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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 je zasnovana in na potresno obtežbo računsko preverjena 12 nadstropna stavba iz križno lepljenega lesa. Gre za preliminarno analizo potencialnih nadomestnih gradenj v Ljubljani, kjer bi se obstoječe tipske več nadstropne stanovanjske stavbe z nezadostno potresno odpornostjo nadomestilo s sodobno zasnovanimi vendar arhitekturno sorodnimi stavbami iz trajnostnih materialov. V nalogi je na osnovi preučene arhivske dokumentacije ene izmed obstoječih tipskih stavb ter z upoštevanjem materialnih in tehnoloških omejitev zasnovana nova stavba iz križno lepljenega lesa. Na osnovi podatkov iz literature in že izvedenih eksperimentov o potresnem odzivu posameznih stenskih elementov in veznih sredstev je bil modeliran njihov odziv. Razvit je bil nelinearen računski model veznih sredstev, ki je bil v nadaljevanju tudi validiran. Na podlagi validiranega odziva posamezne stene se je pristopilo k izdelavi računskega nelinearnega modela načrtovane stavbe. Na osnovi notranjih statičnih veličin linearnega modela so bile ocenjene dimenzije nosilnih elementov (križno lepljenega lesa in spojev), nadalje je bila izvedena nelinearna potisna analiza. Le-ta je predstavljala osnovo za analizo po N2 metodi in metodi načrtovanja pomikov - za oceno ustreznosti odziva in odpornosti zasnovane stavbe na potresno obtežbo. In the thesis, a 12-storey building made of cross-laminated timber is designed and numerically tested for seismic loading. It is a preliminary analysis of potential replacement buildings in Ljubljana, where existing typical multi-storey residential buildings with insufficient seismic resistance would be replaced with modern but architecturally similar buildings made of sustainable materials. With the help of the studied archival documentation of one of the existing buildings and further - considering the material and technological constraints - a new cross-laminated timber building was designed. The response of the individual walls and the connections has been simulated on the basis of literature data and experiments already carried out on the seismic response of individual walls and connection elements. A non-linear computational model of the connection elements was developed and further validated. The validated single wall model was implemented into the development of a numerical non-linear model of the designed building. Based on the internal static quantities determined from the linear model, the dimensions of the load-bearing elements (cross-laminated timber and connections) were estimated and finally a non-linear pushover analysis was performed. This formed the basis for the implementation of the N2 method and the DBD - to further assess the adequacy of the response and resistance of the designed building to various seismic loading.

Nezanimanje ljudi in državnih organov za krepitev potresne odpornosti objektov je posledica pomanjkanja lastnih izkušenj s katastrofalnimi naravnimi pojavi. Varljiv je predvsem občutek varnosti v primeru potresov, saj so močni potresi redki, vendar pa je njihov potencial za negativne posledice zelo visok. Da bi med študentkami in študenti vzpostavili nepristransko dojemanje potresnega tveganja, smo izvedli seizmični stresni test stavbnega fonda Univerze v Ljubljani. Podatke za namen raziskave nam je v večji meri zagotovila Univerza v Ljubljani. Dodatne informacij smo pridobili s pregledom stavb in projektne dokumentacije ter na osnovi že opravljenih analiz. Na ta način smo razvili model izpostavljenosti stavbnega fonda ter ga nato dopolnili z modelom potresne nevarnosti, modelom potresne ranljivosti in modelom posledic potresa na stavbe in ljudi. Vse modele smo nato vključili v analizo potresnega tveganja. V okviru magistrske naloge smo razvili parametričen model za oceno potisnih krivulj stavb, kar omogoča oceno potresne ranljivosti stavbe na osnovi nelinearnih dinamičnih analiz poenostavljenega nelinearnega modela stavbe. Rezultati študije kažejo, da je ogroženost človeških življenj na Univerzi v Ljubljani zaradi nevarnosti potresov previsoka. Srednja letna povratna doba za pojav izgube življenja med študenti zaradi potresov znaša le 6 let, kar presega sprejemljivo potresno tveganje za izgubo življenja v primeru posodobljenega stavbnega fonda za faktor 26. Poleg tega so previsoke tudi finančne izgube, saj smo ocenili, da znaša pričakovani letni strošek za odpravo škode na stavbnem fondu 1.040.000 EUR, kar je skoraj četrtina vseh sredstev iz razvojnega stebra za financiranje Univerze v Ljubljani. The lack of interest on the part of the population and the national authorities in strengthening the earthquake resistance of buildings is a consequence of the lack of their own experience with catastrophic natural phenomena. The feeling of safety in the event of earthquakes is particularly deceptive because strong earthquakes are rare, but their potential for adverse effects is very high. In order to establish an unbiased perception of seismic risk among students, we conducted a seismic stress test of the building stock of the University of Ljubljana. The data for the purposes of this study was mainly provided by the University of Ljubljana, and some of the information was also obtained by inspecting the buildings and project documentation and on the basis of previous analyses. We developed an exposure model for the building stock, which was supplemented by a seismic hazard model, a seismic fragility model and an earthquake impact model for buildings and people. All models were then included in the seismic risk analysis. We developed a parametric model for estimating the pushover curves of buildings, which allows to analyse the seismic fragility of a single building by nonlinear dynamic analyses of a simplified nonlinear building model. The results of the study show that the seismic fatality risk at the University of Ljubljana is too high. The average annual return period for loss of life among students is only 6 years, which exceeds the acceptable fatality risk for an updated building stock by a factor of 26. Moreover, the financial losses are too high. The annual cost of repairing seismic damage to the building stock was estimated at EUR 1,040,000, which represents almost a quarter of all funds allocated to the University of Ljubljana from the Development of Funding pillar.

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 nalogi smo analizirali potresni odziv armiranobetonskih mostov s pomanjkljivo prečno armaturo stebrov. V večini novejših mostov v Sloveniji je strižna armatura določena tako kot je zahtevano v standardu Evrokod 8/2, preostali dve funkciji prečne armature: a) objetje betonskega jedra in b) preprečevanje uklona vzdolžne armature, pa nista vedno ustrezno obravnavani. Količina prečne armature je v kritičnih področjih dostikrat premajhna, razdalja med podprtimi palicami vzdolžne armature pa prevelika. Stremena so pogosto neustrezno oblikovana in izvedena brez primernih kljuk. Vse to lahko povzroči razpad betonskega jedra in uklon vzdolžnih armaturnih palic, kar zmanjšuje razpoložljivo duktilnost stebrov (sposobnost sipanja potresne energije), oziroma deformabilnost konstrukcije. Nalogo smo razdelili na dva delovna sklopa: 1) v prvem delu smo analizirali vpliv pomanjkljive prečne armature na ciklični odziv stebrov, ki so bili eksperimentalno preizkušeni v okviru doktorske naloge Anžlin (2017) 2) v drugem delu smo analizirali vpliv pomanjkljive prečne armature na odziv značilnega viadukta. Vse analize v prvem sklopu naloge smo izvedli, ne da bi poznali rezultate eksperimentov. V prvem delu naloge smo vse obravnavne stebre modelirali s standardnim Gibersonovim modelom s koncentrirano plastifikacijo. Odziv nelinearnih vzmeti smo opisali s Takedovimi histereznimi pravili. Ovojnice histerez smo določili s semi-empiričnimi in parametrično-empiričnimi metodami, ki jih vsebujeta standarda Evrokod 8/2 in Evrokod 8/3. Z vsemi upoštevanimi metodami smo dobili podobne ovojnice histerez, z eno pomembno izjemo, vrednosti za mejni zasuk stebrov so se namreč precej razlikovale. Tiste, ki so bile določene s parametrično-empirični postopkom, so bile v večini obravnavnih stebrov najmanjše in so se zelo dobro ujemale z rezultati eksperimentov. V obravnavnih stebrih je pomanjkljiva prečna armatura zmanjšala deformacijsko kapaciteto stebrov. Spremenila je tudi način porušitve stebrov. V večini stebrov s pomanjkljivo prečno armaturo so se vzdolžne palice globalno uklonile. V stebrih s standardno prečno armaturo je porušitev nastopila, ko so se vzdolžne palice pretrgale. V drugem delu naloge smo primerjali potresni odziv značilnega viadukta, kjer so bili stebri v enem primeru armirani s standardno, v drugem pa z nestandardno prečno armaturo. S primerjavo rezultatov teh analiz smo ugotovili, da pomanjkljiva prečna armatura ni imela bistvenega pomena na nosilnost konstrukcije in potresni odziv konstrukcije, preden je stekla armatura v stebrih. Bistveno pa je vplivala na deformacijsko kapaciteto viadukta. Deformacijska kapaciteta viadukta, ki smo jo definirali kot maksimalni pomik, pri katerem se poruši prvi steber, je bila v primeru standardne prečne armature večja. In this thesis, we present an analysis of seismic response of reinforced concrete bridges with substandard lateral reinforcement of columns. Most of the bridges, that were built in Slovenia in the near past have shear reinforcement according to standard Eurocode 8/2, however the other two functions of lateral reinforcement, which are: a) confinement of the concrete core b) preventing buckling of the longitudinal reinforcement, are not always adequately satisfied. In such cases, the amount of lateral reinforcement in critical areas of the section is mostly inappropriate, while distance between the supported bars of the longitudinal reinforcement is too large. Stirrups are often inadequately designed and constructed without suitable hooks. All of this can lead to the collapse of the concrete core and buckling of the longitudinal reinforcement, which reduces the ductility of columns (the ability to absorb energy), or the deformability of the structure. The thesis was divided in two parts: 1) Cyclic response of columns with inadequate lateral reinforcement detailing, which were experimentally tested in the framework of doctoral thesis Anžlin (2017), was analysed in the first part 2) Influence of inadequate lateral reinforcement details on the response of a characteristic viaduct was examined in the second part. All of the analyses that were performed in first part were done without knowing the results of the experiments. In the first part of thesis, considered columns were modelled using the Giberson material model with lumped plasticity. The response of nonlinear springs was described with the Takeda hysteresis rules. Hysteresis envelopes were determined using semi-empirical and parametric-empirical methods according to Eurocode 8/2 and Eurocode 8/3. With all of the considered methods, similar hysteresis envelopes were obtained, with one notable exception. The values for the ultimate rotation of the columns varied considerably. Those determined by the parametric-empirical procedure were the smallest in most of the considered columns and were in good agreement with the results of the experiments. Inadequate lateral reinforcement of column specimens showed a reduced deformation capacity of columns. They also change the way of failure, in most columns with inadequate lateral reinforcement, a global buckling of longitudinal bars was obtained. In columns with appropriate lateral reinforcement, the failure occurred due to the rupture of longitudinal bars. In the second part of thesis, comparison of seismic response of typical viaduct, in which one case considered columns with standard, and in the other substandard lateral reinforcement, was made. It was observed, that inadequate lateral reinforcement did not have a significant impact on capacity and response of structure before yielding of column longitudinal reinforcement. However, it significantly affected the deformation capacity of the viaduct. The deformation capacity of the viaduct, which was defined as the maximum displacement at which the first column collapses, was higher in the case of standard lateral reinforcement.

Vsebina pričujoče magistrske naloge je povezana z realnim problemom iz inženirske prakse. Predmet analize je ocena potresne odpornosti nosilne konstrukcije stavbe za izobraževanje v Ljubljani. Nosilna konstrukcija je pretežno iz opeke in je bila grajena v petdesetih letih prejšnjega stoletja. Geometrijske in materialne karakteristike nosilne konstrukcije so bile pridobljene s pomočjo tehnične dokumentacije in z izvajanjem preiskav na objektu. Pri tem je bilo uporabljenih več vrst destruktivnih, delno destruktivnih in nedestruktivnih preiskovalnih metod. Nato je predstavljeno teoretično ozadje seizmične analize objektov iz nearmiranega zidovja. Na podlagi pridobljenih informacij o stavbi je bil izdelan idealiziran računski model nosilne konstrukcije s programskim orodjem 3Muri. Omenjen program omogoča nelinearno statično analizo konstrukcije s pomočjo makroelementov. Kot rezultat analize program poda potisne krivulje in največje možne pomike ter pospeške, ki jih je konstrukcija še sposobna prenesti. Ugotovljeno je bilo, da nosilna konstrukcija obravnavane stavbe ne nudi ustrezne potresne odpornosti glede na zahteve veljavnega standarda. V nadaljevanju je analiziranih več različnih smiselno izbranih možnosti za povečanje potresne odpornosti obravnavane stavbe. Pri snovanju utrditvenih ukrepov je upoštevano dejstvo, da se bo v bližnji prihodnosti gradil prizidek k obstoječi stavbi. Najustreznejšo varianto utrditve predstavljajo dodatne nosilne armiranobetonske stene in bodoči prizidek objekta. In the master thesis, we deal with an engineering practice problem. The subject matter is to assess seismic resistance of an educational facility in Ljubljana. Bearing system of the facility, which was built in the fifties, is mainly made of bricks. Geometric and mechanical features of the existent bearing system were examined by technical documentation and by executing research at the facility. Many destructive, partially destructive and non-destructive research methods were used. Later on a theoretical background is presented, which refers to the seismic analysis of objects made of unreinforced masonry. In the program 3Muri an idealized computational model is presented based on obtained information of the facility. The program is based on the macro elements principle and the non-linear method for seismic performance assessment. Pushover curves, the maximum displacement and acceleration of the bearing system are given as the result of analysis of the structure. According to conditions of the valid standard, the bearing system of the discussed building does not reach the seismic resistance. Later on there are analysed different options for improvement of the seismic resistance of the facility. While designing the strengthening measures it has been taken into account that an extension of the building will be built in the near future. Additional reinforced concrete walls and the future extension of the building are presenting final strengthening measures.

diplomskom radu obrađeno je nelinearno ponašanje čeličnog višekatnog okvira s inovativnim sustavima stabilizacije. Cilj rada je bio proučiti tipove konstrukcija koji imaju mogućnost recentriranja nakon djelovanja potresa, tj. smanjenja rezidualnih pomaka. U prvom dijelu rada tema je razrađena kroz teoriju i prikaz dvojnih sustava s mogućnošću recentriranja. U drugom dijelu rada proveden je proračun i usporedba dvaju modela s različitim duljinama potresnih veza. Proveden je nelinearan statički proračun postupnog guranja kako bi se dobile krivulje kapaciteta. Dobiveni rezultati za oba sustava su uspoređeni na temelju mehanizma kolapsa, faktora prekogranične čvrstoće te ciljanog pomaka.

N2 je brza nelinearna statička metoda za projektiranje zgrada otpornih na potres. Rad predstavlja značajke i ograničenja metode, njezin razvoj te mogućnosti primjene na različitim tipovima zgrada. Istaknute su razlike između klasične N2 metode i njezinih proširenja. Također, dana je usporedba N2 metode i sličnih proračunskih pristupa. Ustanovljeno je da se rezultati dobiveni proračunima uz primjenu N2 metode dobro slažu s rezultatima dobivenim uz primjenu znatno složenijih metoda. Na kraju su dane smjernice za daljnje istraživanje., The N2 method is a fast nonlinear static method for the seismic design of buildings. This paper presents main properties and limitations of the method, its development over time, and possibilities of its application for different types of buildings. Differences between the traditional N2 method and its extensions are highlighted. Comparison of the N2 method with similar design approaches is also provided. The results obtained by calculations based on the N2 method are found to be in good agreement with the results obtained by much more complex methods. Guidelines for further research are given in the final part of the paper., N2 ist eine schnelle nicht lineare statische Methode für die Planung von erbebensicheren Gebäuden. Die Abhandlung stellt die Merkmale und die Grenzen der Methode, deren Entwicklung sowie die Möglichkeiten der Anwendung an verschiedenen Gebäudetypen vor. Hervorgehoben werden die Unterschiede zwischen der klassischen N2 Methode und deren Erweiterungen. Des Weiteren wird ein Vergleich der N2 Methode und ähnlicher Berechnungsansätze dargelegt. Es wurde festgestellt, dass die Ergebnisse, die durch die Berechnung durch Anwendung der N2 Methode erhalten wurden, gut zu den Ergebnissen passen, die man durch die Anwendung wesentlich komplexerer Methoden erhalten hat. Am Ende werden Richtlinien für weitere Untersuchungen gegeben.

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.

Predmet diplomskog rada je provjera koncepta projekta konstrukcije tornja Westgate B – verzija od 26 etaža primjenom višemodalne spektralne analize, N2 metode naguravanja, nelinearno-elastičnog odgovora u vremenu. The subject of Thesis is to examine the concept of the project of construction of the tower Westgate B - version of 26 floors by applying the modal spectral analysis, the methods of pushing N2, non-linear elastic response in time.

V diplomski nalogi je bila izdelana ocena potresne odpornosti institutskega trakta stavbe UL FGG na Hajdrihovi ulici v Ljubljani s programoma 3Muri in SAP2000. V začetnem poglavju obravnavamo obnašanje zidanih konstrukcij med potresom in možne porušne mehanizme. Sledita opis določil Evrokoda 8-3, ki obravnava področje ocenjevanja obnašanja obstoječih stavb med potresi, ter opis postopka preverjanja potresne odpornosti zidov. V nadaljevanju je opisana poenostavljena nelinearna N2 metoda. V praktičnem delu naloge je predstavljen obravnavan objekt. Za dosego čim bolj primerljivih rezultatov modelov v obeh programih smo se z modeliranjem v SAP-u želeli čim bolj približati modelu v 3Muriju. Analiza lastnega nihanja je bila preverjena na treh modelih – modelu v 3Muriju, linijskem modelu v SAP-u ter ploskovnem modelu v SAP-u. Pri primerjavi nihajnih časov se je izkazalo, da modela v SAP-u dosežeta zgolj 67–96 % nihajnih časov modela v 3Muriju. Razlike smo pripisali različnemu podajanju masnih vztrajnostnih momentov, da bi njihov vpliv preverili, pa smo izvedli parametrično analizo. Izkaže se, da bi primerljive rezultate obeh programov dosegli s povečanjem masnih momentov v SAP-u na 220 % njihove začetne vrednosti, česar pa s fizikalno utemeljenim argumentom ne moremo upravičiti. Rezultati obenem kažejo, da sta modela v SAP-u med seboj bolj primerljiva, kot sta primerljiva posamezen model v SAP-u in model v 3Muriju. To smo pripisali uporabi različnih metod izračuna – SAP uporablja metodo FEM, 3Muri pa metodo FME. Da bi v čim večji meri eliminirali razlike med modeloma v različnih programih, smo kontrolo enakosti delovanja programov izvedli še na primeru enostavne konstrukcije brez odprtin. Izkaže se, da odstopanja res niso posledica različno definiranih elementov konstrukcije v obeh programih, zato se zdi pripis razlik različnim metodam izračuna smiseln. V nadaljevanju smo z obema programoma izvedli še nelinearno statično »pushover« analizo, pri čemer smo v SAP-u materialno nelinearnost zajeli z uvedbo plastičnih členkov. Ponovno se izkaže, da modela v različnih programih ne izkazujeta primerljivih rezultatov. In this thesis, the seismic performance assessment of the UL FGG building on Hajdrihova st. was investigated by 3Muri and SAP2000 software. In the first chapter the behaviour of masonry buildings under seismic actions are presented with an emphasis on failure mechanisms of structural components. Then follow the provisions of the Eurocode 8-3 standard, which deals with seismic assessment of existing buildings. Further on, the simplified N2 method based on non-linear static (pushover) analysis is introduced. In the practical part of the thesis the UL FGG building is presented. To achieve similar results in both programs we tried to make the model in SAP similar to 3Muri model as much as possible. Eigenvalue analysis was performed on three models – the 3Muri model, the SAP frame model and the SAP shell model. A comparison of natural periods has shown 4 % to 33 % smaller values for SAP models. The reason for differences could be in different mass moments of inertia. To check the influence of MMI, parametric analysis was performed. Results of the analysis have shown the need for enhancement of the SAP model MMI to 220 % of its original value, but this kind of adjustment cannot be physically explained. Analysis also shows that the results for two SAP models are much closer in comparison to each other than the results of any SAP model in comparison to the 3Muri model. This could be the result of different analysis methods – 3Muri using FME and SAP using FEM. In an attempt to eliminate the differences between models in both programs, a simpler model was analyzed. It turns out, the differences between models are not a consequence of the definition of structural components. More likely the difference is caused by not considering the same analysis method. Further on, the non-linear static analysis in both programs was investigated. Non-linear behaviour of the material in SAP model was modeled by defining the plastic hinges into elements of the/an equivalent frame. Again it turned out, the results of SAP and 3Muri models were far from similar.

V diplomski nalogi sta izdelana dva modela za oceno potresne odpornosti povprečne zidane hiše na širšem območju Škofje Loke. V začetnem poglavju obravnavamo obnašanje zidanih konstrukcij in možne porušne mehanizme njihovih elementov. V nadaljevanju je predstavljeno teoretično ozadje metode N2, ki je vključena v Evrokod 8 in s katero smo določili potresno odpornost obravnavanih zidanih objektov. Analizirali in interpretirali smo rezultate analiz za 11 hiš, ki se nahajajo v širšem območju Škofje Loke in so bile zgrajene v letih od 1970 do 1990. Na osnovi načrtov Projektov za pridobitev gradbenega dovoljenja smo vrednotili srednje vrednosti in koeficient variacije za izbrane geometrijske lastnosti stavb, ki imajo pomemben vpliv na njihovo obnašanje. Pričakovani delež tlorisnih površin sten glede na neto površino etaže znaša 11–12 %, delež efektivnih tlorisnih površin sten pa se giblje v območju 60-90 % bruto površine sten, pri čemer je odvisen od smeri objekta. Povprečen zid je širok 2,4 m, njegova efektivna višina pa znaša 80 % etažne višine objekta. V primerjavi izbranih lastnosti hiš s sorodnimi podatki, ki so dostopni na spletnem portalu e-Prostor, smo ugotovili večja odstopanja v vrednostih le teh. Nelinearno statično (potisno) analizo smo izvedli s programom 3Muri. Rezultati so pokazali, da so najbolj ranljivi medokenski slopi zidu, delno pa tudi prekladni deli. Običajno pri mejnem stanju blizu porušitve nastopa kombinacija upogibnih in strižnih poškodb. Glede na mejni pospešek smo izbrali merodajne potisne krivulje in jih normirali glede na težo objekta in njegovo višino oziroma glede na povprečno efektivno tlorisno etažno površino sten v obravnavani smeri in višino objekta. S tem smo dobili dva modela normiranih potisnih krivulj. Pričakovana maksimalna dosežena nosilnost v šibki smeri objekta znaša 15 % celotne teže stavbe oziroma dobrih 60 kN na kvadratni meter efektivne tlorisne površine sten. Prikazana je uporaba modelov na primeru dveh objektov in dodana ocena potresne odpornosti za mejno stanje močnih poškodb, ki kaže na to, da večina obravnavanih objektov ne izpolnjuje zahtev Evrokoda 8-3. Two models for seismic performance assessment of masonry houses in Škofja Loka region are developed. In first chapters the behaviour of masonry buildings under seismic actions with an emphasis on failure mechanisms of structural components are discussed. Follows an overview of the theoretical background of N2 method, which is included in the Eurocode 8 and which was used for determination of the seismic resistance of examined masonry structures. The results of numerical investigation of 11 masonry houses, built in the years from 1970 to 1990, are then presented and discussed. The project design for building permit was used to obtain input data of the buildings. The mean values and the coefficient of variation were assessed for those geometrical features of the buildings, which have great impact on the seismic performance assessment of the buildings. Expected percentage of the floor surface area of the walls in relation to the net surface of the floor varied from 11 to 12 % with respect to the direction of building. The proportion of the effective floor area of the walls is in the range from 60 to 90% of the gross surface area of the walls depending on the direction of the building. Average wall is 2,4 m wide and its effective height amounts to 80 % of the building`s floor height. It was found that the selected characteristics of houses with the corresponding data which are available on the web portal e-Prostor, are significantly different. Nonlinear static (pushover) analysis was performed by using computer software 3Muri. The results show that the combination of bending and shear damage occurred in piers and also spandrels in the region of deformation close to the ultimate limit state. Two models of the normalized expected pushover curves were obtained by taking into account the pushover curves which had a decisive impact on the seismic limit-state peak ground acceleration. The base shear was normalized by the weight of the building or with respect to the average effective floor area of the walls in the given direction and whereas the top displacement was normalized only by the building’s height. Maximum expected capacity in weak direction amounted 15 % of the total weight of the building and more than 60 kN per square meter of effective floor area of the walls. In the last chapter the normalized pushover curves were used for seismic performance assessment of two houses for which it was found that do not fulfil requirements of standard Eurocode 8-3.

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.

Rad obrađuje potresni odziv plitko temeljenih konstrukcija na mekim tlima. Istraživanje u okviru rada je pokrenuto uz glavnu pretpostavku da europski normirani spektri odziva za meka tla nisu dobro definirani te da ne uključuju učinke međudjelovanja tla i konstrukcije. S ciljem definiranja poboljšanog spektra odziva kao osnovnog alata za proračun sigurnih i potresno otpornih konstrukcija, izrađene su i funkcije impedancije i prijenosne funkcije koje omogućuju uključivanje učinaka međudjelovanja tla i konstrukcija u proračunima primjenom metode spektara odziva. Oslonac studiji daju rezultati eksperimentalnih istraživanja provedenih na potresnom stolu na Sveučilištu u Bristolu te u geotehničkoj centrifugi na institutu IFSTTAR. Numerički modeli korišteni za provedbu parametarske studije su uspješno kalibrirani s obzirom na rezultate spomenutih eksperimentalnih istraživanja. U radu je dan prijedlog primjene funkcija impedancije, nastalih u okviru ovog rada, u klasičnim računalnim programima koji primjenu nalaze u znanosti i praksi. Osim toga, dan je prijedlog za primjenu funkcija impedancije u okviru N2 metode., This thesis deals with seismic response of shallow founded structures on soft soils. Research within the thesis is initiated with the main assumption that the European code-based response spectra for soft soils are ill-defined and that they do not include soil-structure interaction effects. With the aim to provide improved response spectrum, as a key engineering tool for design of earthquake resistant structures, both impedance and transfer functions were developed. Those functions enable incorporation of both soil compliance and its capability that dissipates earthquake energy. Parametric study was conducted using numerical models calibrated with regards to experimental results obtained both from testing performed in enhanced gravitational field using geotechnical centrifuge at the IFSTTAR institute and on shaking table of the University of Bristol at 1g. Numerical modelling, and thus parametric study, was governed using equivalent linear method. The last chapter of the work provides proposed methodology for including the developed functions into classical program packages mostly used by engineering practice and academia for structural analysis and design. Also, proposal for application of impedance functions within the framweork of N2 method is provided.

U radu je prikazana analiza djelovanja seizmičkih sila na okvirnu čeličnu konstrukciju koja je izvedena i patentirana u Švedskoj. Konstruktivni sustav za kojeg je provedena analiza prvotno je bio sačinjen od okvirne čelične konstrukcije sa armiranobetonskom jezgrom. Kako bi se ostvarilo trošenje seizmičke energije nelinearnim ponašanjem, konstrukcija je „omekšana“ zamjenom armiranobetonske jezgre čeličnom jezgrom. Priključci su modelirani kao nepopustljivi (rigid), kako bi se spriječile rotacije između konstruktivnih elemenata, te su primijenjeni kriteriji „zgrade posmika“. Konstrukcija je analizirana primjenom dviju linearnih metoda: ekvivalentnog statičkog djelovanja i modalnom analizom, te primjenom dviju nelinearnih metoda: nelinearnom statičkom metodom (N2) i nelinearnom dinamičkom metodom u vremenu (time history). Na kraju je napravljena usporedba rezultata dobivenih ovim metodama te je analiziran utjecaj nelinearnosti na horizontalne apsolutne i relativne pomake katova konstrukcije.