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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.

To improve the durability and serviceability of reinforced concrete structures, different variants of dual-phase reinforcing steel were developed within the research project NEWREBAR. The investigated variant of the new material, termed DPD2 steel, has a specific microstructure that increases the corrosion resistance, but its yielding strength is less than that of Tempcore steel B500B. DPD2 steel has no yielding plateau, which is characteristic of conventional reinforcing steel. Thus, it was investigated whether the current building codes can be used to design earthquake-resistant concrete structures reinforced by DPD2 steel bars. For this reason, three multi-story reinforced concrete frame buildings were designed according to Eurocode by considering DPD2 steel and, for comparison reasons, Tempcore steel B500B. Based on the nonlinear model, which was validated by cyclic test of columns, the seismic performance of DPD2 buildings was found to be improved compared to those designed with conventional B500B reinforcing steel. This can mainly be attributed to the substantial strain hardening of the DPD2 steel, which increases the overstrength factor of the structure by about 10%. However, for the improved seismic performance, the amount of steel in DPD2 buildings had to be increased in the design by approximately 20–25% due to the smaller yield strength of DPD2 steel. Nevertheless, it was demonstrated that Eurocode 8 could be used to design earthquake-resistant frame building reinforced with dual-phase reinforcing steel DPD2.

V diplomski nalogi je narejena ocena potresne odpornosti enodružinske zidane stavbe v Črnomlju, katere del je bil zgrajen leta 1964, dograditev pa je sledila leta 2000. Dela stavbe sta med seboj ločena z vertikalno dilatacijo, zato smo analizo izvedli za oba dela stavbe posebej. Za oceno potresne odpornosti stavbe smo uporabili metodo N2, ki temelji na nelinearni statični (potisni) analizi in je del standarda Evrokod 8. Potisno analizo smo najprej izvedli na nivoju etaž in s tem dobili potisne krivulje etaž, ki smo jih nato združili v potisne krivulje stavbe. Pri določitvi nosilnosti zidov smo upoštevali tri karakteristične mehanizme porušitve, in sicer upogibno porušitev zidovja, strižno porušitev z zdrsom po naležni regi ter strižno porušitev s pojavom diagonalnih razpok. Na zidovju ni bilo opravljenih preiskav, zato so bile materialne karakteristike zidovja povzete iz literature. Pri oceni potresne odpornosti smo upoštevali mejno stanje omejitve poškodb, mejno stanj velikih poškodb in mejno stanje blizu porušitve. Analizo smo izvedli ločeno za smeri X in Y. Na podlagi kontrol smo ugotovili, da je potresna odpornost starejšega dela stavbe višja od potresne odpornosti novejšega dela stavbe, kar je posledica slabe tlorisne zasnove novejšega dela stavbe. Zaključili smo, da stavba ni potresno odporna glede na zahteve standarda Evrokod 8. Dodatno smo izvedli analizo brez upoštevanja strižne porušitve z zdrsom po naležni regi v spodnji etaži, ki se sodeč po izkušnjah pojavlja le v zgornjih etažah. Tudi v tem primeru kontrole mejnih stanj niso bile v celoti izpolnjene, čeprav se je nosilnost stavbe povečala. The earthquake resistance of a single-family detached masonry building in Črnomelj, Slovenia, is evaluated in this bachelor thesis. The building was constructed in 1964 and reconstructed in 2000. As the two parts of the building are connected through a vertical expansion joint, the seismic analysis was performed for each part individually. The building’s earthquake resistance was assessed by the N2 method, which is based on a non-linear static (pushover) analysis and is a part of the Eurocode 8 standard. The pushover analysis was first performed at the storey level, thus obtaining the pushover curves of the storeys, which were then merged into the pushover curve of the entire building. The bearing capacity of each wall was estimated by the simplified model taken into account the flexural failure, the shear failure due to sliding and the shear failure due to formation of diagonal cracks. The material characteristics of the building’s walls were taken from the literature due to the absence of in-situ measurements. In the assessment of earthquake resistance, the damage limitation limit state, significant damage limit state and near collapse limit state were considered. The analysis was conducted separately for the X and Y direction of seismic loading. On the basis of the limit states verification, it was found that the earthquake resistance of the older part of the building performed is better than that of the new part, which is the consequence of the poor design of the plan of the new part of the building. It was concluded that the building is not earthquake resistant accorindg to the Eurocode 8 requirements. Additionally, a pushover analysis without consideration of the shear failure of the walls due to sliding was performed, because such failure modes had been observed only in higher stories in the past earthquakes. In this case, the verifications of limit states were also not entirely fulfilled although the strength of the building was increased.

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.

V diplomski nalogi je narejena ocena potresne odpornosti zidane stavbe po standardu Evrokod 8-3. Uporabljena je metoda N2, ki sestoji iz izvedbo nelinearne statične (potisne) analize na modelu z več prostostnimi stopnjami in oceno potresnih zahtev na modelu z eno prostostno stopnjo. Potisna analiza je izvedena v dveh korakih. Najprej je določena potisna krivulja na nivoju etaž. Pri tem so upoštevani mehanizmi upogibne porušitve, strižne porušitve zaradi prestriga in strižne porušitve zaradi diagonalnih razpok. Pri določitvi materialnih lastnosti zidov je poleg delnih materialnih varnostnih faktorjev upoštevan tudi faktor zaupanja zaradi omejenega poznavanja konstrukcije. V naslednjem koraku so etažne potisne krivulje združene, s čimer je definirana potisna krivulja na nivoju konstrukcije. S transformacijo slednje na ekvivalenten sistem z eno prostostno stopnjo je omogočen račun potresnih zahtev in verifikacija potresne odpornosti. Poleg kontrole mejnega stanja omejitve poškodb in mejnega stanja velikih poškodb, ki jo predvideva standard Evrokod 8-3, je izvedena tudi kontrola mejnega stanja blizu porušitve. Kontrole so izvedene ločeno za smeri obremenjevanja X in Y. Ugotovljeno je, da je mejno stanje omejitve poškodb prekoračeno v obeh smereh obremenjevanja, mejno stanji velikih poškodb in mejno stanje blizu porušitve pa le v smeri Y. Zaključeno je, da stavba ne izpolnjuje zahtev standarda Evrokod 8-3. In the diploma thesis an assessment of the earthquake resistance of the masonry building was made according to the Eurocode 8-3 standard. The N2 method, which consists of the implementation of non-linear static push-over analysis on a multi-degree-of-freedom model and the estimation of seismic demand on single-degree-of-freedom model, was used. The push-over analysis was performed in two steps. Firstly, a push-over curve at the storey level was determined by taking into account the mechanisms of flexural failure, shear failure due to sliding and shear failure due to formation of diagonal cracks. The material properties of the walls were estimated by consideration of the partial material safety factors and the confidence factor due to limited knowledge of the construction. In the next step, the storey push-over curves were joined together, which resulted in the push-over curve on a structural level. By transforming the latter into an equivalent single-degree-of-freedom model it was made possible to estimate the seismic demand and to verify performance of the structure. Besides the verification of the limit state of damage limitation and the limit state of significant damage, which is envisaged by the Eurocode 8-3 standard, the verification of the near collapse limit state was performed independently for X and Y direction of seismic action. It was found that the limit state of damage limitation is not verified in both directions of loading, while the limit state of significant damage and near collapse limit were not verified only in the direction Y. It is concluded that the building does not meet the safety requirements of the standard Eurocodes 8-3.

V magistrski nalogi obravnavamo štiri nadstropni jekleni okvir z zamaknjenimi etažami pri potresni obremenitvi. Okviri so dimenzionirani z različnimi pristopi. Dva okvira sta dimenzionirana po načinu DCM z manjšimi odmikom od pravil, ki jih določa SIST EN 1998-1. Trije okviri so dimenzionirani po načinu DCH. Za okvire so izdelani matematični modeli v programskem okolju Abaqus. Okviri so modelirani s kombinacijo lupinastih in linijskih končnih elementov. Upoštevana je materialna in geometrijska nelinearnost. Na vsakem modelu je izvedena potisna N2 analiza in dinamična nelinearna analiza s tremi akcelogrami. N2 metoda je bila uporabljena za oceno pričakovanega plastičnega mehanizma, distribucijo poškodb in za potrditev vrednosti faktorja obnašanja q. Z rezultati dinamičnih analiz primerjamo velikost akumuliranih plastičnih deformacij, maksimalne pomike tekom potresa in količino sipane energije v plastičnih deformacijah. Vidna so mesta plastičnih členkov. The master’s thesis deals with four story steel frames with staggered floor construction designed for seismic action. Steel frames are designed according to different approaches. Two frames are designed according for DCM with smaller modifications to rules given in SIST EN 1998-1. Three frames are designed according for DCH. All frames are modeled in the SIMULIA Abaqus FEA program. The models are combination of linear beam and shell finite elements. The geometric and material nonlinearity were taken into consideration. The models are subjected to pushover N2 analysis and dynamic nonlinear analysis with three different ground motions. The N2 method was used to estimate the expected plastic mechanisms and the distribution of damage and to revise the behaviour factor. The results of dynamic analysis were used to compare equivalent plastic strain, maximum displacements of frames, plastic dissipation energy, and the distribution of damage.

The paper deals with the effects and costs of implementing a base isolation system for the mitigation of the seismic risk of an existing steel rack structure. Different realistic distributions of the payload mass and occupancy levels, which form different plan asymmetric variants, have been analysed. The results obtained by the pushover analysis (N2 method) are presented as top floor envelopes and as plastic hinge damage patterns. In the presented cost study, the cost of the implementation of the proposed base isolation system is compared with the estimated costs of structural repairs to the damaged structural members of the superstructure, as well as with estimated expenses of the downtime period. The results have shown that base isolation is, in general, not economically feasible for lower ground motion intensities, whereas it could be of great benefit in the case of moderate and high intensities, especially if the downtime period is taken into account. El presente artículo trata sobre los efectos y costes de implementación de un sistema de aislamiento en cimentación para la mitigación del riesgo sísmico de la estructura de un bastidor de acero en altura prexistente. Se han analizado diferentes distribuciones realistas de la masa contribuyente y de los niveles de ocupación, conformando diferentes variantes asimétricas en planta. Se presentan los resultados obtenidos mediante el método N2 (análisis estático incremental no lineal) como envolventes de las plantas superiores y como patrones de deterioro en estado plástico. En el estudio de costos presentado, el coste de implementación del sistema de aislamiento propuesto se compara con los costes estimados de reparación de los elementos superestructurales y los costes derivados del período de desocupación. Los resultados muestran que, en general, el aislamiento en la base no resulta viable económicamente para movimientos de baja intensidad, pero puede ser muy beneficioso en el caso de intensidades moderadas y altas, particularmente cuando el período de desocupación es tenido en cuenta.

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.

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.

Premostitvene konstrukcije nam omogočajo premoščanje naravnih in umetnih ovir ter so ključnega pomena za povezovanje in združevanje ljudi. Zaradi njihove pomembnosti je te konstrukcije potrebno projektirati in zgraditi tako, da tudi v primeru ekstremnih naravnih vplivov (npr. močan potres) ohranijo svoj namen in tako še vedno omogočajo komunikacijo s prizadetimi območji. Ker so močni potresi razmeroma redek dogodek, konstrukcijam zaradi neekonomičnosti v postopku projektiranja ne zagotovimo elastičnega odziva. Konstrukciji običajno zagotovimo nekoliko manjšo nosilnost in s tem dovolimo, da se v konstrukciji v določenih izbranih delih pojavijo poškodbe, ki jih lahko po močnem potresu popravimo. Sposobnost konstrukcije, da prenese poškodbe (plastične deformacije) imenujemo duktilnost konstrukcije. Plastične deformacije pri premostitvenih konstrukcijah običajno dopuščamo le v stebrih, in sicer na mestu stika s temeljem in/ali na mestu stika s prekladno konstrukcijo. V magistrski nalogi je prikazan postopek projektiranja tipičnega krajšega armiranobetonskega mostu v skladu s standardom Evrokod 8/2, ki vsebuje takšen pristop k projektiranju konstrukcij. Kljub temu, da je odziv mostov pri močnih potresih izrazito nelinearen, postopki projektiranja v splošnem še vedno temeljijo na rezultatih linearno-elastične analize. Potresni odziv konstrukcije smo s tem razlogom ocenili tudi s pomočjo poenostavljene nelinearne analize, ki temelji na potisni analizi, ki je bila določena z metodo N2. Metoda vsebuje nelinearno statično analizo modela konstrukcije z več prostostnimi stopnjami (MDOF sistem) in nelinearno dinamično analizo ekvivalentnega modela konstrukcije z eno prostostno stopnjo (SDOF sistem). Ker standard ne predvideva eksplicitne kontrole potresnega tveganja, varnost konstrukcije preverjamo s primerjavo vnaprej določenega ciljnega potresnega tveganja z izračunanim potresnim tveganjem. V sklopu magistrske naloge smo varnost konstrukcije preverili s pomočjo zahtevnejše inkrementalne dinamične analize IDA in nedavno predlagane metode 3R, ki nam pove ali je ciljno tveganje porušitve konstrukcije preseženo. Bridge structures enable us to span natural and artificial barriers and are the key meaning for connecting and the agglomeration of people. Because of their importance it is necessary to design and build them in a way that they even in a case of extreme natural events (e.g. a strong earthquake) keep their purpose and allow communication with affected areas. Because strong earthquakes are a comperatively rare event, we do not assure structures within the process of designing to have an elastic response, because of the uneconomical aspect. Usually we assure structures a bit smaller load capacity and with that we allow damage within chosen elements of the structure that can be renovated after a strong earthquake. Ability of the structure to withstand damage (plastic deformation) is called structure ductility. When designing bridge structures we usually allow plastic deformation in columns at the connection with the foundation and/or at the connection with the slab. In this master's thesis we show a procedure of designing a typical short reinforced concrete bridge in accordance with the standard Eurocode 8/2 that contains such approach for designing structures. Even though that bridge response in case of strong earthquakes is explicitly nonlinear, design procedures generally still base on results of a linear-elastic analysis. Because of this, we also evaluated the seismic response of the structure with help of the simplified nonlinear analysis, which is based on a pushover analysis that was proposed with the N2 method. This method contains the nonlinear static analysis of the structure model with multiple degrees of freedom (MDOF system) and the nonlinear dynamic analysis of the equivalent structure model with a single degree of freedom (SDOF system). Because the standard does not foresee the explicit control of the seizmic risk, we have to evaluate the safety of the structure with comparison of in advance chosen target collapse risk with the calculated collapse risk. In this master's thesis the safety of the structure was evaluated with a more demanding incremental dynamic analysis IDA and recently proposed 3R method, that tells us if the structure target collapse risk is exceeded.

Projektiranje stavb po veljavnih standardih ne omogoča jasnih informacij o varnosti pred porušitvijo, saj vrednotenje verjetnosti porušitve v standardu ni predvideno. V doktorski disertaciji zato predlagamo nov postopek projektiranja, ki temelji na ciljnem potresnem tveganju. Takšno projektiranje je iterativno in zahteva uporabo nelinearne metode analize. Izhodišče je začetna konstrukcija, ki jo postopno prilagajamo dokler ocenjeno potresno tveganje ni manjše od ciljnega tveganja. Predlagan postopek projektiranja pa lahko postane nepraktičen, če je število iteracij veliko. Zato smo predlagali enostavne smernice za prilagajanje armiranobetonskih okvirnih stavb na osnovi rezultatov potisne analize trenutne konstrukcije. Z njihovo uporabo se s primernim večanjem prečnih prerezov elementov in vzdolžne armature stebrov izboljšuje deformacijska kapaciteta in nosilnost stavbe. Poleg smernic za prilagajanje konstrukcije smo vpeljali tudi stopnjevanje zanesljivosti projektiranja, pri čemer se računsko manj zahtevne metode analize uporabijo v začetnih iteracijah, bolj zahtevne, ki so običajno tudi bolj natančne, pa za kontrolo rezultatov projektiranja na osnovi poenostavljenih metod. Del raziskav je bil usmerjen tudi v izboljšanje natančnosti ocene potresnega tveganja. Razvili smo nove enačbe za oceno potresnega tveganja, kjer upoštevamo fizikalno opredeljeni mejni vrednosti intenzitete potresa. Ugotovili smo namreč, da neupoštevanje spodnje in zgornje meje intenzitete potresa v nekaterih primerih povzroči precenjeno vrednost potresnega tveganja. Predlagan postopek projektiranja smo z upoštevanjem novih enačb za oceno potresnega tveganja uporabili na dveh primerih armiranobetonskih okvirnih stavb. Kljub grobi določitvi začetne konstrukcije smo ciljno potresno tveganje dosegli zgolj s štirimi oz. tremi iteracijami. Upoštevanje zgornje meje intenzitete potresa lahko znatno zmanjša ocenjeno verjetnost porušitve, kar posledično vpliva na izbrano konstrukcijo. Most current standards that are concerned with the seismic design of buildings do not provide sufficiently clear information about safety against collapse. For this reason a new procedure for the risk-based seismic design of buildings is proposed, which is iterative and based on the use of nonlinear methods of analysis. The proposed design procedure starts by the selection of an initial structure, which is gradually adjusted by means of iterations until the estimated seismic risk is lower than the target risk. Since the number of such iterations may become excessive, simple guidelines have been developed for the structural adjustment of reinforced concrete frame buildings, which can be used to improve the building's strength and deformation capacity by appropriately adjusting the structural elements selected on the basis of the results of pushover analysis from the current iteration. The concept of differentiation in the reliability of design is also implemented, so that less demanding analytical methods are used in the initial iterations, whereas more demanding, and usually more accurate methods are used to verify the design results obtained by using simplified methods. Part of the research was aimed at the improvement of the accuracy of seismic risk estimation, which is an important component of the proposed design procedure. New equations for seismic risk assessment, which take into account the physically defined limits of ground-motion intensity, have been derived. It was found that sometimes, if the lower and upper limits of the ground-motion intensity are insufficiently taken into account, overestimated values of the seismic risk may be obtained. The suitability of the proposed design procedure, which takes into account the newly developed equations for seismic risk assessment, was demonstrated on two examples of reinforced concrete frame buildings, one having 8 storeys and the other 15 storeys. The target risk was achieved after only four and three iterations, respectively, even though their corresponding initial structures had been only roughly defined. Taking into account the upper bound of the seismic intensity can result in a reduction in the estimated probability of collapse, which can in turn have a significant effect on the final design of the structure.

V diplomski nalogi je obravnavana potresna analizi enodružinske zidane stavbe, zgrajene leta 1993, na obrobju Ljubljane. V prvem delu diplomske naloge je predstavljeno teoretično ozadje določitve potresne obtežbe in nosilnosti tako posameznih zidov kot tudi celotne konstrukcije. Pri določitvi nosilnosti so upoštevani trije značilni porušni mehanizmi, ki nastanejo v zidanih stavbah, pri kombinaciji vodoravne in navpične obtežbe: upogibni mehanizem in oba strižna mehanizma. V drugem delu je izračunana potresna odpornost obravnavanega objekta. Za trdnost materiala so upoštevane srednje vrednosti, ki so zmanjšane za faktor zaupanja. Potrebno je določiti lastne teže posameznih konstrukcijskih sklopov in mase celotne konstrukcije. Potresna sila je določena z metodo z vodoravnimi silami, pri čemer je bil upoštevan največji spektralni pospešek ter faktor obnašanja 1,5. V analizi je bila obravnavana le spodnja etaža, saj so tam največje potresne obremenitve. Najprej je bila ocenjena nosilnost celotne konstrukcije po elastični analizi, pri čemer je upoštevana popolna prerazporeditev sil iz preobremenjenih zidov na zidove, ki imajo še rezerve. Naredili smo tudi poenostavljeno nelinearno analizo pri čemer je bila tako dobljena nosilnost za y smer 797 kN, kar je le za približno 10% manjša vrednost od nosilnosti, ki smo jo ocenili na osnovi rezultatov linearno elastične analize (880 kN). Ugotovljeno je bilo, da projektna potresna obremenitev presega projektno nosilnost zidov iz česar sklepamo, da objekt v celoti ne zadosti zahtevam standarda Evrokod 8. The thesis addresses assessment of seismic resistance of a single-family masonry building, built in 1993, in the suburb of Ljubljana. The theoretical background for determination of design seismic loads and capacity of both masonry walls as well as the whole structure is presented in the first part of the thesis. The determination of the strength of masonry walls is also described with consideration of three failure mechanisms that occur in masonry wall: sliding shear failure, shear failure with diagonal cracks, flexural failure. In the second part follows practical example where we calculate seismic resistance of the building. For the strength of materials we take into account the mean values reduced by a confidence factor. It is necessary to determine the weight of individual structural assemblies and the mass of the whole structure. Seismic force is determined by the method of horizontal forces, where is taken into account the maximum spectral acceleration, and behaviour factor 1,5. Seismic resistance is then checked only for the ground floor since there the greatest storey shear force occurs. Firstly the base shear was calculated on the basis of elastic analysis by taking into account the full redistribution of seismic forces to those walls which still had reserves. The simplified nonlinear analysis was also performed. Sodetermined base shear in y direction amounted to 797 kN, which is only about 10% less than the base shear estimated from linear elastic analysis (880 kN). It was found that design seismic load exceeded the estimated design value of base shear strength, which indicated that the investigated building does not comply the safety requirements of the Eurocodes 8.

V diplomski nalogi je obravnavana poenostavljena nelinearna analiza izbranih družinskih hiš na območju Krškega. Osnovo za modeliranje in analizo obravnavanih objektov sta predstavljala standarda Evrokod 6, ki obravnava zidane konstrukcije in Evrokod 8, ki obravnava potresnoodporno projektiranje konstrukcij. Teoretične osnove in zaporedje postopka računa so predstavljene v prvem delu naloge. Na hitro se naloga dotakne nastanka potresov in njihovega vpliva na okolje, opisane so materialne karakteristike opečnih zidov in podane enačbe za račun nosilnosti zidovja. V nadaljevanju so predstavljene teoretične osnove za oceno potresne odpornosti zidanih objektov. V drugem delu naloge je podan primer potresne analize enega izmed objektov, nato pa je predlagan še model normirane potisne krivulje glede na rezultate potisnih analiz štirih značilnih zidanih hiš na območju Krškega. Predlagamo, da nosilnost značilnega zidanega objekta iz opečnih votlakov za šibko os znaša približno 27 % teže objekta, pomik etaže na meji porušitve pa približno 0.42 % višine etaže. Približno potisno krivuljo za izbran objekt lahko določimo enostavno tako, da normirane prečne sile s predlaganega modela potisne krivulje pomnožimo s težo objekta, normirane pomike pa z višino pritlične etaže, ki se za zidane objekte malo spreminja. Potrebno je poudariti, da so rezultati take ocene vsekakor precej negotovi tako zaradi uporabe precej poenostavljenih nelinearnih modelov, kot tudi zaradi majhnega števila objektov, ki smo jih upoštevali pri določitvi normirane potisne krivulje značilnih zidanih objektov. Zato je uporaba predlaganega modela primerna le za hitre ocene potresne odpornosti večjega števila objektov. The diploma thesis addresses a simplified nonlinear seismic (»pushover«) analysis of selected family houses in the Krško region. Standards Eurocode 6 and 8, which, respectively, deals with masonry buildings and earthquake-resistant design of buildings, were used as a basis for modelling and seismic analysis of the examined houses. The theoretical background and sequences of seismic analysis are presented in the first part of the thesis, where the occurrence of earthquakes and their impact on environment are also briefly addressed. In addition, the mechanical characteristics and the models of resistance of the masonry walls are described. Follow an overview of the theoretical background for seismic performance assessment of masonry buildings. The second part of the thesis presents results of simplified seismic analysis of a family house. At the end of the thesis, the model for normalized pushover curve of masonry buildings in the Krško region is proposed by taking into account the results of seismic evaluation of four examined buildings. It is suggested that an average shear resistance in the weak direction of a building from Krško region, which is constructed by hollow bricks, is around 27 % of its weight, whereas the ultimate storey drifts is around 0.42 % of the storey height. The proposed model makes it possible to assess the pushover curve of the examined building simply by multiplying the normalized shear forces from the model by the weight of the examined building and by multiplying the normalized storey drifts by the storey height. It should be noted that the results of such an assessment is quite uncertain, not only due to the simplified models used for the pushover analysis, but also due to the fact that only a small number of buildings were used in the parametric study. Therefore, the use of the proposed normalized pushover curve is limited and may be suitable only for rapid seismic performance assessment of large number of buildings.

V diplomski nalogi obravnavamo klasično zidan stanovanjski blok zgrajen v 60. letih prejšnjega stoletja v Škofji Loki. V prvem delu predstavimo obnašanje zidanih konstrukcij, ki so izpostavljene potresni obtežbi. Obravnavamo teoretično ozadje za tri možne mehanizme porušitve zidu, iz katerih določimo nosilnost posameznih elementov: strižna porušitev z nastankom diagonalnih razpok, strižna porušitev z zdrsom in upogibna porušitev. Nato predstavimo metodo za določitev projektne potresne obtežbe, na koncu pa pojasnimo osnove poenostavljene nelinearne potisne analize. Drugi del naloge obsega oceno potresne odpornosti dejanskega zidanega objekta. Predpostavili smo nihanje objekta v osnovni nihajni obliki in določili potresne sile po metodi s horizontalnimi silami. Materialne karakteristike smo določili deloma iz projektne dokumentacije in deloma z upoštevanjem določil iz standarda Evrokod. Pri oceni potresne odpornosti smo se omejili na zidove v pritličju, ki so najbolj ranljivi v primeru potresa. V analizi smo predpostavili, da je betonska klet bistveno bolj toga od opečnih zidov nad kletjo. Z izračuni za nearmirano zidovje v skladu z Evrokodoma 6 in 8 smo ocenili, da objekt dosega potrebno potresno varnost v vzdolžni smeri, v prečni smeri pa ne. Ugotovitve iz elastične analize smo potrdili s poenostavljeno nelinearno potisno analizo. Naredili smo tudi kratko primerjavo med projektiranjem po trenutno veljavnih standardih Evrokod in predpisi iz časa projektiranja, takrat je bil v veljavi jugoslovanski predpis iz leta 1964, torej obdobja po močnem potresu v Skopju. Pri primerjavi potresne sile dobljene po takratnih in trenutno veljavnih standardih smo ugotovili, da se bile zahteve v standardih JUS precej blažje, saj je projektna potresna sila dobljena po trenutno veljavnih standardih Evrokod 2,5 krat večja. The thesis addresses the earthquake resistance of the typical masonry apartment building constructed in the 1960s in Škofja Loka. In the first part the seismic response of masonry buildings is presented. Explained are the models of three possible masonry wall failure mechanisms, which are the basis for determining the capacity of single walls taking into account the shear failure due to formation of diagonal cracks, the sliding shear failure and the flexural failure. The definition of the design seismic action and fundamentals of the pushover analysis follow. The second part of the thesis deals with performance assessment of masonry building in Škofja Loka. The seismic demand is firstly assessed by using the lateral force method. Material characteristics were defined according to design project with consideration of provisions of Eurocode standard. Only ground floor is included in seismic performance assessment since it is the most vulnerable. The effects of the concrete basement were neglected in the analysis. The results of the analysis according to Eurocode 6 and 8 have shown that the building meets safety requirements in longitudinal direction, but not in the case of transverse direction. Conclusions on the basis of elastic analysis were confirmed by simplified nonlinear pushover analysis. At the last part of the thesis a comparison between design seismic action according to standard Eurocodes and regulations from 1964, which were the consequence of the catastrophic Skopje Eartquake, are presented. It was found that Eurocode provided the 2,5 times greater design seismic action.

V diplomski nalogi obravnavamo problematiko porušitev jeklenih paličnih daljnovodnih stebrov. Porušitev enega ali več zaporednih stebrov, lahko povzroči prekinitev prenosa električne energije. Posledično se zmanjšajo dohodki iz naslova prenosa energije, poleg tega so precejšnji tudi neposredni stroški zaradi vzpostavitve prvotnega stanja. V teoretičnem delu so na kratko predstavljeni najpogostejši vzroki porušitev in možne zaščite pred porušitvami stebrov zaradi pojava prekomerne dodatne obtežbe na vodnikih. V praktičnem delu diplomske naloge obravnavamo nosilni daljnovodni steber NC74 daljnovoda 2 × 110 kV, pri čemer projektne vplive na konstrukcijo definiramo po predpisih SIST EN 50341-1 ter na podlagi linearno-elastične analize preprojektiramo kritične elemente obstoječe konstrukcije. Sledi nelinearna statična analiza za obtežne kombinacije z žledom, ki so se izkazale za najbolj kritične pri projektiranju. Izkaže se, da so za daljnovodni steber značilne razmeroma majhne dodatne nosilnosti zaradi vpliva prerazporejanja obremenitve na nosilne elemente konstrukcije. Dodatna varnost proti porušitvi je zato v veliki meri posledica stopnje izkoriščenosti elementov pri projektiranju. V zadnjem delu diplomske naloge projektiramo daljnovodni steber po načelih metode načrtovanja nosilnosti. Z namenom, da bi preprečili globalno porušitev konstrukcije, varujemo diagonalne in vertikalne elemente, medtem ko za šibek člen, kjer dopustimo poškodbe, izberemo konzole stebra, na katere so obešeni vodniki daljnovoda. Oslabitev konzole smo dosegli z zmanjšanjem profila najbolj izkoriščenega elementa na konzoli, utrditev trupa stebra pa s povečanjem profilov za diagonalne in vertikalne elemente. Na ta način smo preprečili globalno porušitev konstrukcije, pri čemer se je masa konstrukcije povečala za približno 14%. Za aplikacijo metode v praksi bi bilo potrebno predhodno izvesti verjetnostno analizo pojava izrednih obtežb in stroškovno analizo, s katero bi ugotovili, ali je predlagan način projektiranja ekonomsko upravičen. The issues of collapse of steel-truss transmission towers are addressed in the thesis. The collapse of one or several consecutive towers causes loss of electricity supply. Consequently, a part of income from energy supply may be lost. In addition, collapse of tower cause high direct costs of restoration of transmission line. In the theoretical part of the thesis, the most frequent collapse patterns due to extreme action on conductors, as well as possible solutions for protection of the towers against collapse are presented. The practical part of the thesis, which addresses electric transmission tower NC74 of the 2 × 110 kV transmission line, involves definition of the design action according to standard EN 50341-1 and redesign of critical elements of the existing tower on the basis of linearelastic analysis. Follow nonlinear static analysis for sleet-based load cases, which represented the most critical action for design of the tower. The results of nonlinear static analysis indicated that overstrength due to redundancy of such towers is minor. The estimated overstrength of the tower is thus primarily consequence of the utilization rate of the structural elements in the design. In the last part of the thesis, capacity design procedure is applied to the transmission tower in order to prevent global collapse of structure. The diagonals and the vertical elements of the tower were protected against failure, whereas cantilevers of the tower were selected as week parts of the structure. In order to meet this requirement, the diagonals and vertical elements of the tower were strengthened, and the element of the cantilever, which had the largest utilization rate, was weakened by selecting smaller cross-section of the structural element of the cantilever. This design procedure prevents global collapse of structure for the price of increased mass of the structure, which was in this case approximately 14% larger than that in the case of conventional design. For the application of the proposed design approach in practice, a probabilistic analysis of the occurrence of the extreme actions and the cost-benefit analysis should be performed in order to prove or disprove the economic feasibility of the proposed design approach.

In this thesis a new methodology for the seismic risk assessment of masonry buildings is presented. It is based on a probabilistic approach, which makes it possible to determine seismic risk using various performance measures such as the probability of exceeding a certain damage state, the probability of exceeding a certain economic loss, the expected annual loss, and the loss dependent on a given seismic intensity. Using these performance measures engineers and project stakeholders can make informed decisions as to whether particular existing buildings should be repaired, strengthened, or replaced, or simply choose the best variant in the design of a new building. The methodology consists of four main steps: hazard analysis, structural analysis, damage analysis and loss analysis. The results from these four separate analyses are combined together in a probabilistic manner, using the total probability theorem, thus making it possible to explicitly take into account numerous uncertainties. However, in this study the main focus was on the modelling uncertainties, and on the aleatoric uncertainties which are due to record-to-record variability. A database of experimental data obtained in the testing of numerous masonry specimens was established, and analysed in order to define fragility functions for masonry elements failing in shear or flexure, while also evaluating the uncertainties in the limit-state deformations of the masonry walls. The possibility of reducing the impact of uncertain input parameters by means of non-destructive tests was also explored. By measuring its ambient and forced vibrations, the vibration periods of an old masonry building in Ljubljana were determined, and used to calibrate corresponding structural models. It was shown that such non-destructive experimental investigations can contribute to more reliable seismic performance assessments of buildings, even when the performance assessment procedure is based on a nonlinear method of analysis. In addition to the explicit consideration of uncertainties, damage to the components of buildings was also explicitly simulated on the basis of the relationship between the seismic intensity and the engineering demand parameters which were obtained by simplified nonlinear analysis. The latter consisted of pushover analysis, together with incremental dynamic analysis of a SDOF model. The applicability of the proposed methodology was demonstrated by means of examples of a residential and a commercial building, which were constructed from hollow clay bricks or solid bricks. Under the presumptions of this study, the expected annual loss for buildings constructed with hollow clay bricks was 60 €/100m2 of the gross floor area, and 125 €/100m2 in the case of buildings which were made from older material consisting of solid bricks. Disaggregation of the results showed that weaker earthquakes with lower intensities contribute significantly towards the expected annual losses. It was also found that nonstructural elements, which are key components in the loss assessment model, can contribute more than 50 % of the total loss. The modelling uncertainties have a large impact on the results of the pushover analysis and of those obtained by incremental dynamic analysis, as well as on the probability of exceeding damage states. However their impact on loss estimates is more pronounced in the case of the fragility and loss functions, seismic hazard, and the costs of replacing the building. V doktorski disertaciji predstavimo metodologijo za oceno potresnega tveganja zidanih stavb. Metodologija temelji na verjetnostnem pristopu, kar omogoča vrednotenje potresnega tveganja z različnimi merami kot so verjetnost prekoračitve izbranega mejnega stanja, verjetnost prekoračitve določene ekonomske izgube, pričakovana letna izguba ter pogojne izgube pri izbranih vrednostih intenzitete potresa. Vse omenjene mere potresnega tveganja omogočajo investitorjem informirano odločitev o sanaciji/utrditvi/zamenjavi obstoječih objektov oziroma izbiro najboljše variante pri projektiranju novih. Metodologija za oceno potresnega tveganja je sestavljena iz štirih analiz: analize potresne nevarnosti, analize obnašanja konstrukcije, analize poškodovanosti in analize izgub. Rezultati vsake od ločenih analiz so obravnavani probabilistično in med seboj povezani z izrekom o popolni verjetnosti. Takšen okvir omogoča eksplicitno upoštevanje številnih negotovosti, v okviru disertacije pa smo se osredotočili na upoštevanje modelnih negotovosti in negotovosti v potresni obtežbi. Vzpostavili smo bazo podatkov iz laboratorijskih eksperimentov na številnih zidanih preizkušancih in izpeljali funkcije ranljivosti za zidove, ki se porušijo bodisi v strigu bodisi v upogibu, s čimer smo vrednotili negotovosti v mejnih pomikih zidov. Raziskali smo tudi možnost zmanjšanja vpliva negotovosti vhodnih parametrov z uporabo nedestruktivnih preiskav. Z merjenjem ambientnih in vsiljenih vibracij smo določili nihajne čase stare zidane stavbe v Ljubljani, nato pa smo s parametrično analizo dokazali, da je s kalibracijo matematičnega modela stavbe glede na izmerjen elastični nihajni čas mogoče zmanjšati tudi vpliv negotovosti na rezultate nelinearne analize obnašanja konstrukcije. Poleg vpliva negotovosti smo v oceni potresnega tveganja eksplicitno simulirali poškodovanost komponent. Zvezo med potresnimi zahtevami in intenziteto potresa smo določili s poenostavljeno nelinearno metodo na osnovi potisne analize in inkrementalne dinamične analize na modelu z eno prostostno stopnjo. Predlagano metodologijo smo demonstrirali na primerih stanovanjske in poslovne zidane stavbe, ki sta bili zgrajeni bodisi iz opečnih votlakov bodisi iz polnih zidakov. Pri stavbah iz boljšega materiala je bila ob predpostavkah v tej študiji in izbiri modela pričakovana letna izguba 60 €/100 m2 bruto tlorisne površine, pri stavbah iz starejšega materiala pa 125 €/100 m2. Rezultate smo razčlenili po intenzitetah potresa, pri čemer se je izkazalo, da k pričakovanim letnim izgubam zelo veliko prinesejo šibki potresi, ki ne povzročijo velikih izgub, vendar se glede na uporabljen model potresa pojavijo precej pogosto. Ugotovili smo tudi, da nekonstrukcijske komponente prispevajo več kot 50 % k celotnim izgubam obravnavanih objektov, zaradi česar so ključnega pomena za oceno izgub. Izkazalo se je tudi, da imajo modelne negotovosti velik vpliv na rezultate potisnih analiz, inkrementalnih dinamičnih analiz in na verjetnost prekoračitve mejnih stanj, pri oceni izgub pa prevlada močan vpliv funkcij ranljivosti in funkcij izgub ter vpliv potresne nevarnosti in nadomestitvene vrednosti objekta.

V diplomski nalogi je izdelana ocena potresne odpornosti stare upravne stavbe Rudnika živega srebra Idrija. V prvem delu naloge je predstavljeno obnašanje zidanih stavb med delovanjem potresa in opis tipičnih porušnih mehanizmov zidov. Sledi kratek opis določil standarda Evrokod 8-3, ki obravnava področje ocenjevanja obnašanja obstoječih stavb med potresi. Po korakih je opisana poenostavljena metoda N2, ki temelji na nelinearni statični analizi. Na koncu sledi še predstavitev programa 3Muri, ki smo ga uporabili za račun potisnih krivulj. V drugem delu naloge je sprva opisana upravna stavba, ki je zgrajena iz nepovezanih kamnitih in opečnih zidov. Zaradi nepoznavanja dejanske kvalitete obstoječih materialov smo za obe vrsti zidovja iz literature privzeli po tri nabore mehanskih lastnosti. Pripravili smo pet modelov z različnimi kombinacijami vrednosti mehanskih lastnosti opečnega in kamnitega zidovja, na podlagi katerih smo ocenili potresno odpornost konstrukcije. Na osnovi deterministične analize smo ugotovili, da stavba ni sposobna prenesti pričakovanega projektnega pospeška temeljnih tal ag = 0,23 g in tako ne izpolnjuje zahtev standarda Evrokod 8. Velika ranljivost konstrukcije je bila posledica zelo nizkih vrednosti strižnih trdnosti privzetih materialov, ki smo jih skladno s standardom Evrokodom 8-3 delili še s faktorjem zaupanja CF = 1,35. Različne kombinacije mehanskih lastnosti zidovja so povzročale različne oblike porušnih mehanizmov konstrukcije. Zaradi majhnih razlik med strižnimi trdnostmi privzetih materialov se potresne odpornosti posameznih modelov niso bistveno razlikovale. Vrednosti koeficientov potresne odpornosti SRCu so variirali med 0,09 in 0,12, kar se je dobro ujemalo z vrednostjo, ki je bila ocenjena v projektu POTROG (2013). Ocenjujemo, da so mejni pospeški tal za obravnavan objekt verjetno podcenjeni, kar je posledica varnostnih faktorjev, ki jih je potrebno upoštevati v primeru nepopolnega poznavanja konstrukcije. In this thesis, the seismic performance assessment of the former administration building of RŽS Idrija is investigated. The first part of the thesis presents the behaviour of masonry buildings under seismic actions, and typical failure mechanisms of masonry walls, followed by the provisions of the Eurocode 8-3 standard, which deal with seismic assessment of existing buildings. Further on, the simplified N2 method based on non-linear static (pushover) analysis is introduced, followed by the presentation of 3Muri software. The second part of the thesis begins with a description of the administration building, which was build out of stone and brick masonry walls without adequate floor-to-wall connections. Not knowing the exact quality of the existing materials, three sets of mechanical properties for both types of masonry were obtained from the literature. The seismic performance assessment was based on five models of the structure each with different combination of mechanical properties of stone and brick masonry. The results of the deterministic analysis have shown that the building is incapable of withstanding the expected design ground acceleration ag = 0,23 g and does not meet the requirements of the Eurocode 8 standard. The great vulnerability of the structure is a consequence of very low shear strength values of the masonry, which were assessed from previous studies and, in accordance with Eurocode 8-3, divided by the confidence factor CF = 1,35. Different combinations of mechanical properties of masonry have lead to different types of failure mechanisms of the structure. Due to small differences between shear strength values of the materials the seismic resistance of our models did not differ significantly. The seismic shear coefficient SRCu was between 0,09 and 0,12 which complied with the coefficient estimated in the POTROG (2013) project. It is estimated that the limit-state peak ground acceleration is most likely underestimated, which is the consequence of safety factors that need to be considered in the case of incomplete knowledge of the structure.