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1、外文原文Response of a reinforced concrete infilled-frame structure to removal of two adjacent columnsMehrdad Sasani_Northeastern University, 400 Snell Engineering Center, Boston, MA 02115, United StatesReceived 27 June 2007; received in revised form 26 December 2007; accepted 24 January 2021Available on
2、line 19 March 2021AbstractThe response of Hotel San Diego, a six-story reinforced concrete infilled-frame structure, is evaluated following the simultaneous removal of two adjacent exterior columns. Analytical models of the structure using the Finite Element Method as well as the Applied Element Met
3、hod are used to calculate global and local deformations. The analytical results show good agreement with experimental data. The structure resisted progressive collapse with a measured maximum vertical displacement of only one quarter of an inch (6.4 mm). Deformation propagation over the height of th
4、e structure and the dynamic load redistribution following the column removal are experimentally and analytically evaluated and described. The difference between axial and flexural wave propagations is discussed. Three-dimensional Vierendeel (frame) action of the transverse and longitudinal frames wi
5、th the participation of infill walls is identified as the major mechanism for redistribution of loads in the structure. The effects of two potential brittle modes of failure (fracture of beam sections without tensile reinforcement and reinforcing bar pull out) are described. The response of the stru
6、cture due to additional gravity loads and in the absence of infill walls is analytically evaluated. c 2021 Elsevier Ltd. All rights reserved.Keywords: Progressive collapse; Load redistribution; Load resistance; Dynamic response; Nonlinear analysis; Brittle failure1. IntroductionTheprincipalscopeofsp
7、ecificationsistoprovidegeneralprinciplesandcomputationalmethodsinordertoverifysafetyofstructures.The“safetyfactor,whichaccordingtomoderntrendsisindependentofthenatureandcombinationofthematerialsused,canusuallybedefinedastheratiobetweentheconditions.Thisratioisalsoproportionaltotheinverseoftheprobabi
8、lity(risk)offailureofthestructure.Failurehastobeconsiderednotonlyasoverallcollapseofthestructurebutalsoasunserviceabilityor,accordingtoamoreprecise.Commondefinition.Asthereachingofa“limitstatewhichcausestheconstructionnottoaccomplishthetaskitwasdesignedfor.Therearetwocategoriesoflimitstate:(1)Ultima
9、telimitsate,whichcorrespondstothehighestvalueoftheload-bearingcapacity.Examplesincludelocalbucklingorglobalinstabilityofthestructure;failureofsomesectionsandsubsequenttransformationofthestructureintoamechanism;failurebyfatigue;elasticorplasticdeformationorcreepthatcauseasubstantialchangeofthegeometr
10、yofthestructure;andsensitivityofthestructuretoalternatingloads,tofireandtoexplosions.(2)Servicelimitstates,whicharefunctionsoftheuseanddurabilityofthestructure.Examplesincludeexcessivedeformationsanddisplacementswithoutinstability;earlyorexcessivecracks;largevibrations;andcorrosion.Computationalmeth
11、odsusedtoverifystructureswithrespecttothedifferentsafetyconditionscanbeseparatedinto:(1)Deterministicmethods,inwhichthemainparametersareconsideredasnonrandomparameters.(2)Probabilisticmethods,inwhichthemainparametersareconsideredasrandomparameters.Alternatively,withrespecttothedifferentuseoffactorso
12、fsafety,computationalmethodscanbeseparatedinto:(1)Allowablestressmethod,inwhichthestressescomputedundermaximumloadsarecomparedwiththestrengthofthematerialreducedbygivensafetyfactors.(2)Limitstatesmethod,inwhichthestructuremaybeproportionedonthebasisofitsmaximumstrength.Thisstrength,asdeterminedbyrat
13、ionalanalysis,shallnotbelessthanthatrequiredtosupportafactoredloadequaltothesumofthefactoredliveloadanddeadload(ultimatestate).Thestressescorrespondingtoworking(service)conditionswithunfactoredliveanddeadloadsarecomparedwithprescribedvalues(servicelimitstate).Fromthefourpossiblecombinationsofthefirs
14、ttwoandsecondtwomethods,wecanobtainsomeusefulcomputationalmethods.Generally,twocombinationsprevail:(1)deterministicmethods,whichmakeuseofallowablestresses.(2)Probabilisticmethods,whichmakeuseoflimitstates.Themainadvantageofprobabilisticapproachesisthat,atleastintheory,itispossibletoscientificallytak
15、eintoaccountallrandomfactorsofsafety,whicharethencombinedtodefinethesafetyfactor.probabilisticapproachesdependupon:(1)Randomdistributionofstrengthofmaterialswithrespecttotheconditionsoffabricationanderection(scatterofthevaluesofmechanicalpropertiesthroughoutthestructure);(2)Uncertaintyofthegeometryo
16、fthecross-sectionsandofthestructure(faultsandimperfectionsduetofabricationanderectionofthestructure);(3)Uncertaintyofthepredictedliveloadsanddeadloadsactingonthestructure;(4)Uncertaintyrelatedtotheapproximationofthecomputationalmethodused(deviationoftheactualstressesfromcomputedstresses).Furthermore
17、,probabilistictheoriesmeanthattheallowableriskcanbebasedonseveralfactors,suchas:(1)Importanceoftheconstructionandgravityofthedamagebyitsfailure;(2)Numberofhumanliveswhichcanbethreatenedbythisfailure;(3)Possibilityand/orlikelihoodofrepairingthestructure;(4)Predictedlifeofthestructure.Allthesefactorsa
18、rerelatedtoeconomicandsocialconsiderationssuchas：(1)Initialcostoftheconstruction;(2)Amortizationfundsforthedurationoftheconstruction;(3)Costofphysicalandmaterialdamageduetothefailureoftheconstruction;(4)Adverseimpactonsociety;(5)Moralandpsychologicalviews. Thedefinitionofalltheseparameters,foragiven
19、safetyfactor,allowsconstructionattheoptimumcost.However,thedifficultyofcarryingoutacompleteprobabilisticanalysishastobetakenintoaccount.Forsuchananalysisthelawsofthedistributionoftheliveloadanditsinducedstresses,ofthescatterofmechanicalpropertiesofmaterials,andofthegeometryofthecross-sectionsandthes
20、tructurehavetobeknown.Furthermore,itisdifficulttointerprettheinteractionbetweenthelawofdistributionofstrengthandthatofstressesbecausebothdependuponthenatureofthematerial,onthecross-sectionsandupontheloadactingonthestructure.Thesepracticaldifficultiescanbeovercomeintwoways.Thefirstistoapplydifferents
21、afetyfactorstothematerialandtotheloads,withoutnecessarilyadoptingtheprobabilisticcriterion.Thesecondisanapproximateprobabilisticmethodwhichintroducessomesimplifyingassumptions(semi-probabilisticmethods).As part of mitigation programs to reduce the likelihood of mass casualties following local damage
22、 in structures, the General Services Administration 1 and the Department of Defense 2 developed regulations to evaluate progressive collapse resistance of structures. ASCE/SEI 7 3 defines progressive collapse as the spread of an initial local failure from element to element eventually resulting in c
23、ollapse of an entire structure or a disproportionately large part of it. Following the approaches proposed by Ellinwood and Leyendecker 4, ASCE/SEI 7 3 defines two general methods for structural design of buildings to mitigate damage due to progressive collapse: indirect and direct design methods. G
24、eneral building codes and standards 3,5 use indirect design by increasing overall integrity of structures. Indirect design is also used in DOD 2. Although the indirect design method can reduce the risk of progressive collapse 6,7 estimation of post-failure performance of structures designed based on
25、 such a method is not readily possible. One approach based on direct design methods to evaluate progressive collapse of structures is to study the effects of instantaneous removal of load-bearing elements, such as columns. GSA 1 and DOD 2 regulations require removal of one load bearing element. Thes
26、e regulations are meant to evaluate general integrity of structures and their capacity of redistributing the loads following severe damage to only one element. While such an approach provides insight as to the extent to which the structures are susceptible to progressive collapse, in reality, the in
27、itial damage can affect more than just one column. In this study, using analytical results that are verified against experimental data, the progressive collapse resistance of the Hotel San Diego is evaluated, following the simultaneous explosion (sudden removal) of two adjacent columns, one of which
28、 was a corner column. In order to explode the columns, explosives were inserted into predrilled holes in the columns. The columns were then well wrapped with a few layers of protective materials. Therefore, neither air blast nor flying fragments affected the structure.2. Building characteristicsHote
29、l San Diego was constructed in 1914 with a south annex added in 1924. The annex included two separate buildings. Fig. 1 shows a south view of the hotel. Note that in the picture, the first and third stories of the hotel are covered with black fabric. The six story hotel had a non-ductile reinforced
30、concrete (RC) frame structure with hollow clay tile exterior infill walls. The infills in the annex consisted of two withes (layers) of clay tiles with a total thickness of about 8 in (203 mm). The height of the first floor was about 190800 (6.00 m). The height of other floors and that of the top fl
31、oor were 100600 (3.20 m) and 1601000 (5.13 m), respectively. Fig. 2 shows the second floor of one of the annex buildings. Fig. 3 shows a typical plan of this building, whose response following the simultaneous removal (explosion) of columns A2 and A3 in the first (ground) floor is evaluated in this
32、paper. The floor system consisted of one-way joists running in the longitudinal direction (NorthSouth), as shown in Fig. 3. Based on compression tests of two concrete samples, the average concrete compressive strength was estimated at about 4500 psi (31 MPa) for a standard concrete cylinder. The mod
33、ulus of elasticity of concrete was estimated at 3820 ksi (26 300 MPa) 5. Also, based on tension tests of two steel samples having 1/2 in (12.7 mm) square sections, the yield and ultimate tensile strengths were found to be 62 ksi (427 MPa) and 87 ksi (600 MPa), respectively. The steel ultimate tensil
34、e strain was measured at 0.17. The modulus of elasticity of steel was set equal to 29 000 ksi (200 000 MPa). The building was scheduled to be demolished by implosion. As part of the demolition process, the infill walls were removed from the first and third floors. There was no live load in the build
35、ing. All nonstructural elements including partitions, plumbing, and furniture were removed prior to implosion. Only beams, columns, joist floor and infill walls on the peripheralbeams were present.3. SensorsConcrete and steel strain gages were used to measure changes in strains of beams and columns.
36、 Linear potentiometers were used to measure global and local deformations. The concrete strain gages were 3.5 in (90 mm) long having a maximum strain limit of 0.02. The steel strain gages could measure up to a strain of 0.20. The strain gages could operate up to a several hundred kHz sampling rate.
37、The sampling rate used in the experiment was 1000 Hz. Potentiometers were used to capture rotation (integral of curvature over a length) of the beam end regions and global displacement in the building, as described later. The potentiometers had a resolution of about 0.0004 in (0.01 mm) and a maximum
38、 operational speed of about 40 in/s (1.0 m/s), while the maximum recorded speed in the experiment was about 14 in/s (0.35 m/s). 4. Finite element modelUsing the finite element method (FEM), a model of the building was developed in the SAP2000 8 computer program. The beams and columns are modeled wit
39、h Bernoulli beam elements. Beams have T or L sections with effective flange width on each side of the web equal to four times the slab thickness 5. Plastic hinges are assigned to all possible locations where steel bar yielding can occur, including the ends of elements as well as the reinforcing bar
40、cut-off and bend locations. The characteristics of the plastic hinges are obtained using section analyses of the beams and columns and assuming a plastic hinge length equal to half of the section depth. The current version of SAP2000 8 is not able to track formation of cracks in the elements. In ord
41、er to find the proper flexural stiffness of sections, an iterative procedure is used as follows. First, the building is analyzed assuming all elements are uncracked. Then, moment demands in the elements are compared with their cracking bending moments, Mcr . The moment of inertia of beam and slab se
42、gments are reduced by a coefficient of 0.35 5, where the demand exceeds the Mcr. The exterior beam cracking bending moments under negative and positive moments, are 516 k in (58.2 kN m) and 336 k in (37.9 kN m), respectively. Note that no cracks were formed in the columns. Then the building is reana
43、lyzed and moment diagrams are re-evaluated. This procedure is repeated until all of the cracked regions are properly identified and modeled. The beams in the building did not have top reinforcing bars except at the end regions (see Fig. 4). For instance, no top reinforcement was provided beyond the
44、bend in beam A1A2, 12 inches away from the face of column A1 (see Figs. 4 and 5). To model the potential loss of flexural strength in those sections, localized crack hinges were assigned at the critical locations where no top rebar was present. Flexural strengths of the hinges were set equal to Mcr.
45、 Such sections were assumed to lose their flexural strength when the imposed bending moments reached Mcr.The floor system consisted of joists in the longitudinal direction (NorthSouth). Fig. 6 shows the cross section of a typical floor. In order to account for potential nonlinear response of slabs a
46、nd joists, floors are molded by beam elements. Joists are modeled with T-sections, having effective flange width on each side of the web equal to four times the slab thickness 5. Given the large joist spacing between axes 2 and 3, two rectangular beam elements with 20-inch wide sections are used between the joist and the longitudinal beams of axes 2 and 3 to model the slab in the longitudinal direction. To model the behavior of the slab in the transverse direction, equally spaced parallel beams with 20-inch wide rectangular sections are used. There