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

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Code Requirements for Reinforced Concrete”..

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3. British Standard Institution. BS8 110 “The Structural Use of Concrete, Par.I._(Design,

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