ss

eaiProgressive collapseNonlinear analysis methodDynamic amplification factorGSA guidelines

(DAF). As the column-removed building is loaded into a significantly yielding phase, different assessedresults are obtained by the linear static method and the nonlinear acceptance criterion suggested bythe GSA guidelines. A DAF considering the inelastic dynamic effect may be needed in the GSA linearprocedure. The capacity curve constructed from the nonlinear static analysis is shown to be capable ofpredicting the progressive collapse resistance and the DAF of a column-removed RC building.

2008 Elsevier Ltd. All rights reserved.

1. Introduction

Many practicing engineers and academic researchers havebeen engaged in the prevention of progressive collapse sincethe partial collapse of the Ronan Point apartment building in1968. Especially after the malevolent bombing of the MurrahFederal Building in 1995, several changes to the philosophy andpractice of design for important buildings have been made inthe last decade. Resistance of building structures to progressivecollapse has been an important task for the development ofstructural design codes. Some study results, code approaches, anddesign strategies or standards have been reviewed, discussed,and/or compared in the literatures [17]. Generally speaking, theinvestigated issues include abnormal loading events, assessmentof loading, analysis methods, and design philosophy. In recentyears, the development of analysis methods for evaluating theprogressive collapse potential of an existing or new buildinghas been an imperative subject. Linear static, nonlinear static,linear dynamic, and nonlinear dynamic methods are four basicapproaches for the progressive collapse analysis. Advantagesand disadvantages of these approaches have been discussed byMarjanishvili and Agnew [8,9]. Detailed descriptions of a step-by-step, linear static procedure for progressive collapse analysis have

Corresponding author. Tel.: +886 8 7703202x7193.E-mail address:mhtsai@mail.npust.edu.tw (M.-H. Tsai).

been issued by the US General Service Administration (GSA) [10]and Department of Defense (DoD) [11]. The GSA linear staticanalysis approach has been applied to evaluate the potential ofa steel moment frame and a RC frame for progressive collapse[8,12].Terrorist events are quite few in the history of Taiwan.

Even so, the potential hazard of terrorist attacks always existsbecause of the trend of globalization. Since Taiwan is locatedin an earthquake-hazardous region, most of the RC buildingsare detailed according to the seismic design code. Some studiesindicated that seismic design detailing might help to enhancethe resistance of buildings against progressive collapse [1315].Hence, seismically designed RC buildings are expected to have lowpotential for progressive collapse. In this paper, the progressivecollapse potential of an earthquake-resistant RC building underfour threat-independent, column-removed conditions is evaluatedby using the GSA linear static analysis procedure. Nonlinear staticand dynamic analyses are carried out to verify the linear analysisresult and estimate the progressive collapse resistance for eachcolumn-removed condition. The catenary effect is neglected andonly the flexural failure mode is considered herein. Dynamic effecton the assessed results obtained from the linear or nonlinear staticmethod is discussed. Application of the nonlinear static methodto the estimation of the progressive collapse resistance and thedynamic amplification factor (DAF) of a column-removed buildingis proposed and demonstrated.Engineering Structures

Contents lists availa

Engineering

journal homepage: www.el

Investigation of progressive collapse resiearthquake-resistant RC building subjectMeng-Hao Tsai , Bing-Hui LinDepartment of Civil Engineering, National Pingtung University of Science and Technology,

a r t i c l e i n f o

Article history:Received 20 July 2007Received in revised form28 May 2008Accepted 30 May 2008Available online 21 July 2008

Keywords:

a b s t r a c t

Following the linear static a(GSA), the potential of anthis study. Nonlinear staticcollapse resistance of the budifferent collapse resistanceresistancemay be adopted foto a conservative estimation0141-0296/$ see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2008.05.03130 (2008) 36193628

ble at ScienceDirect

Structures

evier.com/locate/engstruct

tance and inelastic response for aned to column failure

No.1 Hseuh-Fu Road, Neipu, Pingtung 912, Taiwan

nalysis procedure recommended by the US General Service Administrationarthquake-resistant RC building for progressive collapse is evaluated innd nonlinear dynamic analyses are conducted to estimate the progressivelding subjected to column failure. Under an approximate deflection demand,s are obtained. It indicates that different criteria for estimating the collapser these two nonlinear analysis methods. The nonlinear static approach leadsfor the collapse resistance if 2.0 is used as the dynamic amplification factor

3620 M.-H. Tsai, B.-H. Lin / Engineering

Table 1Dimensions of RC member sections (cm)

Floor Column Beam Joist

1F 70 100 50 90 30 65, 20 502F11F 70 90 50 75 30 65, 20 50

2. Descriptions and modeling of the RC building

2.1. Descriptions

The RC building is an 11-storey, moment-resisting framestructurewith a 2-storey basement. Its first storey is an open spacefor the public. The center-to-center plan dimensions are 17.75m inlength and 12.25 m in width from the ground floor to the roof, asshown in Fig. 1. There are three bays with center-to-center spanlength arranged as 5.6 m, 6.55 m, and 5.6 m in the longitudinal(westeast) direction, and two bays with a 6.6 m and a 5.75 mspan in the transverse (northsouth) direction. The storey heightis 3.8 m for the first storey and 3.2 m for the others. In additionto the self weight, a dead load (DL) of 0.98 kN/m2 is applied tothe roof and 0.245 kN/m2 to other floors. The service live load(LL) is 4.91 kN/m2 for the roof and 1.96 kN/m2 for other floors.Conventionally, the structural design consultants in Taiwan uselarger imposed DL and LL on the roof to account for the loading ofspecial waterproof roofing and some accessory facilities (e.g. waterreservoir, ventilation system, etc.), respectively. Table 1 presentsthe section dimensions of the RC members for the building. Acompressive strength equal to 27 500 kN/m2 is used for theconcrete. The design yield strength is 412 000 kN/m2 for the mainreinforcements and 275 000 kN/m2 for the stirrups.The building is located at a soft soil site and its design spectral

response acceleration, SaD, is equal to 0.47g estimated at thefundamental period. All the beams and columns are designedand detailed according to seismic code requirements. The beammembers have at least three continuous #10 steel bars for the topand bottom reinforcement. As required by the seismic demand,more #10 top and bottom bars are provided and continuousthrough the column lines at the beamcolumn joints. The positivemoment strength at each joint face is larger than one half of thenegative moment strength at that face of the joint. Also, sum of thenominal flexural strengths of the columns framing into a joint is atleast 1.2 times larger than that of the beams framing into the joint.Hence, a strong column-weak beammechanismmay be ensured. Ifany interior column on the ground floor is removed, the two-spanbeam will redistribute loads to adjacent columns. Flexural hingesmay form at the two ends of the beams when they cannot resistthe instantaneous loading in an elastic manner. If the plastic hingestrength is insufficient to sustain the loading, the beam deflectionwill further increase to mobilize catenary tensile action, which isthe final protection against collapse.

2.2. Structural modeling

A beamcolumn framemodel is constructed for the RC buildingusing the SAP2000 commercial program [16]. The model isassumed to be fixed on the ground. Self weight of the exteriorwallsis distributed to the spandrel beams. Also, selfweight of the interiorwalls and partitions is estimated and applied to the floor slab asa distributed load. Thereafter, according to the tributary area, selfweight of the slab and all the dead loads and live load on it aredistributed to the beam elements for each floor. The fundamentalperiod of the building model is equal to 1.35 and 1.34 s in thelongitudinal and transverse direction, respectively.

The reinforcement disposition of each member section is

simulated based on the design drawings of the RC building. ThereStructures 30 (2008) 36193628

are twenty types of reinforcement disposition and nine differentspacing of shear stirrup for all beam sections. The nominalmomentand shear strength vary from 620 kN m to 1460 kN m and730 kN to 920 kN, respectively, for the beam members. Flexuralplastic hinges are assigned to both ends of beam elements. Defaultmoment-hinge properties based on the FEMA-273 guidelines [17]are adopted for the hinge model. Different performance levelsare represented by circular symbols with different shadows, asshown in Fig. 2. Although, as recommended by the GSA guidelines,strength increase factors for material properties may be used inthe analysis, they are not considered in this study. Preliminarystudies [18] indicated that collapse of the RC building undercolumn-removed conditions is governed by the flexural failuremode of beam elements. Also, the columnmembers remain elasticeven when the ultimate moment capacities of the connectedbeam sections have been developed. Hence, shear failure is notconsidered and the column members are assumed to be elastic inthis study.

3. Progressive collapse potential

3.1. Loading and criterion

A downward loading combination

Pst = 2(DL+ 0.25LL) (1)recommended by the GSA guidelines is adopted for the linear staticanalysis. DL includes the structural weight and additional deadloads. Pst is defined as the GSA loading herein. In the linear staticanalysis, the GSA loading is applied to the RC building subjectedto column failure, and the demand-to-capacity ratio (DCR) offlexural moment is calculated to assess the progressive collapsepotential. Since the building has a typical structural configuration,the acceptance criterion for the primary structural components isDCR 2.0.When the DCR value is larger than 2.0, a hinge has to beinserted to themember end for releasing themoment. For dynamicanalysis, the DAF, 2, in Eq. (1) is omitted and the downwardloading is changed to

Pdy = (DL+ 0.25LL). (2)

3.2. Collapse potential

Four threat-independent, column-removed conditions, desig-nated as Case 1B, Case 2A, Case 1A, and Case 2B, are consideredfor the building. According to the bay line numbers shown inFig. 1, the removed column of the first storey is 1B, 2A, 1A, and2B for Case 1B, 2A, 1A, and 2B, respectively. Linear static, non-linear static and nonlinear dynamic analyses are carried out toinvestigate the column failure responses of the building. 5% inher-ent damping ratio is assumed for the dynamic analysis. Similar tothe results observed by Sucuoglu et al. [19], most of the down-ward loading originally sustained by the failed column is trans-ferred to the plane frames intersecting at the line of the failedcolumn. Therefore, the DCR values, plastic hinge distribution, anddeflection of those intersected frames are the major concerns inthis paper.Fig. 3a shows the DCR values and the plastic hinges obtained

from the GSA linear static and nonlinear static analysis for Case 1B,respectively. Force-controlledmethodwith force magnitude equalto the GSA loading (Pst) is used for the nonlinear static analyses.Moment distribution of the linear static analysis is presented inFig. 3b. Because of different local axis definitions, the columnmoments are not displayed for the BB frame. It is seen that there

is no DCR value larger than 2. The column-removed building haslow potential for progressive collapse and no moment-released

Fig. 2. The plastic hinge model.

hinge has to be inserted to any member. However, the nonlinearstatic analysis results show several plastic hinges occurred atthe member ends. Similar result is observed from the nonlineardynamic analysis, as shown in Fig. 3c.Based on the performance levels in Fig. 2, the plastic hinges in

Figs. 3a and 3c are classified as immediate occupancy under theGSA loading. It is observed that a DCR value close to or larger than1.0will lead to the formation of a plastic hinge. This implies that theGSA guidelines permit certain flexural ductility to be developed.Similar results are obtained for Case 2A, 1A, and 2B, which arenot shown here. Table 2 summarizes the maximum deflection atthe column-removed point for those four conditions. Approximate

Table 2Maximum deflection under the GSA loading (cm)

Method Case 1B Case 2A Case 1A Case 2B

Elastic static 1.88 1.61 2.11 1.73Nonlinear static 2.15 1.64 2.25 1.82Nonlinear dynamic 1.94 1.56 1.83 1.82

4. Progressive collapse resistance

As expected, onlyminor damage is induced under theGSA staticloading for the earthquake-resistant RC building. The progressiveFig. 1. Plan dimensions of the building.M.-H. Tsai, B.-H. Lin / Engineeringdeflections confirm their insignificantly yielding behavior underthe GSA loading.Structures 30 (2008) 36193628 3621collapse resistance, which is defined as the ultimate downwardloading capacity of the column-removed building, is further

rFig. 3b. Elastic moment distribution for Case 1B.

estimated using the nonlinear static and the incremental dynamicanalysis method.

4.1. Nonlinear static method

Displacement-controlled procedure with a maximum deflec-tion of 20 cm is used to investigate the collapse resistance of thecolumn-removed building. Fig. 4 shows the loaddisplacementresponses of those four column-removed conditions. The ordi-nate represents the exerted loading in terms of the percentage of

static analysis, incremental dynamic analysis is carried out to ver-ify the ultimate loading capacities.

4.2. Nonlinear dynamic method

A series of nonlinear time history analyses under differentdynamic loadings are conducted. A step function multiplied by(DL + 0.25LL) is used to simulate the dynamic loading appliedto the column-removed building. The magnitude of the stepfunction is increased gradually till extremely large deflectionoccurs at the column-removed point. P effect and largedisplacement are considered in the nonlinear dynamic analysis.Typical displacement time histories under (DL + 0.25LL) and2(DL + 0.25LL) for Case 1B are shown in Fig. 5. The peakdisplacement response of each time history is collected toconstruct the loaddisplacement envelopes for the incrementaldynamic analysis, as shown in Fig. 6. It is seen that the ultimateloading capacities are developed at the deflections approximatedto that obtained from the nonlinear static analysis. This is due tothe fact that identical plastic hinge models are adopted for thenonlinear static and nonlinear dynamic analyses. The estimatedcollapse resistance is about 2.15Pdy, 2.75Pdy, 2.4Pdy, and 2.4Pdy,respectively for Case 1B, 2A, 1A, and 2B. Table 3 summarizes theprogressive collapse resistance obtained from the nonlinear staticand nonlinear dynamic analyses.

4.3. Dynamic amplification factor

From Table 3, it is seen that larger loading capacities are3622 M.-H. Tsai, B.-H. Lin / Engineering

Fig. 3a. DCR values and nonlinea(DL + 0.25LL), while the abscissa represents the deflection at thecolumn-removed point. The loaddisplacement responses underStructures 30 (2008) 36193628

static plastic hinges for Case 1B.

the GSA loading are also marked with symbols in the figure. If ex-pressed as a multiplier of 2(DL + 0.25LL), the maximum loadingcapacity is equal to 1.25Pst , 1.62Pst , 1.39Pst , and 1.39Pst for Case 1B,2A, 1A, and2B, respectively. It is realized that Case 1Bhas the small-est progressive collapse resistance as compared to others. How-ever, since the dynamic effect is not considered in the nonlinearobtained from the nonlinear static analysis than from the nonlineardynamic analysis. This difference may be attributed to the

dFig. 4. Loaddisplacement curves from the nonlinear static analyses.

dynamic effect. The DAF is usually defined as the ratio of thedynamic displacement response (dy) of an elastic single-degree-of-freedom (SDOF) system to its static displacement response (st)under an equal applied load. This displacement-based definitionresults in a larger DAF than 2.0 for elasticplastic systems [2022].Considerst = Pst/kst anddy = Pdy/kdy,st = dy leads toDAF = kst/kdy = Pst/Pdy (3)where Pst and Pdy are, respectively, the required static and

Fig. 5. Typical displacement time histories for Case 1B.

respectively. Hence, the DAF may be expressed as the ratio ofthe static force response to the dynamic force response under anequal displacement demand, as explained by Fig. 7. Based on thisforce-based definition, the DAFs for those four column-removedconditions are obtained as shown in Fig. 8. It is seen that the DAFdecreases with increasing displacement of the column-removedpoint. As shown in Table 3, under the displacement demand of theultimate loading, the DAFmay decrease to 1.16, which is similar tothat indicated by Ruth et al. [23]. This reflects that, based on a DAFof 2, the displacement-controlled, nonlinear static analysismethodTable 3Loaddisplacement response and DAF for collapse resistance

Method Case 1B Case 2A Case 1A Case 2B

Nonlinear static (2.50, 12.84)a (3.24, 12.92) (2.78, 12.13) (2.78, 12.82)Nonlinear dynamic (2.15, 12.33) (2.75, 12.30) (2.4, 12.61) (2.4, 12.51)DAF 1.16 1.18 1.16 1.16a Loading multiplier of (DL+ 0.25LL), deflection in cm.M.-H. Tsai, B.-H. Lin / Engineering

Fig. 3c. DCR values and nonlineardynamic force under the same deflection. kst and kdy representthe equivalent static and dynamic stiffness of the SDOF system,Structures 30 (2008) 36193628 3623

ynamic plastic hinges for Case 1B.may lead to a conservative estimation of progressive collapseresistance for a column-removed building.

3624 M.-H. Tsai, B.-H. Lin / Engineering

Fig. 6. Loaddisplacement curves from the incremental dynamic analyses.

Fig. 7. Diagrammatic explanation of the dynamic amplification factor.

Fig. 8. Variation of the DAF for the column-removed conditions.

5. Comparison of inelastic responses

In the GSA linear static procedure, beam sections with DCRslarger than 2.0 are replaced with inserted hinges to simulatethe inelastic response of the column-removed building under

vertical downward loadings. This implies that elasticperfectlyplastic models are assumed for the inserted hinges. In this section,Structures 30 (2008) 36193628

the ability of the GSA linear static procedure for capturing thenonlinear static behavior in the significantly yielding phase isexamined. Also, application of theDAF 2.0 to the GSA linear staticanalysis for a significantly yielding building is evaluated.

5.1. Nonlinear static maximum loading

The GSA linear static analyses are performed for the column-removed building subjected to the maximum loadings estimatedby the nonlinear static method. According to the GSA guidelines,moments of the member ends with DCR > 2.0 are releasedand the linear static analysis is repeated until no DCR value islarger than 2. Fig. 9a shows the final DCR values and static plastichinges for Case 1B, where only three DCR values are larger than2. Performance levels of the plastic hinges are presented by theshading of the hinge circles. There are three moment-releasedhinges at the final run of the linear static analysis. However, asignificantly yielding mechanism is observed from the nonlinearstatic analysis. The maximum deflection obtained from the GSAlinear procedure is 2.6 cm, which is less than 12.84 cm from thenonlinear static analysis. Similar phenomena are revealed by othercolumn-removed conditions, as shown in Figs. 9b9d. The linearstatic approach fails to simulate the nonlinear static response inthe significantly yielding phase.

5.2. Nonlinear dynamic maximum loading

A hinge rotation angle equal to 6 is recommended as thenonlinear acceptance criterion for RC beams in the GSA guidelines.According to the hinge model adopted in this study, all the plastichinge rotation angles are far less than the allowable value underthe nonlinear dynamicmaximum loadings. Thus, based on the GSAnonlinear criterion, progressive collapse may be limited for thefour column-removed conditions.Based on a DAF of 2, the dynamically determined maximum

loadings are doubled to conduct the GSA linear static analyses.This means that the multiplier of the loading combination (DL +0.25LL) is increased to 4.3, 5.5, 4.8, and 4.8, respectively forCase 1B, 2A, 1A, and 2B. Contrary to the result assessed bythe GSA nonlinear acceptance criterion, progressive collapseoccurs for all four conditions. According to the criterion ofremoving failed members (three-hinges failure mechanism), allthose adjacent bays interconnected at the column-removed linecollapse progressively. Fig. 10 shows the final DCR values and theplastic hinges, respectively, obtained from theGSA linear static andthe nonlinear dynamic analysis for Case 1B. The plastic hinges areclassified as life safety by the hingemodel. Therefore, a discrepancybetween the results assessed by the GSA linear static method andby its nonlinear acceptance criterion may arise under an extremedownward loading. The DAF of 2 appears to be invalid as the RCbuilding undergoes significantly yielding behavior.

6. Prediction of the collapse resistance

Nonlinear incremental dynamic analysis is usually a promisingmethod for estimating the progressive collapse resistance. Never-theless, it is time-consuming to perform the incremental dynamicanalysis for the maximum loading capacity. As a consequence, anefficient approach may be needed to predict the progressive col-lapse resistance precisely.The area below the nonlinear static loaddisplacement curverepresents the absorbed energy of the building subjected tothe downward loading. A capacity curve may be constructed

Fig. 9b. DCR values and static plastic hinges for Case 2A under 3.24(DL+ 0.25LL).

by dividing the accumulated stored energy by its correspondingdisplacement [12]. It is mathematically expressed as

PCC (ud) = 1ud ud0PNS(u)du (4)

where PCC (u) and PNS(u) are, respectively, the capacity functionand the nonlinear static loading estimated at the displacementdemand u. Hence, the capacity curve of the column-removed

the corresponding displacement of the column-removed point.Figs. 11a11d show the capacity curves of those four conditionsalong with the associated nonlinear static and incrementaldynamic loaddisplacement curves. It is observed that thecapacity curve approximately coincides with the variation ofthe incremental dynamic curve up to the maximum loadingcapacity. Therefore, the capacity curve may be used to predictthe progressive collapse resistance of the column-removedFig. 9a. DCR values and static plastic hinges for Case 1B under 2.5(DL+ 0.25LL).M.-H. Tsai, B.-H. Lin / Engineeringbuilding is numerically obtained from dividing the accumulatedarea under the nonlinear static loaddisplacement curve byStructures 30 (2008) 36193628 3625building. The predicted collapse resistances are determined by themaximum value of the capacity curve and summarized in Table 4.

Fig. 9d. DCR values and static plastic hinges for Case 2B under 2.78(DL+ 0.25LL).

It is seen that the estimated values agree well with those obtainedfrom the incremental dynamic analyses. Meanwhile, the DAF maybe estimated from dividing the nonlinear static loaddisplacementcurve by the corresponding capacity curve up to the maximumloading, as shown in Fig. 12.

7. Conclusions

Table 4Predicted maximum loadings

Case Multiplier of (DL+ 0.25LL)1B 2.162A 2.781A 2.382B 2.40Fig. 9c. DCR values and static plastic hinges for Case 1A under 2.78(DL+ 0.25LL).3626 M.-H. Tsai, B.-H. Lin / EngineeringThe vulnerability of an earthquake-resistant RC building toprogressive collapse is evaluated in this study. According to theStructures 30 (2008) 36193628GSA linear static analysis approach, the building has a lowpotentialfor progressive collapse. Nonlinear analysis results reveal that

Fig. 11a. The capacity curve of Case 1B.

Fig. 11b. The capacity curve of Case 2A.

Fig. 11c. The capacity curve of Case 1A.

Fig. 11d. The capacity curve of Case 2B.M.-H. Tsai, B.-H. Lin / Engineering

Fig. 10. DCR values and dynamic plastic hinges for Case 1B under Pdythe flexural ductility of beam members may be developed tosome extent in the GSA linear static analysis procedure. Moreover,Structures 30 (2008) 36193628 3627

2.15(DL+ 0.25LL). The dash lines represent the collapsed members.different progressive collapse resistances are obtained by thenonlinear static and the incremental dynamic method. Different

3628 M.-H. Tsai, B.-H. Lin / Engineering

Fig. 12. Estimated DAF from the capacity curves.

acceptance criteria for determining the collapse resistance maybe adopted for these two methods. The nonlinear static analysisgives a conservative estimation for the collapse resistance if thedynamic amplification factor (DAF) is equal to 2.0. Based on aforce-based definition, the DAF is less than 2.0 as the flexuralductility is developed. Also, the linear static analysis procedureand the nonlinear acceptance criterion suggested by the GSAguidelines may have different evaluation results as the column-removed building is loaded into significantly yielding phase. Underthis condition, a different DAF from 2.0 is needed for the GSAloading combination to account for the inelastic dynamic effect.The capacity curve constructed from the nonlinear static analysisis shown to be capable of predicting the progressive collapseresistance and the DAF for a RC building subjected to columnfailure.

Acknowledgments

The writers wish to express their sincere appreciation to thereviewers for very constructive comments. The study presented inthis paperwas supported by theNational ScienceCouncil of Taiwanunder Grants NSC 95-2221-E-020-035. The support is gratefullyacknowledged.

References

[1] Mohamed OA. Progressive collapse of structures: Annotated bibliography andcomparison of codes and standards. J Perform Constr Fac 2006;20(4):41825.

[2] Nair RS. Preventing disproportionate collapse. J Perform Constr Fac 2006;20(4):30914.Structures 30 (2008) 36193628

[3] Ellingwood BR. Mitigating risk from abnormal loads and progressive collapse.J Perform Constr Fac 2006;20(4):31523.

[4] Dusenberry DO. Review of existing guidelines and provisions related toprogressive collapse. In: Workshop on prevention of progressive collapse.Washington (DC): National Institute of Building Sciences; 2002.

[5] Ellingwood BR, Smilowitz R, Dusenberry DO, Duthinh D, Lew HS, Carino NJ.Best practices for reducing the potential for progressive collapse in buildings.Report no. NISTIR-7396. National Institute of Standards and Technology,Technology Administration, US Department of Commerce; 2007.

[6] Starossek U. Progressive collapse of structures: Nomenclature and procedures.IABSE, Structural Engineering International 2006;16(2):1137.

[7] Starossek U, Wolff M. Progressive collapse: Design strategies. In: IABSEsymposium, structures and extreme events. 2005.

[8] Marjanishvili SM. Progressive analysis procedure for progressive collapse. JPerform Constr Fac ASCE 2004;18(2):7985.

[9] Marjanishvili S, Agnew E. Comparison of various procedures for progressivecollapse analysis. J Perform Constr Fac ASCE 2006;20(4):36574.

[10] GSA, Progressive collapse analysis and design guidelines for new federal officebuildings and major modernization projects. General Service Administration.2003.

[11] Department of Defense (DoD) Unified facilities criteria (UFC): Design ofbuildings to resist progressive collapse, UFC 4-023-03, U. S. DoD. 2005.

[12] Abruzzo J, Matta A, Panariello G. Study of mitigation strategies for progressivecollapse of a reinforced concrete commercial building. J Perform Constr FacASCE 2006;20(4):38490.

[13] Corley WG. Applicability of seismic design in mitigating progressive collapse.In: Proceedings of workshop on prevention of progressive collapse. Washing-ton (DC): National Institute of Building Sciences; 2002.

[14] CorleyWG,Mlakar Sr PF, SozenMA, ThorntonCH. TheOklahoma city bombing:Summary and recommendations for multihazard mitigation. J Perform ConstrFac 1998;12(3):10012.

[15] Hayes Jr JR, Woodson SC, Pekelnicky RG, Poland CD, Corley WG, Sozen M.Can strengthening for earthquake improve blast and progressive collapseresistance?. J Struct Eng, ASCE 2005;131(8):115777.

[16] SAP2000 rVersion 8.0. Linear and nonlinear static and dynamic analysis anddesign of three-dimensional structures. Berkeley (CA, USA): Computers andStructures Inc.; 2002.

[17] FEMA. NEHRP guidelines for the seismic rehabilitation of buildings (FEMAPublication 273). Washington (DC): Federal Emergency Management Agency;1997.

[18] Lin BH. Progressive collapse analysis and evaluation of an earthquake-resistantRC building. Master thesis. Taiwan: Department of Civil Engineering, NationalPingtung University of Science and Technology: 2007.

[19] SucuogluH, Citipitioglu E, Altin S. Resistancemechanisms in rc building framessubjected to column failure. J Struct Eng ASCE 1994;120(3):76582.

[20] Kaewkulchai G, Williamson EB. Beam element formulation and solutionprocedure for dynamic progressive collapse analysis. Comput Struct 2004;82:63951.

[21] Kaewkulchai G, Williamson EB. Dynamic behavior of planar frame duringprogressive collapse. In: 16th ASCE engineering mechanics conference. 2003.

[22] Pretlove AJ, Ramsden M, Atkins AG. Dynamic effects in progressive failure ofstructures. Int J Impact Eng 1991;11(4):53946.

[23] Ruth P, Marchand KA, Williamson EB. Static equivalency in progressivecollapse alternate path analysis: Reducing conservatism while retainingstructural integrity. J Perform Constr Fac 2006;20(4):34964.

Investigation of progressive collapse resistance and inelastic response for an earthquake-resistant RC building subjected to column failureIntroductionDescriptions and modeling of the RC buildingDescriptionsStructural modeling

Progressive collapse potentialLoading and criterionCollapse potential

Progressive collapse resistanceNonlinear static methodNonlinear dynamic methodDynamic amplification factor

Comparison of inelastic responsesNonlinear static maximum loadingNonlinear dynamic maximum loading

Prediction of the collapse resistanceConclusionsAcknowledgmentsReferences