load-carrying mechanism to resist progressive collapse of rc buildings

Load-Carrying Mechanism to Resist ProgressiveCollapse of RC Buildings

Kai Qian, M.ASCE1; Bing Li2; and Jia-Xing Ma3

Abstract: The slew of high profile engineering calamities in the past decade has demonstrated the disastrous consequence of progressivecollapse. However, the low probability of such events actually occurring means it is uneconomical to spend extreme resources to design everybuilding against progressive collapse. A more feasible proposition would be to consider alternative fall-back parameters such as secondaryload carrying mechanisms that can help to reduce the severity of the collapse, should it actually occur. However, to date, very limited studieshave been carried out to quantify the effectiveness of such secondary load carrying mechanisms in resisting progressive collapse, especiallymembrane actions developed in RC slabs. Therefore, a series of 6 one-quarter scaled specimens were tested and the failure modes, load-displacement relationships, load redistribution responses, and strain gauge results are presented herein. The contribution of each mechanismon the load-carrying capacity is discussed. A series of analyses are also carried out to better quantify the findings made in the study. DOI: 10.1061/(ASCE)ST.1943-541X.0001046. © 2014 American Society of Civil Engineers.

Author keywords: Progressive collapse; Reinforced concrete; Slab; Three-dimensional; Compressive arch; Catenary; Compressivemembrane; Tensile membrane; Structural safety and reliability.

Introduction

Progressive collapse is defined by the ASCE/SEI 7 (ASCE/SEI2010) as “the spread of an initial local failure from element toelement, which eventually results in the collapse of an entire struc-ture or a disproportionately large part of it.” Generally, buildingsare not designed for accidental loading conditions that may leadto progressive collapse. The collapse of Murrah Federal Buildingin 1995 and World Trade Centers in 2001 indicated that the con-sequence of progressive collapse is severe in terms of both eco-nomic and life losses. However, strength has to be raised tovery high levels to effectively mitigate progressive collapse inconventional design—something that is uneconomical for suchlow-probability events. As such, consideration of secondary loadcarrying mechanisms can be an effective alternative in the designagainst progressive collapse. These secondary load carrying mech-anisms include compressive arch action (CAA) and tensile catenaryaction (TCA) developed in beams as well as compressive mem-brane action (CMA) and tensile membrane action (TMA) devel-oped in slabs. Several researchers (Yi et al. 2008; Sasani andKropelnicki 2008; Su et al. 2010; Tian and Su 2011; Qian andLi 2013b; Yang and Tan 2013) have studied CAA and TCA inresisting progressive collapse. However, to date, limited studieshave been carried out to study the CMA and TMA developed in

RC slabs to mitigate progressive collapse and their individualeffects are unclear and have yet to been quantified. CMA andTMA have long been admitted in structural engineering field(Park 1965; Bailey 2001). However, very limited studies have beenconducted to verify the contribution of CMA and TMA developedin the RC slabs to prevent progressive collapse of RC buildings.Hawkins and Mitchell (1979) had discussed the factors influencingthe initiation and propagation of progressive collapse in flat platestructures. Mitchell and Cook (1984) discussed TMA developed inRC slabs to resist progressive collapse in detail. Qian and Li(2013a) investigated the reliability of CMA and TMA developedin flat slabs in resisting progressive collapse while Qian and Li(2013c) discussed the strengthening schemes to improve the behav-ior of flat slabs in resisting collapse by externally bonded fiber-reinforced polymers. Qian and Li (2012) experimentally investi-gated the performance of RC beam-slab structures under the lossof a corner column scenario. It was found that limited TCA devel-oped in beams; however, TMA developed in slabs could reducethe likelihood of progressive collapse significantly. In this study,6 one-quarter scaled RC specimens were tested. The experimentalresults including the load-displacement curve, failure modes, andlocal strain behavior are presented. The effects of CAA, TCA,CMA, and TMA on the vulnerability of RC structures in resistingprogressive collapse are then discussed. Finally, a series of analyti-cal analyses, which are modified based on previous analytical mod-els, are utilized to predict the contribution of each mechanismanalytically.

Experimental Program

Experimental Setup

To experimentally investigate the behavior of beams and slab bridg-ing over the removed interior column, there is need to consider theboundary conditions on the edges of beams and slab. To simulatethe effects of surrounding slab and beams, the most ideal specimenis 4 × 4 panel, as shown in Fig. 1. However, only a 2 × 2 panel

1Associate Professor, Hunan Univ., Changsha, China; formerly, Re-search Fellow, Natural Hazards Research Center, Nanyang TechnologicalUniv., 50 Nanyang Ave., Singapore 639798. E-mail: [email protected]

2Director, Natural Hazards Research Center, Nanyang TechnologicalUniv., 50 Nanyang Ave., Singapore 639798 (corresponding author).E-mail: [email protected]

3Ph.D. Candidate, School of Civil and Environmental Engineering,Nanyang Technological Univ., 50 Nanyang Ave., Singapore 639798.E-mail: [email protected]

Note. This manuscript was submitted on May 7, 2013; approved onFebruary 6, 2014; published online on July 2, 2014. Discussion period openuntil December 2, 2014; separate discussions must be submitted for indi-vidual papers. This paper is part of the Journal of Structural Engineering,© ASCE, ISSN 0733-9445/04014107(14)/$25.00.

© ASCE 04014107-1 J. Struct. Eng.

J. Struct. Eng.

63

specimen is cast and tested because of cost and space limitation.Furthermore, it is a challenge to properly simulate horizontal androtational constraints applied on the beam and slab edges ascolumns A3 and E3 could provide horizontal constraints to thebeams (B3–D3). Moreover, the torsional stiffness of beamD2–D4 could also apply additional constraints to joint D3. For sim-plicity, the edge columns were designed to fix on the strong steellegs to equivalently simulate the fixed boundary conditions (asshown in Fig. 2). Horizontal and rotational constraints on the edges

of the slab held by fixed columns were provided mainly by thetorsional stiffness of the edge beams. Moreover, specified weights[380 kilograms (kg) for each] were hung at the extended part of theslab to apply additional rotational constraints on the slab, as shownin Fig. 2. A concentrated load was then applied on the top of theinterior column by a hydraulic jack with about a 600-millimeter(mm) stroke. It should be noted that displacement controlled ap-proach was utilized in this push-down test. Dynamic responseof the specimens could be predicted by energy equilibrium method,which will be discussed in behind. To create a symmetric failuremode for the test specimens, a steel assembly (Item 3 in Fig. 2)was installed below the hydraulic jack to ensure concentric loading.It is understandable that the failure of beams connected with theinterior column normally will not occur simultaneously. If the steelassembly (Item 3 in Fig. 2) is not installed and rebar fracture occursin one of the beam-interior column interfaces, the majority of therotation will then be concentrated on that interface with further in-crease of the displacement. This was different from the real situa-tion for RC frames under the loss of an interior column scenario.In multistory frames, the beams in the upper floors would providehorizontal constraints on the lower column and make sure theinterior column could only move vertically after removal of aground interior column.

Specimen Design

Two prototype structures with different span aspect ratio are seis-mically designed in accordance with ACI 318-08 (ACI 2008). Thedistributed dead load on the prototype structure because of a gravityload of 220-mm thick slab was 5.2 kilopascals (kPa). The super-imposed dead load due to ceiling, mechanical ductwork, electricalitems, and plumbing is assumed to be 1.0 kPa. The live load isassumed to be 3.0 kPa. As Singapore is in a low-seismicity zone,the test specimens are assumed to be located on a site class of D,stiff soil profile. The design spectral response acceleration param-eters at short periods, SDS, and at 1 s period, SD1, were 0.45 and

Fig. 1. Plan view of prototype building correspond to specimen S1

1: Load cell 2: Hydraulic jack 3: Steel assembly

4: Specimen 5:Tension/compression load cell

6: Steel plates (weights)

1

2

3

4

6

5

Load cell

Pin

Jack

Fig. 2. An overview of an S-series specimen in position ready for testing


J. Struct. Eng.

64

0.34 gravitational acceleration (g), respectively. For cost andlaboratory space consideration, one-quarter scaled beam-columnsubstructures (S1 and S2) were tested in this study. In order toquantify the effects of slab and transverse beams on the load carry-ing capacity of RC buildings to resist progressive collapse, fouradditional specimens (T1, T2, P1, and P2) were also tested. Thegeometrical properties and reinforcement details of test specimensare given in Table 1.

The typical dimensions and reinforcement details of S1 areshown in Fig. 3. As shown in the figure, S1 is a 2 × 2 bay singlestory beam-slab substructure. Nine columns, twelve beams, and a55-mm thick slab were cast monolithically. The dimensions of thecolumns were 200 × 200 mm, which was enlarged for preventingdamage in the columns. The center-to-center spans of the transverseand longitudinal beams were 1,500 and 2,100 mm, respectively.Moreover, the cross-sectional dimensions of transverse and lon-gitudinal beams were 140 × 80 mm and 180 × 100 mm, respec-tively. As the test specimens were relatively small-scaled, theeffects the cut-off and lap splice of the beam longitudinal reinforce-ments were not simulated, and continuous 4T10 were doublyreinforced in longitudinal and transverse beams. T10 representsdeformed rebar with diameter of 10 mm. Two layers of slabreinforcement were installed in the slab as in practical design.For the bottom layer, continuous R6 with 250 mm spacing wereplaced. R6 represents plain rebar with diameter of 6 mm. However,for the top layer, although the spacing of top slab reinforcementwas also 250 mm, it was cutoff at the center of each panel followingthe design detailing in ACI 318-08 (ACI 2008). The clear cover ofcolumn, beam, and slab were 10, 7, and 7 mm, respectively. For S2,in general, the dimensions and reinforcement details of columns,beams, and slab were similar to that of S1, as shown in Table 1.The only difference between S2 and S1 was that equal spanwas designed in longitudinal and transverse directions. Thus, bothlongitudinal and transverse beams of S2 have cross sectionsof 140 × 80 mm.

For T1 and T2, they had identical longitudinal and transversebeams as S1 and S2, respectively. The only difference betweenT-series and S-series specimens was that no RC slab was incorpo-rated. As vertical displacement was applied on the interior columnvia displacement controlled approach, the effects of the edgebeams, which were not connected with the interior column, werelimited. Thus, only four interior beams connected with the in-terior column were cast in T-series specimens. For P1 and P2,two-dimensional (2D) beam-column substructures were fabricated.P1 and P2 could be treated as longitudinal and transverse beamsof T1, respectively.

Material Properties

The target compressive strength of concrete at age 28 dayswas 25 megapascals (Mpa). The average compressive strength

of concrete f 0c was found to be 19.9, 20.8, 21.5, 22.7, 21.4, and

23.3 MPa for P1, P2, T1, T2, S1, and S2, respectively. The com-pressive strength of each specimen is obtained by six cylinder tests.In order to consider the fact that under higher loading rates concretewould exhibit an increased strength, the dynamic increase factors(DIFs) proposed by Malvar and Crawford (1998), can be employedto predict the dynamic compressive strength of concrete at differentstrain rates. Grade 250 (R6) and Grade 460 (T10, T13, and T16)steel bars were used as transverse and longitudinal reinforcements,respectively. Table 2 gives the measured tensile properties of thebars used in the tests.

Instrumentation

Extensive measurement devices were installed both internally andexternally to monitor the test specimens. A load cell (Item 1 inFig. 2) was used to measure the vertical load applied on the interiorcolumn. The tension/compression load cell (Item 5 in Fig. 2) wasinstalled at three of the steel legs to monitor the load redistributionbehavior of the specimen. A series of linear variable deformationtransformers (LVDTs) and line transducers were placed at variouslocations to measure the deformation at interior joint and deforma-tion shape along the slab and beams, as shown in Fig. 4. Addition-ally, the horizontal movements of the adjacent columns and liftmovement of slab edge were monitored via a series of LVDTs toascertain restraint stiffness and quantify the extent of horizontalconstraints. To obtain the variations of reinforcement strain underdifferent load carrying mechanism, strain gauges were attachedonto the surface of reinforcement at selected points prior to casting.For T- and P-series of specimens, similar instrumentation deviceswere installed.

Experimental Results

Global Behavior and Failure Modes

Specimen P12D beam-column assemblage has span of 4,200 mm due to assum-ing a mid-column had lost. The load-displacement curve of P1 isshown in Fig. 5(a). The first cracks were formed in the beam endnear to adjacent column (BENA) and beam end near to interior col-umn (BENI) at the loads of 8 and 11 kilonewton (kN), respectively.The measured yield load and first peak load were 24 and 32 kN,respectively. Thus, CAA increased the load carrying capacityby 33.3%. It was assumed the difference between the first peakload and yield load are fully attributed into CAA because of theeffects of strain hardening, and stirrup confinements are limitedat this displacement stage. Moreover, it was found that concretecrushing was first observed at BENI at a displacement of 58 mm.However, limited concrete crushing was observed at BENA until

Table 1. Specimen Properties (Unit: mm)

Test ID

Elements Longitudinal rebar Transverse reinforcement ratio Slab reinforcement ratio

Beam-T Beam-L Column-I Beam-T Beam-L Joint (%) Beam-T (%) Beam-L (%) Top (%) Bottom (%)

P1 N/A Type b* 4T13 N/A 4T10 0.8 N/A 0.5 N/A N/AP2 Type a* N/A 4T13 4T10 N/A 0.8 0.6 N/A N/A N/AT1 Type a* Type b* 4T13 4T10 4T10 0.8 0.6 0.5 N/A N/AT2 Type a* Type a* 4T13 4T10 4T10 0.8 0.6 0.6 N/A N/AS1 Type a* Type b* 4T13 4T10 4T10 0.8 0.6 0.5 0.25 0.25S2 Type a* Type a* 4T13 4T10 4T10 0.8 0.6 0.6 0.25 0.25

Note: Beam-T = transverse beam; Beam-L = longitudinal beam; Column-I = interior column; T13 = deformed bar of 13 mm diameter; T10 = deformed bar of10 mm diameter; Type a* = clear span = 1,300 mm, cross section = 140 × 80 mm2; Type b* = clear span = 1,900 mm, cross section = 180 × 100 mm2.


J. Struct. Eng.

65

the displacement reached 182 mm. Furthermore, it should be notedthat the first rebar fracture was observed at the BENI at a displace-ment of 191 mm. Fig. 6 shows the horizontal movement at the ad-jacent column versus vertical movement of interior column. It can

R6@ 250

Top

Reb

ar

Fig. 3. Dimensions and reinforcement details of S1 (units: mm)

Table 2. Properties of Reinforcing Steel

TypesYield strengthfy (MPa)

Yield strainεy (10−6)

Ultimate strengthfu (MPa)

Ratio ofelongation (%)

R6 355 1,910 465 17.5T10 437 2,273 568 13.1T13 535 2,605 611 11.6T16 529 2,663 608 14.3

Notes: R6 = plain round bar of 6 mm diameter; T10 = deformed bar of10 mm diameter; T13 = deformed bar of 13 mm diameter; T16 =deformed bar of 16 mm diameter.

Fig. 4. Arrangement of instrumentation in S1


J. Struct. Eng.

66

be seen that outward movement was observed in the adjacentcolumn, initially. When the vertical displacement reached 152 mm,inward movement was observed, indicating that CAA had trans-ferred into TCA in beams. The inward movement increased signifi-cantly with further increase of the vertical displacement. The testwas stopped when the displacement reached 370 mm (19.5% of thebeam clear span) because of significant increase in the horizontalmovement at adjacent column (as shown in Fig. 6) with furtherincreasing vertical displacement. The failure mode of this specimenis shown in Fig. 7.

Specimen P22D beam-column assemblage has a span of 3,000 mm. Only a briefdescription will be made as P2 had similar performance to P1. Theyield load and first peak load of P2 were measured as 26 and 36 kN.Thus, CAA increased the yield load by 38.5%. Similar to P1, ini-tially, outward movement was observed in the adjacent column.When the vertical displacement reached 134 mm, inward move-ment was observed.

Specimen T1As shown in Table 1, this specimen has transverse and longitudinalbeam similar to those of P1 and P2, respectively. The measured

load-displacement curve of T1 is shown in Fig. 5(a). The first flexu-ral crack was observed at the transverse BENA at a load of 15 kN,and the first flexural crack occurred in the transverse BENI at a loadof 20 kN. Moreover, at this loading stage, flexural cracks were alsoformed in the longitudinal BENA. When the load reached 48 kN,yielding were observed at beam longitudinal reinforcements basedon strain gauge results. The first peak load of T1 (67 kN) was re-corded at a displacement of 32 mm. Thus, CAA increased the loadresistant capacity by 39.6%. Upon further increment of the dis-placement, more cracks were formed along the beams. However,the crack width in longitudinal beams was much narrower than thatin transverse beams. When the displacement reached 80 mm,severe shear crack formed in one of the transverse BENI. Then, amajority of the damage was concentrated at the shear crack withfurther increment of the vertical displacement. After the displace-ment reached 131 mm, the load resistance began to reascend. Therecords of the horizontal movement at one of the adjacent columnsindicate that the initial outward movement changed into inwardmovement after this loading stage, as shown in Fig. 6. The testwas stopped after the displacement reached 250 mm because ofsevere shear cracks concentrated in one of the transverse BENI.The failure mode of T1 is shown in Fig. 8.

Specimen T2This specimen has transverse and longitudinal beam similar to P2.The damage developed in the longitudinal and transverse beamswere almost simultaneously as the beam aspect ratio (the ratioof span length of longitudinal beam to transverse beam) is 1.0.Thus, only the behavior of the transverse beam is presented. Thefirst cracks were observed in the BENI and BENA at the loads of 18and 22 kN, respectively. In addition, the yield load and first peakload were recorded as 48 and 64 kN. Moreover, severe concretecrushing was observed in the BENI and BENAwhen the displace-ment reached 80 mm. When the displacement reached 120 mm,

0

20

40

60

80

100

0 100 200 300 400Displacement (mm)

Ver

tica

l Loa

d (k

N)

P1P2T1T2

P1-PTCA

T1-PTCA

0

50

100

150

200

250


Ver

tica

l Loa

d (

kN)

T1T2S1S2

S1(PTCA+PTMA)

T1-PTCA

(a) (b)

Note: TCA=Tensile catenary actionTMA=Tensile membrane action

Note: TCA=Tensile catenary action

Fig. 5. Load-displacement curves of the test specimens: (a) 3D effects; (b) slab effects

-1

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400Vertical-displacement (mm)

Hor

izon

tal-

disp

lace

men

t (m

m)

P1P2T1-HT2-HS1-HS2-H

Fig. 6. Horizontal movement of adjacent column versus vertical dis-placement of interior column for the tested specimens

Rebar fracture

Concrete crushing

Fig. 7. Damage patterns of P1 at the end of test

Transverse beamShear failure

Longitudinal beam

Fig. 8. Damage patterns of T1 at the end of test


J. Struct. Eng.

.

67

rebar fracture was observed at one of the transverse BENIs. Afterthis displacement stage, catenary action began to develop and moresevere concrete crushing was observed in the BENI and BENA.The test was stopped when the displacement reached 289 mm,which was about 20% of the span of the beam.

Specimen S1The span aspect ratio of this specimen is 1.4. It has identical beamto T1, but a 55 mm thickness RC slab was incorporated. The load-displacement relationship of this specimen is shown in Fig. 5(b).

The first crack was observed in the top surface of the slab at a loadof 44 kN. When increasing the vertical load to 53 kN, cracks at thetop surface of the slab developed and connected as an ellipse. Withfurther increase of the vertical load, diagonal cracks were formed atthe bottom surface of the slab. Further increasing the load to 80 kN,yielding was observed in the beam longitudinal reinforcements.After reaching the first peak load of 115 kN (corresponding to dis-placement of 47 mm), severe concrete crushing occurred at thebeams and slab. This indicated that CMA and CAA began to di-minish. When the displacement reached 75 mm, the load resistancebegan to reascend. This indicated that CMA had transferred intoTMA in slab. As shown in the results from T- and P-series tests,catenary action normally began to develop after the displacementreached about 10% of the beam span. Thus, the reascending of theload resistance at this loading stage could mainly be attributed intothe development of TMA in the slab. Upon further increase of thevertical displacement, a majority of the deformation was concen-trated in the central region (elliptical region) while limited defor-mation was observed in the outer region (compressive ring), asillustrated in Fig. 9. However, the force could not be redistributedinto edge columns through slab after the displacement beyond215 mm, because punching failure occurred at the interior slab-column connection. This was because of severe concrete crushingwas concentrated into the top slab near interior column, whichdeteriorated the integrity of the slab and beams. Meanwhile, thepunching failure accelerates the detachment of the slab and beamswith further increase of the displacement (as shown in Fig. 10).When the displacement reached 210 mm, bottom reinforcementat both longitudinal BENI fractured. The test was stopped at a dis-placement of 305 mm as reinforcement fracture was observed inall beams and severe punching failure occurred in interior slab-column connection. The failure mode of S1 is illustrated in Fig. 10.As shown in Fig. 10(a, top view), a series of concentric ellipticalcracks that was called tensile net, were observed in the center of theslab. The outer region close to the supported edge experienced little

Distance to corner column in transverse direction (mm)

Dis

tanc

e to

cor

ner

colu

mn

in lo

ngit

udin

al d

irec

tion

(m

m)

0 300 600 900 1200 15000

300

600

900

1200

1500

1800

2100

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

Verticaldisplacement

(mm)

Fig. 9. The contour of deformation shape of S1 at a displacement of180 mm (one-quarter of the slab)

(a)

(b)

Tensile net

Compressive ring

Rebar fracture

Fig. 10. Damage patterns of S1 at the end of test: (a) top view; (b) bottom view


J. Struct. Eng.

68

deflection, which was called compressive ring. In order to quantifythe contributions of CMA and TMA developed in the slab inresisting progressive collapse, an analytical model is proposedand described in behind. Moreover, concrete crushing at the slabnear the interior column and reinforcement fracture at the BENIare observed in Fig. 10(b).

Specimen S2The span aspect ratio of this specimen is 1.0. It had identical beamsto T1, but a 55-mm thickness RC slab was included. In general, theperformance of S2 was similar to S1. Moreover, as the key resultsof the test specimens have been tabulated in Table 3, only the maindifferences between S2 and S1 are emphasized herein. Unlike S1(elliptical crack), circular crack was formed in the slab top surfaceat a load of 56 kN. The yielding was first observed in the beamlongitudinal reinforcements at a load of 90 kN, which was slightlyhigher than that of S1. When the displacement reached 42 mm, thefirst peak load of S2 was reached and equaled to 123 kN. By com-paring with its yield load, it was increased by 36.7%. Similar to S1,punching failure also occurred in the interior slab-column connec-tion when the displacement reached 165 mm. However, when the

displacement reached 170 mm, reinforcement fracture was ob-served in one of transverse beams. Further increasing the verticaldisplacement to 200 mm, reinforcement fracture was also observedin another transverse beam. The test was stopped at the displace-ment of 231 mm. The failure mode of S2 is shown in Fig. 11.

Load Redistribution

When a building has a column suddenly removed, the initial force,which was sustained by the lost column, will be redistributed intoadjacent columns. As mentioned in the section of “Instrumenta-tion” earlier, three tension/compression load cells were installedin three of the steel legs to monitor the variation of the load redis-tribution during tests. Fig. 12 illustrates the variation of the loadredistribution with increasing vertical displacement. For S1, at thestage of yield load, 23.5, 18.8, and 3.8% of the load were distrib-uted into transverse adjacent column, longitudinal adjacent column,and corner column, respectively. For T1, at this loading, 27.6 and22.0% of the load were distributed into transverse adjacent columnand longitudinal adjacent column, respectively. Thus, RC slab notonly enhanced the strength of the specimens, but also provided

Table 3. Test Results

TestF�cr

(kN)F�y

(kN)

Initialstiffness(kN=mm)

F�u

(kN)VDLR�

(mm)F�t

(kN)VDFT�

(mm) Fu=Fy Ft=Fu Failure modes

P1 8 24 1.5 32 182 47 370 1.33 1.47 Beam rebar fractureP2 11 26 1.8 36 134 59 299 1.39 1.64 Beam rebar fractureT1 15 48 3.4 67 131 79 250 1.40 1.18 Shear failure at one of the transverse beams near the interior columnT2 18 48 3.9 64 120 90 289 1.33 1.41 Beam rebar fractureS1 44 80 4.8 115 75 169 305 1.44 1.47 Punching failure at interior slab-column connection and beam rebar fractureS2 56 90 6.2 123 58 165 231 1.37 1.34 Punching failure at interior slab-column connection and beam rebar fracture

Note: F�cr, F�

y, F�u, and F�

t = the first cracking load, yield load, the first peak load, and ultimate load from TCA or TMA, respectively; VDLR� and VDFT� = thevertical displacement at load reascending and vertical displacement at final test, respectively.

(a)

(b)

Punching shear failure

Compressive ring

Tensile net

Detachment between

slab and beam

Rebar fracture

Fig. 11. Damage patterns of S2 at the end of test: (a) top view; (b) bottom view


J. Struct. Eng.

69

more load paths for load redistribution. Although the load redistrib-ution of S1 was varying with an increase of the vertical displace-ment, the percentage of the corner column ranged about 3.5–5.8%.For S2 and T2, similar percentages of the load were distributed intotransverse and longitudinal adjacent columns, as similar beamswere designed in transverse and longitudinal directions.

Local Behavior: Reinforcing Bar Strains

The strains in the steel reinforcement were measured at beams andslabs. As some of the strain gauges did not work in T1, the straingauge results of T2 and S2 are presented for comparison. Fig. 13depicts the variation of the steel strain along the transverse beamsof T2, in accordance with different displacement stages. As can beseen, tensile strain were recorded at the top reinforcement nearadjacent column and bottom reinforcement near interior column,which agrees well with the crack pattern. After the displacementreached 126 mm (TCA began to develop), the compressive strainat the top reinforcement near interior column and bottom reinforce-ment near adjacent column began to decrease. Fig. 14 illustrates the

variation of steel strain along the beams of S2. For S2, in general,the strain profiles of the beams were similar to that of T2. However,the compressive strain measured in the top beam reinforcementnear interior column was much less than that of T2, which wasmainly because of slab invoking a flange in compressive region.Moreover, after the displacement went beyond 120 mm, the wholetop beam reinforcement experienced tensile strain from catenaryaction.

As mentioned in the section of “Instrumentation,” strain gaugeswere also placed in the slab reinforcement for S-series specimens.Fig. 15 demonstrates the relationship of strain in the slab reinforce-ment versus vertical displacement of S2. The locations of straingauges in slab reinforcement are shown in Fig. 16. It should benoted that ST and SB stand for slab strain gauges in top layer andbottom layer of slab reinforcement, respectively. As shown in thefigure, initially, ST2, SB1, and SB2 were compressive becauseof bending moment reverse and the slab flange in compressive re-gion of the beam section near the interior column. However, thecompressive strain of three strain gauges began to decrease afterthe displacement reached 58 mm; this might be because of the

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

0 50 100 150 200 250 300 350

Vertical displacement (mm)

Perc

enta

ge o

f lo

ad r

edis

trib

utio

n

FIRST PEAK LOAD

YIELD LOADCORNER COLUMN

TRANSVERSE COLUMN

LONGITUDINALCOLUMN

0.0%

10.0%

20.0%

30.0%

40.0%

0 50 100 150 200 250

Vertical displacement (mm)

Perc

enta

ge o

f lo

ad r

edis

trib

utio

n

FIRST PEAK LOAD

YIELD LOAD

TRANSVERSECOLUMN

LONGITUDINALCOLUMN

(a) (b)

Fig. 12. Varying of the load redistribution with increasing the vertical displacement: (a) S1; (b) T1

-2000

0

(a) (b)

2000

4000

6000

8000

0 200 400 600 800 1000 1200 1400Distance from the adjacent column interface (mm)

Stra

in (

με)

ε

-2000

0

2000

4000

6000

8000

10000

0 200 400 600 800 1000 1200 1400Distance from adjacent column interface (mm)

At 16 mmAt 32 mmAt 126 mmAt 180 mm

εy

Bottom reinforcement

Str

ain

(με)

At 16 mmAt 32 mmAt 126 mmAt 180 mmAt 240 mm

Top reinforcement

y

At 240 mm

Fig. 13. Strain profile of beam longitudinal reinforcement of T2

-2000

0

(a) (b)

2000

4000

6000

8000

Distance from the adjacent column interface (mm)

Str

ain

(με)


ε

Top reinforcement-2000

0

2000

4000

6000

8000

10000

12000

0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400Distance from adjacent column interface (mm)

Stra

in (

με)


ε

Bottom reinforcement

yy

Fig. 14. Strain profile of longitudinal reinforcement of the transverse beam of S2


J. Struct. Eng.

70

development of TMA in the slab. Moreover, at this load stage, sig-nificant tensile strain was recorded at SB3 and SB7, although theywere installed at the bottom layer of the slab reinforcement. How-ever, limited strain was measured in SB8 and SB10 during the test.This indicated that limited damage occurred at the outer regionof the slab, which worked as a compressive ring to balance thetensile force developed in the center of the slab because of TMA.It should be noted that the increase of the steel strains in slabreinforcement become milder after displacement reached 165 mmbecause of punching failure occurred at the interior slab-columnconnection. For the rest of the specimens, similar results were re-corded and were, therefore, not presented.

Discussion of the Test Results

Discussion of the Capacity of Each Load CarryingMechanism

CAA and TCAAs shown in Fig. 5(a), CAA increased the yield load of P1, P2, T1,and T2 by 33.3, 38.5, 39.6, and 33.3%, respectively. However,TCA could increase the yield load of P1, P2, T1, and T2 by95.8, 126.9, 64.6, and 87.5%, respectively. Thus, CAA and TCAare able to enhance the ability of RC bare frames significantly.Moreover, the maximum load at large displacement stage had ex-ceeded the first peak load of the frame specimens. This further

proved that there is a second line of defense to prevent collapseof RC frames at large displacement stage.

CMA and TMAAs shown in Fig. 5(b), CMA together with CAA increased the yieldload of S1 and S2 by 43.8 and 36.7%, respectively. Meanwhile,TMA together with TCA increased the yield load of S1 and S2by 111.3 and 83.3%. Thus, the additional load provided by CMAand TMA further reduced the vulnerability of RC buildings.

Discussion of Three-Dimensional and Slab Effects

Quasi-Static ResistanceThe three-dimensional (3D) effects excluding the slab contribu-tion were quantified by comparing the performance of T-seriesspecimens with the corresponding P-series specimens. As shown inFig. 5(a) and Table 3, T1 increased the initial stiffness, yield load,first peak load, and ultimate load of P1 by 126.7, 100.0, 109.4, and68.1%, respectively. For T2 and P2, the 3D effects increased theinitial stiffness, yield load, first peak load, and ultimate load ofP2 by 116.7, 84.6, 77.7, and 52.5%. Thus, ignoring the resistancefrom transverse beams to resist progressive collapse of RC frame isoverconservative, and a 3D model should be generated in futureanalytical and numerical analyses. The slab effects were quantifiedby comparing the performance of S-series specimens with thecorresponding T-series specimens. As illustrated in Fig. 5(b), S1increased the initial stiffness, yield load, first peak load, and ulti-mate load of T1 by 41.1, 66.7, 71.6, and 114.0%, respectively. ForS2 and T2, RC slab increased the initial stiffness, yield load, firstpeak load, and ultimate load of T2 by 59.0, 87.5, 92.2, and 83.3%.Thus, both specimens indicated that RC slab could further en-hance the static performance of RC buildings to resist progressivecollapse significantly. In order to decompose the contribution ofTMA and TCA developed in RC beam-slab structures at large dis-placement stage, the load resistance of S-series specimens from RCbeams and RC slab are decomposed. As shown in Fig. 17, 54.0% ofthe load resistance was provided by the beams when S1 reachedits first peak load. When the displacement ranged from 126 to215 mm, about 42.0% of the load was resisted by beams while58.0% of the load was resisted by slab. Beyond 215 mm, the beam’scontribution increased significantly because of punching failurethat occurred in the interior slab-column connection. Similarbehavior was observed in S2.

-1000

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250Vertical displacement (mm)

Stra

in (

με)

ST2ST3SB1SB2SB3SB5SB6SB7SB8SB10

εy

Fig. 15. Steel strain of slab versus vertical displacement of S2

(a) (b)

Fig. 16. The location of strain gauges in slab reinforcement: (a) bottom layer; (b) top layer


J. Struct. Eng.

71

Dynamic ResistanceIt should be noted that progressive collapse may be a dynamicevent. Thus, it is necessary to evaluate the 3D and slab effects onthe dynamic resistance of RC buildings by simply analytical analy-sis (capacity curve method). It is mathematically expressed as

PCCðudÞ ¼1

ud

Zud

0

PNSðuÞdu ð1Þ

where PCCðuÞ and PNSðuÞ are the capacity function and the non-linear static loading estimated at the displacement demand u,respectively.

The capacity curve method is first proposed by Abruzzo et al.(2006) based on the conservation of energy. For details of deriva-tion of this method, please refer to Abruzzo et al. (2006). It shouldbe noted that the effects of strain rate and damping were not in-cluded in this method. The accuracy of the capacity curve methodhad been validated by Tsai (2010). The dynamic capacity curvesof tested specimens are shown in Fig. 18. As seen from the figure,the dynamic ultimate load of P1, P2, T1, T2, S1, and S2 are 28.9,34.0, 56.4, 62.1, 119.4, and 121.0 kN, respectively. Thus, both 3Dand slab would also increase the dynamic capacity of RC frameconsiderably. Dynamic tests should be carried out for deeper under-standing of the secondary load carrying mechanisms to mitigateprogressive collapse of RC frames caused by sudden removal ofcolumns in future.

Analytical Analysis

As mentioned earlier, in order to quantify the contribution of eachmechanism to resist progressive collapse of RC buildings, a seriesof analytical analyses, which are mainly modified based on pre-vious research works (Bailey 2001; Park and Gamble 2000), wereproposed.

Yield Load

Using fundamental plastic hinge concepts and estimating the yieldmoment of the beam from classical Whitney stress block, the pre-dicted yield load of P1, P2, T1, and T2 are 24.6, 25.9, 49.2, and51.8 kN, respectively. The measured yield loads of P1, P2, T1, andT2, respectively, are 24, 26, 48, and 48 kN. Likewise using yieldline theory (refer to Fig. 19) and virtual work concepts, the pre-dicted yield loads of S1 and S2 are 77.3 and 88.2 kN, while theirmeasured values are 80 and 90 kN. In both cases these approximatemethods reasonably predict the measured values.

Compressive Arch Action and Compressive MembraneAction

As shown in Fig. 20, if the edges of slabs or beams are restrainedagainst lateral movement by stiff boundary elements, horizontalcompressive force or thrust are induced in the plane of the slabor axial of beam when, as the slab or beam deflects, changes ofgeometry cause the slab edges to tend to move outward and reactagainst the stiff boundary elements. The induced compressive forceenhances the yield load of beams and slabs through moment-axialforce interaction. It should be noted that the horizontal compressiveforce are never great enough for the tension steel not to yield and,therefore, will always result in an increase in the ultimate momentcapacity of the beam or slab sections.

P- and T-Series Specimens

The analytical model proposed by Park and Gamble (2000) fordetermining the CMA of one-way slab is modified to predictthe CAA developing in the beams (similar to that formulated bySu et al. 2010), as shown in Eq. (2)

P ¼ 1

βln

�0.85f 0

cβ1bh

�h2

�1 − β1

2

�þ δ4ðβ1 − 3Þ

þ βð2lnÞ24δ

ðβ1 − 1Þ�εþ t

ln

�þ δ2

8h

�2 − β1

h

�

þ βð2lnÞ24h

�1 − β1

2

��εþ t

ln

�− β1β2ð2lnÞ4

16 hδ2

�εþ t

ln

�2�

− ðT 0 − T − C 0s þ CsÞ2

3.4f 0cb

þ ðC 0s þ CsÞ

�h2− d 0 − δ

2

�

þ ðT 0 þ TÞ�d − h

2þ δ2

�ð2Þ

where P is the resistance capacity of the frames because of CAA orCMA; b is the width of the beam; ln is the clear span of the beam;

0

(a) (b)

20

40

60

80

100

0 30 60 90 120 150 180 210 240Vertical displacement (mm)

Res

ista

nce

deco

mpo

sitio

n (%

)

Slab-contribution

Beam-contribution

54 %

42 %

First PeakStrength

PunchingFailure

0

20

40

60

80

100

0 30 60 90 120 150 180 210Vertical displacement (mm)

Res

ista

nce

deco

mpo

sitio

n (%

)

Slab-contribution

Beam-contribution

54 %

32%

First PeakStrength

PunchingFailure

Fig. 17. Resistance capacity decomposition results of S-series speci-mens: (a) S1; (b) S2

0

20

40

60

80

100

120

140


Dyn

amic

Cap

acit

y (k

N) P1

P2T1T2S1S2

Fig. 18. Dynamic performance of test specimens

2θ

1θ

δ

δ

Fig. 19. Assumed yield-line pattern for beam-slab specimens underconcentrated load


J. Struct. Eng.

72

β is the ratio of the distance from a plastic hinge at mid-span to thenearest support to 2ln; δ is the vertical displacement at the interiorcolumn; h is the depth of the beam; T 0 and T is the tensile resultantforce of the steel at support and beam-interior column interface; C 0and C is the compressive resultant force of the concrete at supportand beam-interior column interface; ε is the strain because of hori-zontal shrinking and creeping; and t is the horizontal movement atthe support. εþ ðt=lnÞ can be determined by Eq. (3)

εþ tln

¼ð 1hbEc

þ 1lnSÞ½0.85f 0

cβ1bðh2 − δ4− T 0þT−C 0

sþCs1.7f 0

cβ1bÞ þ Cs − T�

1þ 0.85f 0cβ1βl2nbδ ð 1

hbEcþ 1

lnSÞ

ð3Þwhere Ec elastic modulus of concrete; S is horizontal rigidity ofvertical support (S is equal to 93 kN=mm).

Based on the modified Park and Gamble (2000) model, the pre-dicted first peak load of P1, P2, T1, and T2 are 34.8, 32.2, 68.4, and63.2 kN, respectively. Whereas the measured values of P1, P2, T1,and T2 is 32, 36, 67, and 64 kN, respectively. Thus, in general, themodified Park and Gamble (2000) could predict the CAA devel-oped in double span beams with fixed boundary conditions well.In order to further validate the analytical model, the experimentalresults from previous tests are reviewed and compared with theo-retical predictions in Table 4. As shown in the table, the theory

could predict the CAA developed in the case of most of the beamsin the table. For the 16 specimens, the mean value for Ptest=Ptheory is0.99, with a standard deviation of 0.08. It should be noted that themeasured vertical displacement corresponding to the first peak loadof the specimens is utilized in theoretical prediction. As the verticaldisplacement at the first peak load is unknown in practical design,the authors suggest the vertical displacement at the first peak load is0.24h based on the data pool of previous tests, as shown in Table 4.It should be noted that more tests should be carried out to furtherprove the accuracy of Eq. (2) and the suggested vertical displace-ment corresponding to the first peak load.

S-Series Specimens

By using the analytical model proposed by Park and Gamble(2000) for determining the CMA of two-way slabs, the CMA de-veloped in slab of S1 and S2 are predicted to 67.8 and 69.1 kN. Asthe CAA developed in the beams, S1 and S2 are 68.4 and 63.2 kN,respectively. Thus, the predicted first peak load of S1 and S2 are135.4 and 132.3 kN. However, the measured first peak load of S1and S2 are 115 and 123 kN. Thus, the predicted first peak load bysum of CMA and CAA is larger than the measured ones, especiallyfor S1. This is mainly because of the maximum value of CMA, andCAA will not occur simultaneously in reality. However, the accu-racy of the proposed analytical model is enough to roughly quantify

Fig. 20. Schematic of CAA or CMA

Table 4. Test and Theory: Double-Span Beams with Lateral Constraints at Beam Ends

InvestigatorSpecimenmark

Dimensionsb × h × ln

(mm ×mm ×mm) lnh

Beam reinforcement ratio (%)Experimentalfirst peakload (kN)

Theoreticalfirst peakload (kN)

PTestPTheory

δh

Positive moment Negative moment

Top Bottom Top Bottom

Authors P1 100 × 180 × 1,900 10.5 0.93 0.93 0.93 0.93 31.6 33.8 0.93 0.21P2 80 × 140 × 1,300 9.3 1.65 1.65 1.65 1.65 35.5 32.2 1.10 0.22

T1-L* 100 × 180 × 1,900 10.5 0.93 0.93 0.93 0.93 66.7 68.4 0.98 N/AT1-T* 80 × 140 × 1,300 9.3 1.65 1.65 1.65 1.65T2-L 80 × 180 × 1,300 9.3 1.65 1.65 1.65 1.65 63.9 63.2 1.01 0.20T2-T 80 × 140 × 1,300 9.3 1.65 1.65 1.65 1.65

Su et al. (2010) A1 150 × 300 × 1,225 4.08 0.55 0.55 0.55 0.55 168.0 176.0 0.95 0.16A2 150 × 300 × 1,225 4.08 0.83 0.83 0.83 0.83 221.0 206.9 1.07 0.19A3 150 × 300 × 1,225 4.08 1.13 1.13 1.13 1.13 246.0 237.2 1.04 0.25A4 150 × 300 × 1,225 4.08 0.55 0.38 0.55 0.38 147.0 156.6 0.94 0.22A5 150 × 300 × 1,225 4.08 0.83 0.55 0.83 0.55 198.0 203.1 0.97 0.22A6 150 × 300 × 1,225 4.08 1.13 0.75 1.13 0.75 226.0 221.4 1.02 0.24B1 150 × 300 × 1,975 6.58 1.13 1.13 1.13 1.13 125.0 128.5 0.97 0.23B2 150 × 300 × 2,725 9.08 1.13 1.13 1.13 1.13 82.9 94.8 0.87 0.33B3 150 × 300 × 2,725 9.08 1.13 0.75 1.13 0.75 74.7 88.9 0.85 0.34C1 100 × 200 × 1,225 6.12 1.30 1.30 1.30 1.30 60.9 54.3 1.12 0.29

Mean= 0.99 0.24Standarddeviation=

0.08 0.05


J. Struct. Eng.

73

the ability of CMA and CAA developed in RC beam-slab struc-tures. For details of the analytical modes used to predict theCMA of two-way slabs, please refer to Park and Gamble (2000).

Catenary Action and Tensile Membrane Action

Further increase of the vertical displacement, concrete crushing be-comes severe, and flexural cracks may penetrate the whole thick-ness of beam and slab depth. Then the load is mainly carried by thereinforcing bars acting as a tensile net or chain action, as shownin Fig. 21.

P- and T-Series Specimens

By using the equations proposed by Yi et al. (2008), as shown inFig. 5(a), the catenary action behavior of P- and T-series specimenswere predicted and compared with the measured performance. Itcan be seen that, in general, the predicted response of TCAmatchedthe measured response of P1 and T1 well, although the predictedresponse exhibited slightly conservative. However, it should benoted that the analytical equations shown in Yi et al. (2008) wereonly workable after TCA had fully developed with large displace-ment stage (0.1ln).

S-Series Specimens

Unlike compressive membrane action developed in RC slabs, stifflateral constraints at the edges of slab is not the necessary conditionfor developing tensile membrane action in RC slabs. Several pre-vious studies, such as Bailey (2001), had found that significanttensile membrane action could develop in RC slabs with even sim-ply support edges. As shown in Fig. 22, the formation of peripheralcompressive ring could provide considerable lateral constraints todeflected slabs for developing tensile membrane forces in the cen-tral region. Moreover, a majority of previous studies regardingmembrane action developed in RC slab simplified the beam-slabstructures into slab with fully fixed edges or simply support edges.In this study, more realistic test models (beam-slab specimens)were conducted. The lateral constrains applied on the edges oftested slab is actually partial constrained. For simplicity, the ana-lytical model proposed by Bailey (2001) was modified to predictthe TMA developed in the slab of S-series specimens. However, thenecessary modifications for predicting the TMA of S-series spec-imens using Bailey (2001)’s analytical model should be given.1. As concentrated load was applied at the top of the interior

column, the yield line in the bottom slab always connectedthe interior column to corner column as shown in Fig. 11,although the span length in transverse and longitudinal

directions are unequal. Thus, the value of the parameter nis 0.5 even the test specimen is not square. Therefore, the dis-tribution of these forces is illustrated in Fig. 23 and shownbelow:

T2 ¼bKTBot

0

2ð1þ kÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiL2 þ l2

p

2ð4Þ

C ¼ kbKTBot0

2

�k

1þ k

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiL2 þ l2

p

2ð5Þ

S ¼ ðC − T2Þtanφ

¼ 1

tanφ×bKTm

0

2ðk − 1Þ ð6Þ

Sinφ ¼ LffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiL2 þ l2

p ð7Þ

where KT0 is the force in steel per unit width in short direc-tion; L and l are longer and shorter span of rectangular slab; kis the parameter defining magnitude of membrane force (k ¼ 1based on force equilibrium in element 1); φ is the angle defin-ing yield line pattern; and b is a parameter defining magnitudeof membrane force.

2. Sawczuk andWinnicki (1965), Bailey (2001), and Bailey et al.(2008) had indicated that there are three possible failure modesin RC two-way slabs under uniform distributed pressure, asshown in Fig. 24. However, the most possible failure mode ofRC beam-slab structures (similar to S-series specimens) afterremoval of an interior column is concrete crushing at the cor-ner of the slab, as shown in Fig. 24(a). This is mainly because

Fig. 21. Schematic of TCA or TMA

Fig. 22. In-plane membrane force of a laterally unrestrained beam-slabstructures at TMA stage


J. Struct. Eng.

74

of the interior beams crossing the center of the slab, as shownin Fig. 3, which prevented the occurring of failure modes 2and 3. Thus, the parameter b could be calculated based onequilibrium of compressive membrane actions (kbKT0), con-crete compressive stress block {0.67fcu0.45

�ðd1 þ d2Þ=2�},

and the tension reinforcement at the edge of the slab(KT0 þ T0=2), as shown in Eq. (8). The maximum depthof the compressive depth of the compressive stress block isassumed to be 0.45 of average d [ðd1 þ d2Þ=2]

kbKT0 ¼ 0.67fcu0.45

�d1 þ d2

2

�−�KT0 þ T0

2

�ð8Þ

where d1 and d2 are the effective depth in short span and longspan, respectively.

Rearranging Eq. (8) results in

b ¼ 1

kKT0

�0.67fcu0.45

�d1 þ d2

2

�− T0

�K þ 1

2

��ð9Þ

For the details of the analytical model, please refer to Bailey(2001). As shown in Fig. 5(b), the proposed analytical modelslightly overestimates the capacity of TCA and TMA developed

in beam-slab structures because of the strain compatibility betweenthe interior beams and slabs that had not been considered well.Moreover, the punching shear failure between the interior columnand slab because of slab concrete crushing was not simulated inthis analytical model.

Conclusions

Based on the experimental and analytical results, the followingconclusions can be drawn:1. The test results show that 3D effects excluding RC slab could

increase the beam action of the frame by as much as 100%,whereas the 3D effects including RC slab could increase thebeam action up by 246.2%. Thus, 3D effects, including RCslab, should be well-simulated in progressive collapse design.However, it was not easy to simulate nonlinear performance ofRC slab in large displacement stage by normal design soft-ware, such as Sap2000 or ETABS. Thus, developing shell ele-ments, which could properly simulate the nonlinear behaviorof RC slab in large displacement stage, become a critical need.

2. Experimental results from S-series specimens indicated thatloads are initially resisted by flexural behavior followed by

Fig. 23. Assumed in-plane stress distribution for membrane action

(a) (b) (c)

Fig. 24. Three possible failure modes: (a) concrete compression failure at the corner of the slab; (b) fracture of reinforcement across the center of slab;(c) fracture of reinforcement across the intersection of yield lines


J. Struct. Eng.

75

compressive membrane action, compressive arch action,tensile membrane action, and tensile catenary action. Tensilemembrane action began to develop at 4.5–5.7% of beam span,which is much earlier than catenary action that began to work(10% of beam span). This may significantly reduce the lifeand possession loss caused by the collapse of nonload bearingelements from large structural deformation.

3. For beam-column structures (S-series), tensile catenary andtensile membrane action responses developed in RC beams,and slabs will significantly reduce the likelihood of structuresin collapse. However, the test results indicated that RC slab isthe main source of the structure’s capacity, carrying as muchas 68% of the load in large displacement stage.

4. By comparison of the analytical and test results, the proposedanalytical model could predict the yield load, first peak load,and ultimate load of bare frames well. However, the analyticalmodels are prone to overestimate the first peak load and ulti-mate load in beam-slab structures. This is primarily becausethe strain compatibility between beam and slab are not in-cluded in the models.

Acknowledgments

The financial assistance provided by the Defence Science andTechnology Agency, Singapore.

References

Abruzzo, J., Matta, A., and Panariello, G. (2006). “Study of mitigationstrategies for progressive collapse of a reinforced concrete commercialbuilding.” J. Perform. Constr. Facil., 10.1061/(ASCE)0887-3828(2006)20:4(384), 384–390.

ACI Committee 318-08. (2008). “Building code requirements for structuralconcrete (ACI 318-08) and commentary (318R-08).” Farmington Hills,MI, 433.

ASCE/SEI. (2010). Minimum design loads for buildings and other struc-tures, Reston, VA.

Bailey, C. G. (2001). “Membrane action of unrestrained lightly reinforcedconcrete slabs at large displacement.” Eng. Struct., 23(5), 470–483.

Bailey, C. G., Toh, W. S., and Chan, B. M. (2008). “Simplified and ad-vanced analysis of membrane action of concrete slab.” ACI Struct.J., 105(4), 30–40.

Hawkins, N. M., and Mitchell, D. (1979). “Progressive collapse of flatplate structures.” ACI Struct. J., 76(7), 775–808.

Malvar, L. J., and Crawford, J. E. (1998). “Dynamic increase factors forsteel reinforcing bar.” 28th DDESB Seminar, Orlando, FL.

Mitchell, D., and Cook, W. D. (1984). “Preventing progressive collapseof slab structures.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(1984)110:7(1513), 1513–1532.

Park, R. (1965). “The lateral stiffness and strength required to ensure mem-brane action at the ultimate load of a reinforced concrete slab-and-beamfloor.” Mag. Concr. Res., 17(50), 29–38.

Park, R., and Gamble, W. L. (2000). Reinforced concrete slabs, Wiley,New York, 716.

Qian, K., and Li, B. (2012). “Slab effects on the response of reinforcedconcrete substructures after loss of corner column.” ACI Struct. J.,109(6), 845–855.

Qian, K., and Li, B. (2013a). “Experimental study of drop-panel effects onresponse of reinforced concrete flat slabs after loss of corner column.”ACI Struct. J., 110(2), 319–330.

Qian, K., and Li, B. (2013b). “Performance of three-dimensional reinforcedconcrete beam-column substructures under loss of a corner columnscenario.” J. Struct. Eng., 10.1061/(ASCE)ST.1943-541X.0000630,584–594.

Qian, K., and Li, B. (2013c). “Strengthening and retrofitting of RC flatslabs to mitigate progressive collapse by externally bonded CFRP lam-inates.” J. Compos. Constr., 10.1061/(ASCE)CC.1943-5614.0000352,554–565.

Sasani, M., and Kropelnicki, J. (2008). “Progressive collapse analysis of anRC structure.” Struct. Des. Tall Spec. Build., 17(4), 757–771.

Sawczuk, A., and Winnicki, L. (1965). “Plastic behavior of simplysupported reinforced concrete plates at moderately large deflections.”Int. J. Solid. Struct., 1(1), 97–111.

Su, Y. P., Tian, Y., and Song, X. S. (2010). “Progressive collapse resistanceof axially-restrained frame beams.” ACI Struct. J., 106(5), 600–607.

Tian, Y., and Su, Y. P. (2011). “Dynamic response of reinforced concretebeams following instantaneous removal of a bearing column.” J. Concr.Struct. Mater., 5(1), 19–28.

Tsai, M. H. (2010). “An analytical methodology for the dynamic amplifi-cation factor in progressive collapse evaluation of building structures.”Mech. Res. Commun., 37(1), 61–66.

Yang, B., and Tan, K. (2013). “Robustness of bolted-angle connectionsagainst progressive collapse: Experimental tests of beam-column jointsand development of component-based models.” J. Struct. Eng.,10.1061/(ASCE)ST.1943-541X.0000749, 1498–1514.

Yi, W., He, Q., Xiao, Y., and Kunnath, S. K. (2008). “Experimental studyon progressive collapse-resistant behavior of reinforced concrete framestructures.” ACI Struct. J., 105(4), 433–439.


J. Struct. Eng.

76

load-carrying mechanism to resist progressive collapse of rc buildings

Documents