Strengthening and Retrofitting of RC Flat Slabs toMitigate Progressive Collapse by Externally

Bonded CFRP LaminatesKai Qian, A.M.ASCE1; and Bing Li2

Abstract: Previous studies indicated that RC flat slabs, especially without drop panels, are of high vulnerability to progressive collapsebecause no beams could assist in redistributing the axial force previously carried by the lost columns. In order to reduce the likelihood ofprogressive collapse, necessary strengthening schemes should be applied. Six specimens of similar dimensions and reinforcement detailswere prepared, two of which were unstrengthened and served as control specimens, while the remaining four were strengthened with twodifferent schemes: orthogonally (Scheme 1) or diagonally (Scheme 2) bonded carbon-fiber-reinforced polymer (CFRP) laminates on the topsurface of the slab. The progressive collapse performance of the strengthened specimens was studied in terms of their load-displacementrelationships, first peak strength, initial stiffness, and energy dissipation capacities. The dynamic ultimate strength and corresponding dy-namic effects of flat slabs after the sudden removal of a corner column was also discussed due to the dynamic nature of progressive collapse.Test results indicated that both schemes were effective in improving the performance of RC flat slabs in resisting progressive collapse. DOI:10.1061/(ASCE)CC.1943-5614.0000352. © 2013 American Society of Civil Engineers.

CE Database subject headings: Progressive collapse; Fiber reinforced polymer; Slabs; Rehabilitation; Laminated materials; Corners.

Author keywords: Progressive collapse; Fiber-reinforced polymer; Flat slab; Corner; Strengthening; Retrofitting.

Introduction and Background

Progressive collapse is a situation in which a local failure causes achain reaction spreading throughout the entire structure culminat-ing in a catastrophic collapse. In general, progressive collapse ischaracterized by a disproportion in size between the triggeringevent and the resulting collapse (Ellingwood 2006; Bao and Li2010; Li et al. 2011). Examples of such structural collapses inthe last decades include the Ronan Point apartment building inLondon, which partially collapsed in 1968 due to a gas explosion,and the Murrah Federal Building in Oklahoma City, which was de-stroyed in 1995 following an explosion of a bomb truck. Due to thecatastrophic consequences, progressive collapse has gained in-creasing interest in the civil engineering research community, es-pecially in terms of the development of design guidelines. Recently,several design guidelines [U.S. General Service Administration(GSA) 2003; U.S. Department of Defense (DoD) 2009] have pro-posed step-by-step procedures to evaluate the vulnerability of struc-tures to progressive collapse. However, the current designguidelines require refinements through further experimental andanalytical studies. For this purpose, a number of experimental tests(Yi et al. 2008; Orton et al. 2009; Su et al. 2009; Yap and Li 2011;

Qian and Li 2012a, b, 2013b) were conducted recently. Althoughthe experimental tests significantly improved the understanding ofthe performance of RC frames in resisting progressive collapse,only beam-column subassemblages or beam-column-slab substruc-tures were tested. Flat slabs have a higher likelihood of progressivecollapse compared to the beam-column-slab structures becausethere are no beams that could assist in redistributing the load pre-viously carried by the lost columns. Thus, Qian and Li (2013a)tested six one-third-scaled flat slab substructures at Nanyang Tech-nological University (NTU), Singapore, to investigate the droppanel effects on the performance of RC flat slabs in resistingprogressive collapse. The test results indicated that flat slabs, es-pecially those without drop panels (flat plate structures), werehighly vulnerable to progressive collapse. Thus, in order to reducethe likelihood of progressive collapse for such specimens, neces-sary strengthening schemes had to be applied.

In recent years, repairs and strengthening of existing structureshave been among the most important challenges in civil engineer-ing. Steel plates have been used in many countries for flexuralstrengthening of concrete beams for several years (MacDonaldand Calder 1982; Zhang et al. 2001). The main disadvantage ofusing steel plates is corrosion, which adversely affects the bondat the steel-concrete interface. Fiber-reinforced polymers (FRPs)have been frequently used in recent decades because FRPs arenot prone to electrochemical corrosion like steel. Moreover, theycan be formed, fabricated, and bonded easier than steel plates.The mechanical properties of FRPs vary with the type and orien-tation of the reinforcing fibers. Thus, the fibers can be placed in anyorientation to maximize the strength in a desired direction. In thisstudy, unidirectional carbon-fiber-reinforced polymer (CFRP) isused to strengthen the flat slabs in resisting progressive collapsedue to the previous advantages.

In order to investigate the performance of the strengthened flatslabs in resisting progressive collapse and study the effectiveness of

1Research Fellow, School of Civil and Environmental Engineering,Nanyang Technological Univ., Singapore 639798 (corresponding author).E-mail: qiankai@ntu.edu.sg

2Associate Professor and Director, Natural Hazards Research Centre(NHRC), Nanyang Technological Univ., Singapore 639798. E-mail:cbli@ntu.edu.sg

Note. This manuscript was submitted on September 4, 2012; approvedon December 14, 2012; published online on December 17, 2012. Discus-sion period open until January 1, 2014; separate discussions must be sub-mitted for individual papers. This paper is part of the Journal ofComposites for Construction, Vol. 17, No. 4, August 1, 2013. © ASCE,ISSN 1090-0268/2013/4-554-565/$25.00.

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the proposed strengthening schemes in upgrading the progressivecollapse resistance of the flat slabs, six one-third-scaled RC flatslabs (3,100 × 3,100 × 70 mm) were tested. Two of them weretested without any strengthening and taken as control specimens.The test observations of these two specimens had been introducedin detail in Qian and Li (2013a). The four newly tested specimens,of similar dimension and reinforcement details as the control spec-imens, were strengthened by externally bonded CFRP laminates.

Experimental Program

Test Specimens

The six flat slabs prepared for this study were divided into threeseries. The first series, consisting of two flat slabs (Con-L andCon-M), was employed as the control group without any strength-ening. L and M indicate that the flat slabs had low and mediumamounts of slab reinforcement, respectively. For the second seriesof specimens (SO-L and SO-M), CFRP strips were externallybonded on the top face of the slab orthogonally (Scheme 1).However, for the third series of specimens (SD-L and SD-M),CFRP strips were externally bonded on the top face diagonally(Scheme 2). The dimensions and reinforcement details of the testspecimens are summarized in Table 1.

The Control Specimens Con-L and Con-M were designed inaccordance with ACI 318-08 [American Concrete Institute (ACI)2008]. The dead load (DL) of the prototype structure due to a210.0-mm-thick slab was 5.1 kPa. The additional dead load wasassumed to be 1.0 kPa. The equivalent additional dead load dueto the weight of in-fill walls was 2.25 kPa. The live load (LL)was assumed to be 2.0 kPa. One-third-scaled substructures werecast and tested in this study. A uniform pressure of 11.0 kPa basedon loading combination (1.2DLþ 0.5LL), which is suggested inDoD (2009), was applied on the surface of the prototype slabs.In order to create the same demand-capacity ratio on the criticalslab section of the scaled-down slabs as that of the prototype slabs,the same magnitude of the pressure (11.0 kPa) should be applied onthe scaled-down models. Based on the service pressure and basicanalysis, the design axial force in the corner column of each speci-men was determined and listed in Table 1. For detail derivation,please refer to Qian and Li (2012a). Fig. 1 illustrates the dimensionsand reinforcement details of the control specimen Con-L. As shownin the figure, one corner column stub, three enlarged columns, and aslab with 70-mm thickness were cast monolithically. The columnstub in the corner represented the remnants of a removed column.The size of the corner stub was 200 × 200 mm. The size of theremaining columns was 250 × 250 mm. It was enlarged to preventdamage occurring in these columns and to ensure equivalent fixedconstraints applied on these columns. The slab reinforcement of

specimens Con-L and Con-M is shown in Fig. 2. The slabreinforcement in the middle strip was composed of R6 rebar at250.0 mm in two layers at the top and bottom, whereas the columnstrip was composed of two layers of R6 rebar spaced at 125.0 and250.0 mm at the top and bottom, respectively. Moreover, reinforce-ments were installed in the slab-corner column connection to pre-vent or delay possible brittle failure of the specimen within thesmall deformation stage due to punching shear.

As the test results from control specimens had indicated, theexisting dimension and reinforcement details could not preventprogressive collapse of the flat slabs if a corner column was sud-denly removed. Thus, in order to upgrade the resistant capacity ofthe flat slabs, another four specimens (SO-L, SO-M, SD-L, andSD-M) were strengthened by externally bonded CFRP laminates.The dimension and reinforcement details of the strengthened spec-imens SO-L and SD-L were similar to the control specimen Con-L.For SD-L and SD-M, their dimension and reinforcement detailswere similar to Con-M. The details of the strengthening schemesare described in following sections. The average concrete compres-sive strengths were approximately 19.5, 31.7, and 29.9 MPa for theCon-series, SO-series, and SD-series specimens, respectively. Theyield strength, yield strain, and ultimate strength of the R6reinforcement were 430 MPa, 2,210 με, and 516 MPa, respec-tively. The material properties of the CFRP are shown in Table 2.

Test Setup

A schematic of the loading apparatus is given in Fig. 3. A hydraulicjack with 600-mm stroke was utilized to apply vertical displace-ment on the corner stub. The loading process was force-controlledbefore the specimens reached their first peak capacities. After that,a displacement-controlled loading process with 10-mm intervalwas applied. Moreover, as shown in Fig. 4, bending moment re-verse occurred at the slab-corner column connection after removalof the corner column. Vierendeel action can be characterized byrelatively vertical displacement between slab-column connectionsand double curvature deformations of column strips and columns.In order to equivalently simulate Vierendeel action applied on thetest specimens or create positive bending moment (tensile at bot-tom) at the column strip near the corner column, a steel assemblywas specially designed. The elevation view of the steel assembly isshown in Fig. 5. As shown in the figure, the steel box with pinscould apply rotational constraint on the corner column. However,if there was no gap between the pin and hole in the box, horizontalconstraints will apply on the corner joint. It should be eliminated orreduced for flat slabs under the loss of a corner column scenario.A 3-mm gap was designed between the pin and the hole in the steelbox. For the detailing of design of gap, please refer to Qian andLi (2012b, 2013b). Furthermore, three steel legs were utilized tosupport the specimens and to provide equivalent fixed support

Table 1. Specimen Properties

TestCorner columnstub (mm)

Slabthickness

Slab toplayer rebar

Slab bottomlayer rebar

Design axialforce (kN) Specimen description

Columnstrip (mm)

Middlestrip (mm)

Columnstrip (mm)

Middlestrip (mm)

Con-L Crosssection ¼200 × 200

ReinforcementRatio ¼ 2.0%

70.0 mm R6 at 125 R6 at 250 R6 at 250 R6 at 250 15.9 Control specimens withoutany strengtheningCon-M 70.0 mm R6 at 60 R6 at 125 R6 at 125 R6 at 125 15.9

SO-L 70.0 mm R6 at 125 R6 at 250 R6 at 250 R6 at 250 15.9 Strengthened by Scheme 1SO-M 70.0 mm R6 at 60 R6 at 125 R6 at 125 R6 at 125 15.9SD-L 70.0 mm R6 at 125 R6 at 250 R6 at 250 R6 at 250 15.9 Strengthened by Scheme 2SD-M 70.0 mm R6 at 60 R6 at 125 R6 at 125 R6 at 125 15.9

Note: R6 = plain rebar with diameter of 6 mm.

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conditions on the adjacent and interior columns. Finally, in order topartially simulate the influence of the continuity of the slabs on theoverall performance, the slab was extended beyond the fixed sup-port by one-fourth of the span in both directions. Five steel weightassemblies were applied on the extended part of the slab to simulatethe influence of the continuity of surrounding slabs on the responseof the specimens.

Instrumentation

A load cell was utilized to measure the vertical load applied on thecorner stub. One linear variable differential transformer (LVDT)with 300.0-mm travel was installed vertically to measure the ver-tical movement of the corner column stub during the test. In orderto monitor the horizontal movement of the corner joint during thetest, a line displacement transducer with 1,200.0-mm travel wasinstalled horizontally. For control specimens Con-L and Con-M,a total of 23 strain gauges were mounted on the reinforcements

at strategic locations in order to monitor the strain variation alongthe corner column and slab during the test. For strengthened spec-imens, strain gauges were not only installed in the corner columnand slab, but were also placed on the CFRP laminates. The loca-tions of the strain gauges placed in the slab reinforcement areshown in Fig. 2, while the locations of the strain gauges in theCFRP laminates are presented in the figures illustrating the retro-fitting schemes (Figs. 6–8).

Test Results and Observations

Behavior and Failure Modes of the Control Specimens

The failure mode of control specimen Con-L is shown in Fig. 9(a).As shown in the figure, severe diagonal cracks passed through thecenter of the slab. Flexural cracks were not only observed in the topface of the slab near the adjacent column, but also in the bottom

R6@

55

Detail of Corner Stub

Tra

nsve

rse

Adj

acen

t Col

umn

Longitudinal Adjacent Column

Detail of Adjacent Column

8T16

R6@55

Interior Column

R6@55

4T16

Elevation View of the Strengthened Specimens

R6@

55

Plan View

Corner Joint Stub

Elevation View of Control Specimens

Fig. 1. Dimensions of the test specimens

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face near the corner column due to Vierendeel action. No damagewas observed at the corner column. In general, the failure mode ofCon-M was similar to that of Con-L. However, the slab diagonalcracks on Con-M were much finer than those on Con-L. On Con-L,only several discrete diagonal cracks formed at the slab top surface.However, for Con-M, numerous cracks were observed in betweenthe diagonal cracks. For a detailed description of the failure modesand crack pattern development, please refer to Qian and Li (2013a).

The vertical load-displacement curve of specimens Con-L andCon-M are shown in Fig. 10. The first peak capacity (before devel-oping the tensile membrane) of specimens Con-L and Con-M were8.5 and 14.3 kN, respectively. Moreover, significant tensile

membrane action was observed in the load-displacement curveat a large displacement stage for both specimens. The maximumresistance capacities due to tensile membrane were 17.3 and18.5 kN for Con-L and Con-M, respectively. Furthermore, Fig. 10also presents the measured horizontal reaction force versus the ver-tical displacement of the corner joint of Con-L and Con-M. Themaximum horizontal tensile force in the transverse direction forCon-L and Con-M was 6.0 and 7.3 kN, respectively. Severe punch-ing failure was observed in the slab-corner column connection ofCon-L and Con-M at the displacements of 410.9 and 380.9 mm,respectively. The punching shear strength of the slab-corner col-umn connections of the control specimens were compared withthe values suggested in the design codes in Qian and Li(2013a). Good agreements had been achieved by comparingwith CEN (2004), CEB-FIP Model Code 1990 [Comité Euro-International du Béton–Féderation International de la Précontrainte(CEB-FIP) 1993], and DIN-1045-1 [Deutches Institut für Normung(DIN) 2001]. However, the punching failure did not prevent furtherincrease of the load resistance with increasing displacement, pos-sibly due to the integrity reinforcement installed in the slab-cornercolumn connection. The key results of the test specimens are shownin Table 3.

Strengthening Schemes

Through analytical analysis of the test results of the control spec-imens, the dynamic ultimate strengths of Con-L and Con-M were

ST5ST4ST1ST2

ST3

ST7

ST6

SB1 SB2SB3 SB4

SB5

SB6

SB7

SB8

(a)

ST7

ST6

ST5ST4ST1ST2

ST3

SB1 SB2SB3 SB4

SB5

SB6

SB7

SB8

(b)

(c) (d)

Fig. 2. Slab reinforcement details: (a) top slab reinforcement of Con-L; (b) bottom slab reinforcement of Con-L; (c) top slab reinforcement of Con-M;(d) bottom slab reinforcement of Con-M

Table 2. Properties of Tyfo Fibrwrap Composite System

Parameters Propertiesa

CFRP with epoxy, Tyfo SCH-41Composite

Type of FRP Unidirectional CFRP sheetUltimate tensile strength in primaryfiber direction

986 MPa

Elongation at break 1.0%Tensile modulus 95.8 × 103 MPaLaminate thickness 1.0 mmaProperties values given are based on test value by supplier (FYFE Asia Pte.Ltd in Singapore).

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predicted as 10.0 and 14.0 kN, respectively. However, the designaxial force of the Con-L and Con-M was 15.9 kN. Thus, both con-trol specimens would collapse if the corner column was suddenlyremoved. Detailed explanation of the dynamic ultimate strengthwas shown in the section of ‘Vulnerability of the Test Specimens’.Because control specimens Con-L and Con-M had indicated thatexisting design and detailing could not prevent progressive collapseif a corner column was suddenly removed, two strengtheningschemes were proposed to upgrade their resistant capacities. Beforethe application of CFRP laminates, the specimens were carefullyprepared by grinding the regions that will be bonded to the CFRPlaminates to achieve a fully smooth surface. The slab-column in-terfaces were rounded at a radius of approximately 20 mm to avoidCFRP cracks due to local stress concentration. The wet layupCFRP application method was employed on the specimens. It in-volves the use of epoxy resin for bonding and impregnation of theCFRP laminates. Putty was applied to prevent debonding due tounevenness. The following describes the procedures for theCFRP-strengthening schemes proposed.

The failure modes of control specimens (refer to Fig. 9) hadindicated that severe flexural cracks were observed in the topslab-adjacent column interfaces and bottom slab-corner column in-terfaces. Thus, in order to upgrade the resistant capacity of the flatslabs, the flexural strength of the column strips should be strength-ened. The strengthening schemes for upgrading the flexural capac-ity of the column strips were the same in both SO and SD series. Asshown in Fig. 6, one layer of CFRP L-wrap (Step 1 in Fig. 6) wasapplied at each slab-column interface. The CFRP sheet was bent at90° and thereafter extended 50 mm along the column and 540 mmalong the slab. Although the theoretical width of the flange of theslab is four times the slab depth (Park and Paulay 1975), the widthsof 225 and 200 mm were selected for CFRP L-wrap near the ad-jacent column and corner column, respectively, for easy connectionwith the columns. The length of the CFRP L-wrap (540 mm) alongthe slab was designed to coincide with the cutoff point of the slabtop reinforcement 0.3 times the clear span, as recommended in ACI318-08 (ACI 2008). Then a CFRP strip with 50-mm width (Step 2in Fig. 6) was wrapped around the column to better bond the CFRPL-wrap along the slab and delay the debonding of CFRP L-wrap atthe slab-column interfaces. Both top and bottom faces of the col-umn strips were flexurally strengthened because the flat slabs notonly had the possibility of losing corner columns, but also had thepossibility of losing exterior or interior columns.

Severe diagonal cracks were observed in the center slab becauseno top reinforcements were installed in the center of the slab. Thus,flexural strength of the center slab also had to be strengthened toreduce the crack width and increase the resistant capacity. For thestrengthening Scheme 1 (SO-L and SO-M), the flexural strength ofthe center slab was strengthened through externally bondedorthogonal (0–90°) CFRP strips with 150-mm width on the top faceof the slab (refer to Fig. 7). For the strengthening Scheme 2 (SD-Land SD-M), as shown in Fig. 8, CFRP strips with 150-mm widthwere diagonally (45–135°) bonded on the top face of the slab. Itwas understandable that Scheme 1 (0–90°) was an easier applica-tion compared with Scheme 2 (45–135°). As illustrated in Park and

Fig. 3. CFRP-strengthened specimen ready for test

Corner JointCorner Joint

Fig. 4. Bending moment diagram and deformed shape of typical planarframe after the removal of a corner column

(V1)

Upper Steel Column

Steel Pins

Steel Box

Corner Stub

(V2)

(V)

X

Z

0

Fig. 5. Detailing of steel assembly

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Gamble (2000), the ultimate moment resistance (mun) and torsionalmoment (munt) per unit width of the slab equal to

mun ¼ muxcos2αþmuysin2α ð1Þ

munt ¼ ðmux −muyÞ cosα × sinα ð2Þ

For the definition of mun, munt, mux, and muy, please refer toFig. 11. For slabs with isotropic reinforcement (mux ¼ muy),mun ¼ mux ¼ muy and munt ¼ 0. Similarly, for orthogonallystrengthened specimens (SO-L and SO-M), the bending moment

strength of the slab in the x- and y-directions were strengthenedto the same extent. Thus, theoretically, the previous conclusionwas still workable and the orthogonal method could increase thebending moment resistance of the slab uniformly. As the failuremode of the control specimens indicated severe diagonal crackformed at center of the slab, an innovative strengthening scheme(45–135°) was designed just for comparison to the orthogonalmethod (0–90°) and it has proven the reliability of Eqs. (1)and (2) for FRP-strengthened two-way slabs. In Scheme 2(45–135°), several CFRP strips were placed perpendicular the maindiagonal crack.

Step1

Step1 Step1

Step1

Step2Step2

FC3 FC4

FC1 FC2: Strain Gauge

CFRP L-Wrap

Fig. 6. Elevation view of the strengthening schemes for column strips

FC3 FC4

M1 M2 M3

M4 M5 M6

M7 M8 M9

M11 M12M10

Step3

Step3

Step3

Step3

Step3

Step4 Step4 Step4 Step4 Step4

Step2 Step2

Step2

Step1 Step1

Step1

Step1

: Strain Gauge

Fig. 7. Plan view of the strengthening Scheme 1 (SO-L and SO-M)

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Behavior and Failure Modes of the SO SeriesSpecimens

The failure modes of specimens SO-L and SO-M are shown inFigs. 12 and 13, respectively. For specimen SO-L, first flexuralcracks were observed at the cutoff point of the CFRP sheet

(Step 1 in Fig. 6) near the longitudinal adjacent column at a loadof 8.0 kN. When the load was increased to 10.0 kN, the flexuralcracks were observed at the cutoff point of the CFRP sheet (Step 1in Fig. 6) near the transverse adjacent column. At the load to12.0 kN, sound due to CFRP laminates debonding was heard.

FC3 FC4

M1

M2

M3

M4

M5

M6

M7

M8

M9

Step2 Step2

Step2

Step3

Step3

Step3

Step3

Step3

Step4

Step4

Step4

Step4

Step1 Step1

Step1

Step1

: Strain Gauge

Fig. 8. Plan view of the strengthening Scheme 2 (SD-L and SD-M)

Fig. 9. Failure modes of control specimens (a) Con-L; (b) Con-M at final

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Hairline cracks formed in the center of the slab accompanied by thedebonding sound with further increment of load to 14.1 kN.Delamination of the CFRP sheet (Step 1 in Fig. 6) occurred atthe top slab near both adjacent columns at this load stage. Whenthe vertical displacement reached approximately 80 mm, severediagonal cracks with a fan pattern were observed at the bottomof the slab (as shown in Fig. 12). When the displacement reachedapproximately 120 mm, debonding of the CFRP sheet was alsoobserved at the bottom slab near the corner column. Moreover,slight debonding was observed in the CFRP strips in the centerof the slab at this displacement stage. When the displacementreached approximately 180 mm, CFRP delamination was observedat the top slab near the corner column (which was at compressiveside). Upon further increment of displacement, the debonding anddelamination of the CFRP strips propagated accompanied withloud debonding sound. Although the debonding and delaminationof the CFRP laminates became more severe with increasing verticaldisplacement, the resistant capacity of the specimen still kept in-creasing. This was attributed to tensile membrane action dominatedby the load redistribution mechanism in the large displacementstage. When the displacement reached 220 mm, the column stripsnear the free edges were pulling up by the CFRP strips (Steps 3 and4 in Fig. 7) as the CFRP strips tried to develop tensile force throughtensile membrane action stage. This was significantly different withthe failure mode of the control specimens. Due to the discontinuityof slabs at the corner bay, the edge strips could not provide enoughconstraints for the CFRP strips (Steps 3 and 4 in Fig. 7) to developtheir tensile strength; therefore, the amount of the tensile membraneaction of the SO-L did not increase significantly compared to

Con-L. If the flat slabs were subjected to the loss of interior columnscenario, the authors believe that more tensile membrane actioncould be developed due to the continuity of the slabs that providemore anchorage for CFRP strips to develop tensile force. At the end

Table 3. Test Results

Test

Firstyield loadPy (kN)

First peakcapacityPcu (kN)

Initialstiffness(kN=m)

Energyabsorption(kN · m)

Start todevelop tensilemembrane (mm)

MCHR intransverse

direction (kN)

MTHR intransverse

direction (kN)

Maximum tensilemembraneaction (kN)

Con-L 7.3 8.5 236.2 4.1 120.3 −4.5 6.0 17.3Con-M 11.6 14.3 393.2 6.3 131.3 −4.2 7.3 18.5SO-L 14.1 16.8 419.6 8.7 160.9 −7.5 6.0 22.3SO-M 17.0 21.3 524.7 8.8 181.5 −7.0 6.9 23.8SD-L 12.2 18.0 449.4 9.1 150.8 −7.6 9.2 22.5SD-M 18.3 22.5 476.2 6.4 171.5 −9.2 3.2 25.6

Note: MCHR = maximum compressive horizontal reaction force; MTHR = maximum tensile horizontal reaction force.

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

0 100 200 300 400 500Vertical Displacement (mm)

Ver

tical

Loa

d (k

N)

Con-LCon-MSO-LSO-MSD-LSD-MCon-L-HTCon-M-HTSO-L-HTSO-M-HTSD-L-HTSD-M-HT

Hor

izon

tal R

eact

ion

Forc

e (k

N)

HT=horizontal reaction force intransverse direction

Fig. 10. Vertical load versus vertical displacement of the testspecimens

muy

muxm

un

munt

Fig. 11. Upgrading of the bending moment resistance of the flat slab

Fig. 12. Failure mode of Specimen SO-L

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of the test, the CFRP sheets (Step 1 in Fig. 6) at the top slab near theadjacent columns as well as the CFRP sheets (Step 1 in Fig. 6) atthe bottom slab near the corner column were totally delaminated.The CFRP wrap (Step 2 in Fig. 6) in the adjacent columns fracturedat the end of the test.

The maximum strain measured in CFRP sheets near the cornercolumn and adjacent column were 0.06 and 0.08%, respectively(as shown in Fig. 14). They were only 6.0 and 8.0% of the rupturestrain of the CFRP-epoxy composite system. This was possiblydue to debonding of the CFRP sheets and the flexural failure sec-tion, which had shifted into the cutoff point of the CFRP sheets(Step 1 in Fig. 6). The maximum strain measured in CFRP stripsfor strengthening the center slab was 0.35%, which was only 35%of the rupture strain of the CFRP-epoxy composite system. Thiswas attributed to the debonding of the CFRP strips due to theabsence of fiber anchors or other mechanical anchors. As illus-trated in Table 3 and Fig. 10, the behavior of SO-L was very stiffcompared to that of control specimen Con-L. This specimenshowed an increase of 97.7% in the load capacity over the controlspecimen.

For SO-M, the global behavior of this specimen was similar tothat of SO-L (as shown in Fig. 13). The first crack formed in the topslab near the adjacent column was at a load of 14.4 kN, which wasmuch higher than SO-L. The delamination of CFRP sheets near theadjacent column of SO-M was not as severe as that in SO-L. How-ever, the punching failure at the slab-corner column connection of

SO-M was much more severe compared to SO-L. Limited punch-ing failure was observed in SO-L, possibly due to the CFRP L-wrap(Step 1 in Fig. 6) applied at the corner column, which increased theflexural strength of the slab and delayed the punching failure. Themaximum strain of the CFRP sheets and strips were 0.15 and0.49%, respectively. As shown in Table 3, the measured first peakcapacity of SO-M was 21.3 kN, which was 49.0% higher than tothe control specimen Con-M.

Behavior and Failure Modes of the SD SeriesSpecimens

The failure modes of SD-L and SD-M are shown in Figs. 15 and 16,respectively. For specimen SD-L, only the most significant discrep-ancies compared to specimen SO-L were emphasized in this paper.First, punching failure was observed at the top slab near the adja-cent columns because there are no CFRP strips applied there (asshown in Fig. 15). Second, severe diagonal cracks at the cutoffpoint of the central CFRP strips (Step 3 in Fig. 8) controlled thefailure of the specimen (as shown in Fig. 15). The maximum strainmeasured in the CFRP sheets for column strip strengthening was0.14%. Moreover, the maximum strain measured in the CFRP stripsfor central slab strengthening was 0.61%. This relatively largestrain could be utilized to explain the reason for higher performancein SD-L than in SO-L. SD-L increased the first peak capacity by111.8% compared to the control specimen Con-L.

Fig. 13. Failure mode of Specimen SO-M

-500

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250 300 350 400

Vertical displacement (mm)

Stra

in (

µε)

FC1FC2FC3FC4

-500

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3500

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

Stra

in (

µεµε) M1

M2M3M4M5M6M7M8M9M10M11M12

Fig. 14. Strain in CFRP laminates for Specimen SO-L

Fig. 15. Failure mode of Specimen SD-L

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For strengthened specimen SD-M, the main damage concen-trated in the diagonal crack at the cutoff point of the central CFRPstrips (Step 3 in Fig. 8) when the displacement reached 150 mm.Thus, no punching failure was observed in the top slab near theadjacent columns (as shown in Fig. 16). Moreover, the debondingof the CFRP sheets near the adjacent column and CFRP strips atthe center slab was much milder compared with SD-L. The maxi-mum strain of the CFRP sheets and strips were 0.27 and 0.29%,respectively. SD-M increased the first peak capacity by 57.3% com-pared to the control specimen Con-M.

Discussion

Vulnerability of the Test Specimens

Because progressive collapse is a dynamic phenomenon, it isnecessary to predict the dynamic ultimate strength of the testspecimens in order to accurately evaluate their vulnerability toprogressive collapse. GSA (2003) assumed the value of thedynamic increase factor (DIF) equals 2. However, Ruth et al.(2006) found that the upper bound of the DIF was 1.5 and 1.4for steel and RC moment-resisting frames, respectively. Qianand Li (2012a) experimentally determined the values of DIF tobe less than 1.38 for RC frames with force-controlled behavior.Thus, using the constant 2 to consider the dynamic effect of flatslabs would be too conservative, and thus the energy-based capac-ity curve method was utilized in this paper. Abruzzo et al. (2006)proposed using the capacity curve method to predict the dynamicultimate capacity of the test specimens based on the conservation ofenergy. After conducting a nonlinear pushdown analysis, the load-displacement curve of the structure can be obtained in which the areaunder this curve represents the strain energy in the structure. At themoment at which the system achieves a balanced condition, this in-ternal energy will be equal to the external work, defined as the prod-uct of the constant applied load (column axial force before damage)and the resulting displacement. If the system does not have adequateductility to dissipate the required energy, the internal and externalwork will never balance each other and it will result in a collapse.Thus, a capacity curve may be constructed by dividing the accumu-lated stored energy by its corresponding displacement. The accuracyof the capacity curve method had been validated by Tsai (2010).However, the dissipated energy due to damping was not consideredin this simplified mode. It is mathematically expressed as

PCCðudÞ ¼1

ud

Zud

0

PNSðuÞdu ð3Þ

where PCCðuÞ and PNSðuÞ = capacity function and nonlinear staticloading estimated at the displacement demand u, respectively.

Based on Eq. (3), the dynamic strengths of Con-L, Con-M,SO-L, SO-M, SD-L, and SD-M were determined as 10.0, 14.0,17.4, 20.7, 18.2, and 1.3 kN, respectively. As shown in Fig. 17,the capacity curve of the control specimen Con-L did not intersectwith the load curve (15.9 kN). This indicated that the new energybalance could not be achieved in Con-L after the removal of a cor-ner column. Thus, the control specimen Con-L was predicted tocollapse if the corner column was suddenly removed. After retro-fitting, the capacity curves of the strengthened specimens SO-L andSD-L intersected with the load curve at the displacements of 288.4and 205.0 mm, respectively. This means that SO-L and SD-Lwould not collapse because new energy balance could be achieved.However, as shown in Fig. 10, the tensile membrane action beganto develop at the displacements of 160.9 and 150.8 mm for SO-Land SD-L, respectively. Thus, for these two specimens, they wouldcollapse without the contributions of the tensile membrane action.Tensile membrane action developed in the flat slabs under the lossof a corner column should be further studied.

Similarly, as shown in Fig. 18, control specimen Con-M wouldcollapse while the strengthened specimens SO-M and SD-M wouldsurvive if the corner column was suddenly removed. For specimensSO-M and SD-M, new energy balance was achieved at the displace-ments of 74.2 and 61.2 mm, respectively, while the tensile mem-brane action began to develop at the displacements of 181.5 and171.5 mm, respectively. Thus, even without the aids of the tensilemembrane actions, these two specimens could survive forprogressive collapse. Moreover, as shown in Fig. 18, the dynamicultimate strength of SO-M and SD-M was much larger than thedesign axial force in the corner column (15.9 kN). Thus, afterstrengthening, the vulnerability of the control specimens forprogressive collapse was reduced significantly.

Effectiveness of the Strengthening Schemes

Specimens with a Light Amount of Slab Reinforcements:Con-L, SO-L, and SD-LAs shown in Table 3, the strengthened specimen SO-L had its firstpeak capacity, initial stiffness, peak tensile membrane action, anddynamic ultimate strength increased by 97.7, 77.6, 28.9, and

Fig. 16. Failure mode of Specimen SD-M

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Loa

d (k

N) Capacity curve SO-L

Load curve

Pushover curve of Con-L

Capacity curveCon-L

Capacity curve of SD-L

Fig. 17. Illustration of the capacity curves of specimens Con-L, SO-L,and SD-L

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74.0%, respectively, compared with the control specimen Con-L.However, for strengthened specimen SD-L, the first peak capacity,initial stiffness, peak tensile membrane action, and dynamicultimate strength were increased by 111.8, 90.3, 30.1, and82.0%, respectively. The initial stiffness was defined as the secantstiffness at the first yield strength in this study. Moreover, it isunderstandable that the survival of the structures subjected tothe scenario of the loss of a column is related to their ability todissipate the input energy. In this study, the definition of energydissipation is the area under the load-displacement curve of eachspecimen. Fig. 19 shows the energy dissipation capacity of the testspecimens. The dissipated energies of specimens Con-L, SO-L, andSD-L at the final stage of the test were 4.1, 8.7, and 9.1 kN·m,respectively. Thus, after strengthening, the energy dissipationcapacity of the flat slab could increase by up to 119.5%.

Comparing the performance of SD-L with that of SO-L, it canbe seen that SD-L generally performed slightly better than SO-L.This was possibly due to the central CFRP strips were placeddirectly perpendicular with the diagonal crack (along the principaltensile stress) in Scheme 2 (45–135°). As explained previously,theoretically Scheme 1 (0–90°) could increase the bending momentcapacity similar to Scheme 2 (45–135°). In reality, the interaction ofthe orthogonal strips could possibly jeopardize the effectiveness.

Specimens with a Medium Amount of Slab Reinforcements:Con-M, SO-M, and SD-MSimilar to the flat slabs with a light amount of slab reinforcement,the strengthened specimens SO-M and SD-M could significantlyimprove the global behavior of the control specimen Con-M to

mitigate progressive collapse. As shown in Table 3, the first peakcapacity, peak tensile membrane action, and dynamic ultimatestrength of SO-M were increased by 49.0, 28.6, and 47.9%, respec-tively. For SD-M, the first peak capacity, peak tensile membraneaction, and dynamic ultimate strength were increased by 57.3,38.4, and 52.1%, respectively. Moreover, the energy dissipationcapacity of SO-M and SD-M increased by 39.7 and 0.0%, respec-tively. Focusing on the resistance capacity, SD-M performed betterthan SO-M. However, SD-M could not upgrade the energydissipation capacity of the control specimen Con-M at all due tolocal failure concentrated in the cutoff point of the central CFRPstrips (Step 3 in Fig. 8) in SD-M. However, as the strengthenedspecimens had much higher compressive strength than the controlspecimens, the upgraded performance in the strengthened speci-mens should partially be attributed to the higher strength of con-crete. In reality, the effectiveness of the proposed strengtheningschemes might be slightly reduced if all specimens had similarmaterial properties.

Conclusions

Six one-third-scaled RC flat slabs were tested to investigate the ef-fectiveness of the proposed strengthening schemes in mitigating theprogressive collapse of the flat slabs. Several key points drawnfrom the tests are concluded as follows:• The control specimens Con-L and Con-M have a high likeli-

hood of developing progressive collapse following the suddenremoval of a corner column. Thus, more attention should bepaid to flat slabs during the evaluation of the RC structuresto mitigate progressive collapse.

• After strengthening, both Con-L and Con-M could survive pro-gressive collapse based on the experimental and analytical ana-lysis. However, the collapse was stopped at the tensilemembrane stage for the strengthened specimens SO-L andSD-L, while for strengthened specimens SO-M and SD-Mthe collapse stopped at the elastic region. Thus, the vulnerabilityof the SO-M and SD-M was lower than that of SO-L and SD-Lbecause the extent of the tensile membrane action in flat slabsunder the loss of a corner column is still under investigation.

• SO-L and SD-L could increase the dynamic ultimate strength ofCon-L by 74.0 and 82.0%, respectively. Moreover, SO-M andSD-M increased the dynamic ultimate strength of Con-M by47.9 and 52.1%, respectively. Thus, Scheme 2 (45–135°) per-formed slightly better as compared to Scheme 1 (0–90°) withrespect to resistance capacity. This can be attributed to the factthat the CFRP strips were directly perpendicular with the mainslab diagonal cracks in Scheme 2. However, for Scheme 1(0–90°), the CFRP strips in two directions worked togetherto resist the tensile principal stress of the slab diagonal cracks.The interaction of the perpendicular CFRP strips mightjeopardize the effectiveness. However, the difference in loadresistant capacity between the SO and SD series was small.Considering the ease of the application, deformation behavior,and ductility, the authors suggest using Scheme 1 (0–90°) inpractice.

• The failure of the strengthened specimens was mainly due todebonding of the CFRP laminates and severe cracks concen-trated in the cutoff point of the CFRP sheets and strips. To in-crease the effectiveness of strengthening, it is suggested thatfiber anchors or other mechanical anchors be applied to CFRPlaminates and to apply continual CFRP sheets (Step 1 in Fig. 6)for column strip retrofitting and continual central CFRP strips(Step 3 in Fig. 8) for central slab retrofitting in real practice.

0

5

10

15

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25

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Loa

d (k

N)

Capacity curve SO-MLoad curve

Pushover curve of Con-MCapacity curve

Con-M

Capacity curve of SD-M

Fig. 18. Illustration of the capacity curves of specimens Con-M,SO-M, and SD-M

0123456789

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Cum

ulat

ed e

nerg

y (k

N.m

) Con-LSO-LSD-LCon-MSO-MSD-M

Fig. 19. Illustration of the energy dissipation capacity of the testspecimens

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Future Works

More analytical and experimental studies should be conducted tostudy the strengthening efficiency of flat slab under the loss of aninterior or exterior column scenario due to tensile membrane actionis more significant for these scenarios. Moreover, further studies areneeded to investigate the performance of flat slabs when FRP lam-inates with better bonding by near surface mounted (NSM) or spikeanchors.

Acknowledgments

This research was made possible through the support of and col-laboration with FYFE Asia Private Limited in Singapore. The sig-nificant assistance from Jeslin Quek of FYFE Asia is gratefullyacknowledged.

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