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Engineering Structures 30 (2008) 3619–3628

Contents lists available at ScienceDirect

Engineering Structures

 journal homepage: www.elsevier.com/locate/engstruct

Investigation of progressive collapse resistance and inelastic response for anearthquake-resistant RC building subjected to column failure

Meng-Hao Tsai ∗, Bing-Hui LinDepartment of Civil Engineering, National Pingtung University of Science and Technology, No.1 Hseuh-Fu Road, Neipu, Pingtung 912, Taiwan

a r t i c l e i n f o

 Article history:

Received 20 July 2007Received in revised form

28 May 2008

Accepted 30 May 2008

Available online 21 July 2008

Keywords:

Progressive collapse

Nonlinear analysis method

Dynamic amplification factor

GSA guidelines

a b s t r a c t

Following the linear static analysis procedure recommended by the US General Service Administration

(GSA), the potential of an earthquake-resistant RC building for progressive collapse is evaluated inthis study. Nonlinear static and nonlinear dynamic analyses are conducted to estimate the progressivecollapse resistance of the building subjected to columnfailure. Under an approximate deflection demand,

different collapse resistances are obtained. It indicates that different criteria for estimating the collapseresistancemay be adopted forthese twononlinear analysis methods. Thenonlinear static approach leads

to a conservativeestimation forthe collapse resistance if ‘‘2.0’’ is used as thedynamicamplification factor(DAF). As the column-removed building is loaded into a significantly yielding phase, different assessed

results 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 linear

procedure. The capacity curve constructed from the nonlinear static analysis is shown to be capable of predicting 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 have

been engaged in the prevention of progressive collapse since

the partial collapse of the Ronan Point apartment building in

1968. Especially after the malevolent bombing of the Murrah

Federal Building in 1995, several changes to the philosophy and

practice of design for important buildings have been made in

the last decade. Resistance of building structures to progressive

collapse has been an important task for the development of 

structural design codes. Some study results, code approaches, and

design strategies or standards have been reviewed, discussed,

and/or compared in the literatures [1–7]. Generally speaking, the

investigated issues include abnormal loading events, assessment

of loading, analysis methods, and design philosophy. In recentyears, the development of analysis methods for evaluating the

progressive collapse potential of an existing or new building

has been an imperative subject. Linear static, nonlinear static,

linear dynamic, and nonlinear dynamic methods are four basic

approaches for the progressive collapse analysis. Advantages

and disadvantages of these approaches have been discussed by

Marjanishvili 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 static

analysis approach has been applied to evaluate the potential of 

a 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 exists

because of the trend of globalization. Since Taiwan is located

in an earthquake-hazardous region, most of the RC buildings

are detailed according to the seismic design code. Some studies

indicated that seismic design detailing might help to enhance

the resistance of buildings against progressive collapse  [13–15].

Hence, seismically designed RC buildings are expected to have low

potential for progressive collapse. In this paper, the progressive

collapse potential of an earthquake-resistant RC building under

four threat-independent, column-removed conditions is evaluated

by using the GSA linear static analysis procedure. Nonlinear static

and dynamic analyses are carried out to verify the linear analysis

result and estimate the progressive collapse resistance for each

column-removed condition. The catenary effect is neglected and

only the flexural failure mode is considered herein. Dynamic effect

on the assessed results obtained from the linear or nonlinear static

method is discussed. Application of the nonlinear static method

to the estimation of the progressive collapse resistance and the

dynamic amplification factor (DAF) of a column-removed building

is proposed and demonstrated.

0141-0296/$ – see front matter© 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2008.05.031

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 Table 1

Dimensions of RC member sections (cm)

Floor Column Beam Joist

1F 70× 100 50× 90 30× 65, 20× 50

2F–11F 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 frame

structure with a 2-storey basement. Its first storey is an open spacefor the public. The center-to-center plan dimensions are17.75 m inlength and 12.25 m in width from the ground floor to the roof, as

shown 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(west–east) direction, and two bays with a 6.6 m and a 5.75 m

span in the transverse (north–south) direction. The storey heightis 3.8 m for the first storey and 3.2 m for the others. In addition

to 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 of special waterproof roofing and some accessoryfacilities (e.g. water

reservoir, 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 the

concrete. 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 spectralresponse acceleration,   S aD , is equal to 0.47 g   estimated at thefundamental period. All the beams and columns are designed

and detailed according to seismic code requirements. The beammembers have at least three continuous #10 steel bars for the top

and bottom reinforcement. As required by the seismic demand,more #10 top and bottom bars are provided and continuousthrough the column lines at the beam–column joints. The positivemoment strength at each joint face is larger than one half of the

negative 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 beam mechanism may be ensured. If any interior column on the ground floor is removed, the two-span

beam 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 hinge

strength is insufficient to sustain the loading, the beam deflectionwill further increase to mobilize catenary tensile action, which is

the final protection against collapse.

2.2. Structural modeling 

A beam–column frame model is constructed for the RC buildingusing the SAP2000 commercial program [16]. The model isassumed to be fixed onthe ground. Selfweight ofthe exterior walls

is distributed to thespandrel beams.Also,self weightof theinteriorwalls and partitions is estimated and applied to the floor slab asa distributed load. Thereafter, according to the tributary area, self 

weight 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 the

longitudinal and transverse direction, respectively.

The reinforcement disposition of each member section issimulated based on the design drawings of the RC building. There

are twenty types of reinforcement disposition and nine differentspacing of shear stirrupfor allbeam sections.The nominal momentand 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 column members 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

P st  = 2(DL + 0.25LL )   (1)

recommended by the GSA guidelines is adopted forthe linearstaticanalysis. DL includes the structural weight and additional deadloads. P st  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) of flexural 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 islarger than2.0, a hinge has tobeinserted to the member end forreleasing the moment.For dynamic

analysis, the DAF, ‘‘2’’, in Eq.   (1)   is omitted and the downwardloading is changed to

P dy  = (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 obtainedfrom theGSA linear static and nonlinear staticanalysis for Case 1B,respectively. Force-controlled method with force magnitude equalto the GSA loading  (P st )  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 B–B 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

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Fig. 1.   Plan dimensions of the building.

Fig. 2.   The plastic hinge model.

hinge has to be inserted to any member. However, the nonlinear

static analysis results show several plastic hinges occurred at

the member ends. Similar result is observed from the nonlinear

dynamic 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 the

GSA loading. It is observed that a DCR value close to or larger than

1.0will lead to the formationof a plastic hinge.This implies that the

GSA guidelines permit certain flexural ductility to be developed.

Similar results are obtained for Case 2A, 1A, and 2B, which are

not shown here. Table 2 summarizes the maximum deflection at

the column-removed point for those four conditions. Approximate

deflections confirm their insignificantly yielding behavior under

the GSA loading.

 Table 2

Maximum deflection under the GSA loading (cm)

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

Elastic static 1.88 1.61 2.11 1.73

Nonlinear static 2.15 1.64 2.25 1.82Nonlinear dynamic 1.94 1.56 1.83 1.82

4. Progressive collapse resistance

As expected, only minor damageis induced under theGSA static

loading for the earthquake-resistant RC building. The progressive

collapse resistance, which is defined as the ultimate downwardloading capacity of the column-removed building, is further

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Fig. 3a.   DCR values and nonlinear static plastic hinges for Case 1B.

Fig. 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 the

column-removed building.   Fig. 4  shows the load–displacementresponses of those four column-removed conditions. The ordi-nate represents the exerted loading in terms of the percentage of 

(DL + 0.25LL ), while the abscissa represents the deflection at thecolumn-removed point. The load–displacement responses under

the GSA loading are also marked with symbols in the figure. If ex-pressed as a multiplier of 2(DL + 0.25LL ), the maximum loadingcapacityis equal to 1.25P st , 1.62P st , 1.39P st ,and1.39P st   for Case 1B,2A,1A, and2B, respectively. It is realized thatCase1B hasthe small-est progressive collapse resistance as compared to others. How-ever, since the dynamic effect is not considered in the nonlinearstatic 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 to

construct the load–displacement 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 2.15P dy, 2.75P dy , 2.4P dy, and 2.4P dy ,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 are

obtained from the nonlinearstaticanalysisthan from the nonlineardynamic analysis. This difference may be attributed to the

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Fig. 3c.   DCR values and nonlinear dynamic plastic hinges for Case 1B.

 Table 3

Load–displacement 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 1.16

a Loading multiplier of  (DL + 0.25LL ), deflection in cm.

Fig. 4.   Load–displacement curves from the nonlinear static analyses.

dynamic effect. The DAF is usually defined as the ratio of the

dynamic displacement response (∆dy) of an elastic single-degree-

of-freedom (SDOF)system to its staticdisplacement response(∆st )

under an equal applied load. This displacement-based definition

results in a larger DAF than 2.0 for elastic–plastic systems  [20–22].

Consider ∆st  = P st /kst  and  ∆dy  = P dy/kdy, ∆st  = ∆dy  leads to

DAF = kst /kdy  = P st /P dy   (3)

where   P st    and   P dy   are, respectively, the required static and

dynamic force under the same deflection.   kst   and   kdy   representthe equivalent static and dynamic stiffness of the SDOF system,

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

respectively. Hence, the DAF may be expressed as the ratio of the 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, theDAF may 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 analysis methodmay lead to a conservative estimation of progressive collapseresistance for a column-removed building.

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Fig. 6.   Load–displacement 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 DCRs

larger than 2.0 are replaced with inserted hinges to simulatethe inelastic response of the column-removed building under

vertical downward loadings. This implies that elastic–perfectlyplastic models are assumed for the inserted hinges. In this section,

the ability of the GSA linear static procedure for capturing the

nonlinear static behavior in the significantly yielding phase is

examined. Also, application of the DAF‘‘2.0’’ to the GSAlinearstatic

analysis 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 estimated

by the nonlinear static method. According to the GSA guidelines,

moments of the member ends with DCR    >   2.0 are released

and the linear static analysis is repeated until no DCR value is

larger than 2. Fig. 9a shows the final DCR values and static plastic

hinges for Case 1B, where only three DCR values are larger than

2. Performance levels of the plastic hinges are presented by the

shading of the hinge circles. There are three moment-released

hinges at the final run of the linear static analysis. However, a

significantly yielding mechanism is observed from the nonlinear

static analysis. The maximum deflection obtained from the GSA

linear procedure is 2.6 cm, which is less than 12.84 cm from the

nonlinear static analysis. Similar phenomena are revealed by other

column-removed conditions, as shown in Figs. 9b–9d. The linearstatic approach fails to simulate the nonlinear static response in

the significantly yielding phase.

5.2. Nonlinear dynamic maximum loading 

A hinge rotation angle equal to 6◦ is recommended as the

nonlinear acceptance criterion for RC beams in the GSA guidelines.

According to the hinge model adopted in this study, all the plastic

hinge rotation angles are far less than the allowable value under

the nonlinear dynamic maximum loadings. Thus, based on the GSA

nonlinear criterion, progressive collapse may be limited for the

four column-removed conditions.

Based on a DAF of 2, the dynamically determined maximumloadings 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 for

Case 1B, 2A, 1A, and 2B. Contrary to the result assessed by

the GSA nonlinear acceptance criterion, progressive collapse

occurs for all four conditions. According to the criterion of 

removing failed members (three-hinges failure mechanism), all

those adjacent bays interconnected at the column-removed line

collapse progressively. Fig. 10 shows the final DCR values and the

plastic hinges, respectively, obtained from the GSAlinear staticand

the nonlinear dynamic analysis for Case 1B. The plastic hinges are

classified as life safetyby the hinge model.Therefore, a discrepancy

between the results assessed by the GSA linear static method and

by its nonlinear acceptance criterion may arise under an extremedownward loading. The DAF of ‘‘2’’ appears to be invalid as the RC

building undergoes significantly yielding behavior.

6. Prediction of the collapse resistance

Nonlinear incremental dynamic analysis is usually a promising

method for estimating the progressive collapse resistance. Never-

theless, it is time-consuming to perform the incremental dynamic

analysis for the maximum loading capacity. As a consequence, an

efficient approach may be needed to predict the progressive col-

lapse resistance precisely.

The area below the nonlinear static load–displacement curve

represents the absorbed energy of the building subjected tothe downward loading. A capacity curve may be constructed

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Fig. 9a.   DCR values and static plastic hinges for Case 1B under 2.5(DL + 0.25LL ).

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

P CC (ud) =1

ud

   ud

0

P NS (u)du   (4)

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

building is numerically obtained from dividing the accumulatedarea under the nonlinear static load–displacement curve by

the corresponding displacement of the column-removed point.

Figs. 11a–11d show the capacity curves of those four conditions

along with the associated nonlinear static and incremental

dynamic load–displacement curves. It is observed that the

capacity curve approximately coincides with the variation of 

the incremental dynamic curve up to the maximum loading

capacity. Therefore, the capacity curve may be used to predict

the progressive collapse resistance of the column-removed

building. The predicted collapse resistances are determined by themaximum value of the capacity curve and summarized in  Table 4.

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Fig. 9c.   DCR values and static plastic hinges for Case 1A under 2.78(DL + 0.25LL ).

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 load–displacement

curve by the corresponding capacity curve up to the maximumloading, as shown in Fig. 12.

7. Conclusions

The vulnerability of an earthquake-resistant RC building toprogressive collapse is evaluated in this study. According to the

 Table 4

Predicted maximum loadings

Case Multiplier of   (DL + 0.25LL )

1B 2.16

2A 2.78

1A 2.38

2B 2.40

GSAlinear staticanalysisapproach, the building hasa lowpotentialfor progressive collapse. Nonlinear analysis results reveal that

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Fig. 10.   DCR values and dynamic plastic hinges for Case 1B under P dy 2.15(DL + 0.25LL ). The dash lines represent the collapsed members.

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

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

the flexural ductility of beam members may be developed tosome extent in the GSA linear static analysis procedure. Moreover,

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

Fig. 11d.   The capacity curve of Case 2B.

different progressive collapse resistances are obtained by thenonlinear static and the incremental dynamic method. Different

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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 the

dynamic 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 GSA

guidelines 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 the

reviewers for very constructive comments. The study presented inthispaper wassupportedby theNationalScience Council 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):418–25.

[2] Nair RS. Preventing disproportionate collapse. J Perform Constr Fac 2006;20(4):309–14.

[3] Ellingwood BR. Mitigating risk from abnormal loads and progressive collapse.

 J Perform Constr Fac 2006;20(4):315–23.

[4] Dusenberry DO. Review of existing guidelines and provisions related to

progressive 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. Progressivecollapseof structures: Nomenclatureand procedures.IABSE, Structural Engineering International 2006;16(2):113–7.

[7] Starossek U, Wolff M. Progressive collapse: Design strategies. In: IABSE

symposium, structures and extreme events. 2005.

[8] Marjanishvili SM. Progressive analysis procedure for progressive collapse. J

Perform Constr Fac ASCE 2004;18(2):79–85.

[9] Marjanishvili S, Agnew E. Comparison of various procedures for progressive

collapse analysis. J Perform Constr Fac ASCE 2006;20(4):365–74.

[10] GSA,Progressivecollapse analysisand design guidelinesfor new federal office

buildings and major modernization projects. General Service Administration.

2003.

[11] Department of Defense (DoD) Unified facilities criteria (UFC): Design of 

buildings to resist progressive collapse, UFC 4-023-03, U. S. DoD. 2005.

[12] Abruzzo J, Matta A, Panariello G. Study of mitigation strategies for progressive

collapse of a reinforced concrete commercial building. J Perform Constr Fac

ASCE 2006;20(4):384–90.

[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] Corley WG,MlakarSr PF,Sozen MA,Thornton CH.The Oklahomacity bombing:

Summary and recommendations for multihazard mitigation. J Perform Constr

Fac 1998;12(3):100–12.

[15] Hayes Jr JR, Woodson SC, Pekelnicky RG, Poland CD, Corley WG, Sozen M.

Can strengthening for earthquake improve blast and progressive collapse

resistance?. J Struct Eng, ASCE 2005;131(8):1157–77.

[16] SAP2000 rVersion 8.0. Linear and nonlinear static and dynamic analysis and

design of three-dimensional structures. Berkeley (CA, USA): Computers and

Structures Inc.; 2002.

[17] FEMA. NEHRP guidelines for the seismic rehabilitation of buildings (FEMA

Publication 273). Washington (DC): Federal Emergency Management Agency;

1997.

[18] LinBH. Progressivecollapseanalysisand evaluation of anearthquake-resistant

RC building. Master thesis. Taiwan: Department of Civil Engineering, National

Pingtung University of Science and Technology: 2007.

[19] SucuogluH, Citipitioglu E, AltinS. Resistance mechanisms in rc buildingframessubjected to column failure. J Struct Eng ASCE 1994;120(3):765–82.

[20] Kaewkulchai G, Williamson EB. Beam element formulation and solution

procedure for dynamic progressive collapse analysis. Comput Struct 2004;82:

639–51.

[21] Kaewkulchai G, Williamson EB. Dynamic behavior of planar frame during

progressive collapse. In: 16th ASCE engineering mechanics conference. 2003.

[22] Pretlove AJ, Ramsden M, Atkins AG. Dynamic effects in progressive failure of 

structures. Int J Impact Eng 1991;11(4):539–46.

[23] Ruth P, Marchand KA, Williamson EB. Static equivalency in progressive

collapse alternate path analysis: Reducing conservatism while retaining

structural integrity. J Perform Constr Fac 2006;20(4):349–64.