
beams. ACI StrJl, 79(3): 290-300.
larger size beams, at a given shear reinforcement Tang, C. and Tan, K. 2004. Interactive Mechanical model for
large size beams exhibit less strength and fail in shear strength of deep beams. Jl of Str Engg 130(10):
a brittle manner. 1534–1544.
Yang, K. Chung, H. Lee, E. Eun, H. 2003. Shear characteris-
4. As the depth of beam increases, the crack width tics of high-strength concrete deep beams without shear re-
also increases. However, with increase in inforcements. Engg Strs 25: 1343–1352.
amount of shear reinforcement, the crack width Zararis, P. 2003a. Shear compression failure in reinforced con-
decreases. crete deep beams. Jl of Str Engg 129(4): 544-553.
5. The shear ductility of RC deep beams increases
as the shear reinforcement increases. The in-
crease is significant in beams with shear rein-
forcement index greater than 0.6.
6. ACI 318 shear strength provisions on deep
beams are conservative and it does not consider
size effect, while BS8110 code provisions are
appropriate for deep-beam design.