experimental investigation of rc beams with rectangular spiral reinforcement in torsion

8/11/2019 Experimental investigation of RC beams with rectangular spiral reinforcement in torsion

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Experimental investigation of RC beams with rectangular spiral

reinforcement in torsion

Constantin E. Chalioris , Chris G. Karayannis

Department of Civil Engineering, Democritus University of Thrace, Xanthi 67100, Greece

a r t i c l e i n f o

Article history:

Received 30 December 2012

Revised 21 March 2013

Accepted 2 May 2013

Available online 6 June 2013

Keywords:

Rectangular spiral reinforcement

Torsion

Reinforced concrete beams

Tests

a b s t r a c t

Recently, the use of continuous spiral reinforcement has been extended in reinforced concrete elements

with rectangular cross-sections. The behaviour of reinforced concrete beams with rectangular cross-sec-

tion and continuous rectangular spiral reinforcement as transverse reinforcement under pure torsion is

experimentally investigated. The presented experimental program comprises 11 beams. Test results of

this study clearly indicated that the use of rectangular spiral reinforcement provided enhanced torsional

capacity and improved post peak performance in the examined beams. Compared to beams with equal

quantity of the commonly used stirrups the measured increase of the torsional strength for the tested

beams under imposed twist that locks the spirals was 18%, 16% and 14% for the beams with transverse

reinforcement spacing at 200 mm, 150 mm and 100 mm, respectively. However, it is stressed that when

spirals are unlocked due to the direction of the external twist the torsional capacity of the beams is

decreased and considerable concrete spalling is observed compared to beams with equal quantity of

the commonly used stirrups.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

The beneficial effect of continuous steel spirals to the capacity,

the concrete confinement and the ductility of Reinforced Concrete

(RC) elements with cyclic cross-section has long been recognised

[14]. Recently, the use of continuous spiral reinforcement has

been extended in RC elements with rectangular cross-sections.

RC subassemblages of external beam-column joints, columns and

infilled frames with rectangular members and Rectangular Spiral

Reinforcement (RSR) as shear reinforcement have been tested un-

der cyclic loading[5,6]. The experimental results of these tests re-

vealed that the application of RSR in many cases improved the

overall seismic performance of the examined specimens in com-

parison with the conventionally reinforced subassemblages[7,8].

The application of spiral transverse reinforcement in circular RC

elements under cyclic deformations with torsional effect hasextensively been investigated [911]. The influence of the spirals

locking and unlocking on the concrete confinement, the concrete

cover spalling and the overall hysteretic response of the RC ele-

ments has also been noted in these works. Further, the problem

of reverse cyclic torsional loading in circular concrete members

with spiral transverse reinforcement has been examined and a

new effective confinement technique consisting of two opposing

and crossing spirals has been proposed [12]. Moreover, a shear

truss analytical model for evaluating the contribution of the spiral

transverse reinforcement in solid and hollow circular RC members

has recently been presented[13].

Furthermore, the use of RSR in shear-critical RC beams with

rectangular cross-section has been studied by Karayannis et al.

[14], whereas Yang et al. [15] examined the shear behaviour of

concreteT-beams that have been reinforced using spiral-type wire

rope as internal shear reinforcement.

The recent technical expansion for massive use of continuous

rectangular spiral reinforcement in rectangular reinforced concrete

elements gives the opportunity for wide using of this kind of rein-

forcement in beams under torsion. Concerning the issue of torsion

in concrete members, it is well-known that torsional cracks form a

spiral pattern due to the principal tensile stresses developing in the

diagonal concrete struts [1618]. Thus, steel spirals that cross

approximately orthogonal the torsional cracks consist one of the

most efficient transverse reinforcement against torsional action.The ratio of the steel longitudinal and transverse reinforcement

along with the geometrical and mechanical properties of the RC

members influence the angle of the diagonal cracking [19] and

therefore the optimum angle of the spiral links that should be pro-

vided has to be considered accordingly.

Further, it has been proved that the unlocking effect due to tor-

sion applied in the reversed direction comparing to the direction of

the spiral reinforcement amplifies the occurrence of spalling and

also softens the core concrete resulting in a reduction of the overall

capacity of the reinforced concrete element [10]. Only a few

innovative spiral reinforcement techniques, such as crossing

spirals and spiral-type wire rope, have already been proposed in

0141-0296/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2013.05.003

Corresponding author. Tel./fax: +30 25410 79632.

E-mail address:[email protected](C.E. Chalioris).

Engineering Structures 56 (2013) 286297

Contents lists available at SciVerse ScienceDirect

Engineering Structures

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order to eliminate the observed shortcomings due to the action of

torsion or/and shear[12,15].

The aforementioned review of literature reveals that most of

the experimental research conducted to investigate the behaviour

of spirally reinforced circular RC elements under predominant tor-

sion or shear. Moreover, the published work on the use of rectan-

gular spiral reinforcement as transverse reinforcement in RC

elements with rectangular cross-section is very limited, mainly

carried out by the authors and therefore this area is still an open

field of study.

In this work, the behaviour of RC beams with rectangular cross-section and RSR as transverse reinforcement under pure torsion

(11 specimens) is experimentally investigated. The influence of

the RSR on the cracking and the post-cracking response is exam-

ined, whereas the locking and unlocking effect of the spirals due

to the direction of the imposed twist is also studied.

Both locking and unlocking effects of the RSR usually occur in

rectangular columns under cyclic torsional loading due to seismic

excitations imposed in asymmetrical RC structures[9,10]. Further-

more, although unlikely, the unlocking case might happen when

the spiral is wrongly placed. For these reasons, the case of the unfa-

vourable influence of the imposed twist that unlocks the spirals is

also investigated herein. The contribution of the examined RSR on

the torsional capacity, the cracking patterns and the overall perfor-

mance of the tested beams is also reported and commented.

2. Experimental program

The experimental program reported in this research includes

eleven (11) beams with rectangular cross-section subjected to

monotonic action of pure torsion. The transverse reinforcement

of six specimens consisted of steel spirals with rectangular shape

(Rectangular Spiral Reinforcement RSR), whereas three speci-

mens had common closed stirrups. Two beams had no transverse

reinforcement and they were used as control specimens.

2.1. Characteristics of the tested beams

All eleven beams have the same total length (1.60 m), the sameexamined length tested under pure torsion (600 mm) and the same

cross-sectional dimensions (200/100 mm), as shown inFig. 1. The

longitudinal reinforcement of 10 specimens is also the same; four

deformed bars of diameter 8 mm (48) at the corners of the rect-

angular cross-section that correspond to a longitudinal reinforce-

ment ratio ofql Asl=Ac 1:0%. Only the control specimen with

the codified name P has no steel bars. The measured yield and

ultimate tensile strength of the longitudinal bars were fsly= 518 -

MPa andfslu= 656 MPa, respectively.

The transverse reinforcement of the beams in the examined

pure torsional region varies. The control specimens P and L

have no transverse reinforcement at all. The other nine beamsare sorted in three groups based on the spacing of the transverse

reinforcement in mm; 200, 150 and 100 mm (see alsoFig. 1andTa-

ble 1). Each group consists of three beams; one with common

closed stirrups and two with RSR. Geometrical details and the incli-

nations of the applied spiral reinforcement are also presented in

Fig. 2. Further, the ratios of the provided longitudinal and trans-

verse reinforcement along with the values of the inclination of

the transverse reinforcement in respect to the longitudinal axis

of the beam are presented inTable 1.

Mild steel bars with diameter equal to 8 mm (8) form the stir-

rups and spirals. The yield and the ultimate tensile strength of the

transverse steel reinforcement were measured fsty= 365 MPa and

fstu= 536 MPa, respectively.

It is mentioned that although bars and stirrups of the tested

beams have the same diameter (8), different grades (deformed

and mild steel, respectively) have been selected in order to repre-

sent the common practice of the previous decades construction.

Furthermore, this way the ratio qlfslyqtfsty

(see alsoTable 1) in the exam-

ined beams of Group-100 (with high transverse reinforcement) is

approximately equal to 1.0 and therefore the torsional cracking an-

gle is expected to be approximately 45.

Fig. 1 displays the steel reinforcement arrangements of the

beams. It is noted that the end parts of the beams are heavily rein-

forced with high volume of stirrups in order to bear without crack-

ing the imposed torsional loading.

Concerning the anchorages of the provided transverse rein-

forcement (stirrups and spirals), the links of the closed stirrups

are effectively anchored as shown in Fig. 1. Further, at each endof the RSR one full spiral step is placed within the corresponding

Nomenclature

a inclination of the diagonal compression struts (crackingangle), deg

aexp measured angle of the diagonal compression struts, degacalc calculated angle of the diagonal compression struts, degAc area of the cross-section of the beam, mm

2

Asl area of the total steel longitudinal reinforcement, mm2

Ast area of one legged steel stirrup or spiral, mm2

b, h width and height of the cross-section of the beam, mmfcm mean cylinder compressive strength of concrete, MPafctm mean tensile splitting strength of concrete, MPafsly measured yield strength of the longitudinal steel bars,

MPafslu measured ultimate tensile strength of the longitudinal

steel bars, MPafsty measured yield strength of the transverse steel rein-

forcement (stirrups or spirals), MPafstu measured ultimate tensile strength of the transverse

steel reinforcement (stirrups or spirals), MPaK initial pre-cracking torsional stiffness, kN m2/radpst perimeter of the steel stirrup, mm

po perimeter of the centreline of the shear flow in spacetruss analysis, mm

s uniform spacing of the steel transverse reinforcement(stirrups or spirals), mm

td effective thickness of the compression zone in the diag-onal compression struts in space truss analysis, mm2

Tcr measured torsional moment at cracking, kN m

Tu measured post-cracking ultimate torsional moment,kN m

Tmax maximum torsional capacity, kN mTmax,exp measured maximum torsional capacity, kN mTmax,calc calculated maximum torsional capacity, kN m#Tcr measured angle of twist per unit length at cracking, rad/

m#Tu measured angle of twist per unit length at the post-

cracking ultimate torsional moment, rad/mql normalised ratio of the steel longitudinal reinforcement,

%qt normalised ratio of the steel transverse reinforcement, %uand u 0 angle (inclination) between transverse reinforcement

and the longitudinal axis of the beam, deg

C.E. Chalioris, C.G. Karayannis / Engineering Structures 56 (2013) 286297 287
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heavily reinforced end parts of the beam. This extra spiral stepworks as an anchorage for the RSR.

The codified names of the torsional beams presented inFigs. 1and 2and Table 1comprise the following two parts of digits. The

600100

200

5005001600

P

pure torsion test region

600

L

8

48

ST200

100

200

SPL200

SPU200

200

T

T

T

ST150

SPL150

SPU150

ST100

SPL100

SPU100

100

100

150

150

150

200

8 8

T

T

T

T

T

T

T

T

T

88

88

8 8

88

88

88

88

8

8

Group-200

Control

Group-150

Group-100

80

80

80

80

80

80

Fig. 1. Geometry and steel reinforcements of the tested beams.

288 C.E. Chalioris, C.G. Karayannis/ Engineering Structures 56 (2013) 286297


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first part indicates the reinforcement; P for the control plain con-

crete beam without longitudinal or transverse reinforcement, L

for the control beam with longitudinal bars only, ST for the

beams with stirrups, SPL for the beams with rectangular spiral

reinforcement under favourably imposed action of the torsional

moment that causes spirals to be locked and SPU for the beams

with rectangular spiral reinforcement under unfavourably imposed

twist that causes spirals to be unlocked. It means that in the latter

case torsion is applied in the reversed direction comparing to the

direction of the spiral reinforcement. The last part denotes the

spacing of the steel transverse reinforcement in mm and appearsonly for the specimens with stirrups or spirals.

The cement used in the beams of the presented experimental

program was locally-manufactured, general-purpose ordinary

Portland type cement (type 35IIa, Greek type pozzolan cement

containing 10% fly ash). Sand with a high fineness modulus and

coarse aggregates with a maximum size of 9.5 mm was used. The

concrete mixture was made using cement, sand, crushed stone

aggregates and water in a proportion 1:2.8:1.2:0.425, respectively.

Chemical admixtures were not used in the mix. The concrete com-

pressive and tensile strength have been measured from compres-

sion and splitting tests of standard cylinders and their mean

values arefcm= 23.0 MPa and fctm= 2.67 MPa, respectively.

2.2. Test rig and instrumentation

The experimental setup of the torsional beams is a commonly

used torsional test rig, as it is shown in Fig. 3. The total length of

the specimens was 1600 mm. Beams were supported on two roller

supports 1300 mm apart. These supports ensured that the beam

was free to twist and to elongate longitudinally in both end direc-

tions during the test. The load was applied through a diagonally

placed steel spreader beam on the ends of two steel arms fixed

at the end parts of each tested beam. The 500 mm long end parts

of the specimens were heavily reinforced with high volume of stir-

rups in order to bear without cracking the imposed torsional load-

ing (see alsoFig. 1). The examined test region was the central part

(600 mm long) of the specimens. In all the examined cases duringthe test procedure, torsional helical diagonal cracking and, finally,

failure were localised within this test region, whereas the heavily

reinforced end parts of the beams remained practically intact.

The load was imposed consistently in low rate (approximately

0.001 rad/min for the pre-cracking part and for the plain concrete

beams and 0.005 rad/min after the full cracking of concrete) and

was measured by a load cell with accuracy equal to 0.025 kN.

The average angle of twist per unit length of the tested beams

was estimated using the measurements of two linear variable dif-

ferential transducers (LVDTs) with high accuracy (0.001 mm).

These two LVDTs measured the opposite deformations of each

specimen as it rotates and were placed at the ends of the centraldeformable part of the specimens 600 mm apart from each other

as shown inFig. 3.

In order to acquire useful information about the failure modes

of the tested beams, the strains of the longitudinal and transverse

steel reinforcements were measured by electrical resistance strain

gauges. Two strain gauges were mounted on each longitudinal bar

and on the stirrups at midspan at the effective central span of the

beams. Measurements for load, deformations and steel strains

were read and recorded continuously through a data acquisition

system. The beams were tested in monotonically increasing torque

moment until the ultimate torsional strength and subsequently in

increasing twist until the total failure of the specimen.

3. Test results and discussions

The torsional behaviour of all the tested beams is presented in

Figs. 46in terms of experimental curves of torsional moment ver-

sus angle of twist per unit length. Each Figure (Figs. 46) depicts

the torsional behaviour of the beams of each group (Group-200,

Group-150 and Group-100, respectively) and the measured tor-

sional responses of the control specimens (beam P without rein-

forcement and beam L without transverse reinforcement) for

comparison reasons.

The measured torsional moment at cracking, Tcr, the angle of

twist per unit length at cracking,#Tcr, the initial pre-cracking tor-

sional stiffness, K, the post-cracking ultimate torsional moment,

Tu, and the corresponding angle of twist per unit length, #Tu, ofthe beams are presented in Table 1. It is noted that the control

Table 1

Test results.

Group Beam codified

name

ql

(%)

qt

(%)

uand u 0

(deg)

Tcr(kN-m)

#Tcr(rad/m)

K(107) pre-cracking

(kN m2/rad)

Tu(kN-m)

#Tu(rad/m)

Tmax(kN-m)

Failure mode

Control P 1.934 0.009 3079 1.934 C

L 1.005 2.098 0.007 3558 2.098 L

Group-

200

ST200 1.005 0.613 9 0 2.171 0.008 3771 2.385 0.051 2.385 T

SPL200 1.005 0.672 66 and

114 *1.997 0.007 3653 2.822 0.092 2.822 T

SPU200 1.005 0.672 66 and

114 *1.924 0.007 3810 1.924 TSp

Group-

150

ST150 1.005 0.818 9 0 2.013 0.008 3084 2.649 0.074 2.649 T

SPL150 1.005 0.859 72 and

108 *2.203 0.009 3617 3.068 0.065 3.068 CF

SPU150 1.005 0.859 72 and

108 *1.944 0.007 3725 2.035 0.033 2.035 CFSp

Group-

c100

ST100 1.005 1.226 90 2.008 0.009 3229 3.254 0.099 3.254 CF

SPL100 1.005 1.253 78 and

102 *2.406 0.010 3628 3.705 0.083 3.705 CF

SPU100 1.005 1.253 78 and

102 *2.029 0.007 3650 2.582 0.067 2.582 CFSp

ql AslAc

andqt Astpst

Acs sinu.

uand u0: angle (inclination) between transverse reinforcement and the longitudinal axis of the beam (u6 90, u0 > 90 and u + u0 = 180).* It refers to the spiral reinforcement links where two inclination angles are measured.

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specimens P and L along with beam SPU200 did not exhibit

increasing post-cracking response, as also shown in Fig. 4. Thus,their maximum torsional moment capacities were equal to the cor-

responding torsional moment at cracking: Tmax=Tcr. For all the

other specimens: Tmax=Tu. The values of the maximum torsionalmoments are also presented inTable 1.

200

150

600

600

100

600

SPL100 & SPU100

SPL150 & SPU150

SPL200 & SPU20070

172

72

7030

30

66

200

114

172

72

72

150

22

53

53

22

108

172

72

78

100

15

35

15

35

102

Fig. 2. Details of the spiral reinforcement.



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From the values of the elastic torsional stiffness and the

slopes of elastic parts of the behavioural curves it is deduced

that the initial pre-cracking torsional rigidity remained practi-

cally unaffected by the amount of the reinforcement used. Fur-

ther, the values of the cracking torsional moment and thecorresponding angle of twist per unit length of the tested beams

reveal that the initial torsional response till the point of the con-

crete cracking is characterised by high value of torsional stiff-

ness. In this elastic stage till the first cracking the percentage

of steel has a minor importance and a reinforced concrete beam

behaves more or less as a homogeneous plain concrete member[20,21].

P

1600

load cell

LVDT

LVDT

steel spreader beam

steel arm

tested beam

roller support

Fig. 3. Test rig and instrumentation.

200

200

T

T

200 T

T

Torsionalmoment(kN-m)

Angle of twist per length (rad/m)

SPL200

ST200

SPU200L

P

Fig. 4. Experimental behaviour of the beams of Group-200 and the control beams.

150

150

T

T

150 T

T

Torsionalm

oment(kN-m)


SPL150

ST150

SPU150

L

P


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The post-cracking torsional response and the values of the ulti-

mate torsional moment of the beams indicate that the transverse

reinforcement strongly affects the torsional capacity and the over-

all behaviour, as it was expected[22]. The increase of the amount

of the steel stirrups provided causes significant increase in the tor-

sional capacity and ductility of the examined beams.

Further, from the test results ofFigs. 46andTable 1it is veri-

fied that beams with RSR under favourable imposed twist (spirals

are locked) exhibit substantially improved torsional performance

with respect to the corresponding beams with stirrups at the same

spacing. On the contrary, the beams with RSR under unfavourable

imposed twist (spirals are unlocked) show considerably reduced

torsional capabilities. Thus, the crucial effect of locking and unlock-

ing of the spirals on the torsional response of the examined beams

is clearly identified. When spirals are locked they resist more effec-

tively to the imposed torsional action and contribute more to the

confinement of the concrete core compared to equal quantity of

the commonly used stirrups. On the contrary in the case where spi-

rals are unlocked which means that torsion is applied in the re-versed direction comparing to the direction of the spiral

reinforcement beams resist less effectively to the imposed torsion

than the corresponding ones with equal quantity of the commonly

used stirrups. In these cases increased spalling and reduced con-

finement of the concrete core are also observed.

Figs. 710 display the crack patterns of the torsional beams at

failure. Based on the cracking formation of each beam, the inclina-

tion of the diagonal compression struts is also marked in these fig-

ures. From these photographs it can be observed that the control

specimen P without bars and stirrups showed an abrupt collapse

by failure of concrete and separation in two parts (Fig. 7a), whereas

the control specimen L without transverse reinforcement also

failed in a similar manner exhibiting brittle torsional failure; it

developed an intense single helical crack whereas the bars pre-vented the splitting of the specimen in two parts (Fig. 7b). Further,

beams with longitudinal and transverse steel reinforcement

showed an increasing post-cracking behaviour along with the for-

mation of a number of helical and diagonal cracks that became

excessively wide as the imposed twist increased (Figs. 810).

Beams with spirals that were locked during the imposed twist

(favourable torsion) exhibited helical and diagonal cracks that

crossed approximately vertical the spiral links (Figs. 8b, 9b, and

10b). On the contrary, cracking of beams with spirals that were un-

locked during imposed twist (unfavourable torsion) was almost

parallel to the spiral links and severe concrete spalling was ob-

served (Figs. 8c,9c, and10c).

Based on the crack patterns and the measurements of the

strains of the longitudinal and transverse steel reinforcement the

following failure modes have been observed (the failure mode of

each tested beam is also denoted inTable 1):

C Concrete failure (absence of steel reinforcement)

CF Concrete failure before steel longitudinal or transversereinforcement yielding

CFSp Concrete failure along with severe spalling of concrete

cover before steel longitudinal or transverse

reinforcement yielding

L Longitudinal steel reinforcement yielded before final

concrete failure (absence of transverse steel

reinforcement)

T Transverse steel reinforcement yielded before concrete

failure, whereas longitudinal reinforcement did not

yield

TSp Transverse steel reinforcement yielded before concrete

failure along with severe spalling of concrete cover,

whereas longitudinal reinforcement did not yield

T

T 100

100

T

T

100

Torsional

moment(kN-m)


SPL100

ST100

SPU100

L

P


(a) Beam P

(b) Beam L

26

Fig. 7. Cracking patterns at failure of the control beams.



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4. Simplified analytical approach

The softened space truss theory[23]is a well-known analytical

model forthe problem of torsion in RC beams with bars andstirrups.

Thespace trussanalysis assumes thatthe externaltorsional moment

Tis resisted by an internal torque resulting from the shear flowq,

which is developed in the centre of a shear flow zone with an effec-

tivewall thicknesstd (see also notationin Fig. 11a). Further, based on

the stresses equilibrium, the following known relationships are de-

rived for the calculation of the inclination of the diagonal compres-

sion struts (cracking angle),a, and the torsional componentsTLand

TT, due to the longitudinal and the transverse steel reinforcement

(bars and vertical stirrups), respectively (Fig. 11b)[23,24]:

tana

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAstfstpoAslfsls

s 1

TL 2AslfslAo

potana and 2a

TT2AstfstAo

s cot a 2b

wherepo is the perimeter of the centreline of the shear flow; Ao is

the area enclosed by the centreline of the shear flow; Aslis the total

area of steel longitudinal bars;Astis the area of one legged steel stir-

rup;sis the spacing of steel stirrups;fslandfstare the stresses of the

longitudinal and the transverse steel reinforcement, respectively.

In the case of beams with spiral reinforcement as transverse

steel reinforcement, instead of the Eqs.(1), (2a), and (2b)that holdfor stirrups, the following relationships can be obtained from the

equilibrium of a section of the vertical wall of the beam, as dis-

played inFig. 11c and d:

For the case of rectangular spiral reinforcement with locking

effect (favourably imposed twist that locks the spirals) the fol-

lowing equations are derived (see alsoFig. 11c):

Force equilibrium along the longitudinal axis results to the

relationship:

FL FT;l qpo cot a 3

The force triangle ofFig. 11c in the perpendicular direction gives:

FT;t qs tana 4

(a) Beam ST200

(b) Beam SPL200

(c) Beam SPU200

38 38

54

38 47

42

Fig. 8. Cracking patterns at failure of the beams of Group-200.

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Substituting the shear flow, q, in Eqs.(3) and (4)with the equation

of Bredt: q T2Ao

, it can be derived:

TL 2FL FT;lAo

potana and 5a

TT2FT;tAo

s cot a 5b

Further, in order to determine the value of the cracking angle, a,based on the amount of the longitudinal and the transverse rein-

forcement, Eqs. (5a) and (5b) are combined and therefore it is

deduced:

tan a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFT;tpo

FL FT;ls

s 6

where FL= Aslfsl; FT,l=Astfstcos u; FT,t=Astfstsin u; u < u0;

u + u0 = 180.

For the case of rectangular spiral reinforcement with unlocking

effect (unfavourably imposed twist that unlocks the spirals) the

following equations are derived (see alsoFig. 11d):

Force equilibrium along the longitudinal axis results to the

relationship:

FL FT;l qpo cot a 7

The force triangle of Fig. 11d in the perpendicular direction also

gives Eq.(4).

In the same way, substituting the shear flow, q, in Eqs.(7) and

(4)with the equation of Bredt:

TL 2FL FT;lAo

potana and 8a

TT2FT

;

tAos cot a 8b

Further, the combination of Eqs.(8a) and (8b)gives:

tan a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFT;tpo

FL FT;ls

s 9

It is noted that the aforementioned analysis is a first simplified ap-

proach that takes into account the inclination of the RSR and the

locking or unlocking effect of the spirals. The proposed approach

can be initially used for the estimation of the inclination of the tor-

sional cracking. Furthermore it is stressed that the locking effect of

the RSR provides extra confinement in concrete that has an active

character that works beyond the known passive confining effect

of the common stirrups. In further investigation and towards takinginto account the active confinement of the spiral reinforcement

(a) Beam ST150

(b) Beam SPL150

(c) Beam SPU150

4343

43

4242


(a) Beam ST100

(b) Beam SPL100

(c) Beam SPU100

48

48 48

37 53




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with favourably imposed twist that locks the spirals triaxial model

of concrete strength might be implemented.

5. Comparisons of analytical and experimental results

5.1. Inclination of torsional cracking

The values of the cracking angle for the specimens with com-

mon stirrups (ST200, ST150 and ST100), RSR with locking effect

(SPL200, SPL150 and SPL100) and RSR with unlocking effect

(SPU200, SPU150 and SPU100) can be calculated based on the

Eqs. (1), (6), and (9), respectively. The calculated and the experi-

mentally measured cracking angles of the tested specimens are

presented inTable 2.

5.2. Ultimate torsional moment

The experimentally observed torsional behaviour of a typical RCbeam comprises two distinct regions; the elastic till the first crack-

ing part and the after cracking part. The different character of the

response in these regions reveals the different nature of the load

resisting mechanism in each case. Based on this observation, the

combination of two different models to evaluate the pre-crackingand post-cracking behaviour has recently been proposed[22].

Analytical predictions for the beams of the present study are

based on this combined approach. The estimation of the elastic re-

sponse till the first cracking and the calculation of the torsional

moment at cracking are achieved using the smeared crack analysis

for plain concrete in torsion[20], whereas for the evaluation of the

ultimate torsional moment at the post-cracking response the mod-

ified softened truss model[23]is used. It is noted that the greater

value from these two aforementioned torsional moments is the

calculated maximum torsional capacity of the beam, Tmax,calc.

The analytical predictions of the ultimate torsional moment for

the examined specimens with stirrups along with the observed val-

ues from thetests arepresented inTable 2. Inthe sametable the ob-

served ultimate torsional moments for the specimens with thespiral reinforcement are also presented for comparison reasons.

Fig. 11. Simplified torsional analysis based on the space truss theory.

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11/12

6. Contribution of the Rectangular Spiral Reinforcement (RSR)

Test results of this study clearly indicate that the use of RSR pro-

vides enhanced bearing capacity and improved performance in the

examined beams. However, it is stressed that the locking and

unlocking effects of the RSR in the torsional beams are very impor-

tant parameters that strongly influence the overall behaviour.

When spirals are locked due to the direction of the external

twist the torsional capacity of the beams is increased, whereaswhen they are unlocked the ultimate strength is decreased, the

post peak behaviour deteriorates and considerable concrete

spalling is observed compared to beams with equal quantity of

the commonly used stirrups. The measured increase of the

torsional strength is 18%, 16% and 14% for the tested beams un-

der favourably imposed twist that locks the spirals and trans-

verse reinforcement spacing at 200 mm, 150 mm and 100 mm,

respectively.

On the contrary, the measured decrease of the torsional

strength is 19%, 23% and 21% for the tested beams under unfavour-

ably imposed twist that unlocks the spirals and transverse rein-

forcement spacing at 200 mm, 150 mm and 100 mm, respectively.

Further, it is noted that in the case of the beams under loading

that unlocks the spirals, slippage of spiral reinforcement has not

been observed. This observation could lead to the conclusion that

spirals under unlocking effect continue to properly work as trans-

verse torsional reinforcement. However, due to the inclination of

the cracking angle as developed in the cases of RSR with unlocking

effect, the effectiveness of the spiral reinforcement is decreased

since in these cases torsional cracking inclination and spiral links

direction are far from normal to each other. This is in contrast with

the case of RSR with locking effect where cracking and spiral links

are approximately normal.

Moreover, inFig. 12 the influence of the steel transverse rein-

forcement ratio on of the torsional behaviour of the tested beams

with stirrups and RSR with locking and unlocking effect is evalu-

ated. FromFig. 12a it is deduced that the increase of the amount

of the provided stirrups from 0.613% to 0.818% and from 0.613%

to 1.226% causes a torsional capacity increase of 11% and 36%,respectively. FromFig. 12b it is further concluded that the propor-

tional increase of the provided RSR ratio with locking effect from

0.672% to 0.859% and from 0.672% to 1.253% also significantly in-

creases the maximum torsional moment per 9% and 31%, respec-

tively, as it was expected. The same more or less conclusion

holds for the increase of the provided RSR ratio with unlocking ef-

fect and the proportional increases of the maximum torsional mo-

ment can also be observed inFig. 12c.

However, a remarkable observation about the negative influ-

ence of the RSR under unfavourably imposed twist (unlocking ef-

fect) has clearly been revealed by the comparison of the tested

beams SPU100 and ST150 (see alsoFig. 12a and c). The behaviour

of beam SPU100 with RSR per 100 mm (qt= 1.253%) under unfa-

vourably imposed twist that unlocks the spirals (Fig. 12c) is very

close to the response of the beam ST150 with stirrups per

150 mm (qt = 0.818%) and significant lower transverse reinforce-

ment ratio (Fig. 12a). More or less the same observation can be ob-

tained for the maximum torsional capacity by the comparison of

the beams SPU150 and SPU100 with the beams ST200 and

ST150, respectively (see the values ofTmax in Table 1).

Table 2

Predictions and experimental values of the torsional cracking angle and the maximum capacity.

Group Beam codified name acalc(deg) aexp (deg) Tmax,calc (kN-m) Tmax,exp (kN-m)

Group-200 ST200 33 38 2.633 2.385

SPL200 31 42 and 54 2.822

SPU200 33 38 and 47 1.924

Group-150 ST150 37 43 2.775 2.649

SPL150 36 42 3.068

SPU150 37 43 2.035

Group-100 ST100 43 48 2.923 3.254

SPL100 42 37 and 53 3.705

SPU100 43 48 2.582

(a) Beams with stirrups

Torsionalmoment

(kN-m)


ST150(0.818%)

ST100

(1.226%)

ST200(0.613%)

+11%

+36%


SPL150(0.859%)

SPL100(1.253%)

SPL200(0.672%)

+9%

+31%


SPU150(0.859%)

SPU100(1.253%)

SPU200(0.672%)

+7%

+35%

Fig. 12. Influence of the steel transverse reinforcement ratio on of the torsional behaviour of the tested beams.



12/12

7. Concluding remarks

The behaviour of RC beams with rectangular cross-section and

Rectangular Spiral Reinforcement (RSR) as transverse reinforce-

ment under pure torsion is experimentally investigated. The influ-

ence of the RSR on the cracking and the post-cracking response is

examined, whereas the locking and unlocking effect of the spirals

due to the direction of the imposed twist is also studied. The re-sults of this study indicate the following concluding remarks:

The overall torsional behaviour is strongly influenced by the

locking or the unlocking effect of the spiral reinforcement. The

use of RSR with locking effect provides enhanced torsional

capacity and improved post peak performance. Compared to

beams with equal quantity of the commonly used stirrups the

measured increase of the torsional strength for the tested

beams under imposed twist that locks the spirals was 1418%.

In the cases that the direction of the external twist unlocks

the spirals, the torsional capacity of the beams is decreased

1923% and considerable concrete spalling is observed com-

pared to beams with equal quantity of the commonly used

stirrups. Although in this case slippage of spiral reinforcement

is not observed, it can be clearly observed that due to the

inclination of the cracking angle as developed in the cases of

RSR with unlocking effect, the effectiveness of the spiral rein-

forcement is decreased since in these cases torsional cracking

inclination and spiral links direction are far from normal to

each other.

The increase of the amount of the provided stirrups from 0.613%

to 0.818% and from 0.613% to 1.226% causes a torsional capacity

increase of 11% and 36%, respectively. Further, the proportional

increase of the provided RSR ratio with locking effect from

0.672% to 0.859% and from 0.672% to 1.253% also significantly

increases the maximum torsional moment per 9% and 31%,

respectively. The same conclusions more or less hold for the

increase of the provided RSR ratio with unlocking effect and

the proportional increases of the maximum torsional moment. Observations based on the comparisons of the experimental

results reveal similarities between the torsional behaviour or

the ultimate capacity of the tested beams with RSR with unlock-

ing effect and the beams with stirrups with less quantity trans-

verse reinforcement of common stirrups.

A simplified analysis approach that takes into account the incli-

nation of the RSR and the locking or unlocking effect of the spi-

rals has been developed. This approach can also be used for the

estimation of the inclination of the torsional cracking in these

cases.

References

[1] Park R, Paulay T. Reinforced concrete structures. John Wiley & Sons; 1975 .[2] Saatcioglu M, Razvi S. Strength and ductility of confined concrete. J Struct Eng

ASCE 1992;118(25):1590607.[3] Sheik S, Toclucu M. Reinforced concrete columns confined by circular spirals

and hoops. ACI Struct J 1993;90(5):54253.[4] Tsitotas MA, Tegos IA. Seismic behaviour of r/c columns and beams with

interlocking spirals. Adv Earthquake Eng 1995;2:44961.

[5] Karayannis CG, Sirkelis GM. Seismic behaviour of reinforced concrete columnswith rectangular spiral shear reinforcement. In: 3rd International conferenceon construction in the 21st century (CITC-III), Advancing Engineering,Management and Technology, Athens; 2005.

[6] Kakaletsis DJ, Karayannis CG, Panagopoulos GK. Effectiveness of rectangularspiral shear reinforcement on infilled R/C frames under cyclic loading. JEarthquake Eng 2011;15(8):117893.

[7] Tsonos AG. Improvement of the earthquake resistance of R/C beam columnjoints under the influence of PD effect and axial force variations usinginclined bars. Struct Eng Mech 2004;18(4):389410.

[8] Karayannis CG, Sirkelis GM. Response of columns and joints with spiral shearreinforcement. WIT Trans Modell Simul 2005;41:45563.

[9] Belarbi A, Prakash S, You Y-M. Effect of spiral reinforcement on flexuralsheartorsional seismic behavior of reinforced concrete circular bridge columns.Struct Eng Mech 2009;33(2):13758.

[10] Prakash S, Belarbi A, You Y-M. Seismic performance of circular RC columnssubjected to axial force, bending, and torsion with low and moderate shear.Eng Struct 2010;32(1):4659.

[11] Li Q, Belarbi A. Seismic behavior of RC columns with interlocking spirals under

combined loadings including torsion. Proc Eng 2011;14:128191.[12] Hindi RA, Browning BJ. Torsionally loaded circular concrete members confined

with spirals. ACI Struct J 2011;108(2):13747.[13]Turmo J, Ramos G, Aparicio AC. Shear truss analogy for concrete members of

solid and hollow circular cross section. Eng Struct 2009;31(2):45565.[14]Karayannis CG, Chalioris CE, Mavroeidis PD. Shear capacity of RC rectangular

beams with continuous spiral transversal reinforcement. WIT Trans ModellSimul 2005;41:37986.

[15] Yang K-H, Kim G-H, Yang H-S. Shear behavior of continuous reinforcedconcrete T-beams using wire rope as internal shear reinforcement. ConstrBuild Mater 2011;25(2):9118.

[16] Karayannis CG. Torsional analysis of flanged concrete elements with tensionsoftening. Comput Struct 1995;54(1):97110.

[17]Karayannis CG, Chalioris CE. Experimental validation of smeared analysis forplain concrete in torsion. J Struct Eng ASCE 2000;126(6):64653.

[18] Karayannis CG, Chalioris CE. Strength of prestressed concrete beams in torsion.Struct Eng Mech 2000;10(2):16580.

[19] Chalioris CE. Analytical model for the torsional behaviour of reinforcedconcrete b eams retr ofit ted with FRP mater ials. Eng St ruct2007;29(12):326376.

[20] Karayannis CG. Smeared crack analysis for plain concrete in torsion. J StructEng ASCE 2000;126(6):63845.

[21] Chalioris CE, Karayannis CG. Effectiveness of the use of steel fibres on thetorsional behaviour of flanged concrete beams. Cem Concr Compos2009;31(5):33141.

[22] Chalioris CE. Experimental study of the torsion of reinforced concretemembers. Struct Eng Mech 2006;23(6):71337.

[23]Hsu TC. Unified theory of reinforced concrete. Boca Raton, FL: CRC Press, Inc.;1993.

[24] ACI Committee 318-02. Building code requirements for reinforced concrete(ACI 318-02) and commentary (ACI 318R-02), Farmington Hills. Michigan:American Concrete Institute ACI Committee 318; 2002.

http://refhub.elsevier.com/S0141-0296(13)00212-5/h0005http://refhub.elsevier.com/S0141-0296(13)00212-5/h0010http://refhub.elsevier.com/S0141-0296(13)00212-5/h0010http://refhub.elsevier.com/S0141-0296(13)00212-5/h0010http://refhub.elsevier.com/S0141-0296(13)00212-5/h0015http://refhub.elsevier.com/S0141-0296(13)00212-5/h0015http://refhub.elsevier.com/S0141-0296(13)00212-5/h0020http://refhub.elsevier.com/S0141-0296(13)00212-5/h0020http://refhub.elsevier.com/S0141-0296(13)00212-5/h0025http://refhub.elsevier.com/S0141-0296(13)00212-5/h0025http://refhub.elsevier.com/S0141-0296(13)00212-5/h0025http://refhub.elsevier.com/S0141-0296(13)00212-5/h0025http://refhub.elsevier.com/S0141-0296(13)00212-5/h0030http://refhub.elsevier.com/S0141-0296(13)00212-5/h0030http://refhub.elsevier.com/S0141-0296(13)00212-5/h0030http://refhub.elsevier.com/S0141-0296(13)00212-5/h0030http://refhub.elsevier.com/S0141-0296(13)00212-5/h0030http://refhub.elsevier.com/S0141-0296(13)00212-5/h0030http://refhub.elsevier.com/S0141-0296(13)00212-5/h0030http://refhub.elsevier.com/S0141-0296(13)00212-5/h0035http://refhub.elsevier.com/S0141-0296(13)00212-5/h0035http://refhub.elsevier.com/S0141-0296(13)00212-5/h0040http://refhub.elsevier.com/S0141-0296(13)00212-5/h0040http://refhub.elsevier.com/S0141-0296(13)00212-5/h0040http://refhub.elsevier.com/S0141-0296(13)00212-5/h0045http://refhub.elsevier.com/S0141-0296(13)00212-5/h0045http://refhub.elsevier.com/S0141-0296(13)00212-5/h0045http://refhub.elsevier.com/S0141-0296(13)00212-5/h0050http://refhub.elsevier.com/S0141-0296(13)00212-5/h0050http://refhub.elsevier.com/S0141-0296(13)00212-5/h0055http://refhub.elsevier.com/S0141-0296(13)00212-5/h0055http://refhub.elsevier.com/S0141-0296(13)00212-5/h0060http://refhub.elsevier.com/S0141-0296(13)00212-5/h0060http://refhub.elsevier.com/S0141-0296(13)00212-5/h0065http://refhub.elsevier.com/S0141-0296(13)00212-5/h0065http://refhub.elsevier.com/S0141-0296(13)00212-5/h0065http://refhub.elsevier.com/S0141-0296(13)00212-5/h0070http://refhub.elsevier.com/S0141-0296(13)00212-5/h0070http://refhub.elsevier.com/S0141-0296(13)00212-5/h0070http://refhub.elsevier.com/S0141-0296(13)00212-5/h0075http://refhub.elsevier.com/S0141-0296(13)00212-5/h0075http://refhub.elsevier.com/S0141-0296(13)00212-5/h0080http://refhub.elsevier.com/S0141-0296(13)00212-5/h0080http://refhub.elsevier.com/S0141-0296(13)00212-5/h0085http://refhub.elsevier.com/S0141-0296(13)00212-5/h0085http://refhub.elsevier.com/S0141-0296(13)00212-5/h0085http://refhub.elsevier.com/S0141-0296(13)00212-5/h0090http://refhub.elsevier.com/S0141-0296(13)00212-5/h0090http://refhub.elsevier.com/S0141-0296(13)00212-5/h0090http://refhub.elsevier.com/S0141-0296(13)00212-5/h0095http://refhub.elsevier.com/S0141-0296(13)00212-5/h0095http://refhub.elsevier.com/S0141-0296(13)00212-5/h0100http://refhub.elsevier.com/S0141-0296(13)00212-5/h0100http://refhub.elsevier.com/S0141-0296(13)00212-5/h0100http://refhub.elsevier.com/S0141-0296(13)00212-5/h0100http://refhub.elsevier.com/S0141-0296(13)00212-5/h0105http://refhub.elsevier.com/S0141-0296(13)00212-5/h0105http://refhub.elsevier.com/S0141-0296(13)00212-5/h0110http://refhub.elsevier.com/S0141-0296(13)00212-5/h0110http://refhub.elsevier.com/S0141-0296(13)00212-5/h0110http://refhub.elsevier.com/S0141-0296(13)00212-5/h0110http://refhub.elsevier.com/S0141-0296(13)00212-5/h0105http://refhub.elsevier.com/S0141-0296(13)00212-5/h0105http://refhub.elsevier.com/S0141-0296(13)00212-5/h0100http://refhub.elsevier.com/S0141-0296(13)00212-5/h0100http://refhub.elsevier.com/S0141-0296(13)00212-5/h0100http://refhub.elsevier.com/S0141-0296(13)00212-5/h0095http://refhub.elsevier.com/S0141-0296(13)00212-5/h0095http://refhub.elsevier.com/S0141-0296(13)00212-5/h0090http://refhub.elsevier.com/S0141-0296(13)00212-5/h0090http://refhub.elsevier.com/S0141-0296(13)00212-5/h0090http://refhub.elsevier.com/S0141-0296(13)00212-5/h0085http://refhub.elsevier.com/S0141-0296(13)00212-5/h0085http://refhub.elsevier.com/S0141-0296(13)00212-5/h0080http://refhub.elsevier.com/S0141-0296(13)00212-5/h0080http://refhub.elsevier.com/S0141-0296(13)00212-5/h0075http://refhub.elsevier.com/S0141-0296(13)00212-5/h0075http://refhub.elsevier.com/S0141-0296(13)00212-5/h0070http://refhub.elsevier.com/S0141-0296(13)00212-5/h0070http://refhub.elsevier.com/S0141-0296(13)00212-5/h0070http://refhub.elsevier.com/S0141-0296(13)00212-5/h0065http://refhub.elsevier.com/S0141-0296(13)00212-5/h0065http://refhub.elsevier.com/S0141-0296(13)00212-5/h0065http://refhub.elsevier.com/S0141-0296(13)00212-5/h0060http://refhub.elsevier.com/S0141-0296(13)00212-5/h0060http://refhub.elsevier.com/S0141-0296(13)00212-5/h0055http://refhub.elsevier.com/S0141-0296(13)00212-5/h0055http://refhub.elsevier.com/S0141-0296(13)00212-5/h0050http://refhub.elsevier.com/S0141-0296(13)00212-5/h0050http://refhub.elsevier.com/S0141-0296(13)00212-5/h0045http://refhub.elsevier.com/S0141-0296(13)00212-5/h0045http://refhub.elsevier.com/S0141-0296(13)00212-5/h0045http://refhub.elsevier.com/S0141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experimental investigation of rc beams with rectangular spiral reinforcement in torsion

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