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High Strength Eccentrically Loaded Slender
Reinforced Concrete Deep Beams with Vertical
Edge Restraints
Ali Belhacene, Ahmed Bouhaloufa, Kaoutar Zellat, Tahar Kadri
LMPC, Civil Engineering Department, university of Mostaganem, Algeria
Abstract Buckling tests were carried out on 6 reinforced concrete deep beams
having height/thickness ratios in the range 25 to 67. Observations were made on
the ultimate loads and failure modes. The variables studied included the
height/thickness ratio h/b, the load eccentricity/thickness ratio e/b. The observed
behavior and failure modes of these beams were compared with those of similar
specimens tested without vertical edge restraints as reported in the literature. The
measured ultimate loads were also compared with values predicted using C.I.R.I.A
guide 2: The design of deep beams in reinforced concrete. The aim of this
experimental program is to study the behavior of slender high strength reinforced
concrete deep beams with edge restraints or fixed ends under two top eccentrically
concentrated loads. The eccentricity applied at the top and the bottom was
intentional. This work is intended to provide more experimental data about the
range of mode of failure of these structures that should be considered in design.
The test beams were of height h=1000mm, overall length L=1700mm and simple
span Lo=1400mm giving a span to depth ratio Lo/h of 1.4. The thickness varied
from 40 to 15 mm giving a height to thickness ratio h/b ranging from 25 to67.
Particular attention has been directed towards the mode of failure, the failure load,
the shear strength and the effect of the end conditions on the behavior of these
particular structures.
1 Introduction
The Reinforced concrete deep beams have useful application in tall buildings,
offshore structures and foundations, however their design is not yet covered by the
BS 8110 which explicitly states that “for the design of deep beams, reference
should be made to specialist literature” [1].
Currently, the main design documents are the American code ACI-318-99 [2] ; the
CEB-FIP model code and the C.I.R.I.A guide N° 2, [3] notes that the new Euro
code EC 2 [4] gives only a very brief reference in this area. For this reason, the
2
C.I.R.I.A guide is the only document which gives recommendations on the
buckling strength of slender deep beams [5].
Experiments on slender deep beams are comparatively difficult to carry out and
require attention to details to prevent injury to personnel or damage to equipment.
Probability for this reason, experimental data on the buckling strength of deep
beams are difficult to find in the literature [6]. At the end of the C.I.R.I.A guides
appendix C (Buckling strength of deep beams) [7], it is pointed out that “there is
no experimental evidence to substantial these procedures”.
Fixed end or partially fixed end conditions in reinforced concrete deep beams are
more likely to occur in actual structures than simply supported end conditions. In
buildings, deep beams supported on walls running
in the transverse directions are effectively fixed or partially fixed, the restraints
being provided by the transverse walls. Other cases with a partial fixation, or fixed
end conditions, are concerning deep beams supported on heavy columns [8].
In the past, although there has been a considerable amount of published work on
single-spam reinforced concrete deep beams with simple supports, very few
publications have dealt with deep beams with fixed boundary conditions.
The objective of this experimental is to study the behavior of simply supported
slender reinforced concrete deep beams with vertical edge restrained under two
top loads with intentional eccentricities at the top and bottom and to provide more
experimental data about the range of failure of slender edge restrained reinforced
concrete deep beam that should be considered in design.
Particular attention has been directed towards: the mode of failure, the out-of
plane lateral displacement, the failure load, the shear strength, the crack patterns
and its propagation at various stages of loading and the effects of the restraints on
the behavior of slender reinforced deep beams.
2 Material and methods
The test specimen (Fig.1) consisted of 6 slender reinforced concrete deep beams-
the test beams (Figs 1, 2 and table 1) were of height h = 1000 mm, overall length
L = 1700 mm, and simple span Lo = 1400 mm, giving a span = height ratio Lo / h
of 1.4. The thickness varied from 40 to 15 mm, giving a height = thickness ratio
h/b ranging from 25 to 67. The beams had rectangular-mesh web reinforcement
(Fig.1). Plain round web bars, of 6 mm diameter and 410 N.mm-2 average yield
stress were used, except for the thinner beams where 2 mm wires of 410 N/ were
used. The main tension reinforcement consisted of three deformed bars placed
near the bottom of the beam.
3
Figure.1 Formwork, dimensions and loading schemes of test specimen
The main tension reinforcement consisted of three deformed bars placed near the
bottom of the beam (Fig.2); previous investigations have shown that such an
arrangement of the main tension reinforcement could substantially increase the
shear resistance of the beam [9;13]. Depending on the beam thickness, the
following bar sizes were used 8 mm (537 N.mm-2), 12 mm (446 N.mm-2), and 16
mm (480 N.mm-2) (Fig.2).
Figure.2 Reinforcement arrangement and dimensions of test beams
Concrete was made from rapid hardening Portland cement and zone M-sand to BS
882 [15]. Table 1 gives the cube strength fcu and the tensile splitting strength ft on
the day of the beam test.
Table.1 Concrete properties and steel ratios for the test specimens
4
Beam Thickness
(mm)
Eccentricity
(mm)
Aspect
ratio
D/b
Concrete properties Steel Ratios
Compressive fcu
N/mm²
Tensile ft
N/mm²
Main
Steel
AS%
Web Steel
Vertic
-al
AV%
Horizon
-tal
AH %
B.67-
0.2(Res)
15 3,0 66 73 4,8 1,004 0,84 0,85
B.50-
0.2(Res)
20 4,0 50 76 5,8 1,695 1,23 0,64
B.40-
0.2(Res)
25 5,0 40 68 4,9 1,357 0,48 1,00
B.33-
0.2(Res)
30 6,0 33 71 5,6 1,130 0,40 0,84
B.29-
0.2(Res)
35 7,0 29 74 5,8 1,722 0,34 0,72
B.25-
0.2(Res)
40 8,0 25 71 6,3 1,507 0,30 0,63
Figure 3 shows the concrete-strain relationships used and these experimental
works-cylinders were of height 200 mm and of diameter 10 mm were used for this
compression test-all the test performed shows clearly that she concrete of high
performance with compressive mean strength of 100 N/mm2 at the day of testing
and a mean value of 72 N /mm2 at 7 days.
Déformation, mm
0,000 0,001 0,002 0,003
Str
ess,
N.m
m-2
0
20
40
60
80
100
120
Test 1Test 2Test 3
Figure.3 Concrete-Stress-Strain relationships (experimental values)
5
3 Testing
In the beam notation, the prefix B denotes a beam of overall length L = 1700 mm
and overall height h = 1000 mm. This is followed by the height/thickness ratio and
then the eccentricity/thickness ratio e/b, the letters the between the brackets stand
for “restraints” for example.
B 67-0.2 (Res) refers to a beam of overall dimension of 1700 mm long by 1000
mm deep having an h/b ratio of 67 and an e/b ratio of 0,2 and the beam was tested
with the vertical edge restrained. The beams were tested under two-point top
loading (Fig. 1,2). Special bearing blocks allowed longitudinal translation, the
bearing blocks also restrained the concrete crushing at the bearing zone, which
was observed in some previous tests [10; 14].
The main frame of the vertical edge restraints consists of four independent I-
sections into which small angles were screwed at regular intervals on the inside
face covering the whole depth of the specimen Fig.4 .
a
b
(a) General scheme of the test rig (b) General photo of test rig
Figure. 4 General arrangement of test rig
Rollers were provided at the same location of these small angles to allow for a
low-friction support and to prevent a possible concentration of loading at a
particular section which might cause the failure of the specimen.
6
Depending on the eccentricity applied and the offset of the specimen, the gap
between the tie columns of the test rig and each independent component of the
frame was filled up with a wooden packing of the appropriate thickness-loads
were applied eccentricity, and the loading scheme used is shown in figure 2.
Continuous profiles of lateral displacements were monitored with a ripple-scanner,
which recorded the x, y, z coordinates simultaneously and continuously, as data in
a form that could be processed directly with a computer. Lateral displacements
were measured at discrete positions using 15 LVDT transducers and data-logger-
concrete strains were measured with demountable strain transducers (Fig.5).
To facilitate crack observation, the beams were cast in smooth formwork; a 100
mm square grid was marked on each face so that cracks could be located
accurately. Typically, the preparation and setting-up of a beam for testing took 3
days and the testing itself took 1 day. During testing an additional LVDT
transducer was used as a deflection limit detector, to cut off the load immediately
the deflection exceeded a preset limit. As a further safety precaution, one man was
engaged to keep a constant lookout to give warning of impending collapse or other
potential dangers.
(a)
(b)
Figure.5 (a) position of instrumentations (b) general arrangement and
dimensions of 100 mm gauge length strain transducers (%)
7
4 Results and discussions
Crack patterns and mode of failure of the specimens for all the beams test flexural
cracks initiated at early stage along soffit of the specimens. The most important
ones were those joining the point load at the supports i.e. diagonal cracks. Due to
the slenderness of the test specimens and due to the eccentricities applied at the
top and the bottom fig.6. Some horizontal cracks appeared as well and which
showed a beginning of buckling but the presence of the vertical edge restrains
have avoided this type of failure observed earlier for the same specimens tested
without vertical edge restrains [15].
Figure.6 Photo of the Side view of the lower part of the top-bearing showing the
applied eccentricity
Shear strength-comparison with the CIRIA guide predictions
All the beams, although restrained failed in shear and their ultimate strengths were
calculated using the CIRIA guide’s equation [8;14;17;18]:
Where:
1= 0.44 for normal weight concrete = 0,32 for light weight concrete
2 = 1.95 N.mm-2 for deformed bars = 0,85 N.mm-2 for plain round bars
b = Beam thickness
ha = Active height
ha = h or L whichever is the lesser
Respectively (Fig.8)
Xe = Effective clear shear span
8
.
Figure.7 Crack patterns at failure (shows also load in KN at which each crack
was first observed and the extent of the crack at that load, beam notation as in
Table 1)
Plate3a B.40-02 (Res) at failure Plate 3b B.33-02 (Res) at failure
Plate 3c B.29-02 (Res) at failure
Figure.8 Plate 3 a, 3.b and c presentation
9
Figure.9 Meaning of symbols of equation (1)
Table 2 Experimental shear strength values comparison with CI.R.I.A guide
predictions
4.1 Load Vs Mid-span deflection:
At the Mid-span of the specimens, the deflection was measured using mechanical
strain gauges at various stage of loading. Results are plotted in figure 10.
As the load, increases the mid-span deflection increases for all the test beam .The
thickness of the test beam have a great effect on the value of the mid-span
deflection. For the same load, the thicker the beam, the lower is the deflection as
the shown in fig.9.The maximum mid-span deflection occurs for the thinner beam
that is B.25-0.2Res and attained the value of 0.075mm for a failure load of about
800 KN. Note that, these deflections are not critical for these type of beams due to
their slenderness. Ordinary beams could have failed at this stage. Note that,
although, the test specimens are slender and eccentrically loaded, they did not
Shear failure loads
Beam
Measured
ultimate
Pm[KN]
CIRIA eqn.
P1[KN]
Pm/P1 Modified
CIRIA
Eqn. P2[KN]
Pm/P2
B.67-
0.2(Res)
300 197,6 1,52 178,8 1,7
B.50-
0.2(Res)
372 311,0 1,19 280,6 1,33
B.40-
0.2(Res)
440 338,0 1,30 305,0 1,44
B.33-
0.2(Res)
600 389,0 1,54 352,0 1,70
B.29-
0.2(Res)
750 524,0 1,43 472,0 1,58
B.25-
0.2(Res)
750 553,2 1,35 500,0 1,50
Mean 1,38 1,54
Standard
deviation 0,12 0,13
10
buckle due to the edge restraints. The same specimens tested without edge
restraints buckled as observed by some authors [14].
Deflection, mm
0,00 0,02 0,04 0,06
Lo
ad, k
N
0
200
400
600
800
B.67 - 0,2 (Res)
B.50 - 0,2 (Res)
B.40 - 0,2 (Res)
B.33 - 0,2 (Res)
B.29 - 0,2 (Res)
B.25 - 0,2 (Res)
Figure.10 Loads Vs Mid-span deflection.
4.2 Load Vs strain (compressive and tensile):
As the line joining the point load to the support was critical, measurements were
taken along this diagonal line. The electrical strain gauges disposed in Rosette at
the back face of the specimens as shown in Figure.5 registered the evolution of
the principal compressive and tensile strain as the load increases. The mechanical
strain gauges placed at the front of the specimen allowed us to measure along the
path load (diagonal line between the point load and the support) the change in
length of the mechanical studs dispose initially 100 mm apart. Results theses
measurements are plotted in Figure 11.
The evolution of stains with the applied eccentric load along the load path is
shown in fig.11a,The stains increases with the load and reaches the maximum
compressive value of 3800 micro-strains for test beam B.33-0.2Res and a
minimum compressive value of about 1000 micro-strains.
The tensile strains increases as well with the increase of the applied eccentric load
as shown in fig.11b.The maximum tensile strains reaches a value of about 5500
micro-strains for the test beam B.50-0.2Res.
11
Micro-Strain
0 1000 2000 3000 4000 5000
Lo
ad
, kN
0
50
100
150
200
250
300
350
B.50 - 0,2 (Res)
B.40 - 0,2 (Res)
B.33 - 0,2 (Res)
B.29 - 0,2 (Res)
B.25 - 0,2 (Res)
(a)
Micro-Strain
0 1000 2000 3000 4000 5000 6000
Lo
ad
, kN
0
50
100
150
200
250
300
350
(b)
(a): Compressive (b): Tensile
Figure. 11 Load-Strain in Experimental Values
5 Conclusions
In practical design, it cannot be guaranteed that loads will be truly central even
when the drawings show that they are, the author’s investigation has shown that
where the vertical edges of a slender deep beam are restrained, then an
unintentional eccentricity of up 0,2 times the beam thickness b will not change the
mode of failure which usually shear when loads are centrally applied.
The mode of failure is strongly dependent on the load eccentricity/thickness ratio
e/b. An increase in the e/b ratio would significantly increase the likelihood of the
failure mode changing from shear to buckling.
The CIRIA guide’s equation was modified as suggested by Chemrouk et al.,
2004[9], however the only effect of modification was that in the previous equation
eX would be taken as the total shear span tX
and not the clear span Xe; Table.2
shows the measured loads together with the predictions using both the CIRIA
guide equation (1) and the modified one as suggested by (Chemrouk et al., 2004)
[9].
In slender deep beams, the end anchorage of the main tension bars is unlikely to
be a problem in practice. In the tests, these bars were not anchored to external
steel blocks and yet no bond failure was observed.
The author’s tests have shown that transition from the shear failure mode to the
buckling mode occurs well above e/b = 0,2.
The authors suggest that further research should be carried out to provide more
detailed information on this point as well as the effects of web steel detailing and
variables such as the shear-span to depth ratio.
The restraint of vertical edges of slender concrete deep beams was an effective
way of increasing the ultimate load and changing the mode of failure from
buckling to shear. This conclusion was derived from comparison of the results of
12
the author’s tests with those of previous tests on comparable specimens without
edge restraints [14].
In the future, the authors try to determine the value of e/b from which the
transition from the shear mode of failure to the buckling mode of failure will
occur.
References
1. American Concrete Institute 1999, (ACI318-99) and commentary (ACI318R-99) “Building
Code Requirements for Reinforced Concrete”..
2. British Standard Institution. BS 112 “Method for Sampling and Testing of Mineral
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1986, 3pp.
3. British Standard Institution. BS8 110 “The Structural Use of Concrete, Par.I._(Design,
Materials and Wormanship”, London, 1985, 117pp.
4. Chemrouk M. and Kong F.K.,2004 “High Strength Concrete Continuous Deep Beams with
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pp: 229-243. Multi-Science publishing co.ltd.
5. Chemrouk M. and Kong F.K., 2003 “Instability of Slender Concrete Deep Beam –Panels
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