Seismic analysis of concrete structures within nuclear industry PEDRAM TABATABAEI ARAGHI

Transcription

1 MASTER OF SCIENCE THESIS STOCKHOLM, SWEDEN 2014 Seismic nlysis of concrete structures within nucler inustry PEDRAM TABATABAEI ARAGHI KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT

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3 Seismic nlysis of concrete structures within nucler inustry Perm Tbtbei Arghi Mster Thesis KTH Royl Institute of Technology Deprtment of Civil n Architecturl Engineering Division of Concrete Structures TRITA-BKN, Mster Thesis 422, Concrete Structures 2014 ISSN ISRN KTH/BKN/EX SE

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5 Abstrct Erthquke hs lwys been hzr for civil structures n keeping the structures integrity uring n fter n erthquke is of vitl importnce. This phenomenon s impct is suen n there is little or no wrning to mke the preprtions for this nturl isster. Much mge hs been one on structures which hve le to mjor collpses n loss of mny lives. Civil structures such s nucler power plnts re esigne to withstn erthqukes n in the event of mjor seismic event, to shut own sfely. The im of this thesis is to present the seismic esign proceures for concrete structures, in bsic n etile esign, ccoring to Eurocoe 8. Also to escribe n unerstn the ifference between Eurocoe 8 n the DNB in seismic nlysis of nucler power plnts. To evlute the use of DNB inste of Eurocoe 8 with Sweish seismic conitions is lso nother im in this thesis. Los n ctions which pply on structure in seismic esign n corresponing lo combintions re presente for Eurocoe 8 n the DNB. An exmple is lso given to clrify the esign of primry seismic bems n columns with high uctility clss (DCH). A cse stuy of nucler structure from test project nme SMART2013 hs been me by nlyzing n compring the results from Eurocoe 8 n the DNB with finite element moel in FEM-Design softwre. Nturl frequencies of the moel re compre with the teste moel in SMART2013-project to evlute the finite element moeling. The moel is seismiclly nlyze with lo combintions from Eurocoe 8 n the DNB with Sweish elstic groun response spectrum with the probbility of Results obtine from the primry seismic bems n columns re compre n nlyze. Being on the sfe n conservtive sie of the esign vlues is lwys preferre in seismic nlysis of vitl n sensitive structure such s nucler power plnts. The results from this thesis shows tht, purely structurl, combintion of Sweish elstic groun response spectrum with the Eurocoe 8 lo combintion will give more conservtive vlues thn the DNB. Key wors: Erthquke, nucler power plnts, seismic esign, Eurocoe 8, DNB, lo combintion, primry seismic bem, primry seismic column, high uctility clss (DCH), SMART2013, finite element nlysis, nturl frequency, seismic nlysis, elstic response spectrum, groun response spectrum III

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7 Smmnfttning I stor elr v värlen hr jorbävningr llti vrit ett hot för byggners integritet. Krktären v en jorbävning är plötslig och förnles v små eller ing vrningr. Om jorbävningen meför tt byggner kollpsr sker oft stor förluster v människoliv irekt eller inirekt. Kärnkrftsverk är nläggningr som imensioners för tt klr jorbävningr och sk kunn gå till säker vställning vi en sån hänelse. Syftet me föreliggne rpport är tt presenter hur betongkonstruktioner imensioners för jorbävning enligt Euroko 8. Rpporten reogör även för skillner melln tt imensioner enligt Euroko 8 och DNB (Dimensionering v nukleär byggnskonstruktioner) smt hur et slår tt nvän Euroko me svensk seismisk förhållnen. Lster och lstkombintioner som nväns vi jorbävningsimensionering v betongbyggner är presenter enligt båe Euroko och DNB. Ett exempel presenters för tt vis hur primär blkr och pelre me hög uktilitetsklss (DCH) imensioners för seismisk påverkn. En fllstuie v en nukleär byggn från ett interntionellt projekt, SMART2013, hr nvänts för tt nlyser och utvärer resultten från Euroko och DNB. Byggnen hr nlyserts me finit element me progrmvrn FEM Design. Moellens riktighet hr verifierts genom tt jämför bln nnt egenfrekvenser me e från officiell rpporter från SMART2013. Byggnen är nlyser för seismisk lst enligt svensk förhållnen me mrkresponsspektr 10-5, och primär blkr och pelre hr nlyserts och utvärerts enligt båe Euroko och DNB. Nyckelor: Jorbävning, kärnkrftverk, jorbävningsimensionering, Euroko 8, DNB, lstkombintion, primär seismisk blkr, primär seismisk pelre, hög uktilitetsklss (DCH), SMART2013, finit element nlys, egenfrekvens, seismisk nlys, elstiskresponsspektr, mrkresponsspektr. V

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9 List of nottions The cross sectionl re of one stirrup Chrcteristic seismic ction Designe seismic ction The concrete re of the cross-section The therml coefficient The exposure coefficient The imeter of confine core (to the centerline of hoops) De weight Displcement The vlue of the consiere seismic ction effect on the vibrtion moe The vlue of the consiere seismic ction effect on the vibrtion moe The seismic ction effect uner consiertion Seismic lo ue to esigne DBE The horizontl force cting on storey Chrcteristic vlue of permnent ction Wter pressure ifference between norml wter level n time vrible wter level Soil pressure ue to movble surfce lo Wter pressure Erth pressure Live lo The floor imension perpeniculr to the irection of the seismic ction The sum of esign vlues of the moments of resistnce of the columns frming the joint The sum of esign vlues of the moments of resistnce of the bems frming the joint The torsionl moment pplie t storey bout verticl xis Process relte los uring norml opertion n shutown perio Process relte los uring opertion isturbnce The norml force from tensioning or externl pressure VII

10 Pre-stresse force Chrcteristic vlue of the ccompnying vrible ction Q k Chrcteristic impose point lo The esign spectrum Snow lo Perio of vibrtion The perio of vibrtion of moe The vibrtion perios of moe The vibrtion perios of moe Upper limit of the perio of the constnt spectrl ccelertion brnch Lower limit of the perio of the constnt spectrl ccelertion brnch Vlue efining the beginning of the constnt isplcement response rnge of the spectrum Nturl perio of vibrtion The funmentl perio of the builing within verticl plne Sher resistnce of ech structurl wll The force tht is neee to be tken by sher reinforcement Sher lo cpcity Web compression filure Velocity Win lo The storey height in meters Nturl frequency of vibrtion Height of the primry seismic bem Height of the wll The lrgest cross-section of the column Depth of confine core (to the centerline of hoops) The esign groun ccelertion VIII

11 Gross cross-sectionl with The lrgest cross-sectionl imension of the column norml to the bem xis Minimum imension of the concrete core (to the insie of the hoops) With of confine core (to the centerline of the hoops) Distnce between consecutive engge brs With of the primry seismic bem Thickness of the web Minimum imension of the trnsverse brs Minimum imeter of sher reinforcement Structurl eccentricity The istnce between the center of stiffness n the center of mss, mesure long - irection, which is norml to the irection of nlysis consiere Accientl eccentricity of storey mss Pek vlue of the erthquke inuce resisting force Chrcteristic compressive strength of concrete The esign vlue of concrete tensile strength Yiel strength of the sher reinforcement Yieling stress Fctor reflecting the previling filure moe in structurl systems with wll Distnce between torsionl restrints Minimum nchorge length Length of the criticl region from the connecting joint Criticl region of the first two storeys Length of the section of wll Cler length of the column Rius of gyrtion of the floor mss in pln Bsic vlue of the behvior fctor Interction between two vibrtion perios tking into ccount the eclining rtio IX

12 Squre root of the rtio of the torsionl stiffness to the lterl stiffness in -irection ( torsionl rius ) Chrcteristic vlue of snow lo Pek vlue of the erthquke inuce resisting eformtion Mximum eformtion Yiel eformtion Normlize esign xil force Minimum sher force cpcity of the concrete q k Chrcteristic impose line lo Climte relte temperture lo The concrete compression zone height The reuction fctor Distnce between stirrups Torsionl rius Behvior fctor The number of storeys bove the fountion/the top of rigi bsement The totl number of longituinl brs lterlly engge by hoops or cross ties The number of moes tken into ccount Nturl cyclic frequency The with of compression flnge Accelertion m z m y m x Effective mss moments in z irection Effective mss moments in y irection Effective mss moments in x irection The totl epth of bem in centrl prt of the istnce between torsionl restrints Nturl circulr frequency The isplcement uctility fctor Prtil coefficient for concrete strength X

13 The vlue by which the horizontl seismic esign ction is multiplie, in orer to form plstic hinges in number of sections sufficient for the evelopment of overll structurl instbility, while ll other esign ctions remin constnt The vlue by which the horizontl seismic esign ction is multiplie, in orer to first rech the flexurl resistnce in ny member of the structure, while ll other esign ctions remin constnt The coefficient for Effect of the pressure trnsverse to the plne of splitting long esign nchorge length The coefficient for Effect of wele trnsverse brs The coefficient for Effect of confinement by trnsverse reinforcement The coefficient for Effect of concrete minimum cover The coefficient for Effect of br form ssuming equte cover Define s the previling spect rtio of the wlls of the structurl system The esign vlue of tension steel strin t yiel Shrinkge Settlement Prtil fctor for pre-stressing ctions The mechnicl volumetric rtio of confining hoops within the criticl region Combintion coefficient for vrible ction Fctor for qusi-permnent vlue of vrible ction Fctor for qusi-permnent vlue of vrible ction Fctor for combintion of frequent vlues of vrible ction Fctor for combintion vlue of vrible ction The stress corresponing to the esign vlue The verge compressive stress Reinforcement content Curvture uctility Require vlue of the curvture uctility fctor Snow lo shpe coefficient The coefficient relte to the br imeter XI

14 The coefficient relte to the qulity of the bon conition n position of the br uring concreting Curvture when the tension reinforcement first reches yiel strength Curvture t ultimte when the concrete compression strin reches specifie limiting vlue ζ n Dmping rtio Nturl circulr frequency Slenerness rtio Inclintion of the compression struts The compression strut inclintion ( in seismic esign) The lower boun fctor for the horizontl esign spectrum Inclintion of the stirrups XII

15 Prefce This thesis ws performe with help n guince of structurl engineering compny KE-guppen AB n the Deprtment of Civil n Architecturl Engineering, ivision of Concrete Structures, t Royl Institute of Technology KTH. The thesis ws one from Jnury to June 2014 uner the supervision of Professor Aners Ansell t KTH n CEO Ptrik Gtter t KE-gruppen AB. I wnt to give my pprecition to Professor Aners Ansell my supervisor n techer t KTH for introucing me to this project n wking my interest in Structurl Engineering within Concrete Structures through his courses n tremenous teching. I lso wnt to show my grtefulness for his priceless guince through this thesis. I woul like to express my eepest thnkfulness n mirtion to CEO Ptrik Gtter for shring his invluble knowlege n interntionl experiences within Erthquke Engineering n Seismic Anlysis of Nucler Power Plnts. I wnt to show my grtitue for his time, support, supervision n vilbility even uring busiest scheule. I woul lso like to especilly show my thnkfulness to Dr. Richr Mlm n LicEng. Cecili Ryell for their remrkble guince n inspirtion tht le to this thesis work. Specil thnks go to MSc. Erik Köster for introucing me to KE-gruppen AB n giving me the honor of being prt of their inspiring compny. I wnt to especilly thnk Structurl Engineer Knut Sävlin for his guince n lwys tking his time to help me throughout this thesis. I lso wnt to show my gret pprecition to ll the stff in KE-gruppen AB for their help n showing interest in my thesis work. Lst but not lest I wnt to thnk my prents for their unconitionl support n love. Stockholm, June 2014 Perm Tbtbei Arghi XIII

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17 Contents 1. Introuction Eurocoe DNB Hnbook Aims, gols n contents of the thesis Seismic los Seismic ction Eurocoe Verticl ctions Lo combintion for verticl ctions Lo combintion for seismic esign sitution Dimensionering v Nukleär Byggnskonstruktioner, DNB Design groun response spectrum Seismic los n lo combintion for seismic sitution Seismic nlysis ccoring to Eurocoe Criteri for regulrity in pln Criteri for regulrity in elevtion Structurl type of the builing Ductility Behvior fctors for horizontl seismic ction Methos of nlysis Mol response spectrum nlysis Design for DCH Mteril requirements Geometricl constrints ULS verifictions n etiling of bems ULS verifictions n etiling of columns XV

18 4. Stuie three storey structure The SMART2013 moel Structurl rwings Los Seismic ction De lo Live lo Geometricl n mteril escription Nturl frequncies Seismic nlysis Moeling Seismic ction De lo Live lo Nturl frequencies Anlysis ccoring to Eurocoe Behvior fctor Lo combintion for verticl ctions Lo combintion for seismic esign sitution Mol response spectrum nlysis Anlysis ccoring to DNB Lo combintion for seismic esign sitution Mol response spectrum nlysis Exmple ccoring to Eurocoe Structurl Regulrity Regulrity in pln Regulrity in Elevtion Structurl type of the builing XVI

19 6.3 Design for DCH Mteril requirements Bems Columns n uctile wlls Design for sher resistnce Design for bening resistnce Discussion n comprison of results Conclusion 93 References 95 XVII

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21 1. Introuction Knowlege within esigning structures with respect to erthquke inuce vibrtions is reltively limite in Sween, compre to interntionlly. The most recent mjor erthquke in Sween hppene in 6th of August 2012 close to Hlmst with mgnitue of 4,1 on the Richter-scle. Also, in 1904 Scninvi experience n erthquke of mgnitue 5.5 on the Richter-scle, in Oslofjoren which ws felt in Sween s well [1]. Sween s focus on erthquke resistnce for structures such s nucler power plnts hs increse significntly since the beginning of the 21st century when 34 countries strte to prticipte in project le by the Europen Commission to prepre nucler power plnts for extreme circumstnces n events such s erthqukes. In erly ys Sween in t hve ny specific requirements regring erthquke when esigning power plnts. The new erthqukespecific regultions tht were presente in 2005 plce emns on the opertors to ensure tht their nucler power plnts meet the requirements [2]. Some builings, such s the Turning Torso in Mlmö, re esigne to meet the requirements of specific erthquke resistnce. Turning Torso is esigne to withstn quke of mgnitue 7 on the Richter-scle [3]. For other structures esigne to meet the erthquke resistnce requirements in Sween, the Öresun brige cn be mentione, esigne to withstn quke with mgnitue of 5.7 on the Richter-scle [4]. Reserches hve been conucte to see if erthquke coul be hzr for Sweish ms. For exmple by Bore n Kulhnek [5]. Their conclusion ws tht there is no hzr ginst ms in south-western Sween, but for ms in mile n north of Sween there is smll risk. In the cse were ms re foune on soil, they stte tht more etile investigtions is neee. This thesis is bout the seismic ction nlysis of concrete structures with focus on nucler power plnts n the esign proceure of seismic esign on concrete builings. To be ble to emonstrte such nlysis moel of typicl, simplifie hlf prt of n electricl nucler builing is stuie. A finite element pproch ws use with the softwre FEM- Design 3D Structure Eurocoe 8 Eurocoe 8 is presente s Design of structures for erthquke resistnce. For ppliction on esign n construction of builings n civil structures in seismic regions. Eurocoe 8 is suite for common structures n but not pplicble on specil structures such s nucler power plnts, lrge ms or offshore structures [6]. The purpose of Eurocoe 8 is to ensure the following in n erthquke event: Humn lives re protecte Dmge is limite Structures importnt for civil protection remin opertionl The Eurocoes re me s hrmoniztion of technicl specifiction but there re lterntive proceures, vlues n recommentions concerning clsses with notes inicting where the ntionl coes my be use inste. An exmple is the seismic zone mps n reference groun ccelertion in chpter of the Eurocoe DNB Hnbook Eurocoe clerly cites tht nucler power plnts s well s other specil structures re beyon the scope of Eurocoe 8. Therefore the Swiish Rition Sfety Authority together with Sweish licensees commissione Scnscot Technology AB rrnge Sfety Guie for Nucler Structures title Dimensionering v Nukleär Byggnskonstruktioner (DNB).The DNB is complement to regultions in Boverkets föreskrifter och llmänn rå om tillämpning v europeisk konstruktionsstnrer, the Sweish coe bse on pplictions of Eurocoes, for Sweish nucler 1

22 power plnts. The DNB hnbook cn be pplie on concrete structures for Sweish nucler power plnts s well s lighter structure such s boiling wter rectors (BWR) or pressurize wter rectors (PWR). The DNB cites tht Eurocoe 8 is not pplicble for nucler power plnts, therefore DNBs instructions for seismic esign is tken from ASCE 4-98 [7]. Accoring to the DNB the seismic esign for structure, system n components cn be one in these three steps: Defining the esign erthquke Ientifying the sfety functions tht must be mintine uring n erthquke Verify tht these sfety functions re mintine uring n fter the erthquke The sfety principle for seismic influence on nucler power plnt is tht the structure, system n components nee to keep their function n mintin the rector in sfe sitution, uring the mximum esign erthquke so clle Sfe Shutown Erthquke (SSE). The term SSE is replce by more common term DBE. The interntionl Atomic Energy Agency (IAEA) in IAEA Sfety Guie recommens tht the structure tht is clssifie to withstn erthquke loing, shoul be ble to withstn the effects of greter erthquke tht it shoul be esigne for DBE, so clle Designe Extension Erthquke (DEE). It lso mentions tht smll chnge on the initil prmeter for esigning erthquke gives source to n impoverishe sitution for the structure. Accoring to the DNB the seismic clssifiction for structure, system n components re in three ctegories; 1, P n N. In this thesis the clss P is in focus, its sfety functions in the bering functionlity re: Mintining the integrity of the lo bering structure Crrying n protecting the system n components with sfety function There re three min methos to verify tht the structurl cpcity of builing will withstn seismic lo: Methos bse on experience Tests Clcultions n ynmic structurl nlysis Methos bse on experience cn be use for structures tht were not esigne to withstn seismic loing or structures tht re esigne for certin mgnitue of seismic loing tht shoul be verifie for higher mgnitue. The most common methos of this type re Seismic Qulifiction Utility Group (SQUG) n Seismic Mrgin Assessment (SMA). Tests re use for equipments tht re hr to verify with other methos, such s electricl components. Tests re lso one on shke bors ccoring to prescribe routines. Clcultions n ynmic structurl nlysis is the most useful n ominting metho for sfety verifiction of structures. In this thesis this is the metho in focus. 1.3 Aims, gols n contents of the thesis The im of this thesis is to present the esign proceures for primry seismic bems n columns in concrete structures ccoring to Eurocoe 8 n to escribe n unerstn the ifference between Eurocoe 8 n DNB in seismic nlysis of nucler power plnts. Evlution of the use of DNB inste of Eurocoe 8 for nucler structures is the gol of this thesis. This is one by stuying nucler builing from test project nme SMART2013, n compring mximum responses from the moel structure tht correspons to lo combintions from DNB n Eurocoe 8. 2

23 Chpter 2 contins escription of horizontl n verticl spectrums tht re use for nucler structures in Sween. Los n lo combintions re presente n expline for use with both DNB n Eurocoe 8. These lo combintions will here be use in the nlysis of nucler builing. In chpter 3, proceure of seismic esign of concrete structures is presente, ccoring to Eurocoe 8. Importnt coes which re use for bsic esign of concrete builing n etile esign proceures for primry seismic bems n columns re lso presente in this chpter. A short escription of the SMART2013-project n the specimen teste in this project is given in chpter 4. The teste structure is use n nlyze in this thesis. In chpter 5 the seismic nlysis of the stuie structure one by the FEM-Design softwre, is presente. The proceure of finite element moeling is briefly expline n the results from the ynmic nlysis re lso presente in this section. An exmple given to clrify the esign of primry seismic bems n columns is presente with clcultions in chpter 6, bse purely on Eurocoe 8. In this chpter the bem subjecte to the highest moment n sher force is esigne. From the clcultions, minimum moment resistnce of the column ttche to the bem is presente. Chpter 7 contins iscussion of the results obtine from DNB n Eurocoe 8. In this chpter the ifference between primry seismic bem n column response from Eurocoe 8 n DNB re compre. An overll structure isplcement is lso stuie. Conclusions rwn from the iscussions re finlly presente in chpter 8. In this chpter recommentions for further reserch re lso presente. 3

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25 2. Seismic los Seismic los on the structures re relte on its elstic response spectrum tht is the trnsltion of groun movement expresse with velocity, isplcement, ccelertion n frequency. In the seismic esign other los re lso inclue which is efine in the lo combintions. 2.1 Seismic ction The seismic ction on nucler structures is efine using n elstic response spectrum. The elstic response spectrum chosen for the stuies in this thesis is suitble for nucler fcilities in Sween n ws publishe by Strålsäkerhetsmynigheten (SSM), former Sweish Nucler Power Inspectorte (SKI) n with ssistnce of Vttenfll n EON, former Sykrft n Oskrshmn Krftgrupp (OKG) [8]. Figure 2.1; Horizontl envelope groun response spectr for typicl Sweish hr rock site with mping rtio of 0.005, 0.02, 0.05, 0.07 n 0.10 ccoring to SKI rpport (1992), from [9]. 5

26 Figure 2.2; Verticl envelope groun response spectr for typicl Sweish hr rock site with mping rtio of 0.005, 0.02, 0.05, 0.07 n 0.10 ccoring to SKI rpport (1992, from [10]. The Pek Groun Accelertion (PGA) mounts to g =0.1g for horizontl spectr n g =0.09g for verticl spectr n it is ssume tht the mping of the system is 5%. The isplcement D is given by: where is nturl circulr frequency n is constnt. A first erivtion of the isplcement gives the velocity: An secon erivtion gives the ccelertion: (2.1) (2.2) (2.3) 6

27 The nturl circulr frequency cn be written s function of nturl cyclic frequency, s: (2.4) It is known tht for the mximum vlue of, the mximum vlue of will be: (2.5) With Eqs. (2.3)-(2.4) the expression for cn be rewritten s: Which clerly shows tht the groun pek ccelertion (PGA) vlue i.e. the mximum vlue of the groun, is vli with mximum vlue of, since ll other prmeters involve re constnts. Another wy to explin the mesurement of the PGA vlue is to imgine mssive n cubic concrete block tht is plce on the groun, subjecte to groun motion. Since the mssive block will hve significntly smll perio, by stuying the reltionship: it is unerstnble tht: (2.6) (2.7) By mesuring the ccelertion of the concrete block the PGA vlue will be observe: With the use of the both horizontl n verticl spectr presente bove, horizontl n verticl esign spectr for the pseuo ccelertion cn be crete. Here this ws me by reing the frequency for ech perio n fining the corresponing ccelertion ccoring to the mping rtio. Design spectr for the pseuo ccelertion re shown in Figures 2.3 n 2.4. (2.8) Figure 2.3; Horizontl esign spectrum for pseuo ccelertion which correspons to Figure 2.1 with PGA=0.11g. 7

28 Figure 2.4; Verticl esign spectrum for pseuo ccelertion which correspons to Figure 2.2 with PGA=0.09g. 2.2 Eurocoe 8 Actions which re inclue in the seismic esign ccoring to Eurocoe 8 n corresponing lo combintion re presente in this section Verticl ctions Accoring to Eurocoe 8 the los tht shoul be consiere in seismic esign re los tht ct verticlly on the structure, other thn the seismic lo itself. The reson is tht these cn be trnsforme into msses. Los tht re consiere on the structure re e lo (self weight of the structure) n live lo tht pplies on ech level of the structure. The verticl los tht shoul be tken in to ccount in seismic esign re (e lo) n (vrible live los). De lo is etermine by the self weight of the structure n ccoring to Eurocoe 1, live lo is etermine ue to the ctegory of the builing [11]. Since the builing tht is to be stuie in the following is nucler fcility, the ctegory of the builing will be E2 (inustril use). Live los re summerize in Tble 2.1 below. Tble 2.1; Ctegories n impose los on floors ue to storge n inustril use, from [11]. Ctegory Specific use Exmple q k [kn/m 2 ] Q k [kn] E E2 Ares susceptible to ccumultion of goos, incluing ccess res Inustril use Ares for storge use incluing storge of books n other ocuments As Eurocoe 1 inictes, there is no specific chrcteristic vlue of the impose lo for Inustril use. Accoring to Eurocoe 1, los in inustril res shoul be ssesse consiering the intene use n the equipment which is to be instlle. Where equipment such s crnes, moving mchinery etc, re to be instlle the effects on the structure shoul be etermine in ccornce with EN [11]. Eurocoe 8 lso mentions tht specil structures, such s nucler power plnts, offshore structures n lrge ms, re beyon the scope of Eurocoe 8 [6]. Therefore, the live lo tht hs been chosen for nlysis of the structure is the sme live lo tht ws pplie on the moel in SMART2013-project, see chpter 4. 8

29 2.2.2 Lo combintion for verticl ctions Accoring to Eurocoe 8, the inertil effects of the seismic ctions shll be evlute by tking into ccount the presence of the msses ssocite with ll grvity los ppering in the following combintion of ction: (2.9) where is the chrcteristic vlue of permnent ction, is the chrcteristic vlue of the ccompnying vrible ction n is the combintion coefficient for vrible ction. The combintion coefficient is clculte by the following eqution: (2.10) where is the fctor for qusi-permnent vlue of vrible ction. Vlues for n cn be tken from Tbles 2.2 n 2.3 where the builing types re summrize in ctegories; A-H. Tble 2.2; Vlues of for clcultion of, from [6]. Type of vrible Ctegories A-C Storey Roof Storeys with correlte occupncies Inepenently occupie storeys 0.5 Ctegories D-F n Archives 1.0 9

30 Tble 2.3; Recomene vlues of fctors for builings, from [12]. Action Impose los on builings Ctegory A: omestic, resientil res Ctegory B: office res Ctegory C: congregtion res Ctegory D: shopping res Ctegory E: storge res Ctegory F: trffic re, vehicle weight 30 kn Ctegory G: trffic re, 30kN vehicle weight 160kN Ctegory H: roofs Snow los on builings Finln, Iceln, Norwy, Sween Reminer of CEN Member Sttes, for sites locte t ltitue H 1000 m.s.l. Reminer of CEN Member Sttes, for sites locte t ltitue H 1000 m.s.l Win los on builings Temprture (non-fire) in builings As seen in the Tbles 2.2 n 2.3, there is no ctegory tht specifies vlue for nucler power plnts. Becuse of the importnce of these kins of builings vlue tht oes not significntly ecrese the lo cting on the structure is preferre. The proper vlues re mounte to n Lo combintion for seismic esign sitution Effects of ctions for seismic esign ccoring to cn be written s in the following expression [6]: (2.11) This combintion cn be expresse s Eq. (2.12). 10

31 (2.12) where is the chrcteristic vlue of permnent ction, is the relevnt representtive vlue of prestressing ction, is the esign vlue of seismic ction, is the chrcteristic vlue of the vrible ction n is the fctor for qusi-permnent vlue of vrible ction. Design vlue of seismic ction cn lso be written s: (2.13) where is the chrcteristic vlue of seismic ction. The vlue for epens on seismic hzr conition of the seismic region n on public sfety consiertion which is presente in Tble 2.4. Eurocoe 8 hs efine 4 ifferent importnce clsses for builings. These re clle importnce clsses I, II, III n IV which re epenent on three min fctors [6]: Consequences of collpse on humn life Importnce for public sfety n civil protection in the immeite post-erthquke perio Socil n economic consequences of collpse Tble 2.4; Importnce clsses for builings, from [6]. Importnce clss Builings I Builings of minor importnce for public sfety, e.g. griculturl 0.8 builings, etc. II Orinry builings, not belonging in the other ctegories. 1.0 III Builings whose seismic resistnce is of importnce in view of the 1.2 consequences ssocite with collpse, e.g. schools, ssembly hlls, culturl institutions etc. IV Builings whose integrity uring erthqukes is of vitl importnce for civil protection, e.g. hospitls, fire sttions, power plnts, etc Dimensionering v Nukleär Byggnskonstruktioner, DNB The inclue los n corresponing lo combintion is ifferent in the DNB compre with Eurocoe. DNB inclues severl components tht is inclue in the lo combintion but the the seismic ction is not increse s Eurocoe 8. This will be more cler in this section Design groun response spectrum There re two esigning situtions ccoring to DNB regring seismic esign: SSE-Sfe Shutown Erthquke: Exceptionl seismic esign DEE-Designe Extension Erthquke: Very rre seismic esign 11

32 The term SSE is now replce by more generl term DBE for the esigning erthquke. The esigne groun response spectrum to ensure the rector sfety within DBE efines ccoring to SKI Technicl Report 92:3, see Figures 2.1 n 2.2. For esigning ccoring to DEE, Strålsäkerhetsmynigheten (SSM) is responsible to give the neee input t [7] Seismic los n lo combintion for seismic sitution Seismic los ccoring to DBE n DEE re respectively which is clssifie s ccientl los. DNB corresponing the two esigning situtions efines lo combintions for ech of the cses DBE n DEE. It cn be seen in Eqs. (2.14)-(2.15) tht DNB consiers lrger mount of fctors in the seismic esign sitution thn the Eurocoe 8. Lo combintion, DBE (2.14) Lo combintion, DEE (2.15) where is the e weight, is the wter pressure, is the erth pressure, is the pre-stresse force, is the shrinkge, is the settlement, is the live lo, is the snow lo, is the win lo, is the climte relte temperture lo, is the wter pressure ifference between norml wter level n time vrible wter level, the soil pressure ue to movble surfce lo, is the process relte los uring norml opertion n shutown perio, is the process relte los uring opertion isturbnce, is the lo ue to esigne DBE, is the lo ue to esigne DEE, is the prtil fctor for pre-stressing ctions n is the fctor for qusipermnent vlue of vrible ction, which cn be tken from Eurocoe n EKS8. 12

33 3. Seismic nlysis ccoring to Eurocoe 8 Some importnt coes tht re neee to be consiere when esigning concrete builings re presente n expline in this section. The purpose of this chpter is to provie bckgroun n explntion tht cn be useful to unerstn the use of instructe coes on seismic esign of concrete builings ccoring to Eurocoe Criteri for regulrity in pln Accoring to Eurocoe 8, builings in seismic esign re ctegorize into being regulr n nonregulr, inicte by criteri tht escribe the regulrity in pln n elevtion of the structure. These regulrities will influence the llowe simplifictions n behvior fctor. Tble 3.1; Consequences of structurl regulrity on seismic nlysis n esign, from [6]. Regulrity Allowe Simpfliction Behvior fctor Pln Elevtion Moel Liner-elstic Anlysis (for liner nlysis) Yes Yes No No Yes No Yes No Plnr Plnr Sptil Sptil Lterl force Mol Lterl force Mol Reference vlue Decrese vlue Reference vlue Decrese vlue Accoring to Eurocoe 8, for builing regulr in pln some conitions shoul be stisfie. These re: The slenerness i.e the rtio between lrger n smller length of the builing, shll not be higher thn 4: (3.1) Structurl eccentricity n the torsionl rius, t ech level, n for ech irection of nlysis n, shll be in greement with: (3.2) (3.3) where is the istnce between the center of stiffness n the center of mss, mesure long - irection, which is norml to the irection of nlysis consiere, is the squre root of the rtio of the torsionl stiffness to the lterl stiffness in -irection ( torsionl rius ) n is the rius of gyrtion of the floor mss in pln. Accoring to Eurocoe 8, in multi storey builings such s the builing tht is to be stuie here, the center of stiffness n the torsionl rius cn be etermine only pproximtely. Therefore, for clssifiction of structurl regulrity, simplifiction cn be me if the following conitions re stisfie: All lterl lo resisting systems, such s cores, structurl wlls, or frmes, run without interruption from the fountions to the top of the builing. The eflecte shpe of the iniviul systems uner horizontl los re not very ifferent. This conition my be consiere stisfie in the cse of frme systems n wll systems. 13

34 3.2 Criteri for regulrity in elevtion For builing to be stisfie s regulr in elevtion, conitions in Eurocoe 8 shll be fulfille. In the cse of setbcks, itionl conitions re pplie. Asymmetric preservtion of the stuie structure implies tht the following conition shoul be fulfille: If the setbck o not preserve symmetry, in ech fce the sum of the setbcks t ll storey s shll not be greter thn 30% of the pln imension t the groun floor bove the fountion or bove the top of rigi bsement [6], see Figure 3.1. Figure 3.1; Criteri for regulrity of builings with setbck, from [6]. 3.3 Structurl type of the builing Accoring to Eurocoe 8, the structurl system of the builings is efine s follows: Wll system Frme system Dul system Frme-equivlent ul system Wll-equivlent ul system Torsionlly flexible system Inverte penulum system The conition for ech one of the mentione systems is efine ccoring to Eurocoe 8 [6]. For the stuie structure here the structurl type of the builing is investigte to wll system ue the system in both verticl n lterl irections, resist the los minly by structurl wlls, whose sher resistnce t the bse excees 65% of the totl sher resistnce of the whole structurl system. 14

35 3.4 Ductility When builings re subjecte to strong groun shking, they re expecte to hve the bility to eform beyon the limit of linerly elstic behvior. This eformtion into the structures inelstic (plstic) rnge is of centrl importnce in erthquke engineering. The bility to eform n to issipte energy, without substntil reuction in strength is clle Ductility. Figure 3.2 shows the ifference between linerly elstic n elstoplstic systems regring their pek eformtion, ue to e.g. erthquke groun motion. Both systems hve the sme stiffness, mss n mping [13]. Figure 3.2 clerly show tht n elstoplstic system cn unergo much lrger eformtions thn its corresponing liner elstic system fter reching its yieling point. Accoring to Eurocoe 8, in seismic esign of concrete builings, structures re clssifie in three uctility clsses DCL (low uctility), DCM (meium uctility) n DCH (high uctility). Design with DCL is recommene only in low seismic cses. Otherwise concrete builings tht re esigne to resist erthquke, shll provie energy issiption cpcity n n overll uctile behvior. To be ble to chieve this behvior, Eurocoe clssifies uctility clsses into two ctegories of DCM n DCH. Figure 3.2; Elstoplstic system n its corresponing liner system, from [13]. Yieling stress. Yiel eformtion. Mximum eformtion. Pek vlue of the erthqukeinuce resisting eformtion. Pek vlue of the erthqukeinuce resisting force. 3.5 Behvior fctors for horizontl seismic ction In ccornce with Eurocoe 8, the behvior fctor is n pproximtion of the rtio of the seismic forces tht the structure woul experience if its response ws completely elstic with 5% viscous mping. The seismic forces use in the esign, is the input for conventionl elstic nlysis moel, tht ensures stisfctory response of the structure. The upper limit of the fctor, to ccount for the energy issiption cpcity, is erive s it is shown in Eq. (3.4). (3.4) 15

36 where is the bsic vlue of the behvior fctor, epenent on the type of the structurl system n on its regulrity in elevtion n is the fctor reflecting the previling filure moe in structurl systems with wll. The bsic vlue of the behvior fctor is given in Tble 3.2, epening on the systems uctility clss: Tble 3.2; Bsic vlue of the behvior fctor,, for systems regulr in elevtion. For systems which re not regulr in elevtion, the vlue shoul be reuce by 20%, from [6]. Structurl type DCM DCH Frme system, ul system, couple wll system 3.0α u /α 1 4.5α u /α 1 Uncouple wll system α u /α 1 Torsionlly flexible system Inverte penulum system where is the vlue by which the horizontl seismic esign ction is multiplie, in orer to first rech the flexurl resistnce in ny member of the structure, while ll other esign ctions remin constnt n is the vlue by which the horizontl seismic esign ction is multiplie, in orer to form plstic hinges in number of sections sufficient for the evelopment of overll structurl instbility, while ll other esign ctions remin constnt. Eurocoe 8 inictes n pproximtion vlue of α u /α l for builings which re regulr in pln. The fctor reflecting the previling filure moe in structurl system is clculte epening on its structurl system. Eq. (3.5) shows the reltion for frme n frme-equivlent ul systems while Eq. (3.6) shows the reltion for wll, wll-equivlent n torsionlly flexible systems. (3.5) (3.6) The fctor is efine s the previling spect rtio of the wlls of the structurl system. Accoring to Eurocoe 8, if the spect rtios h wi /l wi of ll wlls of the structure oes not iffer significntly, cn be clculte by Eq. (3.7). (3.7) where is the height of the wll n is the length of the section of wll. By pplying the behvior fctor to the horizontl n verticl spectr from SKI: report 1992 which re shown in Figures 2.1 n 2.2, reltively smller esign spectrum is obtine. First the equtions for esign response spectr both for verticl n horizontl envelopes which re presente in Eurocoe 8 is stuie. These equtions re influence by the behvior fctor s it is expresse in Eqs. (3.7)-(3.10). Figure 3.3 illustrte the ifferent perios for typicl shpe elstic response spectrum which re use in Eqs. (3.8)-(3.11). 16

37 Figure 3.3; A typicl shpe elstic response spectrum showing ifferent perios, from [6]. (3.8) (3.9) (3.10) (3.11) where is the esign groun ccelertion, is the soil fctor; see Eurocoe 8 Tble 3.1, is the lower limit of the perio of the constnt spectrl ccelertion brnch, is the upper limit of the perio of the constnt spectrl ccelertion brnch, is the vlue efining the beginning of the constnt isplcement response rnge of the spectrum, is the esign spectrum, is the behvior fctor n is the lower boun fctor for the horizontl esign spectrum which is recommene to 0.2 ccoring to Eurocoe 8 [6]. 17

38 3.6 Methos of nlysis There re four methos of nlysis possible for etermintion of the seismic effects on structure ccoring to [6]: Lterl force metho of nlysis. Mol response spectrum nlysis. Non-liner sttic (pushover) nlysis. Non-liner time history (ynmic) nlysis. Metho of nlysis is chosen epening on the structures chrcteristics, see Tble 3.1. The chrctristics of the stuie structure, ccoring to Tble 3.1, inicte tht the proper metho of nlysis to etermine the seismic effects is Mol response spectrum nlysis Mol response spectrum nlysis Accoring to Eurocoe 8 ll moes of vibrtion tht consierbly contribute to the globl response shll be tken into ccount, which my be eeme to be fulfille if the two conitions below cn be emonstrte: The sum of the effective mol msses for the moes tken into ccount mounts to t lest 90% of the totl mss of the structure. All moes with effective mol msses greter thn 5% of the totl mss re tken into ccount. Eurocoe 8 inictes tht if these two conitions cnnot be stisfie for ech relevnt irection, minimum number of moes shll be tken into ccount, fulfilling Eqs. (3.11)-(3.12): (3.12) (3.13) where is the number of moes tken into ccount, is the number of storeys bove the fountion/the top of rigi bsement n is the perio of vibrtion of moe. The mximum vlue of seismic ction effect cn be clculte with two ifferent methos, SRSS (Squre Root of Sum of Squres) n CQC (Complete Quric Combintion), epening on the following conition ccoring to FEM Design theory book: (3.14) 18

39 where n re the vibrtion moes incluing both trnsltionl n torsionl moes, n re the vibrtion perios of moe n, is the seismic ction effect uner consiertion, n re the vlue of the consiere seismic ction effect on the vibrtion moe n n is the interction between two vibrtion perios tking into ccount the eclining rtio. The interction cn be etermine by Eq. (3.15) [14]: (3.15) where. Torsionl effects re, ccoring to Eurocoe 8, clculte by the following expression. The floor imension on the storey will be obtine for ech irection s shown in Figure 3.4. (3.16) (3.17) where is the torsionl moment pplie t storey bout verticl xis, is the horizontl force cting on storey, is the ccientl eccentricity of storey mss n is the floor imension perpeniculr to the irection of the seismic ction. Figure 3.4; Explntion of the floor imension on the storey, from [15]. 19

40 3.7 Design for DCH In the stuie cse, the structure is for nucler fcility n Eurocoe oes not give ny recommention regring wht type of uctility clss hs to be chosen. The engineer shoul choose the best possible solution for the structure tht is to be esigne. Depening of the type of builing n its importnce to eform beyon its elstic rnge uring n erthquke, high uctility clss is chosen, DCH Mteril requirements Primry seismic members of the structure shll not hve concrete strength clss lower thn C20/25. Eurocoe 8 lso recommens tht in criticl regions of primry seismic elements of the structure, strength clss of the reinforcement tht shoul be use is Clss C. Properties of reinforcement steel clsses re shown in Tble 3.3 below. These properties re vli within tempertures between -40 C n +100 C in the finishe structure. Tble 3.3; Properties of reinforcement, from [16]. Prouct form Brs n e-coile ros Wire Fbrics Requirement or quntile vlue[%] Clss A B C A B C - Chrcteristic yiel strength f yk or f 0.2k 400 to [Mp] Minimum vlue k=(f t /f y ) k Chrcteristic strin t mximum force, ε uk [%] Benbility Ben/Reben test - - Sher strength Af yk Minimum Mximum evition from nominl mss(iniviul br or wire) [%] 8 ±6.0 (A is re of wire) ± Geometricl constrints Accoring to Eurocoe 8, the primry seismic bems shoul hve t lest with of 200 mm. Also, it is mentione tht the with to height rtio of these bems shoul stisfy the Eq. (3.18). 20

41 (3.18) where is the istnce between torsionl restrints, is the totl epth of bem in centrl prt of n is the with of compression flnge. Eurocoe 8 inictes tht t istnce between the centroil xis of two members shoul not excee /4. Where is the lrgest cross-sectionl imension of the column norml to the bem xis. Another requirement for the bem is tht the with of the primry seismic bem, shll stisfy the expression below, ccount for the effect of the brs tht re pssing through the joint: (3.19) Accoring to Eurocoe 8, the cross section of the columns shoul not hve imension tht is less thn 250 mm. Eurocoe 8 point out tht the thickness of the web shoul stisfy the following expression: (3.20) where is the storey height in meters. Accoring to Eurocoe 8, irregulrities on forming the couple wlls n rnom openings shoul be voie. These cn be one if the influence is either insignificnt or inclue in the nlysis, imensioning n etiling ULS verifictions n etiling of bems Accoring to Eurocoe 8 clcultion for bening n sher resistnce of bem subjecte to n erthquke loing, shll be performe in ccornce with EN :2004, unless specifie in Eurocoe 8 [6]. The effective flnge with is the re tht prt of the top reinforcement of primry seismic bem cn be plce outsie the with of the web. The effective flnge with for primry seismic bems both frming into exterior n interior column, with n without trnsverse bems, is shown in Figures 3.5 n 3.6. The interioer n exterior bem-column joint is presente in Figure

42 Figure 3.5; Frming exterior column with n without trnsversl bem, from [6].. Figure 3.6; Frming interior column, with n without trnsversl bem, from [6]. Figure 3.7; Interior n exterior bem-column joint, from [17]. sher resistnce Sher resistnce is clculte in ccornce with n shll be performe s clssifie in EN :2004 [6]. Aitionl conitions tht hs to be consiere for esigning the primry seismic bem, regring sher resistnce, is expline in Eurocoe 8. Criticl region of primry seismic bem is 22

43 region of the bem tht most likely will yiel uring seismic loing of the structure. These regions re locte closer to n en cross-section where bem is frme into bem-column joint or ny other cross section. The criticl region, is clculte s in Eurocoe 8, by the following expression: (3.21) where is the length of the criticl region from the connecting joint n is the height of the bem. As cn be seen in Figure 3.8, the mximum istnce between the column-bem joint n the lst sher reinforcement shoul not be more thn or equl to 50 mm. Figure 3.8; Trnsverse reinforcement in criticl regions of bems ccoring to Eurocoe 8 [6]. Locl uctility stisfction for sher resistnce Ductility of structure, s mentione erlier cn be efine s the bility of the structure to eform beyon the limit of linerly elstic behvior n to issipte energy, without substntil reuction in strength. Some fctors tht cn influence this eformbility re the tensile reinforcement rtio, the mount of longituinl compressive reinforcement, the mount of lterl tie n the strength of the concrete. The reinforce concrete sections uctility my be chosen s the curvture uctility [18]: (3.22) where is the curvture t ultimte when the concrete compression strin reches specifie limiting vlue n is the curvture when the tension reinforcement first reches yiel strength. However Eurocoe 8 introuce nother form of clcultion for curvture uctility fctor which is bse on the reltionship between n the isplcement uctility fctor, which is conservtive pproximtion for concrete members ccoring to Eurocoe 8, see Eq. (3.23). (3.23) 23

44 The reltionship between n,, is consiere. hs higher vlue thn in irregulr builings n therefore is use inste of in etermintion of the curvture uctility fctor. To stisfy the locl uctility requirements in Eurocoe 8, vlue of the curvture uctility fctor shoul stisfy one of the expressions showe in Eq. (3.24) epenent on the reltion between n. (3.24) where is the bsic vlue of the behvior fctor, is the funmentl perio of the builing within verticl plne where bening tkes plce, is the perio t the upper limit of the constnt ccelertion. When esigning the reinforcement n importnt fctor is tht in criticl regions the strut inclintion in the truss moel shll be 45. This will give the lower limit of. This inclintion will influence the sher lo cpcity n the so clle web compression filure. The following expressions show tht ecresing vlue of, will result in ecresing vlue for n n incresing vlue for : (3.25) (3.26) where is the inclintion of the compression struts, is the inclintion of the stirrups, is the istnce between stirrups, is the cross-sectionl re of one stirrup, is the yiel strength of the sher reinforcement n is the reuction fctor;. From Eqs. (3.25)-(3.26) it is cler tht Eurocoe 8, put more weight on i.e. sher strength regring the reinforcement.the rtio ξ which is introuce in Eurocoe 8 is reltionship between the mximum n minimum sher force in section enoting the en sections of the bem. Depenent on this rtio the sher resistnce computtion type will be etermine. If The computtion shoul be followe by the proceures introuce in Eurocoe 2 [14]. For locl uctility to be stisfie, some specil rules for sher reinforcements, i.e. hoops, in the criticl regions of the primry seismic bems, shoul be tken into ccount ccoring to Eurocoe 8 [6]: Minimum imeter of the brs use shll be 6 mm Spcing of the hoops shoul stisfy Eq. (3.27). (3.27) where is the epth of the bem, is the imeter of the hoops ), is the minimum longituinl br imeter. 24

45 Sher force crrying cpcity without sher reinforcement A concrete bem is ble to tke sher forces without hving ny sher reinforcement. Inste sher forces will be crrie prtly by the concrete itself n prtly by the flexurl reinforcement in the bem. To clrify how the lo cn be crrie by the bem without sher reinforcement crcke section of concrete bem with flexurl reinforcement cn be stuie in Figure Bening crck 2 First sher crck tht occur by lo increse. 3 Followe crck from 2 4 Followe crck from 2 5 Crck long bening reinforcement. Figure 3.9; Forces which cts on bem lmell n evelopment of sher crck, from [19]. As seen in Figure 3.9, V 1 is the sher force crrie by the concrete itself in the compression zone, where concrete is ble to tke up the sher stresses. V 2 is from friction n interlocking ction between concrete surfces. When the evelope crcks rech certin with, the interlocking n friction ction between the concrete surfces will ecrese, thus the sher force V 3 will inste be trnsmitte to the bening reinforcement s concentrte sher force, so clle owel force. It is lso importnt to mention tht the increse longituinl reinforcement content influence the sher force crrying cpcity of bem without sher reinforcement [20], so tht: If the height of the compression zone increses, the bility to crry sher force V 1 is increse. Incresing reinforcement mkes it more ifficult for the crcks to open, thus more friction ction is obtine between the concrete surfces n the bility to crry V 2 increses. If the trnsversl isplcement of the bem ecreses, the owel forces V 3 increses. The expression for the sher force crrying cpcity of bem without sher reinforcement in Eurocoe 2 is purely empiricl. Thus mthemticl moel with the prmeters tht influence the lo crrying cpcity ws estblishe in wy tht it correspons with lrge number of test results in best possible ccornce. See Eq. (3.28) for the mechnicl moel. (3.28) where is the prtil coefficient for concrete strength, is the fctor which consiers the effective height, is the reinforcement content with re, is the chrcteristic compressive strength of concrete, is the verge compressive stress, is the norml force from tensioning or externl pressure, is the concrete re of the cross-section, is the smllest with of the cross-section with the tensile zone n is the effective height. It is seen in the expression for tht if. But the 25