Performance of Three-Dimensional Reinforced Concrete … ST...Performance of Three-Dimensional...

Performance of Three-Dimensional Reinforced ConcreteBeam-Column Substructures under Loss of a Corner

Column ScenarioKai Qian, A.M.ASCE1; and Bing Li2

Abstract: The vulnerability of conventional RC structures to structural failure caused by the loss of corner columns has been emphasized overthe past years. However, the lack of experimental tests has led to a gap in the knowledge for the design of RC building structures to mitigate thelikelihood of progressive collapse caused by losing a ground corner column. Seven one-third scale RC beam-column substructures were testedto investigate their performance. The variables selected for the test specimens included beam transverse reinforcement ratios, type of designdetailing (nonseismic or seismic), and beam span aspect ratios. Shear failure was observed to have occurred in the corner joint, and a plastichinge was formed at the beam end near the fixed support in the nonseismic detailed specimens. However, plastic hinges were also formed in thebeam end near to the corner joint for the seismically detailed specimen. Vierendeel action was identified as the major load redistribution mech-anism before severe failure occurred in the corner joint, but a cantilever beam redistributionmechanism dominated after the corner joint sufferedsevere damage. The test results were compared with the Department of Defense design guidelines to highlight the deficiencies of the recentlyupdated guidelines. DOI: 10.1061/(ASCE)ST.1943-541X.0000630. © 2013 American Society of Civil Engineers.

CE Database subject headings: Progressive collapse; Reinforced concrete; Beam columns; Substructures.

Author keywords: Progressive collapse; Reinforced concrete; Corner; Three dimensional; Beam-column; Substructures.

Introduction

ASCE SEI 7 (2010) defines progressive collapse as the spread of aninitial local failure from element to element, which eventually resultsin the collapse of an entire structure or a disproportionately large partof it. In less technical terms, it is often thought of as the dominoeffect. The collapses of the Ronan Point Tower in London in 1968and Murrah Federal Building in Oklahoma City in 1995 have de-monstrated the disastrous consequences of a progressive collapse.To prevent progressive collapse, a structure should have continuityto offer an alternate path to ensure the stability of the structure whena vertical load-bearing element is removed. Design guidelines[Department of Defense (DoD) 2005; General Services Adminis-tration (GSA) 2003] have proposed design procedures to evaluatethe likelihood of progressive collapse of a structure following thenotional removal of the vertical load-bearing elements. Althoughsignificant improvements were implemented in the recently updatedDoD design guidelines (2009) [for a detailed description of theseupdated points, please refer to Stevens et al. (2009) and Marchandet al. (2009)], a number of design criteria still need to be subjected tofurther analysis and verification with experimental data.

To better understand the performance of RC frames subjectedto different missing column scenarios, several experimental and

numerical studies have been conducted in recent years. Sasani et al.(2007) conducted an in situ test to study the performance of a RCbuilding with one-way floor slabs supported by transverse frameswhen subjected to the sudden removal of one of its exterior columns.The behavior of a RC moment frame subjected to the loss of aninterior column was also investigated by Yi et al. (2008). Theefficiency of using carbon fiber–reinforced polymer (CFRP) ret-rofitting RC pre-1989 frames, which may be deficient in its conti-nuity subsequent to the loss of an interior column, was investigatedby Orton et al. (2009). The behavior of axially restrained beam-column subassemblages under the scenario of the loss of a columnwas studied by Su et al. (2010). The performance of exterior andinterior beam-column subassemblages following the loss of one ofthe ground exterior columns was experimentally studied by Yap andLi (2011) and Kai and Li (2012a), respectively. However, most ofthe previous research studies were focused on the frames subjectedto the loss of interior or exterior column scenarios, whereas limitedstudies have been conducted for the case of loss of corner columns.Mohamed (2009) investigated the implementation of DoD (2005) toprotect against progressive collapse of corner floor panels when theirdimensions exceeded the damage limits through numerical simu-lation. A case study of a RC building with different bracing con-figurations was analyzed using an alternate load path method. Kaiand Li (2012b) experimentally studied the dynamic performance ofsix beam-column substructures under a loss of a ground cornercolumns scenario. The dynamic responses of acceleration, velocity,and displacement were determined. Moreover, the dynamic effects ofthe beam-column substructure caused by sudden removal of a cornercolumn were evaluated. Sasani (2008) and Sasani and Sagiroglu(2008) conducted an in situ test to examine the dynamic response andthe possibility of a progressive collapse of a RC frame when onecorner column and adjacent exterior columns were simultaneouslydemolished by explosion. They concluded that the three-dimensional(3D) Vierendeel action of the transverse and longitudinal frames was

1Research Associate, School of Civil and Environmental Engineering,Nanyang Technological Univ., Singapore 639798 (corresponding author).E-mail: [email protected]

2Associate Professor, School of Civil and Environmental Engineering,Nanyang Technological Univ., Singapore 639798.

Note. This manuscript was submitted on May 18, 2011; approved onJuly 20, 2012; published online on August 10, 2012. Discussion periodopen until September 1, 2013; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Structural Engi-neering, Vol. 139, No. 4, April 1, 2013. ©ASCE, ISSN 0733-9445/2013/4-584–594/$25.00.

584 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / APRIL 2013

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http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000630mailto:[email protected]

the major mechanism for the redistribution of loads in the structure.However, the accuracy of the numerical results is needed to improvevia comparing with the related experimental results. In addition, thetremendous costs of the in situ tests mean that it is impossible tosystemically investigate the performance of RC frames against pro-gressive collapse via thismethod. Therefore, seven one-third scaleRCbeam-column substructures were designed and tested at NanyangTechnological University (NTU), Singapore, to investigate the per-formance of substructures for progressive collapse caused by losingone of the corner columns. The primary objective of this paper is togain a better understanding of the behavior of RC substructures underthe scenario of being subjected to the loss of one of its ground cornercolumns. In particular, the following variables were studied: variationof beam transverse reinforcement ratio in the plastic hinge region,seismic design detailing, design span length, and span aspect ratio.The results of this study can be used as a basis for the understanding ofthe behavior of RC structures for progressive collapse.

Experimental Program

Experimental Setup

As observed from Mohamed (2009) and Kai (2012), most of thedeformation of a typical RC frame subjected to the loss of a groundcorner column took place in the corner panels, whereas the de-formation of the rest of the panels was negligible. Therefore, onetypical critical panel (corner panel in the second story) was extractedand studied. A schematic of the test setup is shown in Fig. 1. Thesetup can be separated into three components. In Component 1,vertical, axial, and rotational constraints were provided at the en-larged adjacent columns to simulate fixed boundary conditionsprovided by the surrounding structural elements. In Component 2,axial loading in the corner column before the damage was simulatedby applying downward displacements at the corner column stubthrough a hydraulic jack with 600-mm stroke. Both the previousnumerical and experimental studies (Sasani and Sagiroglu 2008)indicated that the direction of the bending moment in the beam endnear to the corner joint (BENC) was changed after removal of thecorner column and resulted in a considerably positive bendingmoment (tensile at the bottom) being formed in the BENC after theremoval of the ground corner column as a result ofVierendeel action.However, as observed in the deformation shape of the corner jointfrom Sasani and Sagiroglu (2008), a slight horizontal movementaccompanied the vertical movement of the corner joint after removal

of the ground corner column, and it indicated that the rotational in theBENC was not fully constrained. Component 3 was used to applythis positive bending moment in the BENC for test substructures.Fig. 2 illustrates the detailing of the steel assembly of this com-ponent. One strong steel column was connected to the corner stub ofthe RC specimen using anchor bolts. Four steel pins with highstrength and stiffness were used to apply the prescribed partialrotational and horizontal constraints in each direction. In otherwords, the steel column could freely move in the vertical direction,but the rotational and horizontal freedoms were partially restrained.The extent of rotational and horizontal constraints applied on thecorner joint was related to the allowance between the steel pin andthe hole in the steel box (as shown in Fig. 2), which was designedwith the aid of ABAQUS. The finite-element model (FEM) wasvalidated by comparing the numerical results to the test resultsattained by Sasani et al. (2007). This model was used to predict therelationship of the horizontal movement and vertical deflection ofthe center of the corner joint by pushover analysis. The FEM resultindicates the center of the joint just above the lost column hasmaximum outward horizontal movement of ∼7.2 mm (0.28 in.),whereas the vertical displacement (D1) is ∼180.0 mm (7.09 in.). Theallowance between the steel pin and the hole was designed as follows:

f ¼ H1TV

¼ H1V þ D1 ¼

7:2625 þ 180 ¼ 8:9� 10

23 ð1Þ

d ¼ V � f2

¼ 350 � 8:9 � 1023

2¼ 1:56 ð2Þ

Therefore, the difference between the diameters of the steel pin to thehole was 3 mm, as illustrated in Fig. 2.

Experimental Substructures

In the current study, the nonseismic and seismic-designed 9-storyRC prototype buildings were designed in accordance with Singa-pore Standard CP 65 (1999) and American Concrete Institute (ACI)318-08 (2008), respectively. The test subjects were assumed to beregular frames for ease of analyzes. Fig. 3 presents basic structuralinformation of the prototype frame in accordance with a typicalnonseismic-designed Specimen F3. For the remaining prototypeframes, the dimensions and reinforcement details are given inTable 1. Considering the spatial limitations in the laboratory anddifficulties of transportation, one-third scale tests were conducted.

Fig. 1. Overview of a specimen in position ready for testing

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The comparisons between the prototype frames with the modelframes are given in Table 1. It should be stressed that the seismic-designed prototype buildingwas assumed to be located on a site classof D, stiff soil profile; the design spectral response accelerationparameters, SDS and SD1, were 0.47 and 0.32, respectively.

The distributed dead load on the prototype structure caused by thegravity load of a 210-mm-thick slab was 5.1 kPa. The super-imposed dead load from ceiling, mechanical ductwork, electricalitems, and plumbing was assumed to be 1.0 kPa. The equivalentadditional dead loads from the weight of in-fill walls and beams

Fig. 2. Details of steel assembly

Fig. 3. Plan and elevation view of the prototype frame in accordance with Specimen F3


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were 2.25 and 1.59 kPa, respectively. The live loadwas assumed tobe 2.0 kPa. Thus, the design axial force in the corner column ofeach specimen as specified byDoD (2009) is determined and listedin Table 2. As illustrated in Fig. 4, each test substructure consisted oftwo doubly reinforced beams connected with a column stub at thecorner and two enlarged adjacent columns at the edges where therotational and horizontal restraints on beamswere applied. The cornercolumn stub representing the removed column was 200 mm squarefor all specimens. Details of the test substructures are summarized inTable 2. The transverse reinforcement ratio given in Table 2 wasdetermined by Eq. (3)

rt ¼ Asv=bvs ð3Þ

Fig. 4 illustrates the typical reinforcement layout of the Specimens F2and F3. The concrete cover of the beam and column was 10 and 20mm, respectively. For F2, the transverse reinforcements were hoopstirrups with 135� bends, and transverse reinforcement was providedin the joint region. For the remaining specimens, nonseismic detailingwas provided, transverse reinforcements were hoop stirrups with 90�bends, and no transverse reinforcement was installed in the jointregion. It should be emphasized that a doubly continuous longitudinalrebarwas installed in the beambecause scaled specimenswere testedin the current study. To prevent bottom longitudinal reinforcementbar pullout at the BENC, 90� hooks were used. The developmentlength of the hooked beam top longitudinal reinforcement into thefixed support was greater than the ACI 318-08 (2008) required

design development length. The description of the anchorage detailsis illustrated in Fig. 4.

Material Properties

The target compressive strength of concrete at 28 days of age was 30MPa. The average compressive strength of concrete f 0c obtained fromthe concrete cylinder samples was found to be 31.5, 32.1, 31.9, 32.5,33.1, 32.8, and 33.3 MPa for Specimens F1, F2, F3, F4, F5, F6, andF7, respectively. Grade 250 (R6) andGrade 460 (T16, T13, andT10)steel bars were used as transverse and longitudinal reinforcements,respectively. Table 3 gives the measured tensile properties of thebars used in the tests.

Instrumentation

Extensive measuring devices were installed both internally andexternally to monitor the responses of the test specimens. A total of100 data channels were active during the testing process. A load cellwas used to measure the applied force on the corner stub, and thedeflection shape of the beam was monitored through LVDTs. Threecompression/tension load cells were installed in each fixed support.Two of them were vertical and were used to determine the verticalreaction force and the bending moment at the fixed support. Theremaining horizontal one (Item 10 or 11 in Fig. 1) was used tomeasure the horizontal constraint force at the fixed support. Tomonitor the horizontal reaction force applied to the corner joint fromthe steel assembly (Item 5 in Fig. 1), two compression/tension load

Table 1. Corelationship between the Prototype Frames and the Corresponding Test Models

Test

Dimensions of theprototype beams (mm) Longitudinal rebar in the prototype beams

Dimensions of the modelbeams (mm)

Longitudinal rebarin the model beams

Beam T Beam L

Beam T Beam L

Beam T Beam L Beam T Beam LTop Bottom Top Bottom

F1 540 3 300 540 3 300 2T20 1 T32 2T20 1 T32 2T20 1 T32 2T20 1 T32 180 3 100 180 3 100 4T10 4T10F2 540 3 300 540 3 300 3T32 3T32 3T32 3T32 180 3 100 180 3 100 4T13 4T13F3 540 3 300 540 3 300 2T20 1 T32 2T20 1 T32 2T20 1 T32 2T20 1 T32 180 3 100 180 3 100 4T10 4T10F4 540 3 300 540 3 300 2T20 1 T32 2T20 1 T32 2T20 1 T32 2T20 1 T32 180 3 100 180 3 100 4T10 4T10F5 720 3 300 720 3 300 2T25 1 T32 2T25 1 T32 2T25 1 T32 2T25 1 T32 240 3 100 240 3 100 4T10 4T10F6 540 3 300 720 3 300 2T20 1 T32 2T20 1 T32 2T25 1 T32 2T25 1 T32 180 3 100 240 3 100 4T10 4T10F7 540 3 300 630 3 300 2T20 1 T32 2T20 1 T32 2T25 1 T32 2T25 1 T32 180 3 100 210 3 100 4T10 4T10

Note:T325 deformed bar of 32mmdiameter; T255 deformed bar of 25mmdiameter; T205 deformed bar of 20mmdiameter; T135 deformed bar of 13mmdiameter; T10 5 deformed bar of 10 mm diameter; Beam L 5 longitudinal beam; Beam T 5 transverse beam.

Table 2. Specimen Properties (mm)

Specimen ID

Elements Longitudinal rebar Transverse reinforcementDesign axial load

(kN)Beam T Beam L Beam T (%) Beam L (%) Joint Beam T (%) Beam L (%)

Modified DetailedSpecimen F1

Type a Type a 0.87 0.87 None 0.23 0.23 18.6

Seismically DetailedSpecimen F2

Type a Type a 1.47 1.47 0.49% 0.95 0.95 18.6

Control Specimen F3 Type a Type a 0.87 0.87 None 0.31 0.31 18.6Modified DetailedSpecimen F4

Type a Type a 0.87 0.87 None 0.72 0.72 18.6

Long Span Specimen F5 Type b Type b 0.65 0.65 None 0.36 0.36 29.1Unequal Span Specimen F6 Type a Type b 0.87 0.65 None 0.31 0.36 23.2Unequal Span Specimen F7 Type a Type c 0.87 0.75 None 0.31 0.36 23.2

Note: Type a, clear span5 2,175 mm, cross section5 1803 100; Type b, clear span5 2,775 mm, cross section5 2403 100; Type c, clear span5 2,775 mm,cross section 5 210 3 100; Beam L 5 longitudinal beam; Beam T 5 transverse beam.


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cells (Item 4 in Fig. 1 or the horizontal load cell in Fig. 2) wereinstalled in both longitudinal and transverse constraints. Theoreti-cally, the horizontal reaction force measured in the fixed support(Items 10 and 11 in Fig. 1) and the constraint (Item 4 in Fig. 1)connected with the steel box should be similar. A series of LVDTs

and linear potentiometers were also placed at various locations ofthe substructure to measure the different types of internal de-formation, such as fixed support rotation, curvature, and diagonaldeformations. It should be noted that two LVDTswith 25-mm travelwere placed in each fixed support to monitor the rigid body rotationof the fixed support (refer to Items 8 and 9 in Fig. 1). The rotationalresponse of eachfixed support in each specimenwas recorded duringthe test, and the additional vertical deflection in the corner jointcaused by this rigid body rotation was determined by assuming thebeams as cantilever beams. The error of the cantilever assumptioncan be ignored because the recorded rigid body rotation is limited(e.g., the maximum rigid rotation in the transverse fixed support ofF3 is 0.00183 rad). The displacement results presented in the fol-lowing sections refer to the net displacement, which is defined as thedeflection after subtracting the additional deflection caused by therigid body rotation at the fixed supports from the total deflection. A

Fig. 4. Dimensions and reinforcement details of F2 and F3

Table 3. Properties of Reinforcing Steel

TypesYield strength,

fy (MPa)Yield strain,ɛy (10

26)Ultimate strength,

fu (MPa)Ratio of

elongation (%)

R6 530 2,650 613 20.3T10 575 2,895 695 21.7T13 520 2,595 637 22.6T16 556 2,897 635 21.1

Note: R6 5 plain round bar of 6 mm diameter; T10 5 deformed bar of10 mm diameter; T135 deformed bar of 13 mm diameter; T165 deformedbar of 16 mm diameter.


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total of about 60 electrical resistance strain gauges were mounted onthe reinforcement at strategic locations to monitor strain variationalong the beams, corner column, and joint during the test regime.Fig. 4 illustrates the specific locations of these strain gauges.

Experimental Results and Discussion

A total of seven beam-column substructures with different designdetailing and span length were constructed and tested to evaluate theperformance of the RC frame when subjected to the loss of a groundcorner column. The test results of the seven specimens are summarizedin Table 4 and are discussed in the following sections.

Vertical Load and Horizontal Reaction versus Deflection

Influence of Transverse Reinforcement Ratio in the BeamPlastic Hinge RegionTo relate the test results with the performance status of eachspecimen, the results were normalized by dividing them with de-sign axial force in the corner column. The failure mode of F3 isillustrated inFig. 5. For F3, the first crack was observed at the beamend near the fixed support (BENF) at a load of 4.3 kN (0.23). Thenumber 0.23 illustrates that the crack began to occur in SpecimenF3 when the load reached 23% of the design axial force. However,the first flexural crack was formed in the BENC at a load of 10.0 kN(0.54). This indicates that Vierendeel action was the major loaddistribution mechanism when the specimen within the elastic re-sponse. Following the first crack, joint shear cracks were observedat a load of 21.0 kN (1.13), whereas the plastic hinges were formedat the BENFs at a load of 22.5 kN (1.21). This yield load obtaineda deflection of 28.9 mm. The ultimate capacity of F3 was 25.8 kN(1.39), which corresponded to a deflection of 44.0 mm. On furtherincreasing the vertical deflection, the vertical load resistance beganto decrease. After the joint shear cracks widened, the strains of thebeam longitudinal reinforcement at the BENC started to decrease,whereas the strain of the longitudinal reinforcement at the BENFincreased rapidly. This indicated that the resistance mechanism ischanging to a cantilever beam mechanism and demonstrated thatcantilever beam redistribution mechanism dominated the loadredistribution after severe shear failure has occurred in the joint.When the vertical deflection reached 275.9 mm, the vertical loadresistance began to ascend again, and this is attributed to thecatenary action developing in the beams. The load resistance at thedeflection of 456.2 mm was 11.9 kN (0.64), but it was suddenlyreduced to 0.0 kN at a deflection of 461.3mmbecause of fracture ofthe top beam longitudinal rebar occurring in the beam ends near tothe fixed supports.

The measured horizontal reaction forces are plotted againstvertical deflection in Fig. 6. The terms PL1, PL2, PL3, PL4, andPL5 in the figure represent the first flexural crack, the first yield ofthe beam longitudinal reinforcement, the ultimate capacity, thenormal failure stage that is defined as the resistant capacitydropping to 75.0% of the ultimate capacity, and the vertical loadresistance beginning to ascend again, respectively. The recordedhorizontal compressive force was limited before the first crackoccurred in the specimen. However, it significantly increased afterthe first crack was observed. As shown in Fig. 6, the recordedresponse of the horizontal reaction force in the fixed support wasalmost identical as that measured in the horizontal constraint nearto the corner column for both the longitudinal and transversebeams. Moreover, similar performance of the horizontal reactionforce was measured in both beams before reaching the maximumforce. However, the degradation of the horizontal reaction force inthe transverse beam was greater than that in the longitudinal beamand led to the tensile force being transferred to the transverse beamearlier than that in the longitudinal beam. For the rest of specimens,the average value of the horizontal reaction force measured in thefixed support and the constraint connected with the steel box waspresented. It should be noted that, for F1, F2, F3, F4, and F5, onlythe horizontal reaction force in the transverse direction was pre-sented. However, for F6 and F7, the horizontal reaction forcesmeasured in both directions were presented because of the unequalspan of the beams.

In general, the crack pattern development of F1 was similar tothat of F3. For F1, the dominating diagonal shear crackwas observedin the BENF after severe corner joint shear cracks occurred. The

Table 4. Test Results

TestYield load

(kN)

Ultimateload(kN)

MCHRBeamT (kN)

MCHRBeamL (kN)

MBMBeam T(kN×m)

TMBMBeam T(kN×m)

MBMBeam L(kN×m)

TMBMBeam L(kN×m)

Beam Trotation

at FF (rad)

Beam Lrotation

at FF (rad)

F1 20.1 23.7 18.3 18.6 15.2 16.6 15.3 16.6 0.199 0.194F2 29.1 36.5 27.3 27.9 24.8 25.6 25.0 25.6 0.209 0.201F3 22.5 25.8 19.6 19.8 15.7 16.6 15.9 16.6 0.208 0.199F4 23.2 27.5 20.2 20.7 16.5 16.6 17.1 16.6 0.187 0.180F5 25.2 26.8 20.5 20.3 20.8 23.5 21.6 23.5 0.164 0.173F6 21.5 26.0 19.3 20.9 16.4 16.6 23.6 23.5 0.197 0.155F7 21.0 23.0 19.6 18.4 16.7 16.6 18.7 20.0 0.201 0.159

Note: MCHR 5 maximum compressive horizontal reaction; MBM and TMBM 5 maximum bending moment and theoretical maximum bending moment,respectively; FF 5 final failure stage defined as total loss of the resistance capacity.

Fig. 5. Cracking patterns of F3 at failure


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dominating shear cracks degraded the vertical load resistance andloosened the beam horizontal axial constraints. Moreover, severebuckling of the compressive rebar was observed in the BENF whenthe displacement reached 120.0 mm because of less confinement ofthe concrete. The ultimate capacity of F1 was 23.7 kN (1.27), whichwas only ∼91.9% of the ultimate capacity of F3. The maximumcompressive horizontal reaction forces in the transverse and lon-gitudinal beams of F1 were 18.3 (0.98) and 18.6 kN (1.0), whereasthat in the transverse and longitudinal beams of F3 were 19.6 (1.05)and 19.8 kN (1.06), respectively. This indicated that the dominatingdiagonal shear crack reduced the compressive arch action that de-veloped in the beam and reduced the ultimate capacity. For F4, nodiagonal shear cracks and limited concrete compressive crushingwere observed in the BENFs because of a higher transverse re-inforcement ratio in the plastic hinge region. The specimen even-tually reached an ultimate capacity of 27.5 kN (1.48), and this is∼106.6% of the ultimate capacity of F3. The failuremodes of F1 andF4 can be found in Kai (2012).

Influence of Seismic Design DetailingF2 was seismically designed, and the dimensions and reinforcementdetails are given in Table 2. For F3, the crack width in the bottom ofthe BENC did not change after severe joint cracks had occurred.However, for F2, more cracks were formed at the bottom of theBENC, and these cracks became wider when the corner joint suf-fered more severe damage. Another significant difference betweenthe crack patterns of F2 andF3was that the core joint concrete stayedrelatively intact because of the joint transverse reinforcement ef-fectively confining the joint concrete of F2 after the cover concretespalled at a deflection of 280 mm. The higher longitudinal re-inforcement ratio provided in the beams significantly increased thefirst yield load and the ultimate capacity of the specimen,whereas thehigher transverse reinforcement ratio provided in the beam plastichinge regions delayed the concrete crushing and buckling of thecompressive beam longitudinal reinforcement at the bottom of theBENF. F2 reached the ultimate capacity of 36.5 kN (1.96) and was∼141.5% of the ultimate capacity of F3. Themaximum compressivehorizontal reaction forces in the transverse and longitudinal beamsof F2 were 27.3 (1.47) and 27.9 kN (1.50), respectively. These weremuch higher than that of F3. The failure mode of F2 can be foundfrom Kai (2012).

Influence of Design Span Length and Aspect RatioF5 had a clear span of 2,775 mm, whereas the clear span of F3 was2,175 mm. However, the span aspect ratio for both specimens is 1.0.The dimensions and reinforcement details are given in Table 2. F5 hada much higher initial stiffness compared with F3. However, the jointdiagonal shear crack was observed at a load of 14.3 kN (0.49) in F5,and itwasmuch lower than that of F3. Because the joint shear cracks inF5 developed earlier and faster than those in F3, limitedflexural crackswere observed in the bottom of the BENC. However, the ultimatecapacity of F5 was 26.8 kN (0.92), which was higher than the ultimatecapacity of F3 by 3.9%. However, it should be emphasized that thedesign axial force in the corner columnofF5based onDoD (2009)was29.1 kN.Thus, F5 could not survive if the corner columnwas lost evenif the dynamic amplification factor was 1.0. However, the test resultspresented in this study excluded the resistant contribution of RC slabs,and as concluded in Kai and Li (2012c), the RC slab could increasethe load-resistant capacity by up to 63% for two-way slabs. The fail-ure mode of F5 is presented in Fig. 7.

F6 had unequal span of the beams. The dimensions and re-inforcement details are tabulated in Table 2. For F6, the crackdevelopments in the longitudinal and transverse beams were dis-tinctly different and need to be described separately. The first crack

Fig. 6. Measured horizontal reaction force versus vertical displacement of F3

Fig. 7. Cracking patterns of F5 at failure


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was observed in the transverse and longitudinal beams at loads of 5.9(0.25) and 10.0 kN (0.43), respectively. Moreover, the first flexuralcracks occurred in the transverse and longitudinal BENC at loads of10.0 (0.43) and 20.0 kN (0.86), respectively. Asymmetrical jointshear crackswere observed. First joint shear cracks occurred at a loadof 17.8 kN (0.77) in the joint face along the transverse direction,whereas the shear cracks occurring in the joint face along thelongitudinal direction were at a load of 19.6 kN (0.84). Despite thatthe cracks in the joint along the longitudinal direction occurred laterthan the ones along the transverse direction, the development of thecracks in the longitudinal direction was faster than the ones in thetransverse direction. The ultimate capacity of F6 was 26.0 kN (1.12)and was ∼100.8% of the ultimate capacity of F3. The maximumaverage horizontal compressive reaction forces in the transversebeam and longitudinal beam were 19.3 (0.83) and 20.9 kN (0.90),respectively. With a further increase in the vertical displacement by120 mm, concrete crushing was observed in the transverse BENF,whereas the bottom compression region of the longitudinal beamwas intact. The concrete crushing was first observed in the longi-tudinal beam at a deflection of 200 mm. The failure mode of F6 ispresented in Fig. 8.

Influence of the Longitudinal Beam Depth for the Specimenswith Unequal SpanSimilar to F6, F7 had an unequal span of the beams. As given inTable 2, the depth of the longitudinal and transverse beam of F7 was210 and 180 mm, respectively. However, the depth of the longi-tudinal and transverse beam of F6 was 240 and 180 mm, re-spectively. For F7, the first flexural cracks were observed in thelongitudinal and transverse BENFs at loads of 3.9 (0.17) and 10.0 kN(0.43), respectively. Moreover, the first shear cracks were observedin both faces of the corner joint when the load reached 10.0 kN(0.43). However, the first flexural cracks at the bottom of thetransverse BENC were observed at a load of 16.1 kN (0.69). Afterthis load stage, both beams had similar crack development andfailure modes. The ultimate capacity of F7 was 23.0 kN (0.99), butthe design axial load in the corner column based on DoD (2009) was23.2 kN. Therefore, similar to F5, F7 will totally collapse if thecorner column is suddenly removed by extreme loads. The maxi-mum average horizontal compressive reaction forces in the longi-tudinal beam and transverse beam were 19.6 (0.84) and 18.4 kN(0.79), respectively. Moreover, concrete crushing occurred in bothbeams simultaneously. Furthermore, more flexural cracks were

observed in the longitudinal beam compared with that of F6. Thecomparison of the load-displacement relationship of tested speci-mens is illustrated in Fig. 9. The failure mode of F7 can be foundfrom Kai (2012).

Strain Gauge Results

Fig. 10 gives the strain profile of the beam longitudinal rein-forcement of F3 corresponding to different performance levels(same as the performance level defined in Fig. 6). For F3, initially,the strains of the top longitudinal reinforcement at the BENF wastensile while the bottom longitudinal reinforcement at the BENCwas compression. This was consistent with the crack pattern ob-servation and indicated that Vierendeel action dominated theload redistribution when the specimen is in the elastic response.Moreover, the inflection points (zero strain point) of both the topand bottom longitudinal reinforcement were moving toward thecorner joint after PL3. This indicates that the resistancemechanismof the specimen was changing to a cantilever beam redistributionmechanism after severe failure had occurred in the corner joint.The strain of the bottom longitudinal reinforcement at the BENFyielded at PL4, whereas that strain at the BENC never yieldedduring the test. In general, the strain profile of F2 was similar to F3.For F2, the bottom longitudinal reinforcement at the BENCyielded at PL3. However, it never yielded at that strain in F3 duringthe test.

Fig. 11 illustrates the strain gauge results of the column longi-tudinal reinforcement and the joint shear reinforcement of F2. Itshould be noted that Rebar C2 was a compressive rebar if the two-dimensional (2D) longitudinal framewas considered, whereas it wasa tensile rebar if a 2D transverse frame was considered. Thus, itresulted in the net strain of C2 being limited. On the contrary, RebarC1 and C4 were tensile and compressive in both 2D frames, re-spectively. Thus, the net strain was much larger than the strain whenonly the 2D frame was considered. As shown in the figure, the strainof the joint transverse reinforcement was initially limited. The strainrapidly increased after the first diagonal shear crack occurred in thecorner joint. One consequence of shear is the expansion of the coreconcrete. The joint transverse reinforcement partially restrained theexpansion and appeared to increase the strain. Finally, the strain ofthe joint transverse reinforcement was kept constant with a furtherincrease in the displacement. The maximum strain of the joint

Fig. 8. Cracking patterns of F6 at failureFig. 9.Vertical load and horizontal reaction force versus displacementof the test specimens


J. Struct. Eng. 2013.139:584-594.

transverse reinforcement was 2,380 mɛ. This indicated that the jointtransverse reinforcements had not yielded. For other specimens,there were no transverse reinforcements in the joint caused by thenonseismic design and detail.

Discussion of the Test Results

Tie Strength Method

The design guideline from DoD (2009) is the revised version of theprevious guideline from DoD (2005), incorporating a number ofimprovements. One of the significant modifications in DoD (2009)compared with DoD (2005) is that horizontal tie forces (internal andperipheral) are no longer permitted to be concentrated in the beams,girders, and spandrels (unless the designer can show that thesemembers are capable of carrying the tensile loads while undergoinglarge rotations, i.e., 0.2 rad).As shown inTable 4, thefinal rotation ofthe majority of the beams in the tested specimens was close to 0.2rad. Thus, the beams can be used instead of the floor system to carrythe required peripheral tie strength. The required peripheral tiestrength Fp (kN) is

Fp ¼ 6wF L1Lp ð4Þ

The allowable tie strength, which is defined as the maximum hori-zontal tensile force that can be developedwhenonly the beam top rebaris considered, could provide enough tie force to satisfy the requiredperipheral tie strength in accordance with DoD (2009) (Table 5).However, the measured maximum tie force was significantly less thanthe required peripheral tie strength because of the partial rotationalconstraint in the corner joint, and limited horizontal constraint could beprovided in the corner joint. Thus, using the tie strength method toresist progressive collapse of the RC frames caused by the loss ofa corner column is extremely unsafe. Enhancing the local resistance ofthe corner column may be an effective alternative choice.

Plastic Hinge Properties

Fig. 12 illustrates the bending moment in a beam fixed supportversus vertical displacement of F3. It can be seen from the figure thatthe bending moment in both the fixed supports was initially in-creasing, with an increase in the vertical displacement. When thedisplacement reached 28.9 mm, the bending moment in both fixedsupports was almost constant with increasing vertical displacement.The bending moment measured in the transverse and longitu-dinal fixed supports began to decrease at a displacement of 130.0

Fig. 10. Strain profile of beam longitudinal reinforcement of F3

Fig. 11. Strain gauge results of the column longitudinal reinforcementand joint shear reinforcement of F2

Table 5. Comparison of the Measured Tie Force with the RequirementTie Force Determined Based on DoD (2009)

TestRTTB(kN)

RTLB(kN)

ATTB(kN)

ATLB(kN)

MTTB(kN)

MTLB(kN)

F1 55.7 55.7 72.2 72.2 8.3 8.8F2 55.7 55.7 122.1 122.1 11.1 11.3F3 55.7 55.7 72.2 72.2 7.9 7.5F4 55.7 55.7 72.2 72.2 7.5 7.5F5 69.7 69.7 72.2 72.2 4.3 3.1F6 55.7 69.7 72.2 72.2 6.9 1.1F7 55.7 69.7 72.2 72.2 1.7 1.3

Note: RTTB and RTLB 5 required tie force in the transverse beam andlongitudinal beam, respectively; ATTB and ATLB 5 allowable tie forcein the transverse beam and longitudinal beam, respectively; MTTB andMTLB5measured tie force in the transverse beam and longitudinal beam,respectively.


J. Struct. Eng. 2013.139:584-594.

and 140.0 mm, respectively. This is possible because of concretecrushing occurring in the beam end near the fixed support. Themeasured and theoretical maximum bendingmoment of each beamwas tabulated in Table 4. Comparing the measured maximumbending moment of each beam with the theoretical value obtainedfrom ASCE 41-06 (2006) indicated that the recommended over-strength factors in ASCE 41-06 (2006), which were referred to byDoD (2009), have been slightly overestimated. Moreover, both thenonlinear static procedure (NSP) and nonlinear dynamic procedure(NDP) need to properly define the plastic hinge properties. Thecurrent version of DoD (2009) has adapted the modeling param-eters of plastic hinges for the beam element from ASCE 41-06(2006). Themodeling parameters measured for each beam of testedspecimens were comparedwith the recommended parameters inDoD(2009). As illustrated in Table 6, the measured value of parameter awas close to the value suggested in DoD (2009). However, thesuggested value of parameter b in DoD (2009) was extremely con-servative. The definitions of parameters a and b are shown sche-matically in Fig. 12.

Conclusions

On the basis of the experimental and analytical study results, thefollowing conclusions can be drawn:1. Specimens with seismic detailing saw a 41.5% increase in

ultimate capacity compared with F3. The behavior improvedmainly because of more longitudinal beam reinforcement

installed in the beam, which increased the flexural capacityof the beam section, and a medium amount of transversereinforcement placed in the corner joint region, which alsoallowed plastic hinge development in the beam end adjacent tothe corner joint.

2. As the beam transverse reinforcement ratiowas increased from0.23 (F1) to 0.31% (F3), the strength of the tested specimenwas enhanced by about 8.9%. This is because of the shearfailure that occurred in the plastic hinge region that reducedthe effectiveness of the compressive arch action and resultedin a lower ultimate capacity. However, when the transversereinforcement ratio was increased from 0.31 (F3) to 0.72%(F4), the strength of the tested specimenwas only enhanced by6.5%. This indicates that the effect of the transverse reinforce-ment ratio in the plastic hinge region for ultimate capacity waslimited as long as the shear failure was not severe in the plastichinge region.

3. F5 reached an ultimate capacity of 26.8 kN,whereas the designaxial force of the corner column was 29.1 kN. Thus, F5 willtotally collapse even though the dynamic increase factor was1.0. This confirmed that the specimen with a longer designspan was more vulnerable than the specimen with a shorterdesign span when they were under similar distributed loads.

4. The plastic hinge properties of RC elements suggested in DoD(2009) are an adaptation of the modeling parameters presentedin ASCE 41-06 (2006). The accuracy of these parameters wasevaluated by comparing them with the parameters obtainedfrom current tests. In general, the value of parameter a re-commended in DoD (2009) is reasonable if the beam section iscontrolled by flexural failure, whereas it is too conservative ifthe beam section is controlled by flexural and shear failure.Moreover, for parameter b, the value suggested in DoD (2009)is extremely conservative. More studies need to be conductedfor assessing these modeling parameters.

5. Although DoD (2009) has implemented significant modifi-cations for tie strength design, no difference was proposedbetween the peripheral tie near to the corner column and the tienear to the exterior column in DoD (2009). After analysis, itwas found that the allowable tie strength determined based onthe reinforcement details was larger than the required tiestrength attained based on DoD (2009); however, the mea-sured horizontal tensile force (tie force) was significantly lessthan the allowable tie strength because of insufficient hori-zontal constraint that could be provided by the corner joint.Thus, it is suggested that the catenary effect (tie strengthmethod) should not be considered in the practical designfor buildings to resist progressive collapse caused by losingone of the ground corner columns.

6. Test results indicated that there are two ways to improve theperformance of RC frames against progressive collapse causedby losing a corner column. The first way to improve theperformance is by increasing the flexural capacity of the beamsection by amplifying the beam longitudinal reinforcementratio. However, it should be pointed out that the increase ofthe beam flexural capacity is also controlled by the flexuralcapacity of the column (strong column-weak beam designphilosophy). The secondway to improve the performance is byupgrading the shear strength of the corner joint by installingmore joint transverse reinforcement to confine the corner joint.It should be emphasized that the failure caused by rebaranchorage and splice is beyond the scope of this study. Forexisting buildings, the use of composite materials to improvethe progressive collapse performance must be investigated inthe future.

Fig. 12. Bending moment at fixed support of F3 versus vertical dis-placement

Table 6. Comparison of the Measured Plastic Hinge Parameters with theModeling Parameters Suggested in DoD (2009)

Test

a inBeamT (rad)

a inBeamL (rad)

a in DoD(2009) (rad)

b inBeamT (rad)

b inBeamL (rad)

b in DoD(2009) (rad)

F1 0.031 0.035 0.05 0.181 0.189 0.06F2 0.058 0.063 0.063 0.198 0.198 0.10F3 0.046 0.046 0.05 0.146 0.177 0.06F4 0.052 0.052 0.05 0.143 0.161 0.06F5 0.042 0.042 0.05 0.134 0.134 0.06F6 0.040 0.038 0.05 0.137 0.140 0.06F7 0.043 0.037 0.05 0.143 0.136 0.06

Note: Beam T 5 transverse beam; Beam L 5 longitudinal beam.


J. Struct. Eng. 2013.139:584-594.

Notation

The following symbols are used in this paper:Asv 5 area of the transverse rebar;a 5 rotation difference of the plastic hinge

between the ultimatemoment capacity andthe yield capacity;

b 5 rotation difference of the plastic hingebetween the failure point and the yieldcapacity;

bv 5 width of the beam;D1 5 vertical displacement;H1 5 horizontal movement of the joint center

just above the damaged column;Lp 5 equal to 0.3 m for one-third scale model;L1 5 span of the frame in the direction under

consideration;SDS,SD1 5 design spectral response acceleration

parameters for a short period and at a 1-speriod, respectively;

s 5 spacing of the beam transversereinforcement;

TV 5 total vertical distance between the centerof steel box to the center of corner joint;

V 5 average vertical distance between twosteel pins in each direction;

wF 5 floor load (12.9 kN/m2 in the current

study);d 5 difference between the diameter of the

hole and the steel pin;rt 5 transverse reinforcement ratio; andf 5 designed rotation of the steel column.

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J. Struct. Eng. 2013.139:584-594.
http://dx.doi.org/10.1016/j.engstruct.2008.11.020http://dx.doi.org/10.1016/j.engstruct.2008.11.020http://dx.doi.org/10.1016/j.engstruct.2008.01.019http://dx.doi.org/10.1061/(ASCE)0733-9445)134:3(478)

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