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In this paper, different aspects of a green roof installation are analyzed on several typical buildings in Belgrade. The analysis is performed for buildings with extensive and intensive green roofs. The goal was to determine their influence on existing buildings' structural capacity and thermal characteristics. According to the impact on the structure and its energy performance, the overall effect and justification of the installation of the green roof are determined

This paper presents the analysis of the potential use of green roofs to enhance the energy efficiency of the residential buildings. Namely, in urban areas, there is a lot of potential for reducing the energy needed for heating and cooling in the existing buildings. Thus, in developed countries, green roofs are recognized as one of the important tools for energy savings, but also in accomplishing environmental protection and raising the quality of life. Current regulation in the Republic of Serbia does not adequately demonstrate the effects of contemporary measures of energy efficiency improvement in buildings. This paper provides an analysis of the possible improvement of energy efficiency by various green roof application models. The aim of this investigation is to generate affirmation of the green roof projects by pointing out the financial benefits and other implications that are significant for sustainable development. The existing building in the center of Belgrade with a flat roof is used as the model for parametric analysis. The key indicator of the investment profitability in this investigation was the energy needed for heating and cooling. Besides the economic impact, other aspects of green roof application are highlighted as well. Numerical analysis is performed for the apartment under a flat roof for three different models of renovation. The values of the reduction of the annual energy need for heating and cooling are compared. The economic profitability analysis considered the life cycle profit analysis for all analyzed cases. The obtained results indicate the benefits of using green roofs at both, the individual and the public levels.

Improving the energy efficiency in buildings in the Republic of Serbia has been recognized as an area with the greatest potential for reducing overall energy consumption. It also has an indirect impact on improving the quality of life and comfort in buildings, protecting the environment and reducing the emission of harmful gases, as well as reducing the cost of heating. Permanent population increase resulted in the urbanization process that had different consequences for the quality of life and a sustainable future. Green roofs in urban areas of developed countries have become a legal obligation and policies and programs that support the greening of roofs are aimed at preserving the environment and ensuring the sustainable development of cities. This paper deals with an analysis of the influence of green roofs on the energy performance of existing buildings in the center of Belgrade. One of the conclusions of this research points out that it is necessary to perform research studies and experimental analyses for the application of green roofs in our climatic conditions. Thus, the research focus should be on legal regulation that would establish calculation and design standards for green roof systems.

In the present paper, implementation of Preisach model of hysteresis to elastoplastic analysis of trusses subjected to cyclic is shown. It is also shown that damage effects can be included in presented analysis by introducing basic concepts of continuum damage mechanics. Using finite element method, equilibrium equations are obtained and algorithm for numerical solution is defined. Some advantages of this approach are underlined through several numerical examples.

U ovoj doktorskoj disertaciji je razmatrano ponašanje rešetkastih konstrukcija u plastičnoj oblasti sa ciljem da se optimizuje numerička analiza ovog problema i da se definiše osnova za proširivanje odgovarajućeg modela na gredne elemente linijskih nosača. Ovaj problem, pri cikličnom opterećenju, dobija novu dimenziju u pogledu tačnosti rezultata nakon određenog broja ciklusa, kao i u pogledu numeričke zahtevnosti odgovarajućeg modela. Model materijala zasnovan na Prajzakovom (Preisach) histerezisnom operatoru, određen kao analitički izraz za vezu napon-deformacija, omogućava numerički efektno modeliranje jednoaksijalnog ponašanja materijala. Koristeći ovaj model, u ovoj disertaciji su definisane jednačine u metodi konačnih elemenata za elastoplastičnu analizu rešetkastih nosača pri cikličnom opterećenju i na osnovu toga je definisan algoritam za proračun u programskom jeziku c++. Za validaciju rezultata i analizu numeričkih karakteristika proračuna zasnovanog na modelu materijala koji je korišćen u disertaciji, u numeričkim primerima su poređeni rezultati dobijeni predmetnim modelom sa rezultatima dobijenim koristeći drugi histerezisni operator (Bouc-Wen) i rezultatima dobijenim koristeći jedan od klasičnih modela plastičnosti (model generalisane plastičnosti). Geometrijska nelinearnost je uzeta u obzir poznatim metodama i definisana u delu numeričkih primera. Stanje napona u materijalu koji se analizira je jednoaksijalno, a u numeričkim primerima sa grednim elementima je usvojena hipoteza o ravnim presecima. Pored postojećeg (Prajzakovog) modela za elastoplastično ponašanje materijala, u ovoj disertaciji je definisan model oštećenja u materijalu preko dva pristupa. U prvom pristupu, definisani histerezisni operator za elastoplastično ponašanje materijala je modifikovan kako bi mogao da modelira oštećenje u materijalu. U drugom pristupu, u definisani algoritam proračuna metode konačnih elemenata predmetnog modela elastoplastičnosti je uveden fenomen oštećenja korišćenjem osnovnih principa mehanike kontinuuma sa oštećenjem. Pored toga, predstavljen je model za proračun histerezisnog gubitka energije u rešetkastim konstrukcijama, zasnovan na predmetnom modelu, kao i osnova za proširenje analize na gredne nosače koristeći numeričku integraciju napona u poprečnom preseku za jednostavne slučajeve savijanja... In this doctoral dissertation, behavior of trusses in plastic domain is investigated in order to optimize numerical analysis of this problem and to define foundation for extending proposed model to the analysis of beam elements. New dimension in this problem arise in the case of the cyclic loading, relating to the accuracy of results after certain number of cycles and computational effort of corresponding model. Material model based on the Preisach hysteretic operator, determined as analytical expression for stress-strain relation, enables numerically effective modeling of uniaxial material behavior. By using this model, in this dissertation, finite element equations for elastoplastic analysis of trusses subjected to cyclic loading are determined, which lead to definition of algorithm for numerical analysis in c++ programming language. In order to validate results and to analyze numerical performance of calculation based on the material model used in this dissertation, in numerical examples, results obtained by analyzed (Preisach) model are compared with results obtained by using other hysteretic operator (Bouc-Wen) and also with results obtained by using one of the classical model of plasticity (generalized plasticity model). Geometric nonlinearity is taken into account by well established methods, and it was defined in several numerical examples. Stress state in analyzed material is uniaxial, and in numerical examples with beam elements, the assumption of engineering beam theory is adopted (cross section is perpendicular to a bending line). Besides existing (Preisach) model for elastoplastic material behavior, in this dissertation damage model in material is defined through two approaches. In the first approach, proposed hysteretic operator for elastoplastic behavior is modified, so that it would have the possibility to model the damage in material. In the second approach, in proposed finite element algorithm for elastoplastic analysis, phenomenon of damage is introduced by using the basic principles of continuum damage mechanics. In addition, model for calculation of hysteretic energy loss in truss structures, based on the considered model, is presented, and finally, the foundation for extending the corresponding analysis on beam elements, by using numerical integration of normal stress in cross section, for simple cases of loading, is proposed...

Although there are a large number of buildings with high energy consumption in Serbia, there is a possibility to reduce it by investing in renovation of such buildings. Windows and doors, which are part of thermal envelope of building, play a very important role in the overall energy efficiency of the building. In this paper, some aspects of reducing energy consumption of buildings in urban area are presented through renovation project and experimental measurements. The results of increased energy efficiency of one public building, obtained by changing doors and windows only, are given. Experimental measurements by thermovision camera in several residential buildings are shown in this paper. These measurements indicate importance of installing adequate windows as part of thermal envelope of buildings. In addition, corresponding data, from overall state of energy efficiency of buildings in Serbia, is presented. Zbornik radova Građevinskog fakulteta

U ovoj doktorskoj disertaciji je razmatrano ponašanje rešetkastih konstrukcija u plastičnojoblasti sa ciljem da se optimizuje numerička analiza ovog problema i da se definiše osnovaza proširivanje odgovarajućeg modela na gredne elemente linijskih nosača. Ovaj problem,pri cikličnom opterećenju, dobija novu dimenziju u pogledu tačnosti rezultata nakonodređenog broja ciklusa, kao i u pogledu numeričke zahtevnosti odgovarajućeg modela.Model materijala zasnovan na Prajzakovom (Preisach) histerezisnom operatoru, određenkao analitički izraz za vezu napon-deformacija, omogućava numerički efektno modeliranjejednoaksijalnog ponašanja materijala. Koristeći ovaj model, u ovoj disertaciji su definisanejednačine u metodi konačnih elemenata za elastoplastičnu analizu rešetkastih nosača pricikličnom opterećenju i na osnovu toga je definisan algoritam za proračun u programskomjeziku c++.Za validaciju rezultata i analizu numeričkih karakteristika proračuna zasnovanog na modelumaterijala koji je korišćen u disertaciji, u numeričkim primerima su poređeni rezultatidobijeni predmetnim modelom sa rezultatima dobijenim koristeći drugi histerezisnioperator (Bouc-Wen) i rezultatima dobijenim koristeći jedan od klasičnih modelaplastičnosti (model generalisane plastičnosti).Geometrijska nelinearnost je uzeta u obzir poznatim metodama i definisana u delunumeričkih primera. Stanje napona u materijalu koji se analizira je jednoaksijalno, a unumeričkim primerima sa grednim elementima je usvojena hipoteza o ravnim presecima.Pored postojećeg (Prajzakovog) modela za elastoplastično ponašanje materijala, u ovojdisertaciji je definisan model oštećenja u materijalu preko dva pristupa. U prvom pristupu,definisani histerezisni operator za elastoplastično ponašanje materijala je modifikovan kakobi mogao da modelira oštećenje u materijalu. U drugom pristupu, u definisani algoritamproračuna metode konačnih elemenata predmetnog modela elastoplastičnosti je uvedenfenomen oštećenja korišćenjem osnovnih principa mehanike kontinuuma sa oštećenjem.Pored toga, predstavljen je model za proračun histerezisnog gubitka energije u rešetkastimkonstrukcijama, zasnovan na predmetnom modelu, kao i osnova za proširenje analize nagredne nosače koristeći numeričku integraciju napona u poprečnom preseku za jednostavneslučajeve savijanja... In this doctoral dissertation, behavior of trusses in plastic domain is investigated in order tooptimize numerical analysis of this problem and to define foundation for extendingproposed model to the analysis of beam elements. New dimension in this problem arise inthe case of the cyclic loading, relating to the accuracy of results after certain number ofcycles and computational effort of corresponding model. Material model based on thePreisach hysteretic operator, determined as analytical expression for stress-strain relation,enables numerically effective modeling of uniaxial material behavior. By using this model,in this dissertation, finite element equations for elastoplastic analysis of trusses subjected tocyclic loading are determined, which lead to definition of algorithm for numerical analysisin c++ programming language.In order to validate results and to analyze numerical performance of calculation based onthe material model used in this dissertation, in numerical examples, results obtained byanalyzed (Preisach) model are compared with results obtained by using other hystereticoperator (Bouc-Wen) and also with results obtained by using one of the classical model ofplasticity (generalized plasticity model).Geometric nonlinearity is taken into account by well established methods, and it wasdefined in several numerical examples. Stress state in analyzed material is uniaxial, and innumerical examples with beam elements, the assumption of engineering beam theory isadopted (cross section is perpendicular to a bending line).Besides existing (Preisach) model for elastoplastic material behavior, in this dissertationdamage model in material is defined through two approaches. In the first approach,proposed hysteretic operator for elastoplastic behavior is modified, so that it would have thepossibility to model the damage in material. In the second approach, in proposed finiteelement algorithm for elastoplastic analysis, phenomenon of damage is introduced by usingthe basic principles of continuum damage mechanics.In addition, model for calculation of hysteretic energy loss in truss structures, based on theconsidered model, is presented, and finally, the foundation for extending the correspondinganalysis on beam elements, by using numerical integration of normal stress in cross section,for simple cases of loading, is proposed...

In the present paper, implementation of Preisach model of hysteresis to elastoplastic analysis of trusses subjected to cyclic is shown. It is also shown that damage effects can be included in presented analysis by introducing basic concepts of continuum damage mechanics. Using finite element method, equilibrium equations are obtained and algorithm for numerical solution is defined. Some advantages of this approach are underlined through several numerical examples. U ovom radu, prikazana je primena Prajzakovog modela histerezisa, u strukturnoj analizi rešetkastih nosača koji su izloženi cikličnom opterećenju. Takođe je prikazano da se efekti oštećenja mogu uključiti u prikazanu analizu uvođenjem osnovnih principa mehanike oštećenja u kontinuumu. Koristeći metodu konačnih elemenata, jednačine ravnoteže i algoritam za numeričko rešavanje je definisan. Neke prednosti ovakvog pristupa su naglašene kroz nekoliko numeričkih primera.

The energy efficiency of typical rural houses in Serbia is presented in this paper. Typical houses from rural areas were analyzed by proper measurements, and by numerical calculations according to current regulations. The first house is a traditional Vojvodina house and it is situated in the suburban part of municipality of Sremska Mitrovica. The second house is a typical Serbian mountainous house and it is located in the municipality of Ra{ka. Experimental data for the analysis were obtained by performing measurements of temperature, humidity and dew point on the characteristic spots in these houses. Recording with thermal imaging camera were also done. Detailed insight in energy performance of observed houses can be defined by analyzing obtained results. Calculation of the annual energy needs for heating is based on the Regulations on energy efficiency of buildings in the Republic of Serbia, which were adopted in 2011. It was concluded that the annual energy need for heating in rural homes significantly exceeds optimal limits for objects of that category, so the special attention should be devoted to analysis of energy efficiency problems in rural areas. U ovom radu je prikazano trenutno stanje energetske efikasnosti seoskih kuća u Srbiji. Analizirane su dva tipa kuća iz ruralnih područja putem odgovarajućih merenja, kao i proračunom prema važećim propisima. Prva je tradicionalna vojvođanska kuća koja se nalazi u predgrađu Sremske Mitrovice. Druga je tipična kuća u brdsko-planinskom regionu Srbije i ona se nalazi u opštini Raška. Eksperimentalni podaci za analizu su dobijeni izvršenim merenjima temperature, vlažnosti i tačke rošenja na karakterističnim mestima na objektima. Takođe je obavljeno i snimanje termovizijskom kamerom. Analizom rezultata merenja, može se definisati detaljna slika energetskih karakteristika posmatranih kuća. Proračun godišnje potrebne energije za grejanje je zasnovan na Pravilniku o energetskoj efikasnosti zgrada u Republici Srbiji koji je usvojen 2011. godine. Zaključeno je da godišnja potrošnja energije za grejanje u seoskim kućama znatno prevazilazi utvrđene optimalne granice za objekte te kategorije, tako da posebna pažnja treba da se posveti analizi problema energetske efikasnosti u ruralnim područjima.

U ovoj doktorskoj disertaciji biće razmatrano elastoplastično ponašanje konstruktivnih mekih čelika privelikim naprezanjima u plastičnoj oblasti. Biće pokazano da je osnovna karakteristika naponskodeformacijskog dijagrama ove vrste čelika, formiranje horizontalnog platoa tečenja između zoneelastičnosti i zone plastičnog ojačanja. Ovaj fenomen, koji se ispoljava u vidu lokalne nestabilnostiatomske rešetke (Lüders band) je samo karakteristika monotong naprezanja, dok kod ponovljenognaprezanja iščezava. Koristeći Preisach-ov histerezisni operator, razvijen je materijalni model, koji savelikom tačnošću opisuje ponašanje ovih čelika pri monotonom aksijalnom naprezanju. Materijalnimodel u vidu analitičkog izraza za vezu dilatacija-napon veoma dobro aproksimira oblasti elastičnosti,horizontalnog platoa tečenja i plastičnog ojačanja, karakterističnih za konstruktivne meke čelikeizložene ovoj vrsti naprezanja... In this doctoral dissertation, the elastoplastic behavior of structural mild steel under large deformationsis explained. It will be shown that the stress-strain diagram's main characteristic of this steel type is theformation of a horizontal yield plateau between the elastic region and the plastic hardening region. Thisphenomenon, manifested in the form of local instability of the atomic lattice (Lüders band), is only acharacteristic of monotonic loading, whereas in the case of alternating loading it disappears. UsingPreisach's hysteresis operator, a material model was developed, describing with excellent accuracy thebehavior of this type of steel under monotonic axial loading. The material model in the form of ananalytical expression for the strain-stress relationship very well approximates the regions of elasticity,horizontal yield plateau, and plastic hardening characterized for structural mild steel under this type ofloading.