nsh

n buninon owhiour, analysis and design of Reinforced Concrete (RC) beams with transverseaspg ls w

plates is presented. Finally, directions for future research based on the gaps which exist in the present

, transided fcessarysupplyand pnd forcreatin

plane always passes through the opening. The ultimate strength,shear strength, crack width and stiffness may also be seriouslyaffected.

Furthermore, the provision of openings produces discontinuitiesor disturbances in the normal ow of stresses, thus leading to stressconcentration and early cracking around the opening region. Simi-lar to any discontinuity, special reinforcement or enclosing of the

trast, and according to Somes and Corley [4], a circular openingmay be considered as large when its diameter exceeds 0.25 timesthe depth of the web. The author however feels that the essenceof classifying an opening as either small or large lies in the struc-tural response of the beam. When the opening is small enough tomaintain the beam-type behaviour, or in other words, if the usualbeam theory applies, then the opening may be termed as small.When beam-type behaviour ceases to exist due to the provisionof openings, then the opening may be classied as a large opening.By assuming the prevalence of Vierndeel action and consideringthe fact that failure occurs after the formation of a four-hinge

Corresponding author. Tel.: +60 126848463.

Materials and Design 40 (2012) 90102

Contents lists available at

an

elsE-mail address: SivaN@uniten.edu.my (S. Naganathan).oor, the height of this dead space adds to the overall height of thebuilding depending on the number and depth of ducts. Thereforethe web openings enable the designer to reduce the height of thestructure, especially with regard to tall building construction, thusleading to a highly economical design.

The presence of transverse openings will transform simplebeam behaviour into a more complex behaviour, as they induce asudden change in the dimension of the beams cross section. How-ever, as the opening represents a source of weakness, the failure

position. Openings are classied as small or big openings and thebest position of the opening is decided based on its size. Web open-ings have been found to take many shapes such as circular, rectan-gular, diamond, triangular, trapezoidal and even irregular shapes.However, circular and rectangular openings are the most commonones in practice [2]. With regards to the size of openings, manyresearchers use the terms small and large without drawingany clear-cut demarcation line. Small openings are dened as thosewhich are circular, square or nearly square in shape [1,3]. In con-1. Introduction

In modern building constructionforced concrete beams are often provducts and pipes. These ducts are nedate essential services such as waterand computer network. These ductsunderneath the soft of the beam acovered by a suspended ceiling, thus0261-3069/$ - see front matter 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.matdes.2012.03.001work are presented. 2012 Elsevier Ltd. All rights reserved.

verse openings in rein-or the passage of utilityin order to accommo-, electricity, telephone,ipes are usually placedaesthetic reasons, areg a dead space. In each

opening close to its periphery, should therefore be provided in suf-cient quantity to control crack widths and prevent possible pre-mature failure of the beam [1].

2. Opening classication

This section presents the classication of Reinforced Concrete(RC) beams with web openings based on the openings size andapproach, the Architectural Institute of Japan (AIJ) approach and the strut and tie method. Moreover,the strengthening of RC beams with openings using Fibre Reinforced Polymer (FRP) material and steelReinforced concrete beams with web ope

A. Ahmed a, M.M. Fayyadh b, S. Naganathan a,, K. NaaDepartment of Civil Engineering, Universiti Tenaga Nasional, 43000 Selangor, MalaysiabDepartment of Civil Engineering, University Malaya, 50603 KL, Malaysia

a r t i c l e i n f o

Article history:Received 8 November 2011Accepted 2 March 2012Available online 16 March 2012

Keywords:A. Concrete and compositeG. Destructive testingH. Failure analysis

a b s t r a c t

The construction of moderservices such as air conditiobeams enable the installatireinforced concrete beamsthe art work on the behavweb openings. A variety ofings, guidelines for openinVarious design approache

Materials

journal homepage: www.ll rights reserved.ects will be highlighted and discussed including the classication of open-ocation, and the structural behaviour of RC beams with web openings.ill also be detailed, for example the American Concrete Institute (ACI)ings: A state of the art review

aruddin a

ildings requires many pipes and ducts in order to accommodate essentialg, electricity, telephone, and computer network. Web openings in concretef these services. A number of studies have been conducted with regards toich contain web openings. The present paper aims to compile this state of

SciVerse ScienceDirect

d Design

evier .com/locate /matdes

mechanism, Mansur [5], recommended certain criteria with whichto classify the size of an opening as either large or small. It can beassumed that hinges form in the chord members at a distance ofh/2 from the vertical faces of the opening. This is shown in Fig. 1,where h is the overall depth of a chord member, and the subscriptst and b refer to the top and bottom chords, respectively.

Small opening, lo 6 hmax Large opening, lo > hmax

where hmax is the larger of ht and hb.That is, when the length of opening I0 is less than or equal to such a case, beam action may be assumed to prevail. Therefore,

A. Ahmed et al. /Materials andhmax, it may be dened as a small opening. For large openings,I0 > hmax. In this denition, it is assumed that the members aboveand below the opening have adequate depth to accommodate thereinforcement scheme. In the case of circular openings, the circleshould be replaced by an equivalent square for the determinationof the value of hmax.

Mansur and Tan [6] provided guidelines to facilitate the selec-tion of the size and location of web openings as illustrated in Fig. 2.

(i) For T-beams, openings should preferably be positioned ushwith the ange for ease in construction. In the case of rectan-gular beams, openings are commonly placed at mid-depth ofthe section, but must also be placed eccentrically withrespect to depth. Care must be exercised to provide sufcientconcrete cover to the reinforcement for the chord membersabove and below the opening. The compression chord shouldalso have a sufcient concrete area to develop the ultimatecompression block in exure and should also have adequatedepth to provide effective shear reinforcement.

(ii) Openings should not be located closer than one-half of thebeams depth D to the supports. This is in order to avoidthe critical region for shear failure and reinforcement con-gestion. Similarly, the positioning of an opening closer than0.5D to any concentrated load should be avoided.

(iii) Depth of openings should be limited to 50% of the overallbeam depth.

(iv) The factors which limit the length of an opening are the sta-bility of the chord members, in particular the compressionchord, and the serviceability requirement of deection.When the opening becomes bigger, it is preferable to usemultiple openings providing the same passageway insteadof using a single opening.

(v) When multiple openings are used, the post separating twoadjacent openings should not be less than 0.5D to ensurethat each opening behaves independently.

Based on the aforementioned review, it is clear that openings cantakemany shapes and sizes. The actual type and location of an open-ing must be clearly decided before the design specication stage.Fig. 1. Forming of hinge in RC beam with opening [5].the analysis and design of a beam with small openings may followa similar course of action to that of a solid beam.

3.1. Traditional design approach

It was recommended that in the case of pure bending, becausethe concrete there would have cracked anyway in exure at ulti-mate, the placement of an opening completely within the tensionzone does not change the load-carrying mechanism of the beam[7,8]. This was illustrated through worked examples supported bytest evidence. Thus, the ultimate moment capacity of a beam isnot affected by the presence of an opening as long as the minimumdepth of the compression chord, hc, is greater than or equal to thedepth of the ultimate compressive stress block, that is, when:

hc 6Asfy

0:85f 0cb1

where As is the area of exural reinforcement, fy is the yield strengthof exural reinforcement, f 0c is the compressive strength of concreteand b is the beam width.

Tests have been conducted with a small opening enclosed byreinforcement and introduced into a region subjected to predomi-nant shear [4,912]. As shown in Fig. 3, the beam may fail in twodistinctly different modes. The rst type is labelled beam-type fail-ure which is typical of the failure commonly observed in solidbeams except that the failure plane passes through the centre ofthe opening (as shown in Fig. 3a). Conversely, in the second typelabelled frame-type failure, the formation of two particular diago-nal cracks, one in each member bridging the two solid beam seg-ments, leads to the failure (as shown in Fig. 3b). It was suggestedthat these types of failures require separate treatment for completedesign [6].

Similar to the traditional shear design approach, in both thecases it may be assumed that the nominal shear resistance, Vn, isthe sum of two components Vc and Vs (attributable to concreteand shear reinforcement across the failure plane).

Vn Vc Vs 2

3.1.1. Beam-type failureSimilar to a solid beam, a 45 inclined failure plane may be

assumed when designing for beam-type failure, with the planebeing traversed through the centre of the opening, as shown inFig. 4 [6]. A simplied approach namely the American ConcreteInstitute (ACI) Code [13] can be followed to estimate the shearresistance Vc provided by the concrete:

Vc 16f 0c

qbwd do: 3

where bw is the web width, d is the effective depth and do is the3. Small openings design approaches

This section presents the design approaches which have beenused for RC beams with small openings. The traditional method,the Architectural Institute of Japan (AIJ) method, the plasticitymethod and the strut and tie method are the main design ap-proaches which are presented in this paper. Mansur and Tan [6]recommended that a circular, square, or nearly square openingmay be considered a small opening provided that the depth (ordiameter) of the opening is in realistic proportion to the beam size,that is, less than approximately 40% of the overall beam depth. In

Design 40 (2012) 90102 91diameter of opening.For shear reinforcement contribution, Vs should be calculated

by using Eq. (3). It may be seen that the stirrups available to resist

e lo

and Design 40 (2012) 90102Fig. 2. Guidelines for th

92 A. Ahmed et al. /Materialsshear across the failure plane are those by the sides of the openingwithin a distance of (dv do):

Vs Av fyvs dv do 4

where dv is the distance between the top and bottom longitudinalrebars and do is the diameter (or depth) of opening; Av = area ofvertical legs of stirrups per spacing s; fyv = yield strength of stirrups.The total amount of web reinforced and thus calculated should becontained within a distance (dv do)/2, or preferably be lumpedtogether on either side of the opening.

3.1.2. Frame-type failureThis type occurs due to the formation of two independent diag-

onal cracks, one on each of the chord members above and belowthe opening, as shown in Fig. 3b. It appears that each member be-haves independently similar to the members in a framed structure.Design reinforcement was recommended for this mode of failureand it was also suggested that the chord member requires inde-pendent treatment [6]. Let us consider the free-body diagram atthe beam opening, as shown in Fig. 5. Clearly, the applied factoredmoment, Mu, at the centre of the opening from the global action is

Fig. 3. The two modes of shear f

Fig. 4. Shear resistance Vs provided by shear reinforcement at an opening [6].resisted by the usual bending mechanism, that is, by the coupleformed by the compressive and tensile stress resultants, Nu, inthe chord members above and below the opening. These stressresultants may be obtained by:

ailure at small openings [6].cation of openings [6].Nut Mud a2 Nub 5

subject to the restrictions imposed by Eq. (5). In this equation, d isthe effective depth of the beam, a is the depth of equivalent rectan-gular stress block and the subscripts t and b denote the top and bot-tom cross members of the opening, respectively.

It was recommended that the applied shear, Vu, may be distrib-uted between the top and the bottom chords in proportion to theircross-sectional areas [14]. Thus:

Vut VuAt

At Ab

6

Vub Vu Vut 7

Knowing the factored shear and axial forces, each member can beindependently designed for combined shear and axial force by theusual procedure for solid beams.

Fig. 5. Free-body diagram at beam opening [5].

3.2. AIJ approach

A formula has been suggested by the Architectural Institute ofJapan (AIJ), [15], and is the standard for structural calculation ofreinforced concrete structures to evaluate the shear capacity Vnof beams which contain a small opening. This empirical formulais considered similar to the traditional approach where the totalshear resistance is provided by both concretes and the steel crossesa 45 failure plane passing through the centre of the opening asshown in Fig. 6. The formula given is as follows:

Vn 0:092KuKpf0c 17:7

M 0:12 11:61do

h

0:846

q0wfyv

q" #bdv

where do is the diameter of the circular opening (or that of a circum-scribed circle in the case of a square or rectangular opening), and svis the spacing between the two stirrups, one on each side adjacentto the opening.

Assuming yielding of stirrups, the concrete compressive stressin the shaded portion is given by:

fcw qv fyv1 cot2s 11where pv is the ratio of shear reinforcement placed adjacent to the

Fig. 7. Determination of Ku.

Fig. 8. Truss action in beam with opening [16].

A. Ahmed et al. /Materials andVd

8where kp = 0.82 (100As/bd)0.23, do is the diameter of the circularopening or diameter of the circumscribed circle in the case of asquare opening, which should be taken as less than or equal toh/3; h is the overall depth of the beam, and M/(Vd) is taken as lessthan or equal to 3.

The term K is a function of the effective depth d to account forthe size effects in shear and has a value of between 0.72 and 1.0 asshown in Fig. 7. fyv is the yield strength of web reinforcement.

Where dv is the distance between the top and bottom longitudi-nal bars, the term pw in Eq. (8) refers to the ratio of web reinforce-ment placed within a longitudinal distance dv/2 from the centre ofthe opening as shown in Fig. 6, and dened as:

q0w Avsina cosa

bdv9

where Av is the area of web reinforcement.

3.3. Plasticity method

In a beam with openings, however, it is difcult to develop anarch mechanism, and consequently, the applied shear is trans-ferred by means of a truss mechanism. A beam has a circular open-ing only when the beam is reinforced transversely by verticalstirrups [16], as shown in Fig. 8.

Note that us is the angle of concrete compression strut in theupper and lower chord members.

The horizontal arrows show bond stress and the vertical arrowsrepresent forces acting on the concrete due to the forces in the stir-rups. The unshaded portion shows the zone where the diagonalcompressive stress eld is not formed. The diagonal compressivestress in concrete around the opening becomes larger as the un-shaded portionwidens or as the opening become large. The effectivedepth dtw for the truss mechanism is dened as:

Atw dv docoss Sv tans 10Fig. 6. Effective web reinforcement for opening [15].Design 40 (2012) 90102 93opening and fyv is the yield strength of the stirrups.The value of fcw in Eq. (11) equating to the effective compressive

strength of concrete vfc gives the value of us as:

cots

Vf 0cqv fyv 1

s12

The shear strength of the beam with an opening is given by:

Vn bdtwqv fyv cots 13This applies when diagonal steel reinforcement bars are provided

and the development length is anchored outside of the stirrupsadjacent to the opening as shown in Fig. 9. Where the compressivestress in concrete is relatively low, the contribution of the diagonalbars to the shear capacity is given by:

Vnd Adfyd sin hd 14where hd is the angle of inclination to the axis of the beam, and Ad isthe cross-sectional area of the diagonal bars. The total shear strengthof the beam can be given by adding the value of vnd to the value of vn.

3.4. Strut and Tie model

The strut and tie method was suggested in order to design a

sive stress block is smaller than or equal to the depth of the com-pression chord, and that instability failure of the compressionchord is prevented by limiting the length of the opening [2]. Inpractice, openings are located near the supports where shear ispredominant. Experiments have shown that a beam with insuf-cient reinforcement and improper detailing around the openingregion fails prematurely in a brittle manner [19]. When a suitablescheme consisting of additional longitudinal bars near the top andbottom faces of the bottom and top chords, and short stirrups inboth the chords are furnished, then the chord members behavein a manner similar to a Vierendeel panel and failure occurs in aductile manner. The failure of such a beam is shown in Fig. 11.Clearly, the failure mechanism consists of four hinges, one at eachend of the top and bottom chords.

94 A. Ahmed et al. /Materials andbeam with a small opening. This model takes into account the factthat the applied loads are transmitted through the member to thesupport by means of a system of tension and compression strutsprovided by the steel reinforcement and concrete, as shown inFig. 10 [17]. They are interconnected at the nodes. Such a trussmodel assumes or requires that:

(i) Forces in the truss member are in equilibrium.(ii) Concrete resists only compression and has effective com-

pressive strength fce equal to fc, where the effectiveness fac-tor v is usually less than 1.0.

(iii) Steel reinforcement is required to resist all tensile force.(iv) The centred axis of each truss member and the lines of

action of all externally applied loads at a joint must meetat the nodes.

(v) Failure occurs when a concrete compressive strut crushes, orwhen a sufcient number of steel tension ties yield to pro-duce a mechanism.

The traditional method is an American method based on the ACICode equations and can be considered a simple method as it isbased on the same considerations for RC beams without openings.

(a) Arrangement of diagonal reinforcement around opening (b) truss actionFig. 9. Beam with small opening reinforced by diagonal bars [16].The AIJ method is a Japanese method which is based on an empir-ical equation where a constant K value must be found from a chart.The plasticity method is based on the load trend between theapplied load on the beam top surface and the supports. The strutand tie method considers the transmission of the applied loadthrough a member to the supports by means of a struts system.Each approach has been applied by a different researcher but asyet no work has been conducted on a comparison between thesemethods. Such a study would be useful in order to establish themost convenient approach for RC beams with small openings.

4. Large opening design approaches

The presence of large openings in reinforced concrete beamsrequires special attention in the analysis and design phase becauseof the reduction in both strength and stiffness of the beam andexcessive cracking at the opening due to high stress concentration[18]. This section presents existing approaches which have beenused for the design of RC beams with large openings. The plastichinge method, with its three revisions, is presented as well asthe plasticity method.

4.1. Plastic hinge method

This approach was proposed by Mansur and Tan [6] in 1996 forthe design of RC beamswith large openings. In the ten years follow-ing this milestone, authors have revised these approaches and in2006 produced the third revision of the original method. This sec-tion presents the mathematical equations of these approaches.

4.1.1. Plastic hinge method ISimilar to a beam with small openings, the incorporation of a

large opening in the pure bending zone of a beam will not affectits moment capacity provided that the depth of ultimate compres-

Fig. 10. Strut and Tie force [17].

Design 40 (2012) 90102The experimental observations of the nalmode of failure devel-oped a method of analysis for predicting the ultimate strength of abeam with a large rectangular opening [20]. It is based on the

collapse load analysis in which the basic requirements of equilib-rium, yield and mechanism are satised simultaneously. The mainingredients of this method, which yields a closed-form solution forthe collapse load, are briey described below for a simply-sup-ported beam subject to a point load, P, at a solid section distance,X, from its right support, as shown in Fig. 12.

For the beam in Fig. 12a, the free-body diagram through the

A. Ahmed et al. /Materials andopening centre and those of the chord members above and belowitmaybe representedby Fig. 12b and c, respectively. Itmaybe notedthat the unknown actions at the centre of the opening are the axialforces (Nt and Nb), the bending moments (Mt andMb), and the shearforces (Vt and Vb) in the chord members. Three equilibrium equa-tions relate these six unknowns in whichMm and Vm are the appliedmoment and shear force, respectively, at the centre of the opening.Thus, the beam is statically indeterminate to the third degree.

In a general situation, the problem is statically indeterminate tothe third degree. Equilibrium provides only three equations. There-fore, three additional equations must be formulated in order tosolve the three unknown actions.

Mt Mb N z Mm 15

Nt Nb 0 16

Vt Vb Vm 17This may be accomplished as outlined below. When the chord

members are symmetrically reinforced then the moments at thetwo ends of each chord member (potential hinge location) arenumerically identical at plastic collapse. That is, M1 =M2 andM3 =M4. From the free-body diagram of the chord members (asshown in Fig. 12c), it may be readily shown that the contra exurepoints occur at the midpoint of the chord members. This means thatMt = 0 and Mb = 0. Eq. (15) then reduces to:

N z Mm 18if the total shear, Vm, through the centre of the opening due to glo-bal action is suitably apportioned between the chord members, thatis, if:

Vt kvVm 19where kv is a known value, then the problem reduces to a staticallydeterminate one and the critical sections at the ends of the chordmembers which are subject to combined bending, shear and axialforce can be designed in the usual way following the provisions ofany current building codes.

There are, however, three schools of thought regarding the dis-tribution of applied shear between the chord members at an open-ing. The rst, as proposed by Lorensten [21], assumes that thecompression chord carries the total shear and the tension chordmerely acts as a link carrying no shear. This is probably true whenthe opening is near the bottom. The second proposal by Nasser etal. [14] and Ragan and Warwaruk [22], distributes the total shearbetween the chord members in proportion to their cross-sectionalareas. The third, suggested by Barney et al. [12], distributes theshear force in proportion to the exural stiffness of the chordmembers. Accordingly:Fig. 11. Failure mode [20].Lorensten21 : k 0 20

Nasser etal:14 : kv At=At Ab 21

Barney etal:12 : kv It=It Ib 22Clearly, the three proposals would lead to widely varying amountsof shear being assigned to each chord. However, such an assump-tion is not necessary if the chord members are symmetrically rein-forced. The salient points in such a design process are described inthe owing steps [23]. Due to the introduction of an opening, addi-tional reinforcement must be provided in the chord member so asto retain the original strength of the beam. This additional rein-forcement may be conveniently arranged in a symmetrical mannerfor the top (compression) chord member as shown in Fig. 13. For thebottom (tension) chord member, which has already been providedwith a relatively large amount of reinforcement near the bottomface, it is difcult to reinforce in a symmetrical manner becauseof the danger of steel congestion and over-reinforcement. Hence itis most likely that the bottom chord will be asymmetrically rein-forced. With the assumption that the top chord is symmetricallyreinforced, the interaction diagrams for positive and negative bend-ing will be numerically identical. The nondimensional interactionchart for the top (compression) chord may be obtained by usingthe method of equilibrium and strain compatibility. A typical line-arised chart, corresponding to the case where the distance betweenthe centroid of the two layers of reinforcement is presented inFig. 14. The chart has been developed using the stressstrain rela-tionship for steel and the compressive stress block for concrete asrecommended in the ACI code [24], and is valid for f 0c < 30 MPaand fy = 400 MPa. The curves in this chart are labelled with valuesof (l q g) where l = fy/0.85 f 0c and q g = 2As/bh; b and h are the over-all depths of the chord members, and they are expressed in terms ofnominal strength with a capacity reduction factor of 0.9.

The interaction chart for the bottom (tension) chord may beobtained in a similar manner. Fig. 15 shows a chart for a typicalvalue of cb and for equal concrete cover for top and bottom rein-forcement. For unequal concrete covers, a similar chart may beplotted by varying the position of the top reinforcement as denedby c0b, keeping cb at a xed value. In Fig. 15 each linearised curvewith a particular (l q g) is subdivided into three curves labelledwith different values of a where a A0s=As A0s, q g As A0s=bh and A0s = area of reinforcement for negative bending, and theyare expressed in terms of ultimate axial load and moment alsousing a capacity reduction factor U of 0.9.

The design steps involved in this simplied method are asfollows:

Z ht hb2

do 0:5 acbhb 24

where No = axial load capacity in direct tension andMo = pure bend-ing moment capacity in positive and negative bending.

The value of bending moments at the two ends (Mu)b,3 and(Mu)b,4 at collapse are calculated from:

Mub Nob NubMob=Nob Mub;3or4 25

M0ub Nob NubM0ob=Nob Mub;3or4 26

Vub Mb;4 Mb;3=o 27

Vut Vm Vub 28

Nut Nub 29

Design 40 (2012) 90102 95Mut;2 Vuto

2 Mut;1 30

and96 A. Ahmed et al. /Materials4.1.2. Plastic hinge method IIIf the bottom chord is also assumed to be symmetrically rein-

forced, the number of design charts may be minimised, leading to

Fig. 12. Beam with a large opening

Fig. 13. Beam before and after intDesign 40 (2012) 90102a considerable simplication of the overall design process [6]. In thiscase, the moment-tension interaction diagram would be numeri-cally identical for positive and negative bending, as represented by

under bending and shear [20].

roduction of the opening [6].

andA. Ahmed et al. /Materialsthe solid line in Fig. 15, and the contra exure point would occur atmid span. With this in mind, Eqs. (27) and (23) reduce to:

Vub 2Mub;4=o 31

Nub MmZ

32

Eq. (32) gives the magnitude of axial force in the chord member di-rectly irrespective of the amount of reinforcement. However, to pro-ceed with the design, it is necessary either to assume a certainquantity of reinforcement or to assign a fraction of the total shearto be carried by the bottom chord. The latter approach is suggestedbecause it offers great exibility.

When assigning the shear force, it should be kept in mind thatthe shear carrying capacity of a chord member depends on themoment capacities of the critical end sections. These in turn

Fig. 14. The interaction diagram for compression chord [6].

Fig. 15. The interaction diagram for tension chord [6].depend on the amount of longitudinal reinforcement and whetherthe depth is sufcient to provide effective shear reinforcement.Thus, if the opening is provided in a T-beam just below the ange,and the ange thickness is inadequate for the placement of stir-rups, the entire shear should be assigned to the bottom chord. Sim-ilarly, a situation may arise where the opening is near the bottomof the beam and the bottom chord member is very shallow com-pared to the top chord. In such a case, the top chord membershould be designed to carry the total shear force. For equally sizedchord members, however, assignment of less than half of the exter-nal shear to the bottom (tension) chord member leads to a moreeconomical design.

Once a suitable shear force is assigned to the bottom chord,(Mu)b,4 can be calculated from Eq. (31) and the required reinforce-ment can be obtained from the appropriate chart in Fig. 15. Thedesign of the top chord member is identical to that used in simpli-ed method 1.

4.1.3. Plastic hinge method IIIMansur [25] has stated that his old method of [20] is relatively

complex and requires the development of new sets of designcharts. The complexity arises mainly due to the consideration ofthe generalised arrangement of reinforcement in the chords. How-ever, the design solution may be considerably simplied if thechord members are reinforced symmetrically. This is a feasibleoption because opening length represents only a small fraction ofthe total span of the beam.

Step 1: Determine longitudinal reinforcement for the compres-sion chord.

First, assuming that the beam contains no openings, design thelongitudinal reinforcement. If the beam is subject to a sagging mo-ment, the main reinforcement, As, will be at the bottom. The topreinforcement will be lighter than the bottom reinforcement andthe same amount is usually continued throughout the length ofthe beam, including the opening region. Thus, the top reinforce-ment in the compression chord is known. Use the same amountand the arrangement at its bottom as additional reinforcement isrequired to restore the strength and avoid brittle failure of thebeam due to the provision of openings.

Step 2: Determine the shear force carried by the compressionchord.

Since the amount and arrangement of longitudinal reinforce-ment in the compression chord are known, and as the axial forceacting on it is given by Eq. (18), the moment capacity of the sectionmay be estimated in the usual manner. Because of symmetry, thecapacity in positive and negative bending will be numerically iden-tical. Therefore, from the free-body diagram of Fig. 12c, the amountof shear force which can be transmitted through the compressionchord at ultimate may be obtained as:

Vut 2Mut;2=o 33

where lo is the length of opening.

Step 3: Determine the moments and forces at critical sectionsand design the tension chord.

The shear force carried by the tension chord will be the differ-ence between the applied shear and that carried by the compres-

Design 40 (2012) 90102 97sion chord in accordance with Eq. (17). Due to reinforcementsymmetry, the contra exure point will be at mid-span. The mo-ment at the critical end section is then given by:

dard design procedure. Reinforcement which has already been

shown in this gure by the direction of arrows with blank circlesas the targets.

4.2. Plasticity method

This approach was proposed by the Architectural Institute ofJapan (AIJ) in 1988 for the design of RC beams with large open-ings. In small openings in plasticity truss models, shear is re-sisted by a beam through a combination of the arch and trussmechanism. In this case, where the top and bottom chord mem-bers are of equal depth and where the distance between the topand bottom longitudinal of reinforcement is dvs. It has been rec-ommended by the Architectural Institute of Japan [26] that ver-tical stirrups be provided uniformly through the chord membersand for a distance equal to dvs cot Us on each side of the open-ing, where us is the angle of inclination of the compression con-crete struts in each chord member, as shown in Fig. 17. Thelongitudinal reinforcement adjacent to the opening should be ex-tended beyond the above vertical stirrups and provided withanchorage hooks bent inside.

The shear force carried by each truss mechanism in the chordmembers is:

98 A. Ahmed et al. /Materials and Design 40 (2012) 90102determined from the global action can now be taken into accountto obtain the desired symmetrical arrangement of reinforcementin the tension chord. Design for shear is identical to a solid beam.Mub Vubo2

34

With the axial tension given by Eq. (18), the required amount oflongitudinal reinforcement can be obtained by following the stan-

Fig. 16. Typical design chart [25].Use of design charts, similar to a column, may expedite the designprocess. A typical design chart (using the capacity reduction factoru = 0.9) for symmetrical arrangement of reinforcement, approxi-mated by straight lines, is shown in Fig. 16, where l = fy/0.85 f 0cand q g = 2As/bh. The simple design steps, as outlined above, are

Fig. 17. Truss action in beam with reiVt bdvpv fyv cots 35where b = width of section, qv = shear reinforcement ratio of stir-rups, and fyv = yield strength of stirrups. Thus, the shear capacityof the beam can be obtained as:

Vu 2bdvsqv fyv cots 36where

cots Vf 0cqv fyv

1s

6 2 37

and

qv fyv 6 Vf0c 38

where fyv = yield compressive strength and v = effectiveness factorfor the compressive strength of concrete:

V 0:7f 0c=200 39nforced rectangular opening [26].

andThe lower limit for cot Us as indicated in Eq. (37) is to ensureaggregate interlocking in crack and to prevent excessive crackwidths.

The required force in the longitudinal reinforcement near theopening in each chord member is given by:

Tsn Asnfy Vul02dvs 40

Tsn Asnfy Vuo2dvs 41

and that in the longitudinal reinforcement away from the openingis:

Tsf Astfy Vuo dvs cots2dvs 42

Fig. 18. Truss action in beam with rectangular opening reinforced with diagonalbars [26].

A. Ahmed et al. /Materialswhere Asn and Asf are the area of longitudinal reinforcement in eachchord member near and away, respectively, from the opening.

Where diagonal reinforcement is provided as shown in Fig. 18,the shear resistance provided is given by:

Ad Adfyd sin hd 43where Ad is the area, fyd is yield strength, and hd angle of inclinationto the beam axis of the diagonal bars.

The plastic hinge approaches are based on the ACI Code equa-tions using a columns chart while the plasticity approach is basedon the force trend between the applied load on the beam top sur-face and the supports. The difference between the three approachesto the plastic hingemethod is the portion of shear carried by the topand bottom chords. No research has been conducted to comparethese three plastic hinge methods nor has the method been com-pared with the plasticity approach.

5. Performance of beams with openings

Among the earliest works on beams with openings, Nasser et al.[12] in 1967 studied the behaviour of rectangular RC beams withlarge web openings. They found that the top and the bottom chordof large opening beams behaved like a Vierendeel panel and thecontra exure points occurred at their mid point. They alsoassumed that the apportionment of applied shear was distributedbetween the top and bottom chord in proportion to their cross-sec-tional area. Test data exists regarding what happens when a smallopening is introduced in a region subjected to predominant shearand the opening is enclosed by reinforcement to investigate thebeams failure mode [4,9,10]. A method has been developed to pre-dict the ultimate strength based on the collapse load analysis of areinforced concrete beamwith large rectangular opening subjectedto a point load [2]. They also assumed that the solid sections of thebeam were rigid and that collapse results from the formation of amechanism with four plastic hinges, one at each end of the topand bottom chords. They found that the ultimate strength increasedwith a decrease in the moment to shear ratio at the centre of theopening and the amount of external shear carried by the top andbottom chord depends not just on the cross-sectional properties,but also on the opening size (length and depth) and location ofthe opening. Later in 1985, a rational design method was used forreinforced concrete beams with large rectangular openings [27].Twelve beams were tested under one point load and subjected tobending and shear force. They observed that an increase in theopening size (length and depth) or momentshear ratio at thecentre of the opening increased both crack width and maximumdeection. They also stated that the diagonal bars for corner rein-forcement were more effective in both controlling crack widthand reducing beam deection, as shown in Table 1. In 1991, thebehaviour of reinforced concrete continuous beams with largeweb openings was studied [28]. Eight beams were tested and itwas found that the location of the opening has very little inuenceon the cracking load, but that openings located in a relatively highmoment region yield smaller collapse load and large deection. Thedeection brought about by Vierendeel action and the mode ofcollapse remain virtually unaffected by the location of opening.

An analysis of the service load of reinforced concrete with largeweb openings in the analytical modelling was proposed by Mansuret al. [17]. They assumed that the beam was treated as a non pris-matic member with two different crosssectional properties (thesoild section and the opening section by replacing the chord mem-bers through equivalent continuous medium). A total of 15 rein-forced concrete T-beams containing large web openings weretested [29], each simulating either negative or positive moment.They found that the presence of a web opening led to a decreasein both cracking and ultimate strength. They also found that theexternal shear may be distributed between chords in accordancewith their exure stiffness based on either gross or cracked trans-formed section. The critical lateral buckling load of deep slenderrectangular beams containing openings along the centre-lines ofthe beams has been studied by Tbevendran and Shandugam [30].The numerical method which was proposed to predict the criticalload was outlined in detail; cantilever beams and simply supportedbeams were considered. The critical loads evaluated numericallyusing the energy approach were compared with those valuesobtained experimentally and a good agreement was achieved.The nonlinear analysis and design of statically loaded simply sup-ported post tensioned and pre-stressed concrete beams and girderswith rectangular openings was investigated by Kennedy and Abda-lla [31]. Several design parameters were varied such as: openinglength and depth, vertical and horizontal locations of the opening,location of the applied load, type of cross section, and opening rein-forcement. The results from the analytical study were substanti-ated by test results from 12 post tensioned pre-stressed concretebeams, eight of which had rectangular sections, whilst the remain-ing four were T-section beams. A rational method of distributingthe shear between the top and bottom chords of the opening wasalso proposed, together with a design procedure against the crack-ing of such chords. The inuence of openings on the response of

Design 40 (2012) 90102 99hybrid reinforced concrete T-beams, with the beams subjected toacyclic load applied at midspan was investigated by Tanijayaand Hardjito [32]. The experimental work involved testing and

strengthening and updating the performance of RC beams withopenings. A total of 10 beams were tested under static loading, sim-

o (m

808080808040208080808080

andinvestigating the structural responses of three hybrid reinforcedconcrete T-beams, partially constructed using light weight con-crete. An opening was provided on the web of each beam, withthe exception of the third one, that is, the beam was provided withan opening in the low exural moment-high shear region and inthe high exural moment-shear region. The behaviour of the spec-imens was discussed based on the observed degradation ofstrength and stiffness as well as the energy dissipation capability.Test results indicated that the presence of web opening caused adecrease in both cracking and ultimate strengths. The deectionductility of a beam with a web opening in the low exural mo-ment-high shear region was seen as approximately equal to thatof a beam with an opening in the high exure-shear region.

A three-dimensional nonlinear nite element model suitable forthe analysis of reinforced concrete beams with large openingsunder exure was developed by Al-Shaarbaf et al. [33]. Numericalstudies including some material parameters such as concrete com-pressive strength, amount of longitudinal tensile reinforcementand opening size on the loaddeection response were conducted.The nite element solution revealed that the ultimate load andpost-cracking stiffness increased with an increase in the concretecompressive strength and the extent of the bottom steel reinforce-ment decreased with an increase in the length or depth of theopening. The bond anchorage and the shear carrying behaviourof pre-stressed concrete beams made of Ultra-High PerformanceConcrete (UHPC) with and without web openings was investigatedby Hegger and Bertram [34]. Results of the shear tests with multi-ple openings in the web showed that the remaining shear resis-tance was approximately 6065% compared to solid beams. The

Table 1Beams details [27].

Specimen Design ultimate load PUD (KN) l (mm) Dt (mm) d

R1 204 400 110 1R2 162 600 110 1R3 132 800 110 1R4 107 1000 110 1R5 89 1200 110 1R6 164 800 130 1R7 92 800 90 2R8 138 800 120 1R9 144 800 130 1R10 137 800 110 1R11 131 800 110 1R12 127 800 110 1

100 A. Ahmed et al. /Materialseffect of small circular openings on the shear, exural, and ultimatestrength of beams made by normal and high strength concrete hasalso been studied [35]. The main factors of this test were thechanges of diameter, the position of opening and the type and loca-tion of reinforcement around the opening as well as changes in thestrength of the concrete. In this investigation nine of the beamstested were made up of normal concrete and ve of the beamswere made up of high strength concrete; all of which were tested.The testing beams were loaded as simple beams with two concen-trated and symmetrical loads. The effect of concrete strength de-pends on parameters such as diameter and the position of theopening. The load under which the rst exural crack is induceddoes not depend on the presence or the lack of opening or its situ-ation, but shear cracks around the opening will induce sooner thanshear cracks around a similar area in a solid beam. The increase ofthe diameter of the opening in beams with an opening made ofnormal concrete will cause a change in the pattern of cracks andthe type of failure from exural failure to frame type or beam typeshear failure. The increase of strength in concrete does not havemuch inuence on the ultimate strength, but it will increase theulating the negative moment regions of reinforced concreteT-beams [36]. Of these beams ninewere fabricatedwith large open-ings through the web whilst the other beams had a solid web. Theystudied the effect of tension reinforcement area, reinforcementaround the opening, strength of concrete and the shear span todepth ratio on the strength of such beams. In general, the presenceof web openings decreased both the cracking and ultimate strength,as well as the stiffness of the beams. Both the shear span to depthratio and concrete compressive strength of T-beams with openingshad a pronounced effect on the load bearing capacity of the testedbeams. Both the top chord and bottom chord member indepen-stiffness and improve the serviceability of the beams. The mostcritical position of an opening in order to reach the ultimatestrength in beams made of normal concrete is near the support.In addition to this, the best place for the location of the openingin these beams is in the middle of a distance between the placeof applied load and support (in the middle of the shear span).The presence of longitudinal bars on the top and bottom of theopening is necessary in order to control the cracks and exuralstrains around the opening. The installation of diagonal bars andsmall stirrups at the top and bottom of the openings will increasethe ultimate strength of the beams with opening.

6. Strengthening with Fibre Reinforced Polymer (FRP) materials

This section presents the use of externally bonded material for

m) Db (mm) eo (mm) a + l/2 (mm) Stirrups spacing

Sb (mm) St (mm)

110 0 1000 40 40110 0 1000 40 40110 0 1000 40 40110 0 1000 40 40110 0 1000 40 40130 0 1000 50 5090 0 1000 30 30

100 10 1000 35 4590 20 1000 30 50

110 0 800 40 40110 0 1000 40 40110 0 1200 40 40

Design 40 (2012) 90102dently resisted the shear force of tee beams with openings madefrom high strength concrete. The predicted ultimate loads basedon this rule agreed with the experimental ultimate loads for beamswith a shear span to depth ratio equal to 2. In general, the behaviourof high strength concrete beams with openings was shown to bequite different from the behaviour of normal strength concretebeams with openings. Table 2 presents the results compiled byZainab [36]. The possibility of reducing the effect of existing circularweb openings in solid beams on both strength and stiffness bymeans of strengthening the openings with Glass Fibre ReinforcedPlastics was investigated in [37]. The experimental program con-sisted of testing 11 simply supported reinforced concrete rectangu-lar beams. The rst beam was solid with no opening and served asthe reference beam. Each of the remaining beams was providedwith one or two circular web openings with different diameters.Table 3 presents the results found in [37]. Several design parame-ters including the opening width and depth, as well as amountand conguration of the Fibre Reinforced Polymer (FRP) sheets inthe vicinity of the opening were investigated by Abdalla [38]. Theexperimental program included the testing of 10 reinforced

Puth Pu/Puth Mode of failure

24.4 1.036 Shear failure at opening

20 0.95 Shear failure at opening20 0.98 Shear failure at opening20 1 Shear failure at opening

20 0.915 Shear failure at opening20 0.96 Shear failure at opening

20 0.88 Flexural shear failure20 0.7 Flexural tension failure

14 1.057 Shear failure at opening20 0.95 Shear failure at opening

CFR

and Design 40 (2012) 90102 101Table 2Beams results [36].

Group no. Beam no. Pcr Pu

R 10 25.4

A A1 4 19A2 4 19.6A3 4.5 20

B B1 4 18.3B2 4 19.2

C C1 6 17.6C2 3 14

D D1 2 14.8D2 4 19

Table 3Beams test result [37].

Specimen Dimensions of openings Concrete strengthfcu (Mpa)

Conguration of

W (mm) H (mm)

SB1 NAa NAa 49 NAa

RO2 100 100 52 Type 1RO3 200 100 49 Type 1RO4 300 100 51 Type 1RO5 300 150 49 Type 1RO6 300 150 49 Type 1UO7 100 100 43 NAa

UO8 200 100 49 NAa

UO9 300 100 52 NAa

UO10 300 150 42 NAa

a NA denotes not applicable.

A. Ahmed et al. /Materialsconcrete beams, ve of which were strengthened with FRP sheetsaround the opening, whilst four were tested without strengthening,and the remaining beam was solid without an opening and wasconsidered as the control beam. The efciency of using Carbon FibreReinforced Polymer (CFRP) sheets to control local cracks aroundopenings and to resist excessive shear stresses in the openingchords was examined. Based on the results of this investigation,they found that the presence of an un-strengthened opening inthe shear zone of a reinforced concrete beam signicantly de-creased its ultimate capacity. With an un-strengthened openingwith a height of 0.6, the beam depth may reduce the beam capacityby 75%. The application of CFRP sheets according to the arrange-ment presented in this research greatly decreases beam deection,controls cracks around the opening, and increases the ultimatecapacity of the beam. The use of FRP sheets to strengthen the areaaround openings may retrieve the full capacity of the beam forrelatively small openings. The shear failure at the opening chordsof strengthened openings occurs due to a combination of shearcracking of concrete and bond failure of the FRP sheets glued tothe concrete. The method was shown to be capable of estimatingthe shear capacity of reinforced concrete beams with CFRPstrengthened openings.

There are two patterns of strengthening by FRP rod. The rstinvolves FRP rods enclosing the opening and the other involves plac-ing FRP rods diagonally throughout the entire depth of the beam.Both were investigated by Pimanmas [39]. The author found thatsimply placing FRP rods around the opening was not fully effectivebecause a diagonal crack can propagate through the beam with thecrack path diverted to avoid intersecting with the FRP rod. WhenFRP rods were placed throughout the entire beams depth, a signif-icant improvement in loading capacity and ductility was achieved,similar to strengthening by pre-fabricated internal steel bars. Theexural failure mode was restored. An experimental study toP strengthing Cracking loadPcr (kN)

Ultimate load Pu (kN) Mode of failure

30 83 Flexure at mid-span25 86 Flexure at mid-span20 73 Flexure at mid-span20 62 Shear at opening15 35 Shear at opening20 34 Shear at opening25 41 Shear at opening13 43 Shear at opening20 41 Shear at opening5 22 Shear at openinginvestigate the efciency of external strengthening of such beamswhen provided with large openings within their shear zones wasconducted by Allam [40]. It was found that both types of materialused for strengthening namely steel plates and CFRP sheets as wellas its conguration scheme, signicantly affected the efciency ofstrengthening in terms of beam deection, steel strain, cracking,ultimate capacity and failure mode of the beam. Test resultsrevealed that the efciency of external strengthening of beamswithopenings increased signicantly when such strengthening wasapplied to both the inside and outside edges of the beam opening.The increase was also found to be more signicant than in thecase of only strengthening the outside edges. Furthermore, it wasdiscovered that using steel plates for strengthening beamswith openings was much more efcient than in the case of CFRPsheets.

Fig. 19. Photos of specimens strengthened with CFRP at failure [41].

This paper has reviewed the existing work related to RC beams

[1] Mansur MA, Tan KH, Lee SL. Collapse loads of RC beams with large openings.

102 A. Ahmed et al. /Materials andASCE J Struct Eng 1984;110(11):260210.[2] Prentzas EG. Behavior and reinforcement of concrete beams with large

rectangular apertures. PhD Thesis, University of Shefeld, UK; 1968. p. 230.[3] Hasnat A, Akhtaruzzaman AA. Beams with small rectangular opening under

torsion, bending and shear. ASCE J Struct Eng 1987;113(10):225370.[4] Somes NF, Corley WG. Circular openings in webs of continuous beams. Shear in

Reinforced Concrete. Special Publication SP-42. Detroit: American ConcreteInstitute; 1974;35998.

[5] Mansur MA. Effect of openings on the behavior and strength of RC beams inshear. Cement Concr Compos 1998;20(6):47786.

[6] Mansur MA, Tan KH. Concrete beams with openings: analysis and design. BocaRaton, Florida, USA: CRC Press LLC; 1999. p. 220.

[7] Tan KH, Mansur MA, Huang LM. Design of reinforced concrete beams withcircular openings. ACI Struct J 2001;98(3):40715.

[8] Mansur MA, Tan KH, WengW. Effects of creating an opening in existing beams.ACI Struct J 2001;98(3):40715.

[9] Hanson JM. Square openings in webs of continuous joists. PCA Research andwith openings. Based on the aforementioned review, it is evidentthat there are gaps in the previous research which must be inves-tigated. Below are the main points which can be considered asconclusions and directions for future work in order to ll the gapswhich exist in the work carried out thus far.

1. Since no research has been conducted regarding the comparisonof existing design approaches of RC beams with small openings,future work must take into consideration such comparisonsbased on a number of experiential samples.

2. Future work must also cover the comparison between the pro-posed three plastic hinge approaches as well as the plasticityapproach based on a number of experimental samples.

3. Strengthening of RC beams with externally bonded steel platesmust be investigated corresponding to different parameterssuch as the steel plates mechanical and geometrical propertiesas well as their congurations.

4. Strengthening of RC beams with externally bonded FRP materi-als, namely CFRP sheets and fabric, GFRP sheets and fabric andso on, must be investigated with different parameters such asthe FRP materials mechanical and geometrical properties andcongurations.

5. Since no repair work has been conducted on RC beams withopenings, it would be extremely benecial were an experimen-tal study to be conducted for the repairing of damaged RCbeams with openings using externally bonded FRP material orsteel plates with different parameters such as materialsmechanical and geometrical properties and congurations.

ReferencesThe interfacial shear stresses found tobe inuencedby the geom-etryparameters suchas thicknessof the FRPplate andadhesive layerin range of the different degrees [41], where the interfacial shearstress concentrations and levels increase obviously with theincrease of the thickness of the FRP plate. A typical failure of a spec-imenstrengthenedwithCFRP is shown in Fig. 19. Thecross-sectionalshape found to has a signicant inuence on the effectiveness of theCFRP-connement under concentric loading [42], where memberwith the circular cross-section beneted the most, followed by themember with the square cross-section and the gain in load capacityof RC members with rectangular cross-sections due to CFRP-connement depends on the aspect ratio of the cross-section.

7. Conclusion and future directionsDevelopment Bulletin RD 100.01D. Portland Cement Association; 1969. p. 114.[10] Salam SA (1977). Beams with openings under different stress conditions. In:Proceeding of 3rd conference on our world in concrete and structures. CI-Premier. Singapore. p. 25967.

[11] WengW. Concrete beams with small openings under bending and shear. MEngThesis, National University of Singapore; 1998. p. 92.

[12] Barney GB, Corley WG, Hanson JM, Parmelee RA. Behavior and design ofprestressed concrete beams with large web openings. PCI J 1977;22(6):3261.

[13] ACI 318. Building code requirements for reinforced concrete and commentary.Farmington Hills, MI: American Concrete Institute; 1995.

[14] Nasser KW, Acavalas A, Daniel HR. Behavior and design of large openings inreinforced concrete beams. ACI J Proc 1967;64(1):2533.

[15] Architectural Institute of Japan. Standard for structural calculation ofreinforced concrete structure; 1988 [in Japanese].

[16] Ichinose T, Yokoo S. A shear design procedure of reinforced concrete beamswith web openings. Summaries of Technical Papers of Annual Meeting. Japan:Architectural Institute of Japan; 1990. p. 31922.

[17] Mansur MA, Tan KH, Weng W. Analysis of concrete beams with circular webopenings using strut-and-tie models. Malay J Civil Eng 2006;18(2):8998.

[18] Mansur MA, Lee YF, Tan KH, Lee SL. Test on RC continuous beams withopenings. J Struct Eng 1991;117(6):1593605.

[19] Siao WB, Yap SF. Ultimate behavior of strengthened large openings made inexisting concrete beams. J Inst Eng 1990;30(3):517.

[20] Mansur MA. Ultimate strength design of beams with large openings. Int JStruct 1988;8(2):10725.

[21] Lorensten M. Holes in reinforced concrete girders. Byggmastaren1962;41(7):14152. English translation from Swedish, XS6506, PortlandCement Association, February1965.

[22] Ragan HS, Warwaruk J. Tee members with large web openings. PCI J1967;12(4):5265.

[23] Tan KH, Mansur MA. Design procedure for reinforced concrete beams withlarge web openings. ACI Struct J 1992;93(4):40410.

[24] ACI-ASCE Committee-426. The shear strength of RC members, (ACI 426R-74)(Reapproved 1980). In: Proceedings ASCE, vol. 99(ST6); 1973. p. 116871.

[25] Mansur MA. Design of reinforced concrete beams with web openings. In:Proceedings of the 6th AsiaPacic Structural Engineering and ConstructionConference (APSEC 2006). Kuala Lumpur, Malaysia, 56 September 2006.

[26] Architectural Institute of Japan. AIJ standard for structural calculation ofreinforced concrete building; 1994. p. 207.

[27] Mansur MA, Tan KH, Lee SL. Design method for reinforced concrete beamswith large openings. ACI J Proc 1985;82(4):51724.

[28] Mansur MA, Tan KH, Lee YF, Lee SL. Piecewise linear behaviour of RC beamswith openings. ASCE J Struct Eng 1991;117(6):160721.

[29] Tan KH, Mansur MA, Huang LM. Reinforced concrete T-beams with large webopenings in positive and negative moment regions. ACI Struct J1996;93(3):27789.

[30] Tbevendran V, Shandugam NE. Lateral buckling of narrow rectangular beamscontaining openings. Comput Struct 1991;43(2):24754.

[31] Kennedy JB, Abdalla H. Static response of prestressed girders with openings.ASCE J Struct Eng 1992;118(ST2):488504.

[32] Tanijaya J, Hardjito D. The inuence of opening on the responses of hybridreinforced concrte T-beams under cyclic loading. In: Proceeding of the 5thCivil engineering conference in the Asian region and Australasian. Structuralengineering conference; 2010.

[33] Al-Shaarbaf IAS, Al-Bayati NAM, Al-Kaisy DIA. Nonlinear nite elementanalysis of reinforced concrete beams with large opening under exure. EngTechnol 2007;25(2):21028.

[34] Hegger J, Bertram G. Shear carrying capacity of ultra-high performanceconcrete beams. Tailor Made Concrete Structures. Walraven & Stoelhorst.London 2008;3417.

[35] Javad VA, Morteza HA. Effect of small circular opening on the shear andexural behavior and ultimate strength of reinforced concrete beams usingnormal and high strength concrete. In: Proceedings of the 13th worldconference on earthquake engineering. Vancouver. Canada. Paper No. 3239;2004.

[36] Zainab EM, Ahmed M, Hassanean YA (2005). Some parameters inuencing thestatic behaviour of rectangular web perforated high strength RC T-beams. 11th

ICSGE. 17-19 May 2005. Ain Shams University. Cairo. Egypt.[37] Abdel Hafez LM, Alaa Eldin, Abou-Elezz YK. Static behavior of repaired RC

beams having web circular openings in shear zone by using GFRP sheets. In:Proceedings of the 9th international conference on structural and geotechnicalengineering. Cairo, Egypt: Ain Shams University; 2002.

[38] Abdalla HA, Torkeya AM, Haggagb HA, Abu-Amira AF. Design against crackingat openings in reinforced concrete beams strengthened with composite sheets.Compos Struct 2003;60:197204.

[39] Pimanmas A. Strengthening R/C beamwith opening by externally installed FRProds: behavior and analysis. Compos Struct 2010;92:195776.

[40] Allam SM. Strengthening of RC beams with large openings in the shear zone.Alex Eng J 2005;44(1):5978.

[41] Bouchikhi AS, Lousdad A, Megueni A. On the reduce of interfacial shearstresses in ber reinforced polymer plate retrotted concrete beams. MaterDes 2010;31:150815.

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Reinforced concrete beams with web openings: A state of the art review1 Introduction2 Opening classification3 Small openings design approaches3.1 Traditional design approach3.1.1 Beam-type failure3.1.2 Frame-type failure

3.2 AIJ approach3.3 Plasticity method3.4 Strut and Tie model

4 Large opening design approaches4.1 Plastic hinge method4.1.1 Plastic hinge method I4.1.2 Plastic hinge method II4.1.3 Plastic hinge method III

4.2 Plasticity method

5 Performance of beams with openings6 Strengthening with Fibre Reinforced Polymer (FRP) materials7 Conclusion and future directionsReferences