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Sc cience eDirect t Materialss Today: Proceediings 5 (2018) 8775–8783

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2D-Line 2 ear static and n non-linea ar dynamic pro ogressive collap pse ana alysis of reinforcced con ncrete bu uilding S..Gowtham m,M.Prakassh, N.Parthaasarathi, K K.S.Satyanaarayanan, V.Thamilar V rasu Department of Civil Engineeriing, SRM Universsity, Kattankulathuur 603203,India

Abstract Progressivee collapse is deefined as the collapse of a building or a structture either partiially or complettely in a progressive manner from elemeent to element rresulting from thhe failure of onne or more key eelements. Theree will be heavy loss of propertyy and life if a progressivee collapse occuurs suddenly. Thhe present studyy investigates a 2D, two bay - Five storey Reiinforced Concreete (RC) bare frame usedd. A linear staticc analysis and nnon-linear dynam mic analysis ussing time historyy method is carrried out using ffinite element software. T Two column removal scenarioos namely corneer and middle ccolumn removaal scenario are considered. In Linear Static analysis Deemand Capacityy Ratio (DCR) vvalues and mem mber acceptancee criteria are coonsidered and N Non-linear Dynaamic Analysis (NDA) Tim me vs Displacem ment, Maximum m Axial force, B Bending momennt results wheree the column is rremoved and iss used as base for comparrison are calculaated to know thee potential for pprogressive colllapse of a structture. © 2017 Published by Elsevierr Ltd. Selection annd/or Peer-review under responsibility of Internationnal Conference Onn Recent Advancces In Material Chhemistry.

Selection andd/or Peer-review unnder responsibilityy of International C Conference On Reccent Advances In M Material Chemistryy

Keywords: P Progressive; two dimensional;corn d er;middle; linear static; nonlinear ddynamic.

1. Introdu uction According to Generaal Service Addministration ((GSA) 2013 gguidelines [1],, progressive collapse is deefined as an extent of ddamage or colllapse that is ddisproportionaate to the maggnitude of the iinitiating evennt. Progressivee collapse is a critical state of a struucture which can be occurrred from any kind abnormaal loading or due to the occcurrence of mpact, bomb bblast, earthquaake, design or construction error etc. It iss important to analysis the adequacy a of vehicle im structure ffor the sufficient load distriibution througghout its membbers during suuch destructivve situations booth in terms of failuree prevention and for proteection of impportant civil and military structures. Inn the United States, the Departmeent of Defense (DoD) and thhe General Serrvices Adminiistration (GSA A) provide detaailed guidelinees regarding methodoloogies to resistt progressive ccollapse of building structurres. Some impportant buildinngs that have ccollapsed in the past annd the reason for their collaapse are listedd here. Ronan Point Tower A Apartment (19968) reason foor collapse Fatal collaapse of one of its corners due d to a naturaal gas explosioon, which desstroyed a loadd-bearing wall,, Sampoong Departmeent Store (19955)- Due to thee removal of several supportt columns on tthe lower flooors in order to make room for escalaators , Twin Towers T of W World Trade Center C (2001) result of terrrorist attacks and the subseequent fires thatfollow wed and Rana Plaza commeercial office coomplex (2013)) Collapse of m majority of strructures due tto change of usage. Affter the collappse of Ronan B Building in 1968, the impoortance about the study of progressive ccollapse was learnt. Maany researchess were conduccted during 200th century to study the natuure of progresssive collapse on different structures and also to m mitigate the daamage that occcur locally to oother part of bbuilding by prroviding suitabble detailing measures and analyzingg using speciall design methoodologies. 2214-7853 © 2017 Publishedd by Elsevier Ltd. Selection andd/or Peer-review unnder responsibilityy of International C Conference On Reccent Advances In M Material Chemist

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Collapse of Twin Towers of World Trade center in 2001 led to development of codebooks and guidelines that deals mainly on progressive collapse design of building. The Department of Defense has developed Unified Facility Criteria code book[2] named ‘Design of buildings to resist progressive collapse’ which deals with the analysis and design of existing buildings and new buildings to withstand progressive collapse. American Federal agency General Service Administration (GSA) introduced some guidelines out of UFC codes named ‘Alternate path analysis & Design guidelines for progressive collapse resistance’ [1]. These guidelines are used extensively for the analytical part of this project. Aldo McKay et al (2009)[3] illustrates a case study of 4 storey RC building with a flat slab system using UFC 4-023-03 for alternate path analysis. Analysis is carried out using extreme load combination 2(1.2DL + 0.5LL) for linear static analysis and 1.2DL + 0.5LL for non-linear dynamic analysis as specified in UFC 4-023-03. Nonlinear hinges where incorporated as per UFC. In dynamic analysis the column removal time step of 1/20th was selected and performed. This was compared with the linear static analysis. It is seen that the dynamic analysis is more accurate and found the building to be adequate to resist progressive collapse whereas the linear static approach requires an upgrade in order to bring the building into compliance. Bhavik R. Patel (2014) [4] studied the effect of failure of load carrying elements; 15 storey RC building was considered in this study. The building was modelled and analyzed for progressive collapse using structural analysis and design software SAP2000. Nonlinear static and nonlinear dynamic analysis were carried out to evaluate the progressive collapse potential of RC building. GSA guidelines were adopted and it was seen in the nonlinear static case that on column removal 50% of loading instead of load amplification of 2 which was specified by GSA. In a nonlinear dynamic analysis full GSA loadings were attempted in column removal case and it is found to be more accurate. Brian I. Song et al (2013) [5] stated progressive collapse performance of an existing steel frame building was evaluated by physically removing four first-story columns from the building and by performing linear static and nonlinear dynamic analysis of the building using SAP2000. Nonlinear dynamic analysis is more accurate and realistic than linear static analysis. In 2D model, columns more affected whereas in 3D model, beams are more affected. For future research, it would be better to consider the actual material properties and connections of the building in the analytical models in order to obtain more reliable results. Kim et al (2010) [6] evaluated the progressive collapse potential of building structure with core and outrigger trusses using nonlinear static and dynamic analysis. 36-storey analysis model structure composed of RC core walls and perimeter frames connected by outrigger trusses at top were prepared. The static pushdown analysis of the structure with mega-columns and outrigger trusses showed that the maximum strength reached only about 20% of the load specified in the GSA guideline when a mega-column in the first story was removed. According to dynamic analysis results, the vertical displacement monotonically increased until collapse as a result of buckling of some of outrigger truss members. It is found that he structure with outrigger and belt trusses remained stable after a perimeter column was removed. ShalvaMarjanishvili et al (2006) [7] compares four methods for progressive collapse analysis by analyzing a nine-storey steel moment resistant frame building , employing complex analytical procedures like linear-elastic static, nonlinear static, linear-elastic dynamic and nonlinear dynamic methodologies. Each procedure is thoroughly investigated and common shortcomings are identified. Step-by-step description of various procedures for progressive collapse analysis was studied by performing example analysis in SAP2000. Analytical and experimental works of progressive collapse are learnt from different journals [8] – [14]. 1.1 Objective and Scope of project The main objective of this study is the behavior of 2D, Two Bay five storey Reinforced concrete (RC) bare frame under gravity load including two column removal scenarios namely corner and middle column removal scenarios. The scopes of this study are listed below, • Linear and non-linear dynamic analysis is to be carried out for two column removal scenarios. A comparative study on linear static and nonlinear dynamic analysis of 2D , two bay five story RC Bare building 1.2. Research Significance Progressive collapse of Reinforced Concrete (RC) buildings are studied in less number and most of the buildings in India are RC buildings thus necessitating the study. No design guidelines are available as per Indian standards. In this paper, it is proposed to study the behavior of two bay, five storey RC building under progressive collapse on


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removal of corner and middle column in two different analysis. Analytical study will be carried out on a 2D frame under gravity loads using finite element analysis software SAP2000 V14. 2. Analytical study The analytical investigation of progressive collapse of a RC building were carried out with the help of commercially available FEM software SAP2000 the methods to study progressive collapse response of building, and preliminary data taken for analytical study are presented. 2.1. Methods to study Progressive collapse The progressive collapse design requirements employ three design/analysis approaches: Tie Forces (TF), Alternate Path (AP), and Enhanced Local Resistance (ELR). In this paper Alternate Path method is used with deformation controlled action. Hence, the guidelines provided in GSA’s ‘Alternate path analysis & design guidelines for progressive collapse resistance’ is used.GSA guidelines (2013) states that building an designed using any one of the following analysis namely • Linear Static Analysis(LSA) • Non-linear Static Analysis(NSA) • Non-linear Dynamic Analysis(NDA) LSA and NDA are carried out and their results are compared with each other. The advantages of one method over other is learnt. Extensive literature review for NSA was carried out to understand which method will be suitable for analyzing progressive collapse. Time History method was used to do NDA and its results are compared with LSA. 2.2. Preliminary Datum Two Dimensional RC frame is modelled in SAP2000. The various datum of model are presented here. Story height is 3m and width of bay is 2.5m. The grades of concrete and reinforcing steel are respectively M30 and Fe415. The cross-section of beam is 300mm x 300mm and for column is 300mm x 450mm. Reinforcements for Beam is main bar of 4no. of 10mm diameter with stirrups of 8mm diameter @ 100mm spacing. Clear cover is 25mm all around the beam. Reinforcements for Column is main bar of 4no. of 12mm diameter with ties of 8mm diameter @ 150mm spacing. Clear cover is 40mm all around the column. The gravity loads that act on model are listed here, self-weight of beams and columns calculated from SAP2000 automatically, dead load of slab 4.69kN/m, dead load of wall 13.23kN/m and live load on slab is 3.75kN/m. Dead load is denoted as DL while live load as LL.Corner and Middle column removal scenarios are taken for linear static and non-linear dynamic analysis. 2.3. Linear Static Analysis Linear static analysis (LSA) is the basic form of analysis done to study about the response of a building. As per UFC 4-023-03 [2], in a linear static procedure, the structural analysis incorporates only linear elastic materials and small deformation theory; buckling phenomena are not included in the model but are assessed through examination of the output. Inertial forces are not considered. The analysis consists of a single step, in which the deformations andinternal forces are solved based on the applied loads and geometry and materials. Thus, it can be said that linear static analysis can be done in a quick way. 2.3.1. Procedure for LSA • • • •

A bare frame model is created without the column that is considered to be failed by external load. Cross section, material property and suitable reinforcements for different sections are chosen. Apply all gravity loads on the frame. Create load case as per GSA guidelines. The analysis is run and then moment, axial load and shear forces are taken from result. The ultimate moment, ultimate axial load and maximum shear force are calculated as per IS: 456 – 2000.

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• •


Find Demand Capacity Ratios (DCR) for each element. Check which elements are failed as per acceptance criteria specified in GSA guidelines.

2.3.2. Load case for LSA As per Cl.: 3.2.11.4.1 of GSA guidelines [1], to calculate the deformation-controlled actions, simultaneously apply the following combination of gravity loads. Apply the following increased gravity load combination to those bays immediately adjacent to the removed element and at all floors above the removed element. GLD=ΩLD [1.2DL+0.5LL] (1) Apply the following gravity load combination to those bays not loaded with GLD G = 1.2 DL + 0.5 LL

(2)

where GLD = Increased gravity loads for deformation-controlled actions for LSA ΩLD = Load increase factor for calculating deformation- controlled actions for LSA DL = Dead loads on frame LL = Live loads on frame G = Gravity loads on frame

Load increase factor is taken as 2 in deformation controlled action. This factor is multiplied to load case to take into account the dynamic nature of progressive collapse and non-linearity that exist in material and geometry of elements. 2.3.3. DCR calculations DCR is defined as the ratio of acting force (internal force) determined in component (moment, axial force and shear) to expected ultimate, un-factored capacity of the component. As per Cl.: 3.2.11.1.2 of UFC 4-023-03, for deformation controlled action, DCR= QUDLim/QCE (3) where DCR = Demand Capacity Ratio QUDLim = Values taken from SAP2000 for particular element QCE = Expected or ultimate strength of element as per IS:456-2000 2.4. Non-linear Dynamic Analysis Nonlinear dynamic analysis (NDA) is the most accurate method of analyzing the response of the building. As per UFC 4-023-03, in a nonlinear dynamic procedure, inertial effects and material and geometric nonlinearities are included. A time integration procedure is used to determine the structural response as a function of time. Here, time history analysis with ramp time function is used to carryout nonlinear dynamic analysis. 2.4.1. Procedure for NDA • Create frame model with column to be removed. Apply the gravity load in nonlinear case and also consider geometric nonlinearity. Run analysis to get axial force of the column to be removed at the point of removal. • Remove column that is to be considered failed. Apply the equivalent axial load at point of column removal in opposite direction (Upward direction). Equivalent load is taken as Dead load pattern. • Load case named ‘Gravity Load’ was developed with gravity loads and equivalent axial load .Run analysis. Check whether the model with equivalent axial load and the model with column produce similar internal forces and displacement. • If the internal forces and displacements are similar, continue with further steps or else change equivalent axial load until similarity occurs. • Create Ramp time function for the equivalent axial load starting from 1 to 0 values in time 0 and 1 respectively. • In load case, develop “Time History Dynamic Response”, which has to start at the end of ‘Gravity Load’ case. Time interval is taken as 0.1s for each step.

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2.4.2. Loaad case for ND DA As perr Cl.: 3.2.13.4..1of GSA guiddelines, to calcculate the defoormation-conttrolled and forrce-controlled actions, apply the following graavity load. GND = 1.2 DL + 0.5LL ((4) where GNDD = Gravity loaads for Non-linear Dynamicc Analysis DL = Dead looads on framee LL = Live looads on frame 3. Linearr Static Analyysis Results DCR vvalues of diffeerent elements for corner andd middle column removal scenario is shown in figures below.

Figure- 1 a)) DCR for Columnns b)DCR for Beaams for corner coolumn removal

Figure-2 aa)DCR of columnns b)DCR of Beam ms for middle coluumn removal

From Figure 1 & 22, the Maximuum DCR valuue for beam inn Moment andd in column tthe maximum m axial force occurs at corner colum mn removal sccenario. In collumn Maximuum Axial DC CR value was found 0.950 that is 48% more thann that of in a middle colum mn removal; in beam Maxiimum Bendingg Moment DC CR value is 11.422 that is 28%more in middle collumn removall scenario. It is found that D DCR values arre not acceptannce criteria off an element but they aare the limitinng values for tthe use of Linnear Static Anaalysis for a paarticular buildding. DCR vallues are less than 2 forr all elements iin the taken reegular buildingg and hence Liinear Static Annalysis can bee used.

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Accepptance criteriaa for an elem ment to avooid failure foor deformatioon controlled action is prresented in Cl.:3.2.11.7.1 of UFC 4-023-03 ass below,ØmQ QCE ≥ QUD (5) where Ø =>Strength = reeduction factoor from the appropriatte material speecific code. m => Componnent or elemennt demand moddifier (mffactor). QCE => > Expected strrength of the ccomponent or eelement. QUD => Innternal force taaken from SAP P2000 after linnear static anaalysis of elemeent. Elements that fail are shhown in figurees as follow,

Figure- 3 Faileed Elements a)for corner c column rem moval b) for middlee column removal

4. Non-lin near Dynamicc Analysis Reesults NDA is done for tw wo column rem moval scenarios and the ressults are preseented here. Thhree graphs arre plotted in SAP2000 namely Verttical Displacem ment vs Timee, Axial forcee vs Time and Bending moment m vs Tim me. Vertical ment is taken aat the point w where column was removed. The beam w with maximum m axial force aand bending displacem moment iss taken for plootting. Figuress of plot are prresented below w,

Figuree-4 Vertical Displacement vs Time a)for corner coluumn removal b) foor middle columnn removal

From Fig.5, it is leaarnt that theree is vibration in the frame model as a reesult of suddeen column rem moval. Thus resulting in compressioon and tensionn forces in m members. The maximum doownward displlacement is 322.68mm for corner collumn removal and 12.19mm m for middle column removaal.

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F Figure-5 Axial loaad vs Time a) for corner column reemoval b) for midddle column remooval

From F Fig.6, there is variation in aaxial force from m negative to positive valuees because of tthe vibration inn the frame. The maximum negativee axial force is 279.4kN andd max. positivve axial force is 120.9kN foor corner colum mn removal while for middle colum mn removal, maaximum negattive value is 333.2kN and max. m positive vvalue is 285.1.

Figuure-6 Bending mooment vs Time a) for corner colum mn removal b) for middle column reemoval

From F Fig.6, for Cornner column reemoval, maxim mum moment in beams is 2774.9kNm at tim me 1.1s and foor Middle column reemoval, maxim mum moment in beams is 2114.3kNm at tim me 2.73s.

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5. Compaarison of Resu ults Displaacements for ccorner and midddle column sccenarios for LSA and NDA are comparedd in Figure bellow,

Figure-7 Compparison of Verticaal Displacements

usions 6. Conclu In thiss paper, the beehaviour of thhe five storey R RC building uunder corner aand middle coolumn removaal with a 2D finite elem ment modellinng using SAP22000.Based onn this model tthe parametricc studies like linear static analysis a and nonlinear dynamic anallysis are considered. 1) In lineear static analyysis, the maxim mum DCR vallue of Axial iss 0.95 at corneer column andd 0.487 for midddle column removval and Maxim mum DCR vallue of Momennt is 1.427 at ccorner columnn and 1.02 forr middle colum mn removal. Based on the GSA gguidelines for symmetrical sstructure the D DCR value is less than 2. Thherefore the strructure is withinn the permissibble limits. 2) Based on the UFC aacceptance criiteria for an eelement showss that the cornner column is more vulnerabble than the middlee column. 3) In nonn-linear dynam mic analysis reesulted in a maaximum deflecction of 33mm m at corner collumn removal and middle o

columnn removal shoows 12mm whhich corresponnds to The hinnge plastic rotation capacityy 0.756 at corrner column o

o

and 0.275 for midddle column reemoval and it is shows thatt is much lessser than the 12 allowable rotation the structuure is expectedd to survive a ppotential proggressive collappse loss scenarrio. Acknowleedgements Fundinng for this ressearch was sponsored by SR RM Universitty by Universiity Committeee research. Anny opinions, findings, conclusions aand recommenndations expreessed in this ppaper are thosee of the authoors and do nott necessarily reflect thee view of the ssponsors. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

Generaal Services Admiinistration Guidelines, ‘Alternate P Path Analysis & D Design guideliness for progressive ccollapse resistancce’ October 24, 2013 Unified Facilities Criterria (UFC), ‘Desiggn of buildings to resist progressivee collapse’ UFC 44-023-03- June 20013 IS:456--2000, ‘Plain and Reinforced Conccrete - Code of Praactice’ ACI 318R-95, ‘Buildingg Code Requirem ments for Structuraal Concrete and C Commentary’ m, Y. Jun and J. Paark, ‘Performancee of Building Struuctures with Outriigger Trusses Subbjected to Loss off a Column’ 2nd S Specialty J. Kim Conferrence on Disasterr Mitigation, June 2010 Aldo McKay, Kirk M Marchand, Manueel Diaz, ‘Alternatte Path Method in Progressive C Collapse Analysiis: Variation of Dynamic and Nonlinnear Load Increasse Factors’, DOI: 10.1061/ (ASCE)) ShalvaaMarjanishvili, Elizabeth Agneew, ‘Comparisoon of Variouss Procedures for Progressivee Collapse Annalysis’ DOI: 10.10661/_ASCE_0887-- 3828_2006_20:44_365 He qinng-feng and Yi wei-jian, ‘Experrimental Study oon Collapse-Resisstant Behavior oof RC Beam-Coluumn Sub-structuure considering Catenaary Action’ 14th World W Conference on Earthquake E Engineering Octoober 12-17, 2008 Rakshiith K G, Radhakrrishna, ‘Progressiive Collapse anallysis of reinforcedd concrete framedd structure’ IJRE ET: International JJournal of Ressearch in Engineerring and Technoloogy


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[10] Said Elkoly, Bilal El-Ariss, ‘Progressive collapse evaluation of externally mitigated reinforced concrete beams’ Research Article [11] Peiqi Ren, Yi Li, Xinzheng Lu, Hong Guan c, Yulong Zhou, ‘Experimental investigation of progressive collapse resistance of oneway reinforced concrete beam–slab substructures under a middle-column-removal scenario’ Research Article [12] LanhuiGuo, Shan Gao, Feng Fu, Yuyin Wang, ‘Experimental study and numerical analysis of progressive collapse resistance of composite frames’ Research Article [13] M. Mahmoudi1, T. Teimoori, H. Kozani, ‘Presenting displacement-based nonlinear static analysis method to calculate structural response against progressive collapse’ International Journal of Civil Engineering [14] Ioannis P. Giannopoulos, ‘Seismic Assessment of a RC Building according to FEMA 356 and Eurocode 8’ Research Article