Structural Analysis and Design to Prevent Disproportionate Collapse

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Feng Fu

Progressive Collapse Design and Analysis of Space Structures

Publication details https://www.routledgehandbooks.com/doi/10.1201/b19662-4 Feng Fu Published online on: 03 Mar 2016

How to cite :- Feng Fu. 03 Mar 2016, Progressive Collapse Design and Analysis of Space Structures from: Structural Analysis and Design to Prevent Disproportionate Collapse CRC Press Accessed on: 28 Sep 2021 https://www.routledgehandbooks.com/doi/10.1201/b19662-4

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The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. K24849.indb 51 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 grid. For a long-span single-layernormally are connections grid, the built be by either can shells asingle-layerLatticed or adouble-layer 3.2.2 roof structure. together by joints to form the auniform linked are resembles shape. apyramid of steel construction bars The type This types. ofurations top grid bottom the layers and different make can by config diagonal Different struts. joints connected nodal with grids practice. construction ofconsist They topcurrent bottom square and Double-layer in used one of are most structures the popular grids 3.2.1 structures. tensegrity and tures, double-layer suchects, as shells, grids, latticed membrane struc proj construction current in used of spacemajor structures types roofs,closed floors, exteriorandcanopies. several are Therewalls, long-span short from enclosures,tures, also and to mid-span frames of struc have types different widelySpace been in used structures 3.2 Abaqus grams a double-layer demonstrated pro is the using space grid structure chapter, end ofthe this aprogressive collapse example analysis for At of space structures. types of different collapsethe mechanism followed of bycollapse adiscussion accidents world the around and chapter, introduced, are of this space forms In different structures 3.1

Introduction Major Types of Space Structures obeLyr Grids Double-Layer atcd Shells Latticed Progressive Collapse Design and ® and SAP2000 and (CSI, 2013). © 2016 Group, by Taylor LLC & Francis Analysis of Space Structures Chapter Chapter 3 - - - - - 1/25/16 11:27AM 51 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 K24849.indb 52 52 3.2 Olympic) for Seoul the (Geiger Games al., et 1986). 3.1 (Figures arenas fencing and and of gymnastic the roof structures thought innovative designed an and “cable dome” circular the in compression elements.” D.H. Geiger al. (1986) et made of Fuller’s use ideahis of “nature on continuous relies tension to embrace islanded was conceived first cept of tensegrity by R.B. Fuller (1975), reflecting due superlight to space their large-span structures weight. con The compression one bars. of are most They solutions the promising for systems composed of cables continuous individual prestressed and self-equilibrium are structures Figure 3.1, shownAs tensegrity in (Photo taken by the author.) by the taken (Photo 3.2.3 the influence vault’s members also the behaviour. between structural modified of supportsThe type dueand location to curvature. zero its easily be shell,asurface can that ofhas which a cylindrical-shaped domes. geodesic domes, and domes, lamella grid three-way domes, ribbed such as various are types, SchwedlerThere domes, pinned. as designed due to its indeterminacy, and be greater redundancy jointscan the to rigid designed provide as rigidity. However, for double-layer grid, FIGURE 3.1 FIGURE A barrel vault is another latticed shell structure. It features forms It forms vault features A barrel shell structure. latticed another is shell structures. lattice oneDomes of are commonly used the

esgiy Systems Tensegrity Structural Analysis and Design to Collapse Prevent Disproportionate

Interior of the fencing arenas for the Seoul Olympic Games. Olympic Games. Seoul for the arenas fencing of the Interior © 2016 Group, by Taylor LLC & Francis - 1/25/16 11:27AM K24849.indb 53 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 as inflatableas structures. Games; Geiger al., et 1986), made Some are Figure 3.2. shown as in Olympic for Seoul the arenas fencing and (such gymnastic the as membrane works structures together shell lattice or with tensegrity of lightweight The space atype are structure. Membrane structures author.)the Progressive Collapse Design and Analysis ofSpaceStructures for very long bridges. although several past codes of practice provide design procedures for progressive collapse prevention of designs space structures, worldwide. reported collapse anumber of incidents have that been space structure been However, 3.4 Section introduced be have in , there it as will still whennot individual loss of triggered be the member an occurs. dancy, most designers presume aprogressive that collapse will redun due ofFor space structural to mosttheir structures, types members. of consist alarge number of structural Space structures 3.3 3.2.4 3.2 FIGURE So far, So requirements few design are codes detailed there with

to Prevent Disproportionate Collapse Disproportionate Prevent to for Space Guidance Structures Design ebae Structures Membrane

Fencing arenas for the Seoul Olympic Games. (Photo taken by (Photo Olympic taken Games. Seoul for the arenas Fencing © 2016 Group, by Taylor LLC & Francis - 1/25/16 11:27AM 53 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 K24849.indb 54 54 ening of roof. the were cracks ening The formed duecaused in stress to high led to a weak this concrete. the turn, it, In in caused cracking which dowels concrete shell were the supporting too deeply embedded into number steel of was the reason that for causes collapse. the main The Scientifiques et Nationalde desFrance, Ingenieurs 2005) a found shell wereand glass. with enclosed forwere access steelwork to largegangways. openings external The back At columns. tied toand the location the of failure, the there were that supportshell rested on supported two longitudinal beams steel tension members,curved were which propped The struts. with Figure 3.3. shownparts, as in ofconcrete aspan shell with 26.2 m,three was which precast in was a300 designedGate with E50. structure The MayOn 23, 2004, of aportion Terminal 2E’s collapsed near ceiling 3.4 CDG_collapse.png https://upload.wikimedia.org/wikipedia/commons/1/1b/Terminal_2E_ 3.3 FIGURE 3.4.1 of incident each introduced. are mechanism failure world the around tures made. is cause of collapse The the the and introduction of collapse an section, incidents of space this struc In The investigation report of the Ministry of Transportation investigation (ConseilThe of Ministry report the with were strengthened externally two sidesThe of structure the

Incidents around the World the Incidents around Collapse Structure Space Partial Collapse of Charles de Gaulle Airport Terminal 2E Terminal Airport Gaulle de Charles of Collapse Partial Structural Analysis and Design to Collapse Prevent Disproportionate

mm thick curved curved thick mm - - 1/25/16 11:27AM K24849.indb 55 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 3.4.2 steel tension struts. member and concrete curved shell and collapse, including design, acombination and of in factorsfor led safety major to the movements. moisture and thermal stage differential from cycles and of construction stress the Progressive Collapse Design and Analysis ofSpaceStructures eral bracing of the top chords was met through diagonals in the the eral bracing of top in the chords diagonals was met through addition, members. the In in lat the stresses caused bending which at top atthe chords one diagonals intersected point the another, and 1978) Civic of Hartford shows the case Center’s the in that frame, moment. However, Associates, investigation the (Lev Zetlin report joint same to into reduce the of member each intersect bending the conventional design of double-layer centrelines the structures, grid for stadium was the adouble-layer construction frame the grid. In collapse. roof, final frame the casuses which period. snow The loading caused excessive deflectionthe spaceof 1978, in Coliseum due largest to snowstorm the a5-year time in code.the bybuilding thatrequired than wasthat ity less significantly capac member was astructural designed with code structural or the snowwas the load exceeded by design load building the the required of winter 2010–2011. the during major collapses The for reason these United northeastern States the in roof collapse incidents occurred that O’Rourke Wikoff and (2014) investigation an described into about 500 Heavy snow major another cause is for collapse the of space structures. The aboveThe design fault caused progressive collapse the between • • • • • margin had little investigationThe structure found the that also Three independent investigationsThree have done. been space The famous collapseOne incident Civic of that Hartford is the Center

tal ties to the columns to the ties tal support itsWeakness and horizon of longitudinal beam the shell concrete the in were where struts the seated stresses punching local High failure alocal from loads to awaytransfer redundancy and Lack of robustness placed reinforcement may that Cracking havemis or resultedinsufficient from actions nal under dead andloadthe exter structure in flexibility High Space Structure, Hartford CivicSpace Center Structure, Grid Double-Layer of Collapse Snow-Induced © 2016 Group, by Taylor LLC & Francis - - - - - 1/25/16 11:27AM 55 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 K24849.indb 56 56 (Feld Carper, 1997). and volatilethe to collapse weld release, structure entire causing the noticed. Amassive amount of would energy have caused by been prevent out-of-plane Associates, 1978). (Lev Zetlin bending interior of frame, the but along edgesto was the there no means Stadium Sultan Mizan Zainal Abidin, 2009): Zainal Stadium Mizan Sultan for collapse the (Investigation Roof on the Collapse Committee at consideration of support the conditions for roof. the pletion, 2009. cause for in collapse the was incomplete primary The double-layer acurved as structed grid. It collapsed com 1year after Terengganu, roof stadiumThe of football in the Malaysia, was con 3.4.4 propagation of deformation dome caused the to collapse. propagated buckling local area. The ontion asmall rapidly, this and snowof due snap-through local load unexpected to- accumula an ofa span 100 of 0.48 rise mand dome m. The collapsed aresult as 1963 Vlad, and (Vlad 2014). pavilion The was abraced dome with in collapse Bucharest Another example in apavilion is constructed 3.4.3 looked acauseit (ENR, because of as uncommon so failure 1978). is before live loads over were usually is of added.failure - means This were loaded critically middle tomembers close the of truss even the due of compression the to torsional buckling members, that and 20%. byunderestimated more than load by 20% (Feld Carper, and 1997). Therefore, dead the loads were dead the altered roof manager the material, increasing struction • • place, was in It noticed once that roof con was the truss the also scoreboard roof to the A faulty the was also weld connecting • reason the investigation the from explains report The committee investigationAnother showed was cause of failure the that the

which waswhich not done. considerationthe in design mode, of support the flexibility required of space the sensitivity roofThe structure frame sis, out. was which not carried more consideration detailed second-order in design analy required complexityThe long of and roof the structure spans into account support the conditions of roof the structure. design wasThe inadequate; take to designer fully the failed in Terengganu, Malaysia (Support Failure) (Support Malaysia in Terengganu, Stadium Mizan Sultan of Collapse Roof Roof Collapse of Pavilion Constructed in Bucharest in Constructed Pavilion of Collapse Roof Structural Analysis and Design to Collapse Prevent Disproportionate © 2016 Group, by Taylor LLC & Francis - - - - 1/25/16 11:27AM K24849.indb 57 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 collapse. for poorgeometry; was workmanship reason another misaligned in ure is demonstrated later in this chapter. demonstrated is ure later this in support considering the analysis fail A modelling space structure. support was one failure for of major collapse the the reasons of the due removal to the of middle the framework. collapsed, followed by collapse collapse the The of was steel pillars. work.going reconstruction Two-thirds (137 of old the structure m) Progressive Collapse Design and Analysis ofSpaceStructures gravity loads. gravity loading, therefore to prevent progressive collapse due to abnormal should members to extra resist made be formargin structural for long-span designs. required normally test is space structure tunnel collapse therefore,the design practice, of real a building; in a wind excessive snow loading due to severe weather. overloaded are whenbers structures the by agravity load, such as following loss ofcollapse mem the some occur couldcritical also loading. service were to full subject members when structures the following loss of the just oneoccur of several critical potentially showed and space progressive that trusses thetical collapse could sented (1988), by Murtha-Smith was performed on hypo analysis an However, individualloss of member an occurs. pre research the in considered progressive that when not triggered be the collapse will members, design practice, in of it structural dancy normally is redun and to Due its large statical indeterminacy structures. span A double-layer one is of conventional the space grid long- structure 3.5.1 explained. be will of spaceent structures types for differ collapse the mechanism section, this form. In structural on their depending varies Therefore,tures. collapse the mechanism 3.1 Section introducedAs in 3.5 On February 20, February On 2013, stadium under collapsed the while again stage, construction roof the poorly, the wasIn erected resulting From these two collapses in one stadium, it can be seen that the oneFrom two collapses the stadium, that in these it seen be can Based on the above discussion, in the design, an extra safety safety extra above design, on the the an Based in discussion, additionIn to snow, found for to areason was be also strong wind showed collapseThe Coliseum of Hartford the progressive that

Collapse Mechanism of Space Structures Mechanism Collapse Collapse Mechanism for Double-Layer Grid Double-Layer for Mechanism Collapse © 2016 Group, by Taylor LLC & Francis , there are different types of space struc types different are , there ------1/25/16 11:27AM 57 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 K24849.indb 58 58 formed in the design to prevent the formed in progressive collapse. should per be of whole the analysis also global structure buckling unstable. It by Therefore,becoming buckling. triggered local often is radius the Ris of and curvature. of structure the loading. It apt when is t to occur of and supporting manner the and of structure the thickness and collapse ofling a space greatlycurvature is influencedthe frame by of single-layer such as buck layer type shells. lattice The structures of a space prone is buckling local frame toThe single- happen in place takes area, often a local which at members in joints. structural members accordingly.individual structural ofPerry–Robertson stability the equations. check Adesigner can Euler’s design formulas are the these and theory behind buckling for 2005). Standardization, (European Committee theories The worldwide givenformulas are in Eurocode such as 3 guidances of flanges or the Thewebs. design buckling corresponding local unstable; it includes of members overalland the the buckling members, global and buckling. of certain buckling local member to need buckling, that checked: be of buckling here. major design practice, types ling In three are there shell,lattice it worthwhile of is buck to introduce major the types Bucharest. in constructed example An aroof members fail. is collapsecritical of pavilion the certain may if triggered shell. be global And buckling cylindrical low shell, adome, such as more a is prone than to overall buckling adouble-layer than Itbuckling found ashal that was also structure. chapter, asingle-layer to space greater sensitivity exhibits frame deformation propagate can and to lead to collapse. large localized and effects inertial with associated is snap-through Parke (1996) found that, for single-layer braced domes, dynamic the by memberinitiated or node and instability. Abedi from Research prone to progressive collapse due to propagation of instability local single-layer such as braced Structures domes are of structure. the collapse may the initiate important, buckling shell, as is tice stability single-layer the such ofas space lat structures, types For certain 3.5.2 Global buckling refers toGlobal arelatively buckling of space large area the frame of agroup of of consists buckling asnap-through buckling Local when individual is the member becomes Member buckling To behaviour of the help buckling the understand readers fully this introduced in space the for that is structures all reason The

Collapse Mechanism of Single-Layer Space Structures Space Single-Layer of Mechanism Collapse Structural Analysis and Design to Collapse Prevent Disproportionate © 2016 Group, by Taylor LLC & Francis / is the thickness where thickness small, the R is tis - - - - - 1/25/16 11:27AM K24849.indb 59 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 3.5.3 Progressive Collapse Design and Analysis ofSpaceStructures programs Abaqus programs ble-layer demonstrated commercial is the using space grid structure howsection, to aprogressive perform collapse of dou the analysis collapsethe of adouble-layer Therefore, space this grid in structure. 3.4.2 mentioned Section As in 3.6 structures. space of behaviour collapse overall on the effect behaviour the that ofadominant members has (2008), Shekastehband and al. (2011) et Shekastehband and shows Moussa and (2002), Kahla system. from Research equilibrium Abedi due self- to their collapse mechanism have their in feature aunique structures conventional tensegrity than spaceDifferent structures, 3.5.4 (Shekastehband al., et 2012; Abedi, and 2013). Shekastehband phenomenon member under failure the structures of these response forces caused by member failure, the inertia when evaluating the of member forces redistribution the and analysis, especially the in Therefore, to itstructure. account important is effects for dynamic whole region ofthe alocal the in energy system, it as kinetic releases may and ultimately cause overallof collapse. structure the to propagate potential the has to of structure portion parts other the to single-layer oftension. asmall failure Similar domes, initial an under of compression struts through cable under and ruptures sion (cables) or compression (struts). may due be These snap- to the Abaqus using analysis support with failure. Detailed spacethe structures should ablebe engineer support the to collapsecheck of potential cause support all failure. Therefore, tlement design, the an will in Terengganu),Stadium in foundation and heavy earthquakes, set (such methods Mizan Improper in space construction as structures. of for one collapse is of keytypes the the reasons failure ofport all 3.2 supFrom that incidents, it Section seen be the introduced in can In tensegrity structures, amember may suddenly ten structures, in fail tensegrity In In fact, member failure has a dynamic effect on the behaviours on the of effect fact, a In dynamic has member failure

Layer Grid Space Structure Using Abaqus Using Layer GridSpace Structure of Double- Analysis Collapse Progressive upr Failure Support Collapse Mechanism of Tensegrity Structures Tensegrity of Mechanism Collapse ® is shown in Section 3.6. Section shown is in ® © 2016 Group, by Taylor LLC & Francis and SAP2000 and (CSI, 2013). , an excessive, an gravity load may cause ® - - - - 1/25/16 11:27AM 59 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 K24849.indb 60 60 connections are modelled members. the are for all connections generally considered Therefore, to simulation, pinned. be the pin in members for diagonal web the of members are members. the All node to node for top bottom the chords, and additional and tubular from members, individualspanning to tubular use is types tural web members. However, struc of these construction normal the the forming top diagonal struts bottom chords, and pinned with grid, 27 mlong on side, each of consisted and 324 pyramids. square was modelled prototype. It the as ture was aconventional square by Fu Parke and research In (2015), adouble-layer space grid struc 3.6.1 FIGURE 3.4 FIGURE SAP2000such as or Abaqus or AutoCAD,Rhino program it import analysis then into an and (3D) such as cient three-dimensional the to model software set in sophisticated. is It of space more the is geometry The effi structure 3.6.2 ratioto-depth of 6. Figure 3.4.in support-to-support The aspan- was span 9 m, giving supported locationscally the shown nodes at in perimeter selected reprinted with permission of CSI.) permission with reprinted set up first in SAP2000, as shown in Figure 3.4. This is because because is 3.4.This in up set first SAP2000,in as shown Figure The heightThe was 1.5 of grid the was verti whole m. The structure formed by of continuoussometimes systems are kinds These

Prototype Space Structure Space Prototype Setting Up a 3D Model a3D Up Setting Structural Analysis and Design to Collapse Prevent Disproportionate

Double-layer grid model in SAP2000. (SAP2000 screenshot SAP2000.Double-layer (SAP2000 model in screenshot grid © 2016 Group, by Taylor LLC & Francis ® . In this analysis, a3D model this was. In - - - - 1/25/16 11:27AM K24849.indb 61 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 defined with the withdefined *ELASTIC theoption,and values 2.06 was curve of nonlinearity.stress–strain material part the elastic The (Abaqus Progressive Collapse Design and Analysis ofSpaceStructures stress of the chosen steel was 355 of chosen N/mm the stress 5 60.3 design, and members were observed. Toof structural the analysis the simplify buckling was local overstressed noand that and overall buckling loading SAP2000 conditionsnormal no using sure member to make rated. Therefore,underand model analysed designed the was first SAP2000 adesign-oriented design code is program with incorpo 3.5 FIGURE load combination of requirement dead load plus 0.25 of live the load. GSA analysis, (2003) the dynamic guideline For nonlinear the has 3.6.3 the analysis is conducted is here. files analysis INP the using using elastic–plastic material behaviour from Abaqus from behaviour material elastic–plastic using steel components were structural modelled the of properties all rial members wereonal modelled *BEAM using elements. mate The can be imported into Abaqus imported be can strains with the appropriate the with strains input format for Abaqus BS5990 from (BSI,obtained 2001) and converted and stresses into true were strength, yield ultimate the and including strains, and stresses steel. Engineering Steel grade structural the S355 for was all used the waswith defined curve *PLASTIC option. of stress–strain part the for Young’s modulus 0.3 and for Poisson’s ratio were plastic The used.

mm wall thickness—were chosen for all the members. yield the The for all chosen thickness—were wall mm In the proposed the model,In of top bottom chord the diag and and all As shown in Figure 3.5, after analysis in SAP2000, in Figure 3.5, analysis shownAs in 3D after the model

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1/25/16 11:27AM 61 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 K24849.indb 62 62 3.6.5.1 Table 3.1. shown are in they neously Several them. deleting removal were selected; scenarios members to removed be The were forcibly removed by instanta as shown in Figure 3.6, shownas wasin observed. no response obvious dynamic member, was which at of grid, centre was the the removed. However, 3.6.5 Readers refer to Chapter can 2for examples. detailed to Chapter several of file parts. 2,consists INP main the Similar dead load was 1.0 analysis load the was the so used, in combination used Civic Center, more analysis conservative, live the to make full the However, reference with collapse to the incident of Hartford the for case 1.for case 3.6 FIGURE 3.6.4

Axial Force(N) –100000 –110000 + ao Abaqus Major ebr Removals Member –40000 –70000 –90000 –80000 –60000 –30000 –20000 –50000 –10000

Structural Analysis and Design to Collapse Prevent Disproportionate

1.0 live (live 1 as load taken is Case 1 Case

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Axial Force(N) Axial Force(N) –40000 –10000 –140000 –120000 –100000 –30000 –20000 –80000 –60000 –40000 –20000 Structural Analysis and Design to Collapse Prevent Disproportionate 0 0

...... 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ...... 2.0 1.8 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 Response of axial force in the Top removed the - cen the forcein near chord of axial Response Response of axial force in the diagonal strut near the removed the near strut diagonal the force in of axial Response © 2016 Group, by Taylor LLC & Francis ® screenshot reprinted with permission from from permission with reprinted screenshot ® screenshot reprinted with permission from from permission with reprinted screenshot Ti Time(S) 1.6 me(S) . . . 3.2 2.6 2.4 2.2 . . . 3.2 3.0 2.8 2.4 2.62.2 . 3.0 2.8 3.4 3.4 1/25/16 11:27AM K24849.indb 65 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 mission from Dassault Systèmes.) Dassault from mission Progressive Collapse Design and Analysis ofSpaceStructures FIGURE 3.11 FIGURE to members close support the overstresses in B. caused the and supports support, at those locations B primarily remaining into the mostbecause by of loads support the carried Awere redistributed adjacentto close bers the support (B) is become overstressed. This removal after that It of seen be mem support can A, some structural removal the after of support. structure the shows in deflection of vertical also which the distribution the location the members and of support Figure 3.10, shown Aare in (Abaqus A. port 3.10 FIGURE port B. It can be seen that after removal B.port after that It of seen be support, the can bottom the C Figure 3.12 bottom chord force the sup showsnear in axial the Figure 3.11 shows contour removal stress after the of support. the

Contour plot of vertical displacement after removal of central sup removal of central after displacement Contour plot of vertical Contour plot of stress. (AbaqusContour plot of stress. ® screenshot reprinted with permission from Dassault Systèmes.) Dassault from permission with reprinted screenshot C © 2016 Group, by Taylor LLC & Francis A A ® screenshot reprinted with per with reprinted screenshot B B - - - - 1/25/16 11:27AM 65 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 K24849.indb 66 66 Abedi, K., and Shekastehband, B. 2008. Static stability behavior of behavior plane B. K.,Abedi, 2008. stability Static Shekastehband, and K.,Abedi, Parke, and G. 1996. of collapse single-layer Progressive braced References of aprogressive possibility the collapse. increase will which it triggered, be as may can of several failure cause the ture members, averysuch as heavy snow load, aprogressive collapse of struc the whole However,the structure. live abnormal under an load condition, collapse the to trigger of unlikely member is of asinglestructural aspace live grid, anormal supporting load—removalstructure—for noteanalysis, due that weof also redundancy the can high to the 3.6.5.4 215 is which for relevant the kN members. capacity, force exceeded buckling axial the the chord as buckled 3.12 FIGURE found in Fu Parkefound and in (2015). aprogressive be trigger and can results collapse. analysis Detailed adjacent member failures supports, to likely cause further are which whenures, because asupport load to the the fails, redistributed is However, to paidbe greatneeds attention to also support fail Structures Space of Journal International structures. double-layer tensegrity Structures Space of Journal International domes. Axial Force(N)

Structural Analysis and Design to Collapse Prevent Disproportionate –300000 –250000 –200000 –150000 –100000 Progressive Collapse Potential Check Potential Collapse Progressive –50000

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Based on the above on the Based 3.4 - - 1/25/16 11:27AM K24849.indb 67 Downloaded By: 10.3.98.104 At: 22:16 28 Sep 2021; For: 9781315228938, chapter3, 10.1201/b19662-4 Feld, J., Carper, K.L. and 1997. Construction Failures 2005. of 3: Eurocode Design for Standardization. Committee European Geiger, D., A., D. Stefaniuk, Chen, and 1986. construction and design The Fuller, R.B. 1975. Thinking of Explorations in Synergetics the Geometry Fu, F., Parke, and G. 2015. resistance progressive collapse of the Assessment 1978.ofENR. flaws. acombination had roof ENR space Collapsed truss CSI (Computer 2013. Structures). and de France. 2005. Scientifiques et Synthese desIngenieurs National Conseil of steelwork use Institution). 2001. in Standards BSI (British Structural Progressive Collapse Design and Analysis ofSpaceStructures Shekastehband, B.,Shekastehband, K., M.R. Abedi, Chenaghlou, 2011. and anal Sensitivity B.,Shekastehband, K. 2013. Abedi, sys and of Collapse behavior tensegrity O’Rourke, M., Wikoff, and J. 2014. during collapse roof Snow-related the winter for pro 1988. E. of space trusses path analysis Murtha-Smith, Alternate investigation con 1978. Associates. engineering of the Report Zetlin Lev N.B.,Kahla, tensegrity on of Moussa, acable B. and 2002. rupture Effect Mizan Roof Collapse at the Sultan on Stadium Investigation Committee 2003. analy collapse Administration). GSAProgressive (General Services 1993-1-1. for Standardization. Committee London: European EN BS 1-1: Part for buildings. rules and structures. steel rules General 22. June pp. Symposium Proceedings IASS of In spaceand frames. of cable two Olympics: domes Korean for the membranes Shells, Collier Macmillan Publishers. Underof double-layer review. space structures. grid Wiley &Sons. Structures. and Computer Tourism, of Urban Transportation, Design, Sea. and Paris: Ministry l’eddondrement de Gaulle. 2E de Paris-Charles d’une du terminal partie de causes les sur TravauxDes administrative de commission la 5950. BS tions. London: BSI. 1: Part welded and Code sec ofbuildings. for practice design—rolled Steel Research due Constructional of loss. Journal systems to member ofysis tensegrity Dynamics and Structural of Journal due Stability International tems to cable rupture. Engineers. of Civil Society 2010–2011:of Implications building for codes Structural of Journal Engineering collapse. gressive 18, January on roof 1978.truss June 12. space Coliseum Hartford of collapse the of the causes the cerning Structures Space of Journal International systems. Vols.Iman. 1–3, December. Terengganu, Kuala Abidin, Terengganu Zainal Darul Mizan Sultan at collapse roof Stadium the on 2009. Abidin. report Final Zainal DC: GSA. Washington, projects. modernization majorand for office new federal buildings guidelines design and sis

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