1、外文原文Response of a reinforced concrete infilled-frame structure to removal of twoadjacent columnsMehrdad Sasan_iNortheastern University, 400 Snell Engineering Center, Boston, MA 02115, UnitedStatesReceived 27 June 2007; received in revised form 26 December 2007; accepted 24January 2008Available onlin

2、e 19 March 2008AbstractThe 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 Method

3、 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 mm). Deformation propagation over the height of the struct

4、ure 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 with the p

5、articipation 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 beamsections without tensile reinforcement and reinforcing bar pull out) are described. The response of the structure due

6、 to additional gravity loads and in the absence of infill walls is analytically evaluated.o a more precise.Common definition.As the reaching of alimit state ”which causes the constructionnot to accomplish the task itwas designed for. There aretwo categori(1)Ultimate limit sate,which corresponds to t

7、hehighest value of the load-bearingcapacity. Examples includelocal buckling or global instabilityc 2008 Elsevier Ltd. All rights reserved.Keywords: Progressive collapse; Load redistribution; Load resistance;Dynamic response; Nonlinear analysis; Brittle failure1. IntroductionThe principal scope of sp

8、ecifications is to provide general principles and computational methods in order to verify safet y of structures. The “ safety factor ” , which according t o modern trends is independent of the nature and combination of the materials used, can usually be defined as the rati o between the conditions.

9、 This ratio is also proportionaltothe inverse of the probability( risk ) of failure of the structure.Failurehas tobe considerednot only asoverall collapseof thestructure but also asunserviceability or,accordingtes of limit stateof the structure; failure of somesections and subsequent transformation

10、of the structure intoa mechanism; failureby fatigue;elastic or plasticdeformation or creep that cause a substantial change of the geometry of the structure;and sensitivity of the structureto alternating loads, to fire and to explosions.(2)Service limit states, which are functions of the use and dura

11、bility of the structure. Examples include excessive deformations and displacements without instability;earlyor excessive cracks;large vibrations; and corrosion.Computationalmethods used to verifystructures withrespectto the different safety conditions can beseparatedinto:(1)Deterministicmethods, in

12、which themainparametersareconsidered asnonrandom parameters.(2)Probabilisticmethods, in which themainparametersareconsidered asrandom parameters.Alternatively,with respect to the differentuse offactorsof safety, computational methods canbe separated into:(1)Allowablestress method, in whichthe stress

13、es computedunder maximumloads are compared withthe strength ofthe material reducedby given safety factors.(2)Limit states method, in which thestructure may be proportioned on the basis of its maximumstrength. This strength,asdeterminedbyrationalanalysis,shallnot be less thanthatrequiredtosupporta fa

14、ctoredloadequal to the sumofthe factoredlive loadand deadload( ultimate state).The stresses corresponding to working ( service ) conditionswith unfactored live and dead loads are compared with pres cribed values ( service limitstate ) . From the four possible combinations of the firsttwo and second

15、two methods,we can obtain some useful computational methods. Generally, t wo combinations prevail:d upon :(1) Random distributionof strength of materialswith respectto the conditions of fabrication and erection ( scatter of the values of mechanical properties through outthe structure ); (2) Uncertai

16、nty of the geometry of the cross-section sand of the structure( faults and imperfectionsdue to fabrication and erectionof the structure );(3) Uncertainty of the predicted live loads and dead loadsactingon thestructure;(4)Uncertaintyrelated to theapproximationof thecomputational method used( deviatio

17、n oftheactualstressesfromcomputed stresses). Furthermore,probabilistictheoriesmeanthat the allowablerisk can bebasedon several factors, such as :(1) Importance of the construction and gravity of the damageby itsfailure; (2)Number of human liveswhich can be threatenedby this failure;(3)Possibilityand

18、/or likelihoodofrepairingthe structure;(4) Predictedlifeof the structure.All these factors arerelated to economicand socialconsiderationssuch as：(1) Initial cost of the construction;(2) Amortization funds for the duration of the construction;. (2)Probabilisticmethods, whichmake use oflimit states.Th

19、e main advantageof probabilisticapproachesis that,at least in theory, itis possibleto scientificallytakeintoaccount all randomfactors of safety, whichare thencombined to define the safety babilisticapproachesdepen(1)deterministicmethods, which make use of allowable stresses(3)Cost of physi

20、cal and materialdamage due to the failureofthe construction;(4)(5)The definitionof all theseparameters, for a given safsafety factorsto the material andto theloads,withoutnecessarily adopting the probabilisticcriterion.Thesecond is an approximate probabilisticmethodwhich introducessome simplifying a

21、ssumptions ( semi-probabilisticmethods )As3 definesAdverse impact on society;Moral and psychological views.part of mitigation programs to reduce the likelihood of mass casualties following local damagein structures, the General Services Administration 1 and the Department of Defense 2 developed regu

22、lations to evaluateprogressive collapse resistance of structures. ASCE/SEI 7 progressive collapse as the spread of an initial local failure fromelement to element eventually resulting in collapse of an entire structure or a thedifficultyof carryingout a completeprobabilisticanalysishas tobe taken in

23、toaccount. For such an analysis the laws of the distributionof the live load and itsinduced stresses,of the scatterof mechanicalproperties ofmaterials,and ofthe geometryof the cross-sections and the structurehaveto be known.Furthermore, itis difficultto interprettheinteraction between the law ofdist

24、ributionofstrengthandthat of stresses because bothdepend uponthenatureof thematerial, onthe cross-sectionsand upontheload acting on the structure.These practicaldifficultiescaconstructionetyatdifferentapplyn be overcomethe optimum cost. However,is toin two ways. The firstfactor, allowsdisproportiona

25、tely large part of it. Following the approaches proposed by Ellinwood and Leyendecker 4, ASCE/SEI 7 3 defines twogeneral methods for structural design of buildings to mitigate damage due to progressive collapse: indirect and direct design methods. General building codes and standards 3,5 use indirec

26、t design by increasingoverall 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 ofstructures designed based on such a method is not readily possible. One approach

27、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 regulationsrequire removal of one load bearing element. These regulations are meant to evaluate general integrity

28、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 initial damagecan affect more than just one column. In t

29、his 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 was a corner column. In order to explode the columns,

30、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.I. A sGuih view of hcxel San IJiego, Center sinicmrr is siudrd in ihis paper.Lig.工 S2.

31、 Buildi ng characteristicsHotel San Diego was con structed in 1914 with a south annex added in1924. The annex in cluded two separate build in gs.Fig. 1 shows a southview of the hotel. Note that in the picture, the first and third stories of the hotel are covered with black fabric. The six story hote

32、l had a non-ductile rein forced con crete (RC) frame structure with hollow clay tile exterior infill walls. The in fills in the annex con sisted of two withes (layers) of clay tiles with a total thick ness of about 8 in (203mm). The height of the first floor was about 190- 800 m). The heightof other

33、 floors and that of the top floor were 100 - 600 m) and 160 - 1000 m), respectively. Fig. 2 shows the sec ond floor of one of the annexbuild in gs. Fig. 3 shows a typical pla n of this build ing, whose resp onsefollowing the simultaneous removal (explosion) of columns A2 and A3 in the first (ground)

34、 floor is evaluated in this paper. The floor system consisted of one-way joists running in the longitudinal direction (North - South), 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 sta

35、ndard concrete cylinder. The modulus 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 mm) square sections, the yield and ultimate tensile strengths were found to be 62 ksi (427 MPa) and 87 ksi (600 MPa), respectively.

36、The steel ultimate tensile strain was measured at . 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 l

37、ive load in the building. All nonstructural elements including partitions, plumbing, and furniture were removed prior to implosion.Only beams, columns, joist floor and infill walls on the peripheral beams were present.3. SensorsConcrete and steel strain gages were used to measure changes in strains

38、of beams and columns. Linear potentiometers were used to measure global and local deformations. The concrete strain gages were in (90 mm) long having a maximumstrain limit of . The steel strain gages could measure up to a strain of . The strain gages could operateup to a severalhundred kHz sampling

39、rate. The sampling rate used in the experiment was 1000 Hz. Potentiometers were used to capture rotation (integral of curvature over a length) of the beamend regions and global displacementm/s).in the building,as described later. The potentiometers had a resolutionof about in mm) and a maximumoperat

40、ional speed of about 40 in/s m/s),while the maximum recorded speed in the experime nt was about 14 in/sB 丄6E4.98 m4 gm m-2-4gtp34gtp34brE34brE3P 3. TSpical plan of Hokl San (South Anne?! I First floor Kmowdl columns arc crossed.14-415 0 (18 rmn)VETTiXflrtlfculuiiin JXHJ 4a) Beiu叮 A3B3 LII stvuiki fl

41、uui; uiid (bi Bcdiii M- A24. Fin ite eleme nt modelUsing the finite element method (FEM), a model of the building wasdeveloped in the SAP2000 8 computer program. The beams and colu mnsare modeled with Berno ulli beam eleme nts. Beams have T or L sect ions with effective flange width on each side of

42、the web equal to four times the slab thick ness 5. Plastic hin ges are assig ned to all possiblelocations where steel bar yielding can occur, including the ends of eleme nts as well as the reinforcing bar cut-off and bend locati ons. The characteristics of the plastic hinges are obtained using secti

43、on analyses of the beams and columns and assuming a plastic hinge length equal to half of the section depth. The current version of A1l -20 SflHTGnnMsffir-3i 口 W (10 EK IIM吟IA2J 口軸-iftlwMl5CIB ITE2 SiS 1A mm).#2 py ur wren M rnm V gTFPHJSAP2000 8 is not able to track formation of cracks in the eleme

44、nts. In order 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

45、and slab segments are reduced by a coefficient of 5, where the demand exceeds the Mcr. The exterior beam cracking bending moments under negative and positive moments, are 516 k in kN m) and 336 k in kN m), respectively. Note that no cracks were formed in the columns. Then the building is reanalyzed

46、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 bend i

47、n beam A1 - A2, 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. Su

48、ch sections were assumed to lose their flexural strength when the imposed bending moments reached Mcr.9.The floor system con sisted of joists in the Ion gitudi nal directi on(North South). Fig. 6 shows the cross sect ion of a typical floor. I norder to acco unt for pote ntial non li near resp onse o

49、f slabs and joists, floors are molded by beam eleme nts. Joists are modeled with T-secti ons, having effective flange width on each side of the web equal to four times the slab thick ness 5. Give n the large joist spac ing betwee n axes 2and 3, two rectangularbeamelements with 20-inch wide sections

50、are usedbetwee n the joist and the Ion gitud inal beams of axes 2 and 3 to model the slab in the Ion gitud inal directi on. To model the behavior of the slab in the transverse direction, equally spaced parallel beams with20-i nch wide recta ngular sect ions are used. There is a differe nee betwee n

51、the shear flow in the slab and that in the beamelements with rectangular secti ons modeli ng the slab. Because of this, the torsi onal stiff ness is setequal to on e-half of that of the gross sect ions The building had infill walls on 2nd, 4th, 5th and 6th floors on the spandrel beams with some open

52、ings . windows and doors). As Fig, 5, Location of bends in beam top re infnicenient (in an adjacent inncKbuilding at u location similar to beam Al A2. close to column A11mentioned before and as part of the demolition procedure, the infill walls in the 1st and 3rd floors were removed before the test.

53、 The infill walls were made of hollow clay tiles, which were in good condition. The net area of the clay tiles was about 1/2 of the gross area. The in-plane action of the infill walls contributes to the building stiffness and strength and affects the building response. Ignoring the effects of the in

54、fill walls and excluding them in the model would result in underestimating the building stiffness and strength.Using the SAP2000 computer program 8, two types of modeling for the infills are considered in this study: one uses two dimensional shell elements (Model A) and the other uses compressive st

55、ruts (Model B) as suggested in FEMA356 10 guidelines. Model A (infills modeled by shell elements)Infill walls are modeled with shell elements. However, the current version of the SAP2000 computer program includes only linear shell elements and cannot account for cracking. The tensile strength of the

56、 infill walls is set equal to 26 psi, with a modulus of elasticity of 644 ksi 10. Because the formation ofcracks has a significant effect on the stiffness of the infill walls, the following iterative procedure is used to account for crack formation:(1) Assuming the infill walls are linear and uncrac

57、ked, a nonlinear time history analysis is run. Note that plastic hinges exist in the beam elements and the segments of the beamelements where momentdemandexceeds the cracking moment have a reduced moment of inertia.(2)The cracking pattern in the infill wall is determined by comparingat joint A3 in t

58、he second floor.stresses in the shells developed during the analysis with the tensile strength of infills.(3) Nodes are separated at the locations where tensile stress exceeds tensile strength. These steps are continued until the crack regions are properly modeled. Model B (infills modeled by struts

59、)Infill walls are replaced with compressive struts as described in FEMA 356 10 guidelines. Orientations of the struts are determined from the deformed shape of the structure after column removal and the location of openings. Column removalRemoval of the columns is simulated with the following proced

60、ure.(1) The structure is analyzed under the permanent loads and the internal forces are determined at the ends of the columns, which will be removed.(2) The model is modified by removing columns A2 and A3 on the first floor. Again the structure is statically analyzed under permanent loads. In this c