design and analysis of heavily loaded reinforced concrete link beams for burj dubai

ACI Structural Journal/July-August 2008 451

ACI Structural Journal, V. 105, No. 4, July-August 2008.MS No. S-2007-030 received January 19, 2007, and reviewed under Institute

publication policies. Copyright © 2008, American Concrete Institute. All rights reserved,including the making of copies unless permission is obtained from the copyright proprietors.Pertinent discussion including author’s closure, if any, will be published in the May-June 2009 ACI Structural Journal if the discussion is received by January 1, 2009.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

This paper presents a study on the shear capacity and behavior ofreinforced concrete link beams designed for the Burj Dubai Tower,which is the tallest building in the world and will be ready foroccupancy in 2009. Several thousand reinforced concrete linkbeams were used in this structure to interconnect structural walls;in some cases, the factored shear forces in these link beams wereup to three times the traditional nominal ACI shear force strengthlimit. This study presents an examination of the factors that controlthe design and behavior of heavily loaded reinforced concrete linkbeams. Nonlinear finite element analysis methods were used tovalidate and inform the design of the reinforced concrete linkbeams for Burj Dubai and to examine if the ACI nominal sectionalshear force limit is appropriate for this type of member. The resultsillustrate the undue conservatism of the ACI design provisions andthe role of nonlinear analyses in design.

Keywords: beam; design; nonlinear finite element analysis; reinforcedconcrete; shear; strut-and-tie model.

INTRODUCTIONThe Burj Dubai Tower, when completed, will be the

world’s tallest structure. Whereas the final height of thismulti-use skyscraper is a “well-guarded secret,” it willcomfortably exceed the current record holder of 509 meter(1671 ft) tall Taipei 101. The 280,000 m2 (3,000,000 ft2)reinforced concrete tower will be used for retail, an Armanihotel, residences, and offices. The goal of the Burj DubaiTower is not simply to be the world’s highest building—it isto embody the world’s highest aspirations.

Designers purposefully shaped the structural concrete forthe Burj Dubai to be Y-shaped in plan to reduce the windforces as well as to keep the structure simple and fosterconstructibility. The structural system can be described as abuttressed core, as shown in Fig. 1 and 2. Each wing, with itsown high-performance concrete core and perimetercolumns, buttresses the others via a six-sided central core, orhexagonal hub. The result is a tower that is extremely stifftorsionally. The design team purposely aligned all thecommon central core and column elements to form abuilding with no structural transfers.

Each tier of the building steps back in a spiral pattern thatcauses the tower’s width to change at each setback. Theadvantage of this stepping and shaping is to “confuse thewind.” The wind vortexes never become organized becauseat each new tier the wind encounters a different buildingshape that reduces the overall wind loads on the structure.Due to the tapering of the tower, the primary demand on thelink beams is from gravity load redistribution, flow from thetaller core to the perimeter of the structure. The 280,000 m2

(3,000,000 ft2) tower and 185,000 m2 (2,000,000 ft2)podium structures are currently under construction, as shownin Fig. 2. The project is scheduled for completion in 2009.

The center hex reinforced concrete core walls provide thetorsional resistance of the structure similar to a closed pipeor axle, as shown in Fig. 3. The center hex walls are

Title no. 105-S43

Design and Analysis of Heavily Loaded Reinforced Concrete Link Beams for Burj Dubaiby Ho Jung Lee, Daniel A. Kuchma, William Baker, and Lawrence C. Novak

Fig. 1—Tower rendering.

Fig. 2—Construction photo of tower.

ACI Structural Journal/July-August 2008452

buttressed by the wing walls and hammer head walls, whichbehave as the webs and flanges of a beam to resist the windshears and moments. Outriggers at the mechanical floorsallow the columns to participate in the lateral load resistanceof the structure; hence, all of the vertical concrete is used tosupport both gravity and lateral loads. The walls had

concrete strengths ranging from C80 to C60 cube strengthand contained portland cement and fly ash. Local aggregateswere used for the concrete mixture design. The wall andcolumn sizes were optimized using virtual work/LaGrangemultiplier methods.1 This results in a very efficient structure.

The structure was analyzed for gravity (including P-Δanalysis and creep and shrinkage), wind, and seismic loadsby a three-dimensional analysis model that consisted ofthe reinforced concrete walls, link beams, slabs, mats, piles,and the spire structural steel system. The model consisted ofover 73,500 shells and 75,000 nodes.

RESEARCH SIGNIFICANCEThis paper examines methods for the design and analysis

for reinforced concrete link beams that are cast integral withwall piers. In particular, the appropriateness of thestrut-and-tie method and shear design stress limits for thisclass of member are reviewed. The results of this investigationindicate that much higher shear stress levels should bepermitted in ACI 318, as this would greatly extend the utilityof this class of member.

OVERVIEW OF LINK BEAM DESIGNThe demands on the link beams vary greatly and are

dependent on the location of the link beam relative to asetback with the largest shear forces being generated in thebeams closest to a setback. The typical link beams used inthe Burj Dubai are quite stocky with a shear-span ratio (l/2h)of 0.85, a width of 650 mm (2.13 ft), and a height of 825 mm(2.7 ft). For the design of reinforced concrete link beams, theconventional deep beam design method in the ACI 318-992

and the strut-and-tie method in ACI 318-023 were used, withAppendix A enabling the design of link beams somewhatbeyond the conventionally designed maximum deep beamstress limit of 10 in psi (0.83 in MPa), which isbased on ACI 318-99,2 Section 11.8.4, as will be discussedin the following. In the case of members subjected to verylarge shear forces, embedded built-up structural steelsections were provided within the core of the concrete linkbeams to carry the entire shear and flexure demand.

This study was principally conducted during the structuraldesign of the Burj Dubai and used to check and inform thedesign by the different methods and to examine the conditionand stiffness of the reinforced concrete link beams underservice and factored loads. In addition, a study was made ofthe appropriateness of nominal shear stress limits for linkbeams. A series of nonlinear analyses were conductedthat can account for the influence of many factors onresponse including the amount of flexural reinforcement,the distribution of vertical and horizontal web reinforcement,the span-depth ratio, and the confinement provided by wallsat the ends of the link beams. The nonlinear finite elementanalysis tools used in this investigation were ABAQUS,4

ADINA,5 and VecTor2.6

DESIGN DETAILS OF LINK BEAMSThe geometry, factored loads, and design methods of four

Burj Dubai link beams, LB1 to LB4, are shown in Table 1.These link beams, which have the same external dimensions,capture the range of typical shear design force levels forwhich different design solutions were used. Table 2 and Fig. 4present details on Link Beams LB1 and LB2, as well as LinkBeams LB2A and LBRCMAX that are more heavily reinforcedand hypothetical link beams whose behavior is evaluated in the

fc′ fc′

Ho Jung Lee is an Engineer with SC Solutions, Inc., Sunnyvale, CA. He received hisBS and MS from the Seoul National University, Seoul, South Korea, and his PhD fromthe University of Illinois at Urbana-Champaign, Urbana, IL.

Daniel A. Kuchma, FACI, is an Assistant Professor in the Department of Civil andEnvironmental Engineering at the University of Illinois at Urbana-Champaign. Hereceived his PhD from the University of Toronto, Toronto, ON, Canada. He is amember of ACI Subcommittee 318-E, Shear and Torsion.

William Baker is a Partner of Skidmore, Owings & Merrill LLP, Chicago, IL.

Lawrence C. Novak is an Associate Partner of Skidmore, Owings & Merrill LLP.

Fig. 4—Design details for analyzed link beams. (Note: 1 mm =0.0394 in.)

Fig. 3—Three-dimensional view of single floor.


nonlinear analyses. Link Beam LB1 was designed by thedeep design method specified in ACI 318-99.2 Link BeamLB2 was designed by the strut-and-tie model in Appendix Aof ACI 318-02.3 Vertical shear or tie reinforcement in LinkBeams LB1 and LB2 was determined using the selecteddesign approaches to support their factored design loads.Horizontal web reinforcement close to the minimum amountsuggested for deep beams in ACI 318-023 was used in LinkBeams LB1 and LB2. The design of Link Beam LB2 using thestrut-and-tie method in the ACI 318-023 provisions, unchangedin ACI 318-05,7 is described in the next section. As previouslymentioned, a pure reinforced design concrete solution was notpossible for all members by ACI 318-02,3 or would be by ACI318-05,7 such that composite members with steel-embeddedsections were used to support the shear design in memberssubjected to very large shear and flexural forces, including LinkBeams LB3 and LB4. An objective of this study was to investigatewhether or not it was possible to develop a pure reinforcedconcrete solution to support the very large shear forces in LinkBeams LB3 and LB4. To this end, the behavior of more heavilyreinforced members, Link Beams LB2A and LBRCMAX, asdescribed in Table 2 and Fig. 4, will also be examined.

The concrete cylinder compressive strength used in thedesign of these link beams was f ′c = 64 MPa (9280 psi); aconcrete cube strength of 80 MPa (11600 psi) was specifiedand actual cube and cylinder breaks indicate considerablystronger concrete. The design yield strength of flexural rein-forcement used in the link beams was 460 MPa (67 ksi) andof the vertical stirrups and horizontal web reinforcement was420 MPa (61 ksi). Reinforcement with a yield strength of460 MPa (67 ksi) was actually provided, but in accordancewith Section 11.5.2 of ACI 318-02,3 the effective strengthwas taken as 420 MPa (61 ksi). Nonlinear finite elementanalyses of these reinforced concrete link beams (LB1, LB2,LB2A, and LBRCMAX) were performed as will be presented.

STRUT-AND-TIE MODEL USED IN LINK BEAMThe strut-and-tie method has recently developed as a rational

method in the design of discontinuity (D)-regions in structuralconcrete such as deep beam, squat walls, pile caps, and otherelements in which plane sections do not remain plane. Thestrut-and-tie method provides a conceptually simple designmethodology based on the lower-bound theorem of limitanalysis.8 Provisions for using the strut-and-tie method wereincluded as Appendix A in ACI 318-02.3

The strut-and-tie model used for the design of Link Beam LB2is shown in Fig. 5. The design yields the required amount ofhorizontal and vertical tie reinforcement and the requiredstrength of diagonal concrete struts and nodal zones. Minimumhorizontal web reinforcement was provided in the link beamseven though it was not specifically required when the strut-andtie design procedure is used. In this link beam design, the amountof horizontal and vertical ties can simply be increased to supportlarger shear loads until the strength is limited by the strength ofthe diagonal struts and nodal zones.

The use of Appendix A in ACI 318-023 and ACI 318-057

provides for a direct design of the diagonal strength of struts soas to avoid a diagonal compressive failure. This permits amember to be designed for a higher shear stress than the limit fordeep beams in ACI 318-99.2 This deep beam stress limit was alsoset to guard against diagonal compression failures but is notconsidered to be necessary for deep beams as will be discussed inthe following. In the design of Link Beam LB2 byAppendix A of ACI 318-02, the conservative assumption ofnarrow bottle-shaped diagonal struts were made even thoughthe results of the analyses indicate that there is a uniformfield of diagonal compression throughout these members.Thus, it was considered that the nominal capacity calculatedfor this strut-and-tie model by ACI 318-02 would lead to aconservative design.

MAXIMUM SHEAR STRENGTH SPECIFIEDIN CODE PROVISIONS

There is a large variation in the nominal shear design stresslimit that is specified in codes of practice even though thereason for this limit is the same as guarding against a diagonal

Table 1—Geometry, loading, and design methods for link beams

Beam ID

Geometry Factored loads

Design method usedWidth,

mmDepth,

mmSpan,mm

Shear,kN

MomentkN-m

LB1 650 825 1400 1705 1194 Conventional (ACI 318-99, Section 11.8)

LB2 650 825 1400 2805 1164Strut-and-tie(ACI 318-02,

Appendixes A and C)

LB3 650 825 1400 3750 2625 Steel plate

LB4 650 825 1400 5250 3675 Built-up steel I-beam

Notes: Factored loads are equal for both ends of link beams. Ratio of ultimate load tosustained day-to-day (gravity only) service loads is approximately 2.5. Walls adjacentto link beams are 650 mm thick and are typically reinforced with a minimum ofT20mm at 350 mm on each vertical and horizontal face. 1 in. = 25.4 mm; 1 kip =4.448 kN; and 1 ft-kip = 0.356 kN-m.

Table 2—Reinforcing details of link beams analyzed in study

Beam ID

Reinforcement Stirrups

Top bars

Bottom bars

Side bars each face Size

Spacing, mm Type

LB1 5-T32 5-T32 5-T12 T16 150 Two hoops

LB2 12-T32 12-T32 4-T12 T16 125 Two hoops

LB2A 18-T32 18-T32 4-T12 T16 80 Three hoops

LBRCMAX 27-T32 27-T32 4-T12 T16 75 Five hoops

Notes: T32, T20, T16, and T12 are deformed reinforcing bars with respective diameters of32, 20, 16, and 12 mm. In LB2, top and bottom bars were used in two layers each. LB2Aand LRCMAX were not used in Burj Dubai project. They are included for purpose ofexamining appropriateness of current ACI 318-05 limit on maximum shear stress. LB2Ahas significantly more longitudinal tension reinforcement and transverse reinforcementthan LB2. LBRCMAX is analyzed to figure out maximum shear capacity of reinforcedconcrete link beam. In LB2A and LBRCMAX, top and bottom bars were placed in twolayers and three layers each, respectively. 1 in. = 25.4 mm.

Fig. 5—Strut-and-tie model used in design of Link Beam LB2.(Note: 1 in. = 25.4 mm; 1 kip = 4.448 kN; 1 psi = 6.89 ×10–3 MPa; and 1 ft-kip = 1.356 kN-m.)

454 ACI Structural Journal/July-August 2008

compression failure. For the limits shown in Table 3, therange in maximum permitted shear stress is more than afactor of two for the 64 MPa (9280 psi) concrete used in thedesign of the Burj Dubai. The ACI conventionally designedbeam shear limit of 10 (psi) (0.83 [MPa]) wasderived from simply supported beam tests in which there isa funneling and thus magnification of diagonal compressivestresses as they flow from the top of the beam to its supportand in which anchorage failures are common. The AASHTOLRFD9 and CSA (Canadian) code10 shear stress limit of0.25f ′c for reinforced concrete members was derived fromthe modified compression field theory.11) In this approach,the influence of diagonal tensile strains on the capacity of auniform diagonal compression field is directly considered.The flow of diagonal forces in link beams, which aresupported over their ends, are expected to be uniform asillustrated later and thus the limit in the LRFD and CSAprovisions is more appropriate. For the reinforced concretelink beams used in the Burj Dubai, there is the further structuraladvantage of the confinement effect from the pier walls. Thewalls on both sides help to prevent vertical expansion of the linkbeams at their ends, which limits diagonal cracking. Theuse of a higher shear design stress limit in these link

fc′ fc′

beams is investigated in the nonlinear finite element analysesthat are presented in the next section.

NONLINEAR FINITE ELEMENT ANALYSISThe structural behavior of reinforced concrete link beams

is influenced by many factors including the amount of flexuralreinforcement, vertical and horizontal shear reinforcement, thespan-depth ratio, and the confinement effect of the adjacentpier walls. Nonlinear finite element analyses can be used toevaluate the effect of these parameters. In this section, thenonlinear finite analyses of the Burj Dubai link beams (LB1and LB2) and the more heavily reinforced link beams (LB2Band LBRCMAX), as described in Table 2, are presented.

Three different programs, ABAQUS, ADINA, andVecTor2, were used for the finite element analysis of thesereinforced concrete link beams. In ABAQUS, the concretedamaged plasticity model was selected. This model is basedon the work of Lubliner et al.12 and Lee and Fenves.13 Theconcrete damaged plasticity model is intended to provide ageneral capability for the analysis of concrete structuressubjected to static and dynamic loading under low confiningpressures. It is based on the combination of nonassociatedmulti-hardening plasticity and scalar damaged elasticitymodels. The program ADINA provided the option to adjustvarious concrete strength and ductility parameters as well asfailure envelopes to better represent the concrete behaviorfor a specific application. The program VecTor2 implementsthe rotating-angle smeared-crack model of the modifiedcompression field theory and quadrilateral elements areused in the analyses.

Before conducting the finite element analyses of these linkbeams, the finite element models were calibrated and validatedusing experimental results that accounted for the effects ofcomplex geometries, loadings, and edge effects. Becausethis study focuses on the strength of the link beams, it wasinvestigated to see if the selected parameters for the concretematerial model in ABAQUS, ADINA, and VecTor2 predictwell the strength of link beams tested to failure in laboratories.One of the comparisons used the link beam tested undermonotonic loading by Galano et al.14 that had a shear spanratio of 0.75. This ratio was the closest to that of the BurjDubai link beams (shear ratio = 0.85) for the identified testdata. The geometry and reinforcement details of the tested

Fig. 6—Geometry and detailing of link beam tested by Galanoet al.14

(Note: 1 in. = 25.4 mm; and 1 psi = 6.89 × 10–3 MPa.)

Fig. 7—Predicted load-deformation response of link beamtested by Galano et al.14 (Note: 1 in. = 25.4 mm; and 1 kip =4.448 kN.)

Table 3—Maximum nominal shear design stress permitted by code provisions

Design codeMaximum shear strength,

Vn, max

ACI 318-02 and ACI 318-05

AASHTO STD1

AASHTO LRFD3

AASHTO segmental bridges2

CSA (1994)10

CSA (2004)11

JSCE14

Notes: Vc equals nominal shear resistance provided by concrete, fc′ equals concretecompressive strength, bw equals width, d equals distance from compression face tocentroid of longitudinal tension reinforcement, bv equals web width including adjustmentfor presence of ducts, dv equals effective shear depth, and Vp equals component indirection of applied shear of effective prestressing force.

Vc 8 fc′ bwd+

Vc 8 fc ′bwd+

0.25fc′ bvdv Vp+

12 fc ′bwd

0.25fc′ bvdv Vp+

0.25fc′ bvdv Vp+

15 fc ′bwd


link beam are shown in Fig. 6. Four-node plane stress isopara-metric elements were used in the analyses. Reinforcing steelwas modeled as two-node truss elements. The top section ofthe left wall is restrained and the shear force is applied to thebottom section of the right wall by displacement control; thesame prescribed vertical displacement is used along thesection. The analysis results are presented in Fig. 7 and thestrengths predicted by ABAQUS, ADINA, and VecTor2 areshown to predict the experimentally measured capacityreasonably well. The results of other validation studies weresimilar. Therefore, the selected parameters for the concretemodel in ABAQUS, ADINA, and VecTor2 were taken to besufficiently accurate for capacity evaluation of the four linkbeams in this study.

The load and boundary conditions of the finite elementmodel for the Burj Dubai link beams are shown in Fig. 8. Thewall boundary is extended vertically up to the depth of thelink beam and horizontally up to the length of the link beam.This extension with the constraints put in the finite elementmodel provides a realistic boundary for the investigation oflink beam capacity that was expected to lead to conservative(lower bound) estimations of capacity. The load andboundary conditions are the same as that of the link beamtested by Galano et al.14 except the stiff perimeter steel wasused to account for the constraining effect of the wall as theboundary of the model. The additional benefit of axialcompression in the walls, as investigated by other analysesnot presented in this paper, was found to only have a veryminimal beneficial effect on the capacity of the link beams;it is the link beam end restraint rather than axial compressionin the wall piers that influences the behavior of the linkbeams. Thus, the axial load acting on the walls was notconsidered in the reported analyses. The strain variation ofreinforcing steel identified in Fig. 8 was investigated as wellas the crack patterns and capacity of the link beams.

Additional information on the finite element models isnow presented and this is followed in the next section by thepredicted capacity and behavior of the link beams. Increating the finite element models, it was necessary to selectand specify material models and select convergence limits.In all analyses, the response of the reinforcement was linearelastic and perfectly plastic. The default value of theconvergence limit in VecTor2 was used, a convergencevalue of up to 0.01 was used in ADINA, whereas the stabilitycommand was used in ABAQUS, but its use was found tohave little effect on the predicted behavior. The philosophyof VecTor2 is that the user is not required to select nonbasicmaterial parameter values and thus only the compressivecylinder strength was specified and all other default valueswere accepted. ADINA and ABAQUS require the user toselect many other parameter values. The selections made inthese programs are given in the following.

In ADINA, the required concrete material input parameterswere tangent modulus at zero strain (44,000 MPa [6380 ksi]),Poisson’s ratio (0.15), uniaxial cut-off tensile stress (4.83 MPa[700 psi]), post-cracking uniaxial cut-off tensile stress (4.83 MPa[700 psi]), uniaxial maximum compressive stress (–64 MPa[–9280 psi] for unconfined concrete; –102.4 MPa [–14848 psi] forconfined concrete) and corresponding compressivestrains (–0.002 for unconfined concrete; –0.0032 for confinedconcrete), ultimate uniaxial compressive stress (–54.4 MPa[–7888 psi] for unconfined concrete; –87 MPa [–12615 psi]for confined concrete), and ultimate uniaxial compressivestrain (–0.003 for unconfined concrete; –0.0048 for confined

concrete). These input parameters define the stress-straincurve of concrete.

In ABAQUS, the compressive and tensile response wasdefined similarly as in ADINA, but the prediction byABAQUS was based on the concrete damaged plasticitymodel. In this model, the value of the flow potential eccentricityparameter has a significant effect on the concrete response. Thisvalue was set to be 20 based on the calibration with experimentaldata, whereas the dilation angle was similarly selected to be 36.Default values were used for the other input parameters inthe concrete damaged plasticity model.

DISCUSSION OF PREDICTED LINKBEAM BEHAVIOR

The finite element analysis results of Link Beam 1 (LB1)are shown in Fig. 9 through 11. ABAQUS, ADINA, andVecTor2 all predicted similar responses for Link Beam LB1.According to Fig. 9, the predicted capacity is much largerthan the factored design load. Therefore, the use of the deepbeam design method as specified in the ACI 318-992 Code isconsidered to lead to a very conservative design for this linkbeam. Crack patterns at the loading steps similar to thefactored design load and at the ultimate load are shown inFig. 10. At the factored design load, flexural cracks occur atthe boundary regions of the link beam under tension,

Fig. 8—Load and boundary conditions used in modeling ofBurj Dubai link beams.

Fig. 9—Predicted load-deformation response of LinkBeam LB1. (Note: 1 in. = 25.4 mm; and 1 kip = 4.448 kN.)


whereas no shear cracking was observed in the centralportion of the link beam. The development of straining in thelongitudinal and shear reinforcement is presented in Fig. 11.The longitudinal tensile strain increased gradually withincreasing shear force until the capacity of the member wasreached at the point of longitudinal yielding. As shown inFig. 11(b), the transverse reinforcement strain rapidlyincreased with the formation of diagonal cracks, but thetransverse strain at the capacity of the member was less thanthe yield strain of 0.0021. At the ultimate load, severe flex-ural cracks occurred and extensive shear cracking waspredicted. In summary, the finite element analysis resultspredict that the failure mode of Link Beam LB1 was yieldingof longitudinal tension reinforcement and that shear failuresdid not occur. It is also observed that Link Beam LB1, asdesigned by the deep beam design method in ACI 318-99,2

was more conservatively designed for shear than for flexure. The predicted load-deformation response of Link Beam 2

(LB2) by the nonlinear finite element analyses is shown inFig. 12 in which the predicted capacity is considerably largerthan the factored design load. The strut-and-tie method specifiedin ACI 318-057 was therefore observed to lead to a conservativedesign for this link beam. ABAQUS, ADINA, and VecTor2provide similar predictions of behavior of this link beam.Two different concrete models were used in the ADINAanalyses. One is an unconfined concrete stress-strain modeland the other is a confined concrete model. ADINA andABAQUS do not directly consider the confinement effect bythe pier walls at the end of the link beams. Thus, if theunconfined model is used in ABAQUS and ADINA for the

analysis of Link Beam LB2, the capacity of Link Beam LB2is slightly decreased due to concrete crushing at the ends ofthe link beam. This is not expected in practice because thepier walls provide significant restraint to the vertical expansionof the link beam and this increases the concrete compressivestrength at the ends of these link beams. VecTor2 directlyconsiders concrete confinement and softening withoutadditional input from users. When the confined concrete

Fig. 11—Predicted development of reinforcement strains inLink Beam LB1. (Note: 1 kip = 4.448 kN.)

Fig. 12—Predicted load-deformation response of LinkBeam LB2. (Note: 1 psi = 6.89 × 10–3 MPa, 1 in. = 25.4 mm;and 1 kip = 4.448 kN.)

Fig. 10—Predicted crack patterns by ADINA for LinkBeam LB1. (Note: 1 kip = 4.448 kN.)


model is used in ABAQUS and ADINA for the analysis ofthe link beams, it gives similar results to those of the VecTor2default model. The predicted development of reinforcementstrains for Link Beam LB2 is shown in Fig. 13. For LinkBeam LB2, the strain in the transverse reinforcementreaches yield before yielding of the longitudinal reinforcement.The capacity and mode of failure of Link Beam 2 is predictedto occur at the point of yielding of both the longitudinal andtransverse reinforcement.

The finite element analysis results of hypothetical LinkBeams LB2A and LBRCMAX, which contained higherlevels of longitudinal and shear reinforcement, are shown inFig. 14 through 17. ABAQUS, ADINA, and VecTor2provide similar predictions of the behavior of these link beams.Without consideration of the confinement effect by the walls,the analysis results predict a maximum shear stress capacitylimit that is 70% larger than the conventionally designedbeam shear stress limit of 10 (psi) (0.83 [MPa]) that isspecified in ACI 318-05.7 If the confinement effect by thepier walls is considered in the analysis through the use ofthe confined concrete stress-strain model, the shear stresscapacity of the reinforced concrete link beam can be 2.5 timesthe ACI shear stress limit. This is illustrated in thepredicted behavior of Link Beam LBRCMAX in whichvery significant amounts of longitudinal and transversereinforcement were provided. For both Link Beams LB2Aand LBRCMAX, the predicted transverse reinforcement

fc′ fc′

strains were considerably smaller than yield strain at thepoint of yielding of the longitudinal reinforcement.Therefore, it is predicted that the capacity of these linkbeams is limited by their flexural capacities.

Sectional analyses of Link Beams LB2A and LBRCMAXwere also performed using the sectional analysis programResponse 2000.15 Response 2000 15 is also based on themodified compression field theory and employs the engineeringbeam theory assumption that plane sections remain plane.Unlike with the nonlinear finite element analyses,Response 200015 cannot account for the beneficial effects ofconfinement and strut action. Under combined shear andbending loads, the sectional capacities predicted byResponse 200015 for Link Beams LB2A and LBRCMAXwere 6026 and 7600 kN (1355 and 1709 kips), respectively.The state of cracking in Link Beam LBRCMAX was alsopredicted by program Response 200015 as shown in Fig. 18at its ultimate capacity. The member analysis by Response200015 for Link Beam LBRCMAX supports the conclusionfrom the nonlinear finite element analyses that a shearforce close to the LRFD and CSA limit can be supportedby a reinforced concrete link beam of the dimensions usedin the Burj Dubai.

The strength results of this investigation are summarizedin Fig. 19, which presents a comparison of the factored shear

Fig. 14—Predicted load-deformation response of hypotheticalLink Beam LB2A. (Note: 1 in. = 25.4 mm; and 1 kip =4.448 kN.)

Fig. 15—Predicted load-deformation response of hypotheticalLink Beam LBRCMAX. (Note: 1 in. = 25.4 mm; and 1 kip =4.448 kN.)

Fig. 13—Predicted development of reinforcement strains inLink Beam LB2. (Note: 1 kip = 4.448 kN.)


design loads for link beams (LB1 to LB4) in the Burj Dubaiand the predicted shear capacities by the nonlinear finiteelement analyses for Link Beams LB1, LB2, LB2A, andLBRCMAX. The shear force corresponding to the ACI318-057 conventionally designed beam shear stress limit of10 (psi) (0.38 [MPa]) is also shown. The results ofthe analyses predict that the designs are very conservative

fc′ fc′

for Link Beam LB1 that was designed by the ACI 318-992

deep beam provisions and for Link Beam LB2 that wasdesigned by the strut-and-tie model of Appendix A in ACI318-02.3 In the Burj Dubai, composite link beams with largeembedded sections were used to support the shear andflexure demand when this demand was in excess of whatcould be designed for by ACI 318 sectional or strut-and-tiedesign procedures. The results of the analyses for hypotheticalLink Beams LB2A and LBRCMAX suggest that it would havebeen possible to support the large shear force demands in LinkBeams LB3 and LB4 with reinforced concrete link beams;however, reinforcing bar congestion and constructibilityconcerns would need to be evaluated for Link Beams LB2A andLBRCMAX.

CONCLUSIONSIn this paper, the design and capacity of heavily loaded

reinforced concrete link beams were investigated bynonlinear finite element analyses using the programsABAQUS,4 ADINA,5 and VecTor2.6 The following is asummary of results from this study:

1. The effect of the pier walls at the ends of the link beamswas predicted by the analyses to reduce the vertical transverseexpansion at the ends of the members and thereby reduce thedemands on transverse reinforcement. The pier walls alsoprovided confinement that enabled the link beams to supportlarger compressive stresses at their ends. Furthermore, theyenabled a more uniform field of diagonal compression andvertical distribution of shear over the depth of the memberthroughout the entire length of the link beam;

Fig. 17—Predicted development of reinforcement strains inhypothetical Link Beam LBRCMAX (Location A in Fig. 8).(Note: 1 kip = 4.448 kN.)

Fig. 18—Predicted cracking in hypothetical Link BeamLBRCMAX by Response 2000 at ultimate load (V = 1709 kips[7600 kN]). (Note: 1 in. = 25.4 mm; and 1 kip = 4.448 kN.)

Fig. 19—Comparison of shear demands and capacities inlink beams.

Fig. 16—Predicted development of reinforcement strains inhypothetical Link Beam LB2A. (Note: 1 kip = 4.448 kN.)


2. The use of the deep beam design method in the ACI318-992 provisions leads to very conservative shear designsfor link beams as suggested by the results of multiplenonlinear finite element analyses. The ACI 318-992 shearstress limitation for deep beams, which is a function of thespan-depth ratio and imposed to guard against a diagonalcompression failure, unnecessarily limits the load-carryingcapacity of stocky link beams supported over their heightssuch as those used in the Burj Dubai project;

3. The strut-and-tie model in Appendix A of ACI 318-023

and ACI 318-057 permits reinforced concrete link beams to bedesigned for substantially higher loads than would be possibleby the use of ACI sectional design methods. In the use of thestrut-and-tie model, a direct check is made to ensure that thediagonal compressive struts have adequate capacity. There-fore, a design completed by the strut-and-tie model negates theneed to satisfy any sectional shear stress limitation;

4. The results of nonlinear finite element analyses indicatethat reinforced concrete link beams have significantly largershear capacities than the nominal strengths calculated by thestrut-and-tie model of ACI 318-05.7 The capacity of themembers was predicted to be controlled by yielding of thelongitudinal reinforcement; the compressive and nodal stresslimits in ACI 318-057 were found to be conservative; and

5. There is a wide variation in the maximum shear stresslimits in codes of practice. The difference is more than afactor of two between the sectional design models in ACI318-057 (10 [psi] [0.83 (MPa)]) and the Canadianand AASHTO LRFD Design Codes (0.25f ′c ) for link beamscast with 64 MPa (9280 psi) concrete, as used in the BurjDubai. The higher shear stress limit in the Canadian andAASHTO LRFD code was found to be appropriate for shortlink beams that are supported over their height at theirends by continuous wall piers.

ACKNOWLEDGMENTSThe analyses presented in this paper were performed for Skidmore,

Owings & Merrill LLP (SOM) LLP, Chicago, IL, under the direction ofW. Baker, L. Novak, A. Ozkan, and S. Korista.

REFERENCES1. Baker, W.; Novak, L.; Sinn, R.; and Viise, J., “Structural Optimization

of 2000’ Tall 7 South Dearborn Building,” Proceedings of the 2000 ASCEStructures Congress, Track: 14th Analysis and Computational Conference,2000.

2. ACI Committee 318, “Building Code Requirements for StructuralConcrete (ACI 318-99) and Commentary (318R-99),” American ConcreteInstitute, Farmington Hills, MI, 1999, 369 pp.


4. ABAQUS, Version 6.4.3, Hibbitt, Karlsson & Sorensen, Inc.,Pawtucket, RI, 2004.

5. ADINA, “A Finite Element Program for Automatic Dynamic Incre-mental Nonlinear Analysis,” Version 8.3, ADINA R & D, Inc., 2006.

6. Vecchio, F. J., “VecTor2, Nonlinear Finite Element Analysis Programof Reinforced Concrete,” University of Toronto, Toronto, ON, Canada, 2002.


8. Schlaich, J.; Schafer, K.; and Jennewein, M., “Toward a ConsistentDesign of Structural Concrete,” PCI Journal, V. 32, No. 3, 1987, pp. 75-149.

9. AASHTO, “AASHTO LRFD Bridge Design Specifications,” thirdedition, Washington, DC, 2004, 1450 pp.

10. CSA Committee A23.3, “Design of Concrete Structures (CSAA23.3-04),” Rexdale, ON, Canada, 2004.

11. Vecchio, F. J., and Collins, M. P., “The Modified Compression FieldTheory for Reinforced Concrete Elements Subjected to Shear,” ACIJOURNAL, Proceedings V. 83, No. 2, Feb. 1986, pp. 219-231.

12. Lubliner, J.; Oliver, J.; Oller, S.; and Oñate, E., “A Plastic-DamageModel for Concrete,” International Journal of Solids and Structures, V. 25,1989, pp. 299-329.

13. Lee, J., and Fenves, G. L., “Plastic-Damage Model for CyclicLoading of Concrete Structures,” Journal of Engineering Mechanics,ASCE, V. 124, No. 8, 1998, pp. 892-900.

14. Luciano, G., and Vignoli, A., “Seismic Behavior of Short CouplingBeams with Different Reinforcement Layouts,” ACI StructuralJournal, V. 97, No. 6, Nov.-Dec. 2000, pp. 876-885.

15. Bentz, E. C., and Collins, M. P., “Response 2000,” http://www.ecf.utoronto.ca/~bentz/r2k.htm, 2000.

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design and analysis of heavily loaded reinforced concrete link beams for burj dubai

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