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Quite often we have a lot of measurement data and would like to find some relation between them. One common task is to see whether some measured data or a curve of known shape fit into the cumulative measured data. The problem can be visualized since data could generally be presented as curves or planes in Cartesian coordinates where each curve could be represented as a vector. In most cases we have measured the cumulative 'curve', we know shapes of other 'curves' and would like to determine unknown coefficients that multiply the known shapes in order to match the measured cumulative 'curve'. This problem could be presented in more complex variants, e.g., a constant could be added, some missing (unknown) data vector could be added to the measured summary vector, and instead of constant factors we could have polynomials, etc. All of them could be solved with slightly extended version of the procedure presented in the sequel. Solution procedure could be devised by reformulating the problem as a measurement problem and applying the generalized inverse of the measurement matrix. Measurement problem often has some errors involved in the measurement data but the least squares method that is comprised in the formulation quite successfully addresses the problem. Numerical examples illustrate the solution procedure.

U radu su prikazani rezultati eksperimentalne analize utjecaja odabranih parametara materijala i uvjeta ispitivanja na ponašanje asfaltne mješavine. Provedena je parametarska numerička analiza na ponašanje materijala definirano Burgerovim reološkim modelom. Rezultati eksperimentalne i numeričke analize uspoređeni su kvalitativno kako bi se ustanovio utjecaj pojedinog parametra na ponašanje materijala definirano dijagramom sila-pomak.

Parameter estimation is essential for proper modeling of materials and structures. The main problem of parameter estimation is that some parameters could not be directly measured, but somehow deduced from available experimental data. The consequence is that relevant parameters are obfuscated with measurement error and thus unusable. We propose parameter estimation based on the novel inverse procedure capable of accurate extraction of non-measurable parameters from experimental results.

This paper presents application of a novel method for parameter estimation in a stochastic model of fiber reinforced concrete. Fiber reinforced concrete (FRC) is a new material with increasing application. Numerical model of FRC is not so well established as that of ordinary concrete. It is even more truth for procedures for material parameter estimation. Deterministic model of FRC has to deal with a large number of fibres and identification from that type of model is generally difficult. In this work we present a stochastic model of FRC based on the fiber bundle model. Fiber bundle model allows introduction of a probability distribution function into the model and simple performance of Monte Carlo experiments. Introduction of order statistics and the Levenberg – Marquardt procedure leads to formulation of the inverse model that permits identification of material parameters. Numerical examples illustrate the properties and stability of the proposed method.

In the case of heat exchange of open surfaces like pavement, radiation plays a crucial role since that is the mechanism that accounts for the majority of heat energy exchange. During the day solar radiation heats the surface and during the night surface cools itself radiating heat. Heat exchange problems involving radiation lead to a non-linear formulation, which can be simplified with careful parameterization. Namely, contribution of radiation should be expressed through radiated heat instead of direct influence of distant body temperature. The consequence is introduction of a non-linear convective heat transfer coefficient between the pavement and the open air.

In this work we are trying to substitute pullout tests with three-point bending tests. In order to achieve that, a relation between the two tests (pullout and three-point bending) has to be established. It is assumed that this relation is deterministic and so a combination of stochastic - deterministic model is a result. Stability and accuracy of the stochastic-deterministic inverse model is going to be assessed through additional experiments that are under way.

Paper presents experimentation on fiber reinforced concrete (FRC) samples for determination of its fatigue properties. Investigation comprises dynamic and static experiments with force and displace- ment recording. The recordings are a basis for inverse determination of model parameters. The under- lying mathematical model of fatigue is based on a combination of a statistical and deterministic rela- tions among parameters.

Fiber-reinforced concrete (FRC) is a material with increasing application in civil engineering. Here it is assumed that the material consists of a great number of rather small fibers embedded into the concrete matrix. It would be advantageous to predict the mechanical properties of FRC using nondestructive testing ; unfortunately, many testing methods for concrete are not applicable to FRC. In addition, design methods for FRC are either inaccurate or complicated. In three- point bending tests of FRC prisms, it has been observed that fiber reinforcement does not break but simply pulls out during specimen failure. Following that observation, this work is based on an assumption that the main components of a simple and rather accurate FRC model are mechanical properties of the concrete matrix and fiber pullout force. Properties of the concrete matrix could be determined from measurements on samples taken during concrete production, and fiber pullout force could be measured on samples with individual fibers embedded into concrete. However, there is no clear relationship between measurements on individual samples of concrete matrix with a single fiber and properties of the produced FRC. This work presents an inverse model for FRC that establishes a relation between parameters measured on individual material samples and properties of a structure made of the composite material. However, a deterministic relationship is clearly not possible since only a single beam specimen of 60 cm could easily contain over 100000 fibers. Our inverse model assumes that the probability density function of individual fiber properties is known, and that the global sample load- displacement curve is obtained from the experiment. Thus, each fiber is stochastically characterized and accordingly parameterized. A relationship between fiber parameters and global load-displacement response, the so- called forward model, is established. From the forward model, based on Levenberg-Marquardt procedure, the inverse model is formulated and successfully applied.

Main aim of this work is to predict steel fiber distribution in fiber reinforced concrete (FRC), e.g. fiber segregation, with impulse excitation method. The method is based on measuring resonant frequencies of vibration in prismatic specimens excited by impact hammer. Prior to testing, specimens are exposed to X- rays in order to validate reliability of test results. Additionally, possible internal cracks and other defects are explored. The test are performed on specimens with different concrete mixtures and different known defects. Two types of acceleration transducers are used to record response signal. By use of discrete Fourier transform, acceleration in time domain is transformed into frequency domain. Further, resonant frequencies are determined as frequency response peaks. From fundamental resonant frequency dynamic modulus of elasticity of FRC is calculated according to standard ASTM C215. From the test result analyses, influence of fiber distribution and some internal defects, such as cracks, voids etc. can be observed. Since this method is non- destructive, same specimens are conducted to four point bending test and standard compression test, in order to obtain static modulus of elasticity

Fiber reinforced concrete (FRC) is a material with increasing application in civil engineering. Here it is assumed that material consists of a great number of rather small fibers embedded the concrete matrix. It would be advantageous to predict mechanical properties of FRC using nondestructive testing ; unfortunately, many testing methods for concrete are not applicable to FRC. In addition, design methods for FRC are either inaccurate or complicated. In three-point bending tests of FRC prisms, it has been observed that fiber reinforcement does not break but simply pulls out during specimen failure. Following that observation, this work is based on an assumption that the main components of a simple and rather accurate FRC model are mechanical properties of the concrete matrix and fiber pullout force. Properties of a concrete matrix could be determined from measurements on samples taken during concrete production and fiber pullout force could be measured on samples with individual fibers embedded into concrete. However, there is no clear relationship between measurements on individual samples of concrete matrix with a single fiber and properties of the produced FRC. This work presents an inverse model for FRC that establishes a relation between parameters measured on individual material samples and properties of a structure made of the composite material. However, deterministic relationship is clearly not possible since only a single beam specimen of 60 cm could easily contain over 100000 fibers. Our inverse model assumes that probability density function of individual fiber properties is known and that global sample load – displacement curve is obtained from the experiment. Thus, each fiber is stochastically characterized and accordingly parameterized. A relationship between fiber parameters and global load – displacement response, the so-called forward model, is established. From the forward model, based on Levenberg – Marquardt procedure, the inverse model is formulated and successfully applied.

Rad prikazuje numerički postupak za uspostavljanje odnosa između ponašanja dvije različite konstrukcije, odnosno određivanje mjerila (faktora skaliranja) između dvije konstrukcije. Ovo novo rješenje zasnovano je na ideji sličnosti matrica i linearnim transformacijama, uz ograničenja da se mjerilo između konstrukcija određuje tek nakon provođenja diskretizacije te da obje konstrukcije moraju biti u elastičnom području. Mjerilo konstrukcije može se odrediti u polju opterećenja ili pomaka (ovisno o tome dovode li se u vezu sile ili pomaci konstrukcije) gdje se skaliranje statičkog modela konstrukcije zasniva na principu ekvivalentnosti matrica, dok je skaliranje dinamičkog modela konstrukcije bazirano na Smith normalnoj formi. Skaliranje konstrukcije u operatorskom prostoru (matrice krutosti ili fleksije stavljaju se u međuodnos) trebalo bi biti bazirano na Sylvester matričnoj jednadžbi. Međutim, takav pristup nije praktičan te je zamijenjen Levenberg-Marquardt metodom za dobivanje približno ekvivalentnih matrica krutosti. Numerički primjeri ilustriraju predloženi drugačiji pristup.

Quite often, an engineer needs to relate different structures in order to compare their loading or displacements. One could relate a structure and its model or two structures of different type that should serve the same purpose, etc. In this work, authors have related a beam and a truss of quire different sizes by scaling their loading and their displacements. Scaling of loading is very important in wind turbines analysis and all cases when loading cannot be measured directly. In such a case, forces have to be reconstructed from measurements of other parameters, e.g. displacements or strains.

In order to gain additional insight into large structure a model is usually built which leaves us with a problem of transfer of parameters between the model and the structure. Problem is addressed on the general level but after discretization and is formulated as a relationship between relevant parameters of the structure and its model. Scaling matrices in parameter and in measurement space are determined.

Moving loading problem comprises modeling and analysis of some stationary structure and moving vehicle or any other moving structure (crane, pantograph, rotating discs etc.), as well as studying their interaction. Three segments of this problem can be distinguished: moving load modeling, structure modeling and coupling of these two models for interaction. Therefore this problem is very complex and difficult to solve. Vehicle-structure interaction is generally nonlinear problem and involves simultaneous solving of couple of systems of differential equations [1], which requires application of some numerical techniques. Finite element method (FEM), which is the most representative in engineering because of its versatility, is not appropriate for moving loading problem for many reasons (bulky system matrices, determination which of the elements is loaded in every time step, extremely computer and time demanding). Many researchers avoided this problem using significant reduction in degrees of freedom of structure or loading system, often even both. This extensive model simplification raises the question, whether such analysis gives realistic and objective insight into vehicle and structure behavior. In this paper different moving loadings in the context of vehicle- structure interaction are analysed. Simply supported plate structure is modeled with flat shell strip elements [2] upgraded to be suitable for moving loading and interaction analysis. Numerical analysis of vehicle- structure interaction is performed to obtain insight and guidelines for structure and vehicle modelling from the aspect of realiability of structure. Presented numerical model, owing to modified flat strip called vehicle strip element, enables realistic (3D) modeling of both vehicle and structure as well as deep insight in the interaction mechanism between them. Plate structure is chosen here to compare vehicle models, although presented model upholds more complicated structures. It is shown that full vehicle model gives the best agreement with measured data, and is better for complete interaction modelling, since it takes into account all degrees of freedom of the vehicle.

In order to introduce more realistic structure and moving load model, stiffened plate under the influence of full vehicle model is analysed. Flat shell strips are used for space discretisation. Motion of full vehicle model is described with 12 differential equations, and together with equation of plate they are solved using impulse acceleration method. Results are compared with measurements taken from literature and they show good agreement.

The paper shows an application of the spectral method formulated as matrix operators in dynamics of structures applied on the special case of plate under the action of a moving system consisting of mass, force and spring. The plate description includes complex loading and Dirichlet and Neumann boundary conditions that have been imposed using Lagrange multipliers. An example of a simply supported plate - free plate illustrates the application of spectral matrix operators.

— Stiffened plate analysis under the influence of standard european five-axle vehicle (semi- trailer) is presented. Flat shell strip is used for spatial discretization in order to reduce the number of unknowns and enable structure and vehicle models to be authentic as far as possible. Vehicle is introduced as 3D model with 12 degrees of freedom. Structure-vehicle interaction model presented here is described with the system of 13 differential equations which is solved using iterative procedure called impulse acceleration method. Results are compared with experimental data from literature. The results show that moving force and moving mass vehicle models are not appropriate for idealization of long heavy trailers. Since semi-trailers are standard in transportation classification it is important to know how they affect the bridge behavior. Dynamic influence is considerably reduced in relation to the plate bridge structure. While plate structure sustains 3D vehicle model only for small loading mass, it is not case with stiffened plate, so realistic results can be obtained.

Predmet istraživanja bila je izrada detaljnog modela interakcije pokretnog vozila i stvarne mostovne konstrukcije, uzimanjem u obzir svih stupnjeva slobode vozila i oblika poprečnog presjeka konstrukcije. Načinjena je parametarska analiza da bi se istražilo koji parametri vozila i konstrukcije i u kolikoj mjeri utječu na njihovo ponašanje. Cilj je procijeniti da li je modeliranje mostova kao plošnih nosača dovoljno za dobivanje točnih rezultata i koji model opterećenja daje rezultate najbliže stvarnima, dobivenim eksperimentalnim ispitivanjem. Analizirana su dva tipa konstrukcije: slobodno oslonjena ploča bez i sa uzdužnim ukrutama. Promatrano je pet tipova pokretnog opterećenja: pokretna sila, pokretna masa, pokretna masa s oprugom (sa 2 stupnja slobode), dvodimenzionalni model vozila (sa 5 stupnjeva slobode) i trodimenzionalni model vozila (sa 9 stupnjeva slobode). Konstrukcija je diskretizirana ravnim konačnim trakastim ljuskama. Za diskretizaciju i sprezanje modela vozila s modelom konstrukcije uveden je pokretni konačni trakasti element. Predložen je drugačiji iterativni postupak za analizu interakcije vozila i konstrukcije primjenom metode konačnih traka. Provedena je parametarska analiza utjecaja brzine kretanja opterećenja, odnosa mase opterećenja i mase konstrukcije, oblika i krutosti poprečnog presjeka konstrukcije i geometrijskih karakteristika površine konstrukcije na dinamički progib konstrukcije. Model plošnog nosača opterećenog pokretnom silom i pokretnom masom testiran je usporedbom numeričkog rješenja sa rješenjem u zatvorenom obliku. Rezultati analize interakcije složene prostorne konstrukcije (ploča s ukrutama) i punog modela vozila verificirani su usporedbom s rezultatima dinamičkih ispitivanja izvedenih na konstrukciji cestovnog mosta. Iz dobivenih dinamičkih i statičkih progiba, za prelazak dva vozila preko mostovne konstrukcije izračunati su dinamički faktori i uspoređeni s vrijednostima iz literature.

Modeling of long structures supported by the ground and under moving loading, such as railways and airports, is very complex work, which combines several numerical models: structure model, ground model and loading model. Usual engineering practice in analysis of structures supported by the ground and under the influence of a moving loading is to use Winkler model. This model has several drawbacks : does not allow propagation of transversal waves but through the structure, because shear stiffness is not included ; ground deformation is present only under the structure, there is no deformation beyond edges of the structure ; linear relation between applied load and displacement. Undesirable consequence is wave reflection on the structure, which induces very high frequencies. This paper describes models developed for dynamic analysis of long structures subjected to the moving load and lying on the ground having endless boundary conditions (no reflection of transversal waves). Ground has been modeled as Pasternak foundation that takes the shear stiffness into account. The models allow propagation of the transversal waves also through the ground with the advantage that the same model is applicable in both static and dynamic analysis. Structural modeling adopts two approaches : i) beam model based on quarter point beam elements, supported by the Pasternak ground model, ii) finite strip model with equal boundary conditions [2]. Moving loading is described as moving force or moving mass enabling the comparison between them. Loading is time and velocity dependent. The later one requires more effort and the newly developed Impulse Acceleration Method has been adopted [1]. Several numerical examples enable insight into quality of the results obtained and provide comparison between the various assumptions.

Poznato je da je primjena ekološki prihvatljivih materijala posljednjih godina, koje je moguće reciklirati, sve poželjnija. Izuzetak tome nije ni građevinarstvo. Uz stalna istraživanja i pokuse pronalaze se razni materijali kao alternativa klasičnima. Jedan od njih je i bambus, biljka iz porodice trava, čija je primjena veoma raznolika. Bilo da se koristi kao vanjsko ili unutrašnje uređenje ili dio konstrukcije. Cilj završnog rada je istražiti svojstva bambusa kao građevinskog materijala. Prikazati njegova svojstva i ponašanje te analizirati već gotove konstrukcije uz primjenu raznih sadržaja, literature i laboratorijskih istraživanja., It is known that the use of more environmentally friendly materijals, which can be recycled, is increasingly desirable in recent years. Construction is no exception to this. With constant research and experiments, various materials are found as an alternative to the classic ones. One of them is bamboo a plant from the grass family, whose application is very diverse. Whether is bit used as external or internal decoration or part of the structure. The aim of the final year project is to investigate the properties of bamboo as a building material. Show its properties and behavior and analyze already made constructions with the applocation of various contents, literature and laboratory research.

U ovom radu prezentirat će se pojava toplinskog šoka u staklu. Provest će se ispitivanje na fasadnom elementu, takozvanom shadow box. Na elementu podvrgnutom sunčevom zračenju i uvjetima statičkog zasjenjenja mjerit će se temperatura u nekoliko točaka i analizirat će se dozvoljena vlačna naprezanja u staklu preko vrijednosti temperaturnih razlika. Osim ispitivanja, za isti element provest će se proračuni toplinskih utjecaja, svedeni na uvjete stacionarnog stanja. Za to će se koristiti dva računalna programa, Vitrages Decision i Bisco. Zaključno, rezultati će se analizirati obzirom na dopuštene vrijednosti maksimalnih temperaturnih razlika u staklu radi sprječavanja pojave loma. Također, provest će se usporedba izmjerenih i proračunatih vrijednosti u svrhu provjere podudarnosti rezultata i prihvatljivosti uporabe pojedinog računalnog programa za analizu ovakvog specifičnog elementa., The occurrence of thermal shock on the glass will be presented in this paper. The examination will be conducted on the facade element - the shadow box. The temperature will be measured at several points and the permissible tensile stresses in the glass will be analyzed through the value of the temperature differences on an element subjected to solar radiation and static shading conditions. In addition to testing, calculations of thermal effects, reduced to steady-state conditions will be carried out for the same element. Two computer programs - Vitrages Decision and Bisco, will be used for this. In conclusion, the results will be analyzed regarding the permissible values of the maximum temperature differences in the glass in order to prevent breakage. Apart from that, a comparison of measured and calculated values will be carried out to verify the consistency of the results and the acceptability of using a particular computer program for the analysis of this specific element.

Tema ovog rada je prijenos topline kroz višeslojno staklo. Opisani su osnovni oblici izmjene topline. Za svaki od oblika prijenosa definirane su formule za izračun gustoće toplinskog toka. Opisan je prijenos topline kroz jednoslojno, dvoslojno i troslojno staklo uz pripadajuće formule. U prvom dijelu je izveden proračun prijenosa topline kroz sva tri stakla provođenjem i konvekcijom. Pomoću Excela i Hp Prime kalkulatora napravljeni su dijagrami dobivenih rezultata. U drugom dijelu opisan je proces prijenosa topline pod utjecajem Sunčeve radijacije. Uz pomoć programa Wolfram Mathematica dobiven je izračun prijenosa topline kroz jednoslojno, dvoslojno i troslojno staklo. Na kraju rada na temelju dobivenih rezultata izvršena je njihova analiza i usporedba., The topic of this paper is thermal transmittance through multilayer glass. Basic forms of heat exchange are described. Formulas for calculating the heat flow density are defined for each form of transfer. Heat transfer through single-layer, two-layer and three-layer glass is described along with the corresponding formulas. In the first part, the calculation of heat transfer through all three glasses by conduction and convection was performed. Diagrams of the obtained results were made using Excel and Hp Prime calculator. The second part describes the process of heat transfer under the influence of solar radiation. With the help of the Wolfram Mathematica program, the calculation of heat transfer through one-layer, two- layer and three-layer glass was obtained. At the end of the thesis, based on the obtained results, their analysis and comparison were performed.

Anchor channels are a type of cast-in-place fastener that are well suited for supporting curtain walls and other applications in commercial construction because they provide flexibility when connecting structural or nonstructural elements. In modern high-rise buildings, composite slabs consisting of profiled steel decking with an in-situ cast concrete topping are commonly used. In some countries, it is also common to install the attachment point of the curtain wall in a recess of the concrete member often called a “pocket”. Therefore, the specific geometry of the composite slab and pockets is a major factor to consider when designing anchor channel connections. However, the influence of complex geometry on the concrete capacity has not been investigated and design is based on engineering judgement. The main aim of this thesis is to investigate the behavior of anchor channels in composite slabs and pockets, for both tension and shear loads. Extensive numerical parametric studies and several experimental campaigns have been carried out to evaluate the difference in the capacity between slabs with complex geometry and equivalent plain concrete slabs under un-cracked conditions. In the numerical studies, the 3D nonlinear FE code based on the microplane model was employed. The numerical models were validated against the corresponding experimental tests and showed excellent agreement. Based on the results, the existing design models valid for plain concrete slabs have been modified and enhanced to improve their predictability, especially in the case of thin members. Moreover, additional modification factors have been proposed to account for the influence of complex geometry on the concrete capacity., Sidreni kanali su tip sustava za pričvršćivanje koji se postavlja na odgovarajuću poziciju prije ugradnje betona. Vrlo su prikladni za oslanjanje ovješenih fasada i drugih primjena u komercijalnoj gradnji zbog prilagodljivosti prilikom povezivanja konstruktivnih ili nekonstruktivnih elemenata. Sidreni kanali se prilikom oslanjanja ovješenih fasada postavljaju po obodu relativno tankih međukatnih ploča, pri čemu nosivost uslijed otkazivanja betona postaje mjerodavna za dimenzioniranje. U modernim višekatnim konstrukcijama često se koriste spregnute ploče od profiliranih trapeznih limova i sloja lijevanog betona na mjestu ugradnje. U nekim zemljama, uobičajeno je da se povezivanje ovješenih fasada vrši unutar udubljenja u betonskoj ploči koje se naziva „džep“. Stoga, specifičnu geometriju spregnutih ploča i „džepova“ važno je uzeti u obzir prilikom dimenzioniranja spojeva sa sidrenim kanalima. No, utjecaj složene geometrije na nosivost betona nije istražena i proračun je baziran na inženjerskim prosudbama. Osnovni cilj ove disertacije je istražiti ponašanje sidrenih kanala u spregnutim pločama i „džepovima“ za vlačna i posmična opterećenja, a naglasak je na oblicima sloma uslijed otkazivanja betona. Provedene su opširne numeričke parametarske analize i nekoliko eksperimentalnih programa kako bi se odredila razlika u nosivosti između ploča sa složenom geometrijom te ekvivalentnih monolitnih betonskih ploča za neraspucani beton. U numeričkim simulacijama korišten je 3D nelinearni program baziran na metodi konačnih elemenata. Osnovna značajka ovog programa je mikroravninski konstitutivni model, a osnovna ideja je praćenje jednoosnih naprezanja i deformacija u unaprijed definiranim smjerovima (mikroravninama). U programu su pukotine modelirane koristeći tzv. pristup razmazanih pukotina, a kako bi se osigurala objektivnost rezultata neovisno o veličini konačnih elemenata primijenjena je tzv. metoda trakastih pukotina. Numerički modeli su verificirani na osnovu usporedbe s odgovarajućim eksperimentalnim rezultatima, pokazujući izvrsnu podudarnost. U radu su ponajprije istraženi važeći proračunski modeli u normama za vlačna i posmična opterećenja. Naime, izuzetno je bitno da se referentna nosivost, tj. nosivost u monolitnim betonskim pločama, može čim preciznije odrediti kako bi se mogli primijeniti modifikacijski faktor koji će uzeti u obzir složenu geometriju spregnutih ploča i „džepova“. Prilikom istraživanja ponašanja u monolitnim pločama, fokus je stavljen na tanke ploče zbog njihove sve češće primjene u praksi. Na osnovu numeričkih rezultata uočeni su nedostaci kod važećih proračunskih modela i predložene su promjene kako bi se poboljšala njihova točnost. Dodatno su osmišljeni i eksperimenti koji su potvrdili predložene promjene. Kod primjene sidrenih kanala u spregnutim pločama i „džepovima“ varirani su brojni parametri kako bi se istražilo što više mogućih konfiguracija u praksi. Neki od tih parametara su: tip limova, orijentacija limova, debljina ploča, pozicija sidrenih kanala, dimenzije „džepova“, itd. Na osnovu brojnih rezultata predloženi su dodatni modifikacijski faktori za određivanje nosivosti sidrenih kanala u spregnutim pločama i „džepovima“, posebno za vlačno i posmično opterećenje. Validacija navedenih faktora provedena je pomoću serije pomno osmišljenih eksperimenata. Osnovni znanstveni doprinos ovog rada očituje se u unaprjeđenu postojećih saznanja i modela za proračun sidrenih kanala u monolitnim betonskim pločama, te potpuno nova saznanja o njihovoj primjeni u spregnutim betonskim pločama i „džepovima“. Rezultati ovog rada i prijedlozi za proračun od iznimne su važnosti za primjenu sidrenih kanala kod oslanjanja ovješenih fasada koja je sve raširenija diljem svijeta, a posebno u Europi i SAD-u.

Cilj ovog rada je razvoj numeričkog modela za izračun distribucije temperature u kolničkim konstrukcijama s obzirom na mjerene meteorološke podatke uz uvođenje nelinearnog koeficijenta prijenosa topline koji je funkcija temperaturne razlike kolnika i okolnog zraka. Prednost ovog modela je što isti izračunava toplinsko zračenje kolnika (toplinu vraćenu u okolni zrak) što je u važan dio procesa prijenosa topline kod „otvorenih“ prostora. Tijekom perioda 2011. – 2012. godine vršena su preliminarna mjerenja temperatura površina različitih tipova površina kolnika uz praćenje meteoroloških parametara u svrhu utvrđivanja vrsta materijala koji doprinose nepovoljnim toplinskim uvjetima u gradovima. Zatim, tijekom perioda 2013. – 2015. godine provedena su mjerenja temperatura površina asfaltnih kolnika koji su se u preliminarnim mjerenjima pokazali kao nepovoljni, a u velikoj mjeri su prisutni u gradovima. Mjerenja su obuhvatila i mjerenja sunčevog zračenja i meteoroloških parametara. Mjerenja su vršena u svrhu validacije i kalibracije parametara modela. Numerički model temelji se na nestacionarnoj diferencijalnoj jednadžbi diskretiziranoj metodom konačnih elemenata sa posebnim konačnim elementom toplinskog toka prema tlu. U radu je dokazano da je nelinearni koeficijent konvektivnog prijenosa topline, koji je ovisan o vremenu i temperaturnoj razlici kolnika i okolnog zraka, neophodan za opis ovakvog problema. Razvijeni model uključuje kalibraciju koeficijenta konvektivnog prijenosa topline s obzirom na lokalne meteorološke uvjete inverznim iterativnim postupkom., The aim of this paper is to develop a numerical model for calculating the temperature distribution in pavement structures with according to the measured meteorological data, with the introduction of a non-linear heat transfer coefficient which is a function of temperature difference between pavement and ambient air. Developed model calculates heat radiated from the pavement back in the air, which is an important part of the heat transfer process in the open air surfaces. During the period 2011-2012, preliminary measurements of surface temperatures (different types of pavement materials) were performed with monitoring of meteorological parameters, in terms of determining the types of materials that contribute to the increased temperatures in cities. During the period 2013-2015, the temperature of the asphalt surfaces, solar radiation and meteorological parameters were measured. The measurement was performed for the purpose of validation and calibration of model parameters. The mathematical model is based on a nonstationary differential equation, discretized by use of finite element method with a special finite element for heat flux towards the soil. It is proved that a nonlinear heat transfer, coefficient, which is a function of time and temperature difference between the pavement and the surrounding air, is necessary to describe this phenomena. The developed model includes heat transfer coefficient calibration for specific local conditions through the iterative inverse procedure.

U ovom radu analizirana su svojstva svježeg i očvrsnulog betona s udjelom od 70% recikliranog asfalta. Dobiveni rezultati uspoređeni su sa svojstvima referentnog betona izrađenog od prirodnog drobljenog agregata i sa svojstvima betona izrađenog s agregatom od recikliranog betona. Na uzorcima svježeg betona određena je konzistencija betona rasprostiranjem, udio pora i gustoća betona. Na uzorcima očvrsnulog betona određena je gustoća betona, tlačna čvrstoća, vlačna čvrstoća savijanjem i cijepanjem, te vodopropusnost i koeficijent toplinske provodljivosti. Na temelju analize dobivenih rezultata možemo odrediti optimalni postotak zamjene prirodnog drobljenog agregata recikliranim asfaltom uz zadržavanje zadovoljavajućih svojstava svježeg ili očvrsnulog betona., In this paper, properties of fresh and hardened concrete with 70% replacement with recycled asphalt aggregate are analyzed. Obtained results were compared with the properties of reference concrete made from natural crushed stone and with the properties of concrete made from recycled concrete aggregate. Flow table test, air content and density were determined on fresh concrete samples. Density, compressive strength, flexural and tensile splitting strength were determined on the samples of hardened concrete, as well as water permeability and thermal conductivity were determined too on this samples. Based on the analysis of given results, we can determine optimal percentage of replacement of natural crushed stone with recycled asphalt aggregate, while maintaining fresh or hardened concrete properties.