Search

V magistrski nalogi je izdelana nelinearna seizmična analiza po predlogu delovne različice novega Evrokoda 8 na primeru zahtevnejše starejše zidane stavbe - palače. V prvem delu naloge so predstavljene spremembe pri preverjanju potresne odpornosti obstoječih zidanih stavb, ki se nanašajo na nosilnost zidov, deformacijsko kapaciteto zidov in izvedbo nelinearne analize. Temu sledi opis konstrukcije obravnavane stavbe, nabor materialnih karakteristik, nabor vplivov in opis modeliranja konstrukcije. Podani so predlogi utrditvenih ukrepov za izboljšanje obnašanja konstrukcij med potresnim delovanjem. Vpliv potresne obtežbe modeliramo z upoštevanjem Evrokodovega elastičnega spektra. Opisu modeliranja tako sledi opis načina definicije spektrov pospeškov po novi delovni različici Evrokoda. Z upoštevanjem zahtev obstoječe različice Evrokoda in delovne različice novega standarda izvedemo potisno analizo in s pomočjo metode N2 ocenimo njeno potresno odpornost. Najprej je opravljena analiza objekta v obstoječem stanju, čemur sledi analiza treh ojačitvenih variant. V zaključku primerjamo razlike med trenutno veljavnim standardom in novo delovno različico Evrokoda. Temu sledi primerjava rezultatov analize po obeh različicah standarda. In the master's thesis, a non-linear seismic analysis was made according to the proposal of the draft version of the new Eurocode 8 on the case study of cultural heritage brick building - palace. In the first part of the thesis, changes in the verification of the seismic resistance of the existing brick buildings were presented. The changes related to the load-bearing capacity of the walls, the deformation capacity of the walls, and the performance of non-linear analysis. This was followed by a description of the structure of the analysed building, defining material characteristics, defining influences, and a description of the modelling of the structure. Proposals for different strengthening measures were given to improve the behaviour of structures during seismic action. The influence of seismic loading was modelled by considering the Eurocode elastic spectrum. Following the modelling description a description of the acceleration spectra as defined according to the new working version of the Eurocode was presented. Considering the requirements of the existing version of the Eurocode and the draft version of the new standard, we have performed a push-over analysis and evaluated its seismic resistance using the N2 method. Firstly, an analysis of the building in its existing state was carried out. It was then followed by an analysis of three strengthening options. In conclusion, we have compared the differences between the currently valid standard and the new draft version of the Eurocode. This was followed by a comparison of the results of the analysis according to both versions of the standard.

V magistrskem delu so predstavljene spremembe pri potresnoodpornem projektiranju konstrukcij, ki jih uvaja predlog novega standarda Evrokod 8. Novosti smo analizirali na praktičnem primeru 5-etažnega jeklenega objekta iz momentih okvirov in okvirov z ekscentričnimi povezji. Preučili smo nove definicije razredov duktilnosti, faktorjev obnašanja, faktorja občutljivosti za stavbe in kontrolo vplivov teorije drugega reda, kontrole etažnih pomikov v novih mejnih stanjih ter pravila za projektiranje jeklenih konstrukcij. Pravila iz trenutnega standarda Evrokod 8 za razred duktilnosti DCH smo primerjali s predlaganimi pravili za nova razreda duktilnosti DC2 in DC3. Potresnoodporno analizo smo izvedli za ravninske modele momentnih okvirov in okvirov z ekscentričnimi povezji z metodo z vodoravnimi silami. Za momente okvire smo izvedli tudi poenostavljeno nelinearno statično analizo. Ugotovili smo, da projektiranje momentnih okvirov po predlogu novega standarda Evrokod 8 dovoljuje nekoliko lažje in vitkejše konstrukcije z manjšimi dimenzijami elementov. Pri tem za dimenzioniranje niso več merodajni vplivi teorije drugega reda, temveč omejitve etažnih pomikov. Nasprotno, upoštevanje pravil predloga novega standarda Evrokod 8 povečuje zahteve nosilnosti in stabilnosti elementov ekscentričnega povezja. Sam postopek projektiranja ekscentričnega povezja se ne razlikuje od obstoječega. Zahteve poostruje povečanje potresnega dela obtežbe potresnega projektnega stanja. Obremenitve elementov ekscentričnih povezij v DC3 in DC2 so bile večje do te mere, da je bilo najbolj smiselno povečati število povezij in ohraniti primerljive dimenzije elementov. The master thesis deals with the changes in the seismic resistance design of structures introduced by the proposal of the new standard Eurocode 8. The novelties were analysed on a practical example of a 5-storey steel building stabilised with moment resisting frames and frames with eccentric bracings. The new definitions of ductility classes, behaviour factors, the interstorey drift sensitivity coefficient and the control of second order effects, the limitations of interstorey drifts in the new limit states and the specific rules for steel buildings were examined. The code requirements from the current Eurocode 8 for ductility class DCH were compared to the proposed rules for the new ductility classes DC2 and DC3. Seismic analysis was performed for planar models of moment resisting frames and frames with eccentric bracings using the lateral force method. A nonlinear static analysis (pushover) for the moment resisting frames was also performed. It was found that the design of moment resisting frames according to the proposal of the new Eurocode 8 allows somewhat lighter and slimmer structures. In this case, the influences of the second order effects are no longer governing, but rather by the limitations of interstorey drifts. On the contrary, following the changes of the new Eurocode 8 means higher resistance and stability requirements for frames with eccentric bracings. Seismic resistance design of frames with eccentric bracings does not differ from current process. The resistance and stability requirements are intensified by the increase of the seismic part of the seismic design state. The internal forces in the frame with eccentric bracings designed for DC2 and DC3 were greater to the point that it was more reasonable to increase the number of eccentric bracings and maintain comparable element dimensions.

Diplomska naloga obsega preučitev metode s horizontalnimi silami, ki je najenostavnejša metoda potresne analize standarda Evrokod 8. V prvem delu je prikazana primerjava metode glede na obstoječo in novo različico standarda. Na kratko so predstavljene tudi zahteve za modeliranje konstrukcij in kontrola omejitve poškodb na osnovi pomikov, ki jih je treba preveriti pri projektiranju objekta ne glede na uporabljeno vrsto potresne analize. Drugi del naloge vključuje analizo učinka sprememb v metodi s horizontalnimi silami na primeru treh armiranobetonskih konstrukcij. Ugotovili smo, da se rezultati, dobljeni ob uporabi obstoječe različice standarda, med seboj lahko občutno razlikujejo za radi različnih pristopov za račun nihajnega časa. Obenem pa ob upoštevanju najnatančnejšega pristopa iz obstoječega standarda (tj. Rayleigh-eve metode) so razlike do rezultatov, dobljenih z novim standardom, majhne. Večje spremembe ob uveljavitvi novega standarda lahko pričakujemo zaradi spremenjenih projektnih parametrov, ki niso vezane izključno na metodo s horizontalnimi silami, tj. elastičnega spektra pospeškov, faktorja obnašanja ter razmerja med dejanskimi in računskimi pomiki. The thesis includes an examination of the lateral force method, which is the simplest seismic analysis method from the Eurocode 8 standard. The first part of the thesis shows a comparison of the method with respect to the existing and the new version of the standard. The requirements for the modelling of structures and verification of damage limitation based on displacements, which must be verified regardless of the type of seismic analyses, are also briefly presented. The second part of the thesis includes an analysis of the effect of differences in the lateral force method by means of three examples of reinforced concrete structures. It was found that the results obtained with the existing version of the standard can differ significantly due to different approaches for the calculation of the fundamental vibration period. However, if the fundamental vibration period is calculated by the most accurate approach, the differences to the results obtained with the draft of the new and existing standard are small. It is expected that other design factors of the new standard that are not exclusively associated with the lateral force method will have greater impact on the design than the application of the lateral force method. These design factors are the elastic acceleration spectrum, the behavior factor and the ratio between the actual and calculated displacements.

Diplomska naloga obsega preučitev definicije elastičnega spektra pospeškov glede na osnutek novega standarda Evrokod 8 in analizo elastičnih spektrov pospeškov za izbrane lokacije v Sloveniji. V nalogi so prikazani vplivi različnih parametrov na elastične spektre. Na kratko je predstavljen tudi razvoj nove karte potresne nevarnosti. Primerjani so elastični spektri pospeškov glede na trenutno veljavni standard in glede na osnutek novega standarda. V primeru uporabe osnutka novega standarda je spekter določen po dveh različnih postopkih, ki se razlikujeta glede na obseg neodvisnih vhodnih podatkov. Poleg tega diploma vsebuje primerjavo spektrov pospeškov, določenih na podlagi dveh nacionalnih študij Agencije Republike Slovenije za okolje, in dveh evropskih študij o potresni nevarnosti. Ugotovili smo, da so vrednosti elastičnega spektra pospeškov, izračunane skladno z osnutkom novega standarda, lahko precej različne od vrednosti, določene po trenutno veljavnem standardu. Poleg tega smo ugotovili, da so spektralne vrednosti v območju srednje visokih in visokih nihajnih časov zelo odvisne od izbire postopka določitve spektra pospeškov, kot to predvideva osnutek novega standarda. The graduation thesis includes an examination of the definition of the elastic acceleration spectrum according to the draft of the new Eurocode 8 and the analysis of the elastic acceleration spectra for selected locations in Slovenia. It presents the effects of various parameters on the elastic acceleration spectra. The development of a new seismic hazard map is also briefly presented. The elastic acceleration spectra according to the currently valid standard are compared to those based on the draft of the new standard. According to the draft of the new standard, the spectra can be determined by two different procedures, which vary in the scope the independent input data. In addition, the thesis presents spectra determined on the basis of two national studies performed by the Slovenian Environment Agency and two European seismic hazard studies. We found that the values of the elastic acceleration spectrum, calculated by the draft of the new standard, can be quite different from the values determined according to the currently valid standard. In addition, we found that when applying the draft of the new standard, the spectral values in the range of medium and long vibration periods are highly dependent on the choice of the procedure for determining the spectra according to the new standard.

Podjetje želi standardizirati izbiro izvedbe spoja hladilne enote na steno transformatorskega kotla, saj je to eno izmed trdnostno kritičnih mest. V uporabi je veliko število geometrijsko različnih hladilnih enot, ki različno obremenjujejo izvedbe spoja. Zato izdelamo program, ki bo vrnil informacijo o primernosti izvedbe spoja za poljubno geometrijo hladilne enote. Omejimo se le na standardizacijo iz vidika trdnosti. Konstrukcijo analiziramo po metodi končnih elementov za dve vrsti obremenitve – obremenitev lastne teže in superponirane potresne obremenitve, določene po standardu Evrokod 8. Company wants to standardize process of choosing a mechanically critical subassembly – connection between cooling unit and wall of the power transformer tank. Loading of mentioned connection depends on geometry of cooling units. Geometries in use have large variety, therefore we develop a program which returns information of appropriateness of connection type for specified loading – cooling unit geometry. Connection assembly is analysed by finite element analysis, considering standard earth gravity and superposed earthquake loading, defined by Evrokod 8.

V magistrskem delu predstavljamo postopek in rezultate potresnoodpornega projektiranja visoke armiranobetonske (AB) stavbe v skladu s standardom Evrokod 8 (EC8). Obravnavamo 22-nadstropno stavbo, ki ima mešan konstrukcijski sistem ekvivalenten stenastemu sistemu. V programu ETABS smo razvili linearno-elastičen prostorski računski model konstrukcije in ga uporabili za potresno analizo objekta, ki smo jo izvedli z uporabo modalne analize ob upoštevanju projektnega in elastičnega spektra pospeškov. Osnovna nihajna časa konstrukcije za X in Y smer znašata 2,10 s in 3,24 s, celotna projektna potresna sila pa znaša okoli 6,5 % teže objekta, ne glede na horizontalno smer potresne obtežbe. Pri verifikaciji potresne zmogljivosti stavbe smo se osredotočili na kontrolo etažnih zamikov in na dimenzioniranje AB jedra v pritličju, kjer je predvideno območje sipanja energije. Ugotovili smo, da so potresne zahteve v smislu etažnih zamikov sprejemljive le, če smo v kontroli upoštevali zamike izračunane na osnovi elastičnega spektra pospeškov. V primeru visokih stavb je takšen način kontrole zamikov smiseln. Pri dimenzioniranju AB jedra smo predpostavili srednjo stopnjo duktilnosti DCM. Vzdolžno in prečno armaturo v steni jedra smo najprej izračunali z neodvisnim "peš" izračunom v skladu s standardom EC2 in EC8, nato pa še z avtomatskim izračunom programa ETABS. S "peš" izračunom smo za potreben delež vzdolžne armature v AB jedru dobili vrednost 0,63 %, medtem ko je izračun s programom ETABS izkazal za okoli 8 % več vzdolžne armature. Na to odstopanje v glavnem vpliva različno upoštevanje razporeditve armature po prerezu. Pri izračunu prečne armature je prišlo do nekoliko večjih razlik. Z neodvisnim "peš" izračunom smo določili 166 cm2/m potrebne prečne armature v celotnem prerezu jedra, program ETABS pa je izračunal približno 22 % več prečne armature. Do takšne razlike pride predvsem zaradi upoštevanja krajše dolžine posameznih delov stene (medosna razdalja) in krajše ročice notranjih sil pri izračunu s programom ETABS. In the master's thesis, we present the procedure and results of the earthquake-resistant design of a tall reinforced concrete (RC) building according to the Eurocode 8 standard (EC8). The analysed building has 22 storeys and a dual structural system equivalent to a wall system. A linear-elastic spatial model of the building structure was developed in the ETABS program and used for seismic analysis of the building, which we conducted based on the modal response spectrum method considering the design and elastic acceleration response spectra. Fundamental periods of the structure for the X and Y directions are 2,10 s and 3,24 s, and the total design seismic force is about 6,5 % of the weight of the building, regardless of the horizontal direction of the seismic load. In verifying the seismic performance of the building, we focused on the verification of interstorey drifts and the design of the reinforcement of RC core in the ground floor, where the energy dissipation area is foreseen. We found that seismic requirements in terms of interstorey drifts were met only if the interstorey drifts were calculated on the basis of the elastic acceleration response spectrum. In the case of tall buildings, such an approach of verifying interstorey drifts makes sense. In the design of the RC core, we assumed ductility class medium (DCM). The longitudinal and transverse reinforcement in the core wall was first calculated by an independent "hand" calculation in accordance with the EC2 and EC8 standards and then by an automatic calculation in the ETABS program. With the "hand" calculation, we obtained 0,63 % for the longitudinal reinforcement ratio in the RC core, while the calculation in the ETABS program resulted in about 8 % more longitudinal reinforcement. This difference was mainly influenced by the different considerations of the reinforcement distribution across the cross section. There were slightly larger differences in the calculation of the transverse reinforcement. With an independent "hand" calculation, we determined 166 cm2/m of the required transverse reinforcement in the entire core cross section, while the ETABS program calculated approximately 22 % more transverse reinforcement. This difference is mainly due to the consideration of the shorter length of individual parts of the wall (length based on centroidal axes) and the shorter lever arm of internal forces considered in the ETABS calculations.

Major earthquakes have demonstrated that Natech events can be triggered by liquid overtopping in liquid storage tanks equipped with floating roofs. Thus, research on the dynamic behaviour of steel storage tanks with floating roofs is still required. In this paper, the seismic risk against liquid overtopping in a real steel storage tank with a floating roof was analysed using a simplified model that was validated by a refined finite element model based on the arbitrary Lagrangian-Eulerian approach. The simplified model utilizes the Lagrangian of a floating roof-fluid system and is capable of providing a response history of the floating roof. It was demonstrated that it could predict the maximum vertical displacement very accurately, while some differences were observed in the response history of vertical displacement. The computational time for a single response history analysis based on the simplified model amounted to a few minutes, which is significantly less demanding compared to hours required for response history analysis in the case of the refined FE model. The simplified model is thus appro-priate for the seismic fragility analysis considering the overtopping limit state. It is shown that the fragility curves are significantly affected by the liquid filling level. The risk for liquid overtopping is quite high in the case of a full tank. However, by considering the variation of filling level during the year, the overtopping risk was observed reduced by approximately 30%. Alternatively, the approximate fragility analysis for the liquid over-topping can be performed by utilizing the Eurocode formula for the vertical displacement of liquid. This approach is straightforward, but the formula does not account for the higher mode effects, which may result in overestimated seismic intensity causing overtopping, as discussed in the paper

Predmet rada predstavlja analiza dva različita modela dimenzionisanja i utezanja krajeva armiranobetonskih zidova složenih poprečnih preseka, koji se sastoje od spojenih odnosno ukrštenih pravouganoih segmenata. U prvom modelu, zidovi su razmatrani kao integralni elementi složenog preseka sa rebrima i flanšama, prema uputstvima Evrokoda 8. U drugom modelu, zidovi su tretirani kao skupovi nezavisnih pravougaonih delova. Analizirani su zidovi „I” i „T” poprečnih preseka, uzimajući u obzir uticaj momenta nosivosti na zahtevani nivo duktilnosti zidova. Razlika u pomenutim modelima, sa aspekta oblikovanja detalja za lokalnu duktilnost, ogleda se u rasporedu, dužini i zahtevanim nivoima utezanja ivičnih elemenata armiranobetonskih zidova.

Glavni cilj diplomske naloge je predstavitev in uporaba novosti, ki jih na področju potresnoodpornega projektiranja armiranobetonskih montažnih stavb uvaja delovna različica novega Evrokoda 8. Predstavljene so nekatere novosti pri projektiranju montažnih stavb glede na trenutno veljavni standard. Opišemo način definicije spektrov pospeškov, določitev strižne armature v stebrih in izpopolnjena navodila za dimenzioniranje mozničnih stikov med stebri in gredami. Uporabo novega Evrokoda 8 nato demonstriramo tako, da projektiramo različice enoetažne armiranobetonske montažne stavbe. Stavbo sprojektiramo po trenutnem standardu (SIST EN 1998-1) za srednji razred duktilnosti in po delovni različici novega standarda, kjer upoštevamo novo uvedeni razred duktilnosti DC3. Pri projektiranju se omejimo na stebre in stike med stebri in gredami, ki so se med preteklimi potresi izkazali za kritične elemente konstrukcije. Prikazana je primerjava rezultatov projektiranja po obeh standardih. Sprojektirani konstrukciji primerjamo tudi z vidika nosilnosti in deformacijske kapacitete, pri čemer za določitev deformacijske kapacitete uporabimo model za mejni pomik, ki ga prav tako uvaja nova različica standarda Evrokod 8. Izkaže se, da se nosilnost stebra poveča, deformacijska kapaciteta obravnavanih stavb pa se praktično ne spremeni zaradi uporabe nove različice standarda. The main goal of the thesis is to present and use the novelties that are introduced by the draft of new Eurocode 8 in the field of earthquake-resistant design of precast reinforced concrete buildings. Some novelties in the design of precast reinforced concrete buildings in comparison to the current version of the code are presented. We describe the definition of the acceleration spectra, requirements for the shear reinforcement in columns and improved instructions on how to design a dowel connection between a column and a beam. The use of the draft of the new Eurocode 8 is then demonstrated by designing variants of a single storey reinforced concrete building. The building is designed for ductility class medium according to the current standard (SIST EN 1998-1). In addition, it is designed according to the working draft of the new standard, where the newly introduced ductility class DC3 is taken into account. The design is limited to columns and beam-to-column connections, which proved to be the critical structural components in past earthquakes. A comparison between the results of the design is presented. The designed structures are compared in terms of strength and deformation capacity. The deformation capacity was calculated by utilizing the model introduced by the draft of the new Eurocode 8. It turns out that the strength of columns increases, but the deformation capacity is practically not affected by the design rules introduced in the draft of the new standard.

V magistrskem delu analiziramo vpliv delovne različice novega standarda Evrokod 8 na potresnoodpornost reprezentativne armiranobetonske stavbe, ki je že bila sprojektirana v skladu z obstoječo različico Evrokoda 8. Učinke standardov ovrednotimo tako, da konstrukcijo obravnavane stavbe ponovno sprojektiramo z upoštevanjem zahtev delovne različice novega standarda in ocenimo njeno potresno odpornost. V prvem delu predstavimo nosilno konstrukcijo obravnavane stavbe, geometrijo, material, modeliranje vplivov in konstrukcije ter prikažemo armaturne načrte konstrukcije, sprojektirane po obstoječi različici standarda. V drugem delu opišemo novosti pri dimenzioniranju, ki jih prinaša delovna različica novega standarda. Nato nosilno konstrukcijo ponovno sprojektiramo na projektni potresni vpliv in rezultate projektiranja predstavimo v obliki armaturnih načrtov. V zadnjem delu primerjamo potresno odpornost obravnavanih stavb. Za obe konstrukciji stavbe definiramo nelinearen model, izvedemo potisno analizo in s pomočjo metode N2 določimo vrednost pospeška tal, ki povzroči mejno stanje blizu porušitve. Vpliv potresne obtežbe modeliramo na dva različna načina, z upoštevanjem Evrokodovega elastičnega spektra in z uporabo spletne aplikacije za napovedovanje IDA krivulj. Ker smo novo konstrukcijo projektirali za razred duktilnosti DC2, so projektne potresne obremenitve večje, kar je posledica nižjega faktorja obnašanja. Posledično je večja tudi količina računsko potrebne armature. Nosilnost nove konstrukcije je zato večja, deformacijska kapaciteta pa se ne spremeni bistveno. Zato je potresna odpornost obravnavanih različič stavbe v smislu mejnega pospeška tal približno enaka. Na osnovi rezultatov potresnih analiz lahko sklenemo, da delovna različica novega standarda Evrokod 8 ne prinaša bistvenih razlik na potresno odpornost obravnavane stavbe, pri pogoju, da se nova karta projektnega pospeška tal v prihodnosti ne bo bistveno spremenila. In the master thesis, we analyse the impact of the working version of the new Eurocode 8 standard on the earthquake-resistance of a representative reinforced concrete building, which has already been designed according to Eurocode 8 standard. The effects of standards are evaluated by redesigning the building structures requirements of the working version of the new standard. In the first part, we present the load-bearing structure of the analysed building, geometry, materials and the modelling of the building and loads. Drawings of the reinforcement designed according to the existing version of Eurocode 8 standard are also shown. In the second part, we describe novelties in the design that are introduced in the working version of the new standard. The structure is then redesigned for the seismic design loads, and the design results are presented by reinforcement drawings. In the last part of the thesis, the earthquake resistance of both buildings is compared. For each building structure, a non-linear model is defined, pushover analysis is performed, and the peak ground acceleration that causes the near-collapse limit state is estimated with the N2 method. The effect of seismic action is modelled in two ways, by considering the Eurocode elastic acceleration spectrum and by using the web-based methodology for the prediction of approximate IDA curves. Because we designed the new structure for the ductility class DC2, the seismic design loads were increased due to the lower behaviour factor. As a result, the amount of calculated reinforcement is also increased. The load-bearing capacity of the new structure is, therefore, higher, but the deformation capacity does not change significantly. Thus, the earthquake resistance of the new building, if expressed in terms of ultimate peak ground acceleration, is approximately equal to that designed according to Eurocode 8. Based on the results of seismic analyses, we can conclude that the working version of the new Eurocode 8 standard does not affect the seismic resistance of the analysed building significantly, provided that the seismic design maps will not change considerably in the future.

The shear modulus, known as Gmax, is a key parameter for predicting the static and dynamic behavior of soils. Its value decreases by increasing the shear strain. This is because of reducing the soil’s stiffness as a result of increasing the shear deformation. The increasing of the shear modulus by increasing the shear strain is affected by some of the soil properties, such as the Void ratio (e), the Over consolidated ratio (OCR), the Normal stress (σ), the Plasticity index (PI), the Water content (ω%), the Shear strain rate, the Soil structure, and the Loading history, etc. In this paper, undrained, direct shear tests were conducted to study the effect of the plasticity index (PI) and the normal stress (σ) on the shear behavior and the shear modulus of remolded clays. The results show that the normalized shear modulus at a constant strain will generally increase as the σ and PI increase, and the common empirical equations for undisturbed soils at γ = 0~0.1 might be applicable for the disturbed soils too. Ljubljana se nahaja v plitvem sedimentnem bazenu zapolnjenim s kvartarnimi sedimenti. Območje sodi med seizmično najbolj aktivne v Sloveniji in ga je v preteklosti prizadelo več večjih potresov. Razmeroma mehki sedimenti pomembno prispevajo k ojačenju potresnega nihanja tal na tem območju, obstoječe potresne mikrorajonizacije v Ljubljanskem bazenu pa zaradi pomanjkanja geofizikalnih podatkov in podatkov iz vrtin niso zanesljive. Za dopolnitev mikrorajonizacije smo zato izvedli raziskave povprečne hitrosti strižnega valovanja v vrhnjih 30 m (Vs30) sedimentov na 30 točkah. Uporabili smo skupno modeliranje podatkov spektralnega razmerja horizontalnih in vertikalne (HVSR) komponente tri-komponentnih posamičnih meritev mikrotremorjev in disperzijskih krivulj pridobljenih s ploskovnimi meritvami mikrotremorjev analiziranih z metodama razširjene prostorske avtokorelacije (ESAC) in refrakcijskih mikrotremorjev (ReMi). Fazno-hitrostne disperzijske krivulje dobljene z obema metodama se zelo dobro ujemajo. Dobljene vrednosti Vs30 so večje v severnem in severo-vzhodnem delu mesta (300–600 m/s), kjer prevladujejo pleistocenski in holocenski glaciofluvialni sedimenti reke Save, predvsem prod in pesek. V južnem delu mesta (140–300 m/s) ustrezajo najnižje vrednosti Vs30 jezerskim in rečnim sedimentom Ljubljanskega barja. Pridobljeni rezultati se dobro ujemajo s porazdelitvijo različnih sedimentov v bazenu. V primerjavi z obstoječo mikrorajonizacijo, ki temelji na EC8 klasifikaciji, pa kažejo novi podatki na celotnem raziskanem območju na boljše seizmogeološke pogoje, na splošno za eno stopnjo boljšo vrsto tal po EC8 klasifikaciji. Ugotovljena prostorska porazdelitev Vs30 na območju Ljubljane predstavlja zato pomembno dopolnitev obstoječe mikrorajonizacije.

V diplomski nalogi je narejena kontrola starejše jeklene hale, ki je bila sprva enoetažna, kasneje pa ji je bila vgrajena dodatna etaža. Uradno dokumentacijo smo pridobili samo za prvotno stanje hale, zato so bili elementi dodatne etaže izmerjeni, nekateri deli pa predpostavljeni. Najprej so bili določeni vplivi na konstrukcijo. Fasadne lege so bile preverjene v ravninskem modelu, globalna analiza pa je bila narejena v prostorskem modelu. Ugotovljeno je bilo da prvotno stanje objekta ustreza zahtevam novih standardov. Nato sem preveril, obstoječe stanje objekta ob predpostavki uporabe etaže. Izkaže se, da je projekt potrebno dodatno zavetrovati v ravnini etaže ter dodati podpore za prenos sile iz strešne ravnine v glavne stebre konstrukcije. Popravki so v nalogi tudi predstavljeni. Prikazana je tudi kontrola nekaterih spojev. Na koncu sem preveril tudi nosilnost temeljnih tal objekta. Izkaže se, da temelj ni primeren za prevzem potresne obtežbe. This diploma thesis represents the analysis of older steel hall. At first it was one-storey hall, later a floor was added. The official documentation was obtained just for its original state, so the elements of the additional floor were measured, while some parts were assumed. At first the effects on the structure were determined. The verefication of side rails was made in planar model, while global analysis was made in spacial model. It was found that the original condition of the building meets the requirements of the new standards. Then the curent state of the building was checked with assuming the use of the floor. It turns out that we need additional horizontal stabilization in the plane of the floor and that we need to add supports for the transfer of force from the roof plane to the main pillars of the structure. The corrections are also presented in the thesis. Control of some joints is also shown. I also checked the load capacity of the foundation ground of the building. It turns out that the foundation is not suitable for the seismic load.

Kupci energetskih transformatorjev, ki so namenjeni na potresno ogrožena območja, podajajo pri naročilu tudi zahtevo po potresni odpornosti transformatorja. Slednjo zagotavlja ustrezna izvedba več detajlov. Eden izmed njih je vpetje aktivnega dela na kotel in na pokrov. Potresni sunki lahko namreč povzročijo premik aktivnega dela znotraj ohišja, kar povzroči zmanjšanje izolacijskih razdalj in privede do električnega preboja. K problemu smo pristopili z analizo obstoječih potresnih opor in s študijem rešitev, ki jih uporablja konkurenca. Na podlagi zahtev in razpoložljive tehnologije v podjetju smo pripravili lastne rešitve. Za potrebe vrednotenja konstrukcij smo proučili standard Evrokod 8, ki ureja področje potresno-odporne gradnje stavb. Standard smo prilagodili za posebno področje transformatorjev in zapisali postopke za izračun projektnega potresnega vpliva. Zasnovane konstrukcijske rešitve smo nato vrednotili s statično in spektralno analizo. Ugotovili smo, da so zasnovane potresne opore ustrezno konstruirane in sposobne prenašati predvidene obremenitve. Orders for power transformers that are to be stationed in areas with higher seismic activity, contain a demand for adequate earthquake resistance of the product. This request is acceded, among others, with proper fixation of the transformer's active part in the housing. Seismic waves may cause shifts of the active part inside the housing, thus reducing insulation distances which lead to electric discharge. The problem was approached by analysing current earthquake supports and the ones used by competition. Taking available technology in the factory into consideration, own innovative solutions were developed. Eurocode 8 standard which regulates design of earthquake resistant structures was adapted to specific structures of transformers and used for calculation of design seismic action. New designs were then evaluated using static and response spectrum analysis. It was ascertained that the new design of earthquake supports is adequate and can withstand expected loads.

V nalogi smo primerjali dva postopka za oceno rotacijske kapacitete armiranobetonskih stebrov, ki sta vključena v standarda Evrokod 8-2 in Evrokod 8-3. Rezultate analiz smo ovrednotili z eksperimentalnimi rezultati. V ta namen smo ustvarili bazo podatkov za različne stebre, ki so bili preizkušeni s cikličnimi testi. Še posebej so nas zanimali stebri s pomanjkljivimi konstrukcijskimi detajli. Rotacijsko kapaciteto smo določili na osnovi analize ukrivljenosti najbolj obremenjenih prerezov stebrov. Ukrivljenost smo primerno integrirali vzdolž stebra. Pri tem smo upoštevali, da se velike vrednosti ukrivljenosti pojavijo predvsem v območju plastičnega členka. Dolžino plastičnega členka obravnavani metodi določita različno. Razlika je lahko tudi več kot dvakratna. Navkljub temu so razlike v ocenjenih vrednostih rotacijske kapacitete bistveno manjše, saj je bila v večini primerov ocenjena vrednost maksimalne ukrivljenosti večja v primeru postopka Evrokod 8-2, pri katerem je bila dolžina plastičnega členka manjša. Ujemanje analitičnih rezultatov z eksperimenti je boljše v primeru kvadratnih stebrov, vendar so lahko tudi v takšnih stebrih analitične napovedi rotacijske kapacitete bistveno večje od dejanske, še zlasti v primerih stebrov z zelo pomanjkljivimi konstrukcijskimi detajli. Oba analizirana postopka sta večinoma primerna za analizo stebrov, ki so narejeni v skladu z zahtevami sodobnih standardov za projektiranje konstrukcij na potresnih področjih. Vendar bi bilo postopek Evrokod 8-2 treba nekoliko korigirati, saj je ocena maksimalne tlačne deformacije v betonu pogosto prevelika. Za oceno rotacijske kapacitete stebrov z zelo pomanjkljivimi konstrukcijskimi detajli bi bilo za analizo bolje izbrati kakšen drug postopek, ki ga dovoljuje standard Evrokod 8-3. In the Master thesis, we considered two methods that are included in Eurocode 8-2 and Eurocode 8-3 standards, to estimate the rotational capacity of reinforced concrete columns. The numerical results were evaluated with experimental results. For this purpose, the experimental database was composed from various columns that were exposed to cyclic load tests. Columns with deficient structural details were of special interest. Rotation capacity was determined on the basis of the full moment-curvature analysis. Obtained curvature was integrated along the length of the column. The fact that maximum curvatures are expected in the area of the plastic hinge, was also considered. The estimation of the plastic hinge length is up to two times different with respect to the type of considered method. However, the difference of the estimated rotation capacity of the column is smaller in most cases due to larger estimates of the maximum curvature using Eurocode 8-2 method, where the length of the plastic hinge is smaller. Numerical results of the square columns are a better match to the experimental results than the rectangular columns, however those estimates can be significantly larger than the actual rotation capacity, especially when considering columns with deficient structural details. Both considered methods are appropriate for the analysis of the columns that are constructed in accordance with the modern standards for the design of structures in the seismic areas. Due to frequent overestimates of maximum concrete compression strain, Eurocode 8-2 method should be modified somehow. To assess the rotation capacity of the columns with significantly deficient structural details, alternative procedure defined in the Eurocode 8-3 should be taken into account.

Analysis of conceptual design of reinforced concrete (RC) structure with secondary seismic elements in compliance with Eurocode 8 is presented in this paper. The application of this concept is complex due to the requirements regarding the classification and calculation of design internal forces, although the contribution of these elements in the total structural stiffness is neglected. The basic calculations of 8-story RC structure are performed with the main goal to emphasize and explain the problems of utilization of this concept. Its advantages are clearly presented and critical analysis of application in aseismic structural design is performed. The results of comparative analysis of structural design in which some structural elements are treated as a primary or as a secondary are presented. U radu je analiziran koncept proračuna armirano-betonske konstrukcije sa sekundarnim seizmičkim elementima prema zahtevima Evrokoda 8. Iako se doprinos krutosti ovih elemenata zanemaruje prilikom seizmičkog odgovora konstrukcije, primena ovog koncepta je kompleksna zbog niza zahteva u pogledu klasifikacije i načina proračuna statičkih uticaja. S ciljem da se istaknu i objasne specifičnosti primene, pokažu prednosti, ali i kritički razmotri upotreba opcije sekundarnih elemenata, izvršen je proračun osmoetažne armiranobetonske konstrukcije. Prikazane su dve metode za klasifikaciju sekundarnih elemenata, način proračuna uticaja u njima, kao i rezultati uporedne analize u kojoj su određeni elementi konstrukcije razmatrani kao primarni i kao sekundarni.

V diplomski nalogi je prikazan postopek statične analize in dimenzioniranje nosilnih elementov jeklene konstrukcije. Stavba je pravokotne tlorisne oblike, dimenzij 12,10 m in 32,20 m. Višina objekta je 9,50 m. Objekt ima dve etaži. V pritličju je predvidena proizvodnja in skladiščenje, v nadstropju so pisarne. Projekt je narejen v skladu z veljavnimi predpisi in standardi Evrokod ter pripadajočimi slovenskimi nacionalnimi dodatki. Dimenzioniranje na potresno projektno stanje je prikazano na dva načina in sicer, konstrukcije z majhnim sipanjem energije ter konstrukcije s sposobnostjo sipanja energije. Dimenzionirani so tudi štirje značilni spoji obravnavane jeklene konstrukcije. Fasada in streha je iz ognjeodpornih panelov. Dimenzioniranje temeljev ni vključeno v diplomsko nalogo. The Graduation Thesis shows the process of structural analysis and design of key elements of the steel structure. The building has a rectangular floor shape, dimensions of 12.10 m and 32.20 m. Building height is 9.50 m. Construction is a two storey facility. On the ground floor is planed production and storage unit, on the first floor there would be offices. The project is designed in accordance with the valid European standards Eurocodes and related Slovenian national annex. Design of structure for earthquake resistance is shown in two ways, constructions with low energy dissipation and constructions with ability of energy dissipation. In Thesis is also shown design of four typical connections. The facade and roof is made of fire resistant panels. Dimensioning of the foundations is not included in the Thesis.

V doktorski disertaciji smo predlagali iterativni postopek in zaključen izraz za izračun projektnega pospeška tal na osnovi ciljne zanesljivosti. Ta način omogoča vpogled v odnos med ciljno zanesljivostjo, povratno dobo projektnega potresa, nosilnostjo in deformacijsko kapaciteto objekta. Projektni pospešek tal na osnovi ciljne zanesljivosti smo uporabili kot osnovo za izpeljavo faktorja obnašanja. Z novo definicijo faktorja obnašanja smo razložili t.i. »empirično komponento« faktorja obnašanja, saj smo na osnovi ciljne zanesljivosti pojasnili, da mora biti faktor obnašanja za običajne objekte precej manjši od produkta redukcijskega faktorja dodatne nosilnosti in duktilnosti. Nova definicija faktorja obnašanja zato omogoča bolj racionalno odločitev glede prave vrednosti faktorja obnašanja in izračun faktorja obnašanja za poljubno izbrano potresno tveganje, kar smo demonstrirali na primeru večetažne armiranobetonske okvirne stavbe s privzeto srednjo stopnjo duktilnosti. Za obravnavan primer smo pokazali, da faktor obnašanja, ki ga predpisuje Evrokod 8, približno ustreza ciljni verjetnosti porušitve 5∙10-5. V drugem delu disertacije smo preučevali vpliv projektnih dejavnikov po standardu Evrokod 8 na potresne parametre konstrukcije. Za obravnavane konstrukcije se je izkazalo, da imajo projektni dejavniki, ki navadno zahtevajo precej dela projektanta, relativno majhen vpliv na potresne parametre konstrukcij. Po drugi strani pa imajo projektni dejavniki, ki zahtevajo relativno malo dela (npr. upoštevanje projektnih vrednosti materialnih karakteristik), razmeroma velik vpliv na potresne parametre konstrukcij, kar bi lahko bil eden izmed vzrokov za modernizacijo postopkov potresnoodpornega projektiranja stavb. V disertaciji smo preučevali tudi možne pristope za izračun projektnih prečnih sil na osnovi ciljne zanesljivosti in nelinearne dinamične analize. Ugotovili smo, da moramo strižno porušitev praktično preprečiti, če želimo, da morebitne strižne porušitve stebrov nimajo vpliva na verjetnost porušitve. Na ta način smo potrdili načelo metode načrtovanja nosilnosti, čeprav se je izkazalo, da je projektna prečna sila, ki je določena v skladu s standardom Evrokod 8, včasih podcenjena. Strižna porušitev je bila tudi v teh primerih preprečena, vendar le zaradi upoštevanja kriterija o minimalnem deležu armiranja. Zato smo predlagali alternativni postopek za določitev projektnih prečnih sil na osnovi inkrementne dinamične analize, ki se izvede za skrbno izbrane akcelerograme. A new methodology for the calculation of the risk-targeted design peak ground acceleration has been proposed. The closed-form solution of this methodology provides a useful insight into the relationships between seismic risk, the return period of the design earthquake, the strength and deformation capacity of the building. It can thus provide a basis for the derivation of risk-targeted behaviour factor, which can be used to explain the so-called empirical component of the conventional behaviour factor. The first part of the dissertation clearly shows that, in order to achieve adequate collapse safety of new buildings, the value of the behaviour factor should be much smaller than the product of overstrength and ductility reduction factor. This new definition of the behaviour factor thus allows for more rational decisions about what the adequate values of the behaviour factor are, and better estimations of the behaviour factor for a selected collapse risk. This was demonstrated for the case of a reinforced concrete frame building with prescribed ductility class medium. It is demonstrated for the building in question that the behaviour factor pursuant to Eurocode 8 nearly corresponds to a target collapse risk of 5∙10-5. The second part of dissertation explores the impact of design factors on the seismic response of structures. It was shown for the analysed structures that those design factors, which are usually derived upon extensive consideration by the designer, often only have a small impact on the seismic performance of a structure. On the other hand, the application of simple design factors (e.g. design values of the material characteristics) can significantly improve the calculated seismic response of a structure, even though some designers are not even aware of these design factors. This suggests that standards dealing with earthquake-resistant design of buildings could perhaps be modernized. In the last part of the dissertation, some possible approaches to the calculation of design shear forces were examined based on target reliability and nonlinear dynamic analysis. It was found that the shear failure of columns has to be prevented in order to ensure that the impact of this type of failure is neglectable in the context of collapse risk. This confirms the adequacy of the capacity design approach. However, it is discussed that shear failure of columns designed in line with Eurocode 8 is sometimes prevented due to minimum requirements for shear reinforcement and not due to the design shear force, which is estimated on the basis of the capacity design approach. Hence, a methodology was proposed for the estimation of design shear forces based on incremental dynamic analysis. It was shown that merely a few carefully selected ground motions can suffice to estimate the maximum shear forces in columns.

Bistvo diplomskega dela je bila primerjava računskih modelov konstrukcije, predvsem v smislu opazovanja vpliva modeliranja konstrukcije na velikost projektnih torzijskih učinkov. Zanimalo nas je, kako modeliranje torzije vpliva na izračun nihajnih časov, ter posledično na izračun projektnih potresnih sil in posledično tudi pomikov. Analizo z različnimi modeli in primerjavo rezultatov smo izvedli na primeru enostavne dvoetažne stavbe. Aktualni standard EN 1998-1:2006 pri potresni analizi objekta dovoljuje poenostavitve, ki so odvisne od pravilnosti konstrukcije (tlorisna pravilnost konstrukcije in pravilnost po višini). Tako je za tlorisno pravilne konstrukcije, kot je bila obravnavana konstrukcija, dovoljena uporaba poenostavljenih ravninskih modelov, kjer s posrednim načinom (faktor ) modeliramo učinke torzije. Poleg ravninskega modela smo zaradi primerjave rezultatov izvedeli še analize za dva prostorska modela. Primerjava vseh period ravninskih in prostorskih modelov direktno ni možna, saj pri prostorskih dodatno nastopijo nihajni časi, ki pripadajo torzijskemu nihanju (pri ravninskih jih ni), zato smo primerjave rezultatov omejili na prva dva direktno primerljiva nihajna časa. Odstopanja med modeli (predvsem pri pomikih) so posledica različnih načinov modeliranja. Pomembna ugotovitev, ki sledi iz rezultatov, se nanaša na premik masnega središča, za katerega nam EC8 predpisuje, da ga moramo premakniti za naključno ekscentričnost. Rezultati so namreč pokazali, da premik masnega središča ne vpliva bistveno na nihajni čas, temveč predvsem na nihajne oblike. Tako v modelu za določitev nihajnih časov ni potrebno modelirati ekscentričnosti ampak zgolj v modelu za določitev posledic sile F_b. The prime goal of the Diploma thesis was to compare the computational models of the structure, with the emphasis on observation of influences of structural’s modelling on the magnitude of the design torsional effects. The main question was how torsion’s modeling impacts the calculation of the periods, and consequently the calculation of the design seismic forces, and further, also displacements. The analysis of the various models and comparison of the results was performed on a simple two storey building. Current European Standard EN 1998-1: 2006 allows simplification within seismic analysis of structures, and those are dependent on the structure’s regularity (regularity in plan, and regularity in elevation). Thus, for the structures, regular in plan, as our considered structure, EC8 allows for implementation of simplified plane models, where the effects of torsion are taken into the account by the indirect method (factor ). To obtain a common platform for the model comparison we further analyzed the considered structure by two spatial model. A direct comparison of all periods from planar and spatial models is not possible, since the spatial model further offers periods that to belong to the torsional oscillations (and are not available from the plane model). Therefore, so we limited the comparison of results to the two first directly comparable periods. Discrepancies between the models’ results (especially in displacements) are the result of different ways of modeling. An important conclusion that follows from the obtained results refers to the displacement of the centre of mass, which is prescribed by EC8 to take into account accidental torsional effects. The results have namely shown that the displacement of the center of gravity does not significantly affect the periods, but primarily the eigenshapes. Thus, is not necessary to model the displacement of the centre of mass in the model for determining the periods, but exclusively in the model where the effects of force Fb are determined.

Predstavljena je spletna aplikacija za analizo potresne ranljivosti zidanih stavb, ki je bila razvita v programskem jeziku PHP. V prvem delu naloge so na kratko opisane zidane stavbe ter njihovo obnašanje med potresi. V nadaljevanju so podane teoretične osnove poenostavljene nelinearne analize za določitev potresne odpornosti zidanih stavb. Metoda temelji na poenostavljeni potisni analizi, pri kateri se upošteva etažni strižni mehanizem, in inkrementalni dinamični analizi, ki se izvede na ekvivalentnem sistemu z eno prostostno stopnjo. Rezultati analize so poenostavljene krivulje IDA, s katerimi se opiše odnos med intenziteto potresa in potresnimi zahtevami. Na osnovi teh rezultatov se za različna mejna stanja poškodovanosti določi vzorec mejnih pospeškov, ki predstavlja vhodni podatek za račun krivulj potresne ranljivosti objekta. V nalogi so predstavljeni tudi akcelerogrami, ki smo jih uporabili za inkrementalno dinamično analizo, kot tudi postopek izračuna krivulje potresne ranljivosti stavbe. V petem poglavju so opisani postopki in principi ter programski jeziki, s katerimi smo izdelali spletno aplikacijo. Sledi predstavitev in demonstracija uporabe spletne aplikacije v kateri smo združili različne metode v eno aplikacijo. Za izbrano zidano stavbo smo pokazali, da so mejni pospeški, ki smo jih določili z uporabo spletne aplikacije, podobni rezultatom iz modela ekvivalentnega okvira. Nekoliko večje razlike smo opazili pri razporeditvi poškodovanosti za izbrana mejna stanja. V zaključku so predlagane še možnosti razširitve in uporabe aplikacije. In this thesis a web application for seismic vulnerability analysis of masonry buildings, which was developed in PHP programming language, is presented. Firstly, masonry buildings and their behaviour during the seismic event are briefly described. Follows a description of the theoretical background of the simplified nondlinear analysis for seismic performance assessment of masonry buildings. The method is based on simplified pushover analysis with consideration of storydshear plastic mechanisms and the incremental dynamic analysis, which is performed by equivalent single degree of freedom model. Results of the analysis are simplified IDA curves. They can be used to estimate a sample of maximum acceleration causing different limit states, which represents the input data for the calculation of the structure’s seismic fragility curves. Different set of accelergorams, which were selected to be used in the web application, and the procedure for calculation of seismic fragility curves are also presented. In the fifth chapter, the procedure, principles and programming languages used to create the application are described. Follows description and demonstration of the use of web application. For the investigated masonry building it is shown that the limitdstate accelerations obtained by the web application are similar to the results based on the equivalent frame model. Some larger difference can be observed in the distribution of damage in structural elements for a designated limit state. In the conclusion, possibilities for future development and use of the application is discussed.

Vrednost gradbene konstrukcije (t.i. primarne konstrukcije) pogosto predstavlja manjši delež celotne investicije, preostanek pa predstavljo vgrajeni nekonstrukcijski elementi in oprema (t.i. sekundarna konstrucija). Kljub tako velikemu deležu se opremi v splošnem posveča majhna pozornost pri projektiranju, približni postopki, ki so v veljavi v predpisih, pa so zelo netočni in posledično neprimerni. Eden izmed načinov, s katerim lahko ocenimo vpliv potresa na opremo, so etažni spektri pospeškov. Zaradi prezahtevnega točnega postopka v inženirski praksi, ki vključuje uporabo analize časovnega odziva, se bomo v magistrskem delu osredotočili na približno metodo, imenovano direktna metoda za izračun etažnih spektrov pospeškov, ki sta jo razvila Vukobratović in Fajfar. Metoda je uporabna tako za sisteme z eno prostostno stopnjo kot tudi z več prostostnimi stopnjami, upoštevamo pa lahko tako linearni kot tudi nelinearni odziv gradbene konstrukcije. Kljub enostavnosti postopka, ki uporablja zaključene izraze, daje metoda zadovoljive rezultate in je tako primerna in uporabna za vsakdanjo inženirsko prakso. The value of the building structure (the primary structure) often represents a smaller part of the entire investment when compared against the built-in non-structural elements and equipment (secondary structure). Despite being represented by a large share, not much attention is given to the equipment when designing, while the approximate methods which are in effect in the regulations are inaccurate and consequently unsuitable. One of the ways to evaluate the effect of an earthquake on the equipment is floor response spectra analysis. Due to a very demanding process in the engineering practice that includes the use of time history analysis, this master thesis will focus on an approximative method called the direct method of calculating floor response spectra which was developed by Vukobratović and Fajfar. The method is used for a single-degree-of-freedom systems as well as in mutiple-degree-of-freedom systems, and can also be considered for implementation with either elastic or inelastic response of the building structure. Despite the simplicity of the process, that utilises closed-form expressions, the method gives satisfactoy results and is thus regarded as suitable and useful for common engineering practice.

V magistrskem delu obravnavamo potresno odpornost prizidka Inštituta za informacijske znanosti v Mariboru v skladu s standardom Evrokod 8. V prvem delu smo se osredotočili na linearno statično potresno analizo objekta. Želeli smo določiti najbolj optimalen način modeliranja v programu ETABS, ki bi nam pri najkrajšem času modeliranja in izračuna podal sprejemljivo točne rezultate. S tem namenom smo izdelali 15 modelov. Modele smo ločili na inženirsko uporabne ter generične modele, ki zaradi nepravilnosti v praksi niso uporabni, vendar pripomorejo k razumevanju vrednotenja napačnega modeliranja konstrukcije. Rezultati dokazujejo, da se geometrijo modelov do neke mere izplača poenostaviti. V praksi so uporabni tako ploskovni, linijski ali kombinirani modeli. Za kateri model se bomo odločili pa je odvisno predvsem od zasnove konstrukcije in vrste potresne analize. Uporaba togih odsekov za povezovanje vertikalnih elementov z gredami ter povezovanje linijskih in ploskovnih elementov je pomembna za pravilno modeliranje togosti konstrukcije. Ročni vnos mase konstrukcije v masna središča na nivojih etaž zahteva nekoliko več časa za modeliranje, vendar se s tem pospeši sama analiza in omeji prostostne stopnje na trikratnik števila etaž. Glede na primerjavo rezultatov analize modela z ročnim in avtomatskim deljenjem, smo prišli do zaključka, da ročno deljenje ni smotrno, saj zahteva veliko časa, rezultati pa niso bistveno bolj točni. Določili smo tudi optimalno velikost končnih elementov, ki znaša 0,5/0,5 m. V drugem delu magistrske naloge smo na obravnavanem objektu predstavili poenostavljeno nelinearno analizo – N2 metodo. Gre za kombinacijo nelinearne statčine analize modela konstrukcije z več prostostnimi stopnjami (MDOF sistem) in nelinearno spektralno analizo ekvivalentnega modela konstrukcije z eno prostostno stopnjo (SDOF sistem). V modelu za nelinearno potisno analizo smo upoštevali bilinearen odnos med momentom in rotacijo na robovih linijskih elementov. Na osnovi rezultatov potisne analize smo določiti kapaciteto pomika za tri mejna stanja na nivoju konstrukcije, ki jih navaja Evrokod: mejno sanje omejitve poškodb (DL), mejno stanje pomembnih poškodb (SD) in mejno stanje blizu porušitve (NC). V našem primeru bi objekt dosegel mejno stanje blizu porušitve pri pospešku 0,53 g za modalno oziroma 0,67 g za enakomerno porazdelitev sil. Evrokod 8-1 eksplicitno ne podaja mejnega pospeška pri katerem bi bila konstrukcija še sprejemljiva. Smatra se, da je objekt ustrezen, če je projektiran skladno s standardom. Za bolj utemeljeno oceno obnašanja bi morali izhajati iz sprejemljive verjetnosti prekoračitve mejnih stanj, kar presega okvire magistrske naloge. This master thesis deals with the seismic performance assessment of building of Institute of Information science in Maribor. The analyses are performed in compliance with Eurocode 8. First part of the thesis focuses on linear elastic seismic analysis of building with an objective to achieve optimal modeling of the building by using ETABS. Fifteen different models, which were split into two groups, were developed. First group contains models that are accurate and can be used to solve real problems, while the second group contains generic models that are mostly used to enhance our understanding of calculation errors that can be introduced with incorrect models. Results show us that in some cases models can be simplified. Shell, frame and combined models are useful in practical situations. For specific situation we should choose the type of model based on structure type and type of seismic analysis. The use of stiff elements for connection of vertical elements with beams and connection of frame and area elements is important for correct modeling of construction stiffness. Data about mass was also manually entered into the center of mass on storey level. Such an approach is slightly more time consuming, but significantly simplify the analysis and its results. However, it was also found that manual meshing of shell elements is too time consuming and don't have large impact on analysis results. At the end optimal size of finite elements was determined to 0,5/0,5 meters. The second part of the thesis presents simplified non-linear analysis N2 method, which was applied to the investigated building. The N2 method is combination of nonlinear static (pushover) analysis of entire building in combination of inelastic spectra based on an equivalent model with single degree of freedom (SDOF system). In model for non-linear pushover analysis, bilinear relationship between moment and rotation was taken into account at the edges of frame element. On basis of results, given by pushover analysis, limit-state displacements were determined for three states proposed by Eurocode standard: damage limitation state (DL), significant damage state (SD) and near collapse state (NC). The peak ground acceleration causing collapse was estimated to 0,53 g and 0,67g in the case of modal distribution of forces and uniform distribution of forces, respectively. It is assumed that the seismic performance of the building is acceptable since it is designed according to Eurocode 8-1. For more informed decision-making the estimated limit-state peak ground acceelerations should be compared to those values based on tolerable risk, which is beyond objectives of this thesis.

V okviru te diplomske naloge je bila izvedena potresna analiza montažne armiranobetonske hale. Največji poudarek je bil na preučevanju modeliranja betonskih polnil in njihovega vpliva na odziv konstrukcije med potresom. V nalogi so predstavljena pravila in računski postopki, ki so bili uporabljeni pri modeliranju konstrukcije. Vpliv polnil v poljih med stebri smo določili s poenostavljenim modelom, kjer se polnilo modelira z dvema diagonalama v ravnini zidu. Potresno analizo smo izvedli z metodo s horizontalnimi silami, ki je predvidena v Evrokodu 8. Za modeliranje smo uporabili program ETABS v9.7.4. Izdelana sta bila dva modela in sicer, model objekta z upoštevanjem polnil in model brez polnil, ki je služil za primerjavo rezultatov. Ugotovili smo, da so pomiki pri konstrukciji s polnili v povprečju manjši za 38%. Razlike smo opazili tudi pri notranjih statičnih količinah stebrov. Na mestu, kjer se na steber priključuje polnilo, katerega višina je precej manjša od višine etaže, se pojavi moment, ki je za 43 % večji od momenta pri čistem okvirju. Še večja razlika je v prečnih silah, saj so le-te tudi do petkrat večje od sil, ki smo jih določili na osnovi modela brez upoštevanja polnil. A seismic analysis of precast reinforced concrete building is presented in this graduation thesis. The main objective was to estimate the impact of concrete infills on seismic response of structure. In the first part of thesis the principles and analytical procedures for modelling of such structures are described. The effect of concrete infills was taken into account with a single-strut model. The modelling of structure and all the analysis were according to Eurocode 8 performed by software ETABS v9.7.4. For comparison, two different models were developed. The first one is a model which accounts for the effect of concrete infill, whereas the second model consisted of bare frame, which is often used in practice. It was found that infills reduced storey drift for approximately 38%. There are some differences in bending moments, too. In the case, where the infill which having the height much smaller than the height of column, connects to column, bending moments were observed for 43% greater in comparison to those based on the bare frame. However, much greater difference was observed for the shear forces in the columns, which were around five times greater than that observed in the case of bare frame.

V diplomski nalogi je testiran algoritem programa SAP2000 za dimenzioniranje betonskih okvirnih konstrukcij na DCM stopnjo duktilnosti po standardu Evrokod 8. Uporabo programa smo testirali na primerih šest-etažne in enajst-etažne armiranobetonske okvirne stavbe. Podrobno je opisano dimenzioniranje gred in stebrov v okvirnih konstrukcijah po metodi načrtovanja nosilnosti, ki jo uvaja Evrokod 8. Diplomska naloga je razdeljena na 3 dele. V prvemu so obravnavani vplivi na konstrukcijo ter analiza konstrukcije. Sledi prikaz dimenzioniranja prostorskih okvirov na stopnjo duktilnosti DCM. V zadnjem delu primerjamo rezultate dimenzioniranja s programom SAP2000 s ”peš” računom. Ugotovili smo tri pomanjkljivosti algoritma programa SAP 2000 in sicer pri izračunu projektne prečne sile v gredi in stebru po metodi načrtovanja nosilnosti ter pri kontroli upogibne nosilnosti stebrov po metodi načrtovanja nosilnosti (pogoj Mc ≥ 1,3Mb). Vzroka napake nismo uspeli ugotoviti, ker program ne poda podrobnega postopka izračuna, čeprav je algoritem v priročniku programa SAP2000 v skladu s predpisanim postopkom dimenzioniranja po standardu Evrokod 8. Dimenzioniranje elementov s programom SAP2000 brez upoštevanja standarda Evrokod 8 daje korektne rezultate. Assessed is the adequacy of the SAP2000 algorithm for design of reinforced concrete frames for ductility class medium according to Eurocode 8. The use of the program was demonstrated by means of a six-storey and eleven-storey reinforced concrete frame building. Described is design process of beams and columns according to the capacity design rules prescribed by Eurocode 8. The thesis is divided into three parts. The first part deals with the description of the actions on the building and assessment of corresponding internal forces. Next, the structures are designed for ductility class medium. In the third part, results obtained by SAP2000 are compared by those obtained according to hand calculations. Three shortcomings were found in the SAP algorithm. Namely, the design shear force of beams and columns was not assessed entirely according to capacity design approach prescribed by Eurocode 8. Similar observation can be made for the check of columns bending capacity (strong column – weak beam). The source for such inconsistency could not be found since the program does not provide a detailed output. However, SAP2000 gives correct results for the design of beams and columns without consideration of Eurocode 8 principles.

Seismic design of masonry buildings is a very common task of civil engineers in their daily practice. It is very important for structures in seismic areas bearing in mind that the brick buildings typically have a much lower seismic resistance compared to modern reinforced concrete and steel structures. In this paper several types of masonry structural elements have been examined, which appear within the newly or already constructed masonry buildings. Seismic analysis of masonry structures has been analyzed in accordance with the provisions of European engineering regulations Eurocode 6 and Eurocode 8 relating to masonry. The paper presents the practical guidance and procedures for seismic analysis of masonry buildings. Seizmički proračun zidanih zgrada je nezaobilazan zadatak građevinskih inženjera u svakodnevnoj praksi. On je veoma značajan za objekte u seizmičkim područjima imajući u vidu da zidane zgrade po pravilu imaju znatno manju seizmičku otpornost u odnosu na savremene armirano betonske i čelične objekte. U radu je razmatrano više tipova zidanih elemenata konstrukcije koji se pojavljuju u okviru novoprojektovanih ili već izgrađenih zidanih objekata. Seizmički proračun zidanih objekata analiziran je u skladu sa odredbama evropske inženjerske regulative Evrokod 6 i Evrokod 8, koji se odnosi na zidane konstrukcije. Data su praktična uputstva i procedure za seizmički proračun zidanih zgrada.

Design of masonry structures implies a combination of traditional and contemporary knowledge. By introducing Eurocodes, their design is equated with the design of other type of structures. According to the division of contents of European standards for structural design, the Eurocode 6 provides general rules for design, while Eurocode 8 provides additional rules that should be taken into consideration in design of masonry structures for earthquake resistance. This paper provides a review of the most important provisions for the calculation and design concept for masonry structures in compliance with European standards EN 1996 and EN 1998. The basic design concept of masonry structures in seismically active areas is to allow the reduction of expected seismic activity within linear analysis which are obtained based on elastic response spectrum, where the level of design seismic forces depends on the adopted structural system and prescribed behavior of the structure during earthquakes. Projektovanje zidanih konstrukcija predstavlja kombinaciju tradicionalnih i savremenih saznanja, a uvođenjem Evrokodova izjednačava se njihovo projektovanje sa projektovanjem drugih tipova konstrukcija. Saglasno podeli sadržaja evropskih standarda za projektovanje konstrukcija, Evrokod 6 navodi opšta pravila za projektovanje, dok su u Evrokodu 8 data dodatna pravila koja treba uzeti u obzir pri projektovanju zidanih konstrukcija u seizmičkim uslovima. U radu je dat pregled najvažnijih odredbi za proračun i koncept projektovanja zidanih zgrada saglasno evropskim standardima EN 1996 i EN 1998. Osnovni koncept projektovanja višespratnih zidanih zgrada u seizmički aktivnim područjima ogleda se u tome da se u okviru linearne analize dozvoli redukcija očekivanih seizmičkih dejstava dobijenih na osnovu elastičnog spektra odgovora, pri čemu nivo redukcije seizmičkih sila zavisi od usvojenog konstrukcijskog sistema i propisanog ponašanja konstrukcije.

Za zagotovitev potresne varnosti konstrukcije je potrebno določiti maksimalne projektne obremenitve konstrukcije v skladu s predpisom. Standard EN 1998-1:2006 pri analizi konstrukcije dovoljuje poenostavitve, ki so odvisne od tlorisne pravilnosti konstrukcije, in od pravilnosti konstrukcije po višini. Za konstrukcije, ki so pravilne po višini, je dovoljeno uporabiti metodo z vodoravnimi silami. Pri konstrukcijah, ki ne izpolnjujejo pogojev za pravilnost po višini, je potrebno uporabiti zahtevnejšo modalno analizo s spektri odziva. Čeprav ta metoda za konstrukcije pravilne po višini ni obvezna, jo je za take konstrukcije vseeno dovoljeno uporabiti namesto metode z vodoravnimi silami. Bistvo diplomskega dela je primerjava rezultatov metode z vodoravnimi silami in modalne analize s spektri odziva za izračun potresnih vplivov konstrukcije, ki je pravilna po višini. Za izbrano obravnavano konstrukcijo, pravilno tudi v tlorisu, smo tako na osnovi ravninskih modelov z obema metodama izračunali velikosti projektnih potresnih sil, ter pripadajoči horizontalni etažni pomiki. Tako smo ugotovili smiselnost uporabe metode modalne analize s spektri odziva pri konstrukcijah, pravilnih po višini. Primerjava rezultatov obeh metod je pokazala, da izračunane vrednosti opazno variirajo z izbiro metode. To ensure the seismic safety of structures it is necessary to determine the maximum design load of structure in accordance with the regulations. Standard EN 1998-1:2006 at the analysis of the structure allows for certain simplifications, which depend of the structure floor correctness as well as the regularity of structure height. For height correct structures, may be used the lateral force method. Structures that do not qualify for the correctness of the height, it is necessary to use more challenging modal response spectrum analysis. Although this method is not required for height correct constructions, it is allowed to be used instead of the lateral force method of analysis. Essence of the thesis is a comparison of the results of both approaches (lateral force method of analysis and modal response spectrum analysis) to calculate the seismic effects of height correct structure. For the selected structure which is properly also in plan, based on planar models with both methods we calculated sizes of project seismic forces, and their horizontal displacements. In this way we can get an insight into the advisability of using the modal response spectrum analysis in the height correct structures. The results of computational analysis in our case showed that the calculated values vary significantly with the choice of method.

Pri potresno odporni gradnji objektov moramo izpolniti vse zahteve varnosti, ki jih podajajo predpisi, zato moramo določiti maksimalne obremenitve objekta. V diplomskem delu je obravnavana jeklena konstrukcija s šestimi etažami. Analizirala sem, kako na velikost projektnega potresnega vpliva vplivajo različni izbrani postopki izračuna prvega nihajnega časa. Samo na takšen način sem lahko ocenila, kako je velikost potresnega vpliva povezana z izbiro metode analize in posledično, kakšni so stroški gradnje objekta. Masa in togost konstrukcije sta konstrukcijska parametra, ki imata preko prvega nihajnega časa največji vpliv na velikost potresnega vpliva, zato je v ospredju diplomskega dela opazovanje vpliva izbire modeliranja konstrukcije na velikost in porazdelitev potresnega vpliva. Rezultati so pokazali, da se pojavijo opazne razlike v izbiri velikosti profilov stebrov konstrukcije glede na izbrano metodo, po kateri sem računala nihajne čase in velikosti potresne sile. Z ekonomskega vidika to pomeni, da vrednost stebrov celotne jeklene konstrukcije variira z izbiro postopka izračuna nihajnega časa in da je smiselno narediti analizo za različne tipe profilov, npr. za profile HEM in HEA. The earthquake-resistant construction of buildings requires that all safety requirements defined by the regulations must be fulfilled. The peak-design load of the structure needs to be determined in order to meet these conditions. This diploma thesis concernes a steel-structure with six floors. The main objective of the thesis was to investigate how various selected period-calculation methods affect the magnitude of an earthquake’s effect. In this way it was exclusively possible to evaluate the influence of the analyse methods’ selection with the magnitude of the earthquake’s effect and, consequently, to the erection costs. Structural mass and stiffness are those structural design parameters that have the greatest impact on the first period governsing the design magnitude of the earthquake’s effect. Therefore, the core of this diploma thesis is oriented towards selecting the structure’s modelling, and its effect on the magnitude and distribution of the seismic impact. The results obtained clearly that significant differences occur regarding the sizing of the structure’s columns’ profiles originating from the method implemented for evaluation of the first period, as well as the seismic forces’ distributions. From an economical point of view, this means that the selecting of columns’ cross-sections dimensions for the whole steel structure clearly varies with the choice of period-evaluation method. Consequently, this further suggests that an analyse for different types of cross-section profiles, for example HEM and HEA profiles, should be carried out.

The main contribution of the Ph. D. thesis consists in the development of an original analytical model for the inelastic shear behaviour of reinforced concrete walls under seismic conditions. A wide review of literature, which consists of experimental results and mathematical models representing seismic behaviour of reinforced concrete (RC) elements, was made in order to identify the shear deformation and load transfer mechanisms in RC walls. The findings were utilized for the development of a new analytical model, which is based on the multi-vertical-line-element-model (MVLEM). The MVLEM was upgraded by adding multiple horizontal springs representing shear behaviour, which were linked to the displacements in vertical springs. Thus the interconnection between axial, flexural and shear behaviour was achieved. The constitutive rules for horizontal springs were set according to the mathematical models of shear transfer mechanisms found in the literature. The new element was implemented into up-to-date software for seismic analyses of buildings OpenSees. The experimental results of a large scale wall specimen tested on shake table were used in order to verify the reliability of the element. Further, the new element was utilised for a probabilistic study to assess the seismic risk of exemplar RC walls. Parallel to the main task, a critical review of Eurocode 8 procedures for determining the seismic shear demand in RC walls was made. The sources of shear magnification in RC walls, which must be accounted in the seismic design, were investigated. The results of a large parametric study demonstrated that the valid Eurocode 8 procedure needs some corrections, thus an enhanced procedure was proposed.

Zaradi zagotovitve potresne varnosti vsake konstrukcije je potrebno določiti njene maksimalne obremenitve v skladu s predpisom. Bistvo diplomskega dela je tako potresna analiza dvoetažne jeklene konstrukcije z določitvijo velikosti potresnega vpliva glede na izbiro postopka za izračun prvega nihajnega časa konstrukcije. Konstrukcijska parametra, ki preko prvega nihajnega časa najbolj neposredno vplivata na velikost potresnega vpliva, sta masa in togost konstrukcije in zato smo se v diplomskem delu orientirali v opazovanje vpliva modeliranja mase in togosti konstrukcije na velikost in porazdelitev potresnega vpliva. Rezultati računskih analiz so pokazali, da vrednosti opazno variirajo z izbiro postopka nihajnega časa. In order to ensure seismic safety of a structure it is necessary to adequately model the seismic effects on the structure in accordance with the regulations. The essence of the thesis is thus a seismic analysis of two-storey steel structure with the focus on the selection of procedure for the calculation of the structure’s first period and its influence on the magnitude of seismic impact. The mass and rigidness of the structure are certainly the most significant structural parameters that directly govern the value of the first period. Therefore, the thesis observes the impact of structure’s mass and rigidness modeling on the size of the seismic force and its distribution. The results of completed numerical analysis showed that the seismic forces vary noticeably regarding the selected method for the evaluation of the first period.