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The robustness of a reinforced concrete (RC) five-storey building (frame system stiffened by walls) is analysed in the paper. A high ductility class structure is designed in accordance with structural Eurocodes. The response of the structure to eight different scenarios of the ground floor vertical element loss is analysed. Nonlinear Static Analysis (NSA) and Nonlinear Dynamic Analysis (NDA) methods are used for the robustness analysis. Fragility curves of the building are derived from statistical analysis of these results. The values obtained through NSA and NDA, damage limit states of the system, and fragility curves, are compared. The influence of the position of the removed element on robustness of the structure is also analysed.

Research at faculties in Serbia after WWII, even though they were fruit of individual efforts, resulted in significant theoretical contributions. Organized, mostly applied research was conducted within institutes with participation of scholars and researchers of the faculties. Since 1952, the Association of Yugoslav Laboratories (AYL) consolidated the research, thus providing a considerable contribution to the structural engineering in Serbia. This contribution in the field of theory and practice was the basis for the notable achievements that glorified our structural engineering worldwide. Theoretical contributions contained in the doctoral dissertations in the field of Theory of structures and Geotechnics are significant, so they were listed in the paper. Majority of these studies became a part of research project as late as in 1976, and they are briefly presented in the paper. The synthesis of project results from fundamental and technological development research was published in numerous monographs, articles, papers and proceedings of scientific and professional meetings and some of them are commented in this paper. The necessity to introduce technical regulations which have already been adopted in the EU countries EN 1990 to 1999, i.e. the Eurocode, was emphasized. There is a brief discussion of several research directions which are topical nationwide as well as worldwide.

Built heritage is incessantly exposed to natural disasters including numerous earthquakes. Therefore, it is important to take measures to reduce vulnerability and increase the protection of buildings depending on the exposure to seismic hazard and the importance of the building. Studying the history of construction reveals examples of building constructions aimed at protecting against earthquakes. For this reason, such examples are presented here, starting with the buildings from the distant past until now. The documentation related to the action of earthquakes throughout history and the procedures in planning the building protection measures in order to preserve the heritage from dilapidation were commented. The paper, also, presents some examples of incorrect use of materials and construction technologies that damage the original structural fabric, and thus, the value of a certain cultural property.

Safety and functionality of concrete road bridges are of a special importance for the traffic flow continuity in different circumstances including after earthquakes, floods, as well as after vessel or vehicle impact on piers. This is why almost all countries use Bridge Management Systems (BMS). They include the bridge inspection manuals, guidelines, report writing, bridge condition evaluation and determination of priorities (rating) for maintenance work or rehabilitation to achieve the design service life of bridges. This paper presents a comparative analysis of some documents of certain countries and associations, related to BMSs and their main components.

Thermal properties of the wall structure elements made from gel and straw (?Ethno-eco-passive houses?) have been investigated. The gel was made from a mixture of clay, lime, and water. A 1-D mathematical model based on the continuum mechanics, for predicting the thermal conductivity, is proposed. The results obtained by applying the proposed mathematical model were compared with the measurement data of experimental tests, using the Isomet 2114 instrument. The program envisages the measurement of thermal conductivity of three specimens, 5-year-old, comprising three series within 365 days. In the theoretical analysis, the same parameters of thermal stability were treated as in the experiment. The average value of the material thermal conductivity is 0.0990 W/mK, so it can be concluded that, the composite material intended for the envelope of the proposed constructive system ?Ethno-eco-passive house? is verified as thermally suitable.

The objective of this study is to investigate seismic response of bridges with unconventional configuration such as skewed and curved bridges. The influence of skewness and horizontal curvature on seismic performances of bridges, with a special focus on their influence on the probabilistic seismic demand model (PSDM), is analysed. Since the studies of seismic performances of bridges are nowadays formulated in probabilistic frameworks it is important that the established (PSDMs) meet specific criteria so they can be considered a reliable tool in seismic assessment of bridge structures. Twelve types of bridges are considered in this study by varying two bent types, three values of skewness and two values of curvature. Nonlinear dynamic analyses are conducted for all the considered samples. Longitudinal, transversal and resultant column drift ratios are considered as the bridge response. Five earthquake intensity measures are investigated and each of them are calculated from both horizontal components. In addition, the resultant measures are obtained by applying the SRSS rule on the components. The formed PSDMs are analysed in order to examine their efficiency, proficiency and sufficiency. Adverse effects of skewness and curvature on seismic performances of bridges are noticed in the conducted analyses by comparing mean values of column displacement ductility, established prediction models and fragility demand curves. It was noticed that these effects are more prominent for bridges with single pier bents with one weak direction in comparison with double pier bents. Finally, it is found that more accurate models (efficient and proficient) are obtained when structure dependant measures are used in PSDMs. Modified models including resultant measures and resultant response are proposed for fragility analysis of curved and skewed bridges.

The revitalization of existing masonry buildings, built decades ago, is a very topical and complex structural engineering issue, especially when the building was built in the area of significant seismic activity. A large number of masonry buildings in the city of Niš, as well as in other places in Serbia, were built in the period before the adoption of technical regulations on the design and construction of seismically resistant structures and they are at insufficient safety level in the event of an earthquake. Therefore, it is necessary that structural strengthening meets the seismic resistance requirements laid down in Eurocode 8 or other relevant codes. In order to choose the method of structural strengthening, detailed seismic analyses must be carried out in several variants along with the application of relevant technical regulations. The effects of five analyzed structural strengthening methods were checked against the provisions of Eurocode 8, Part 1 and Part 3, which relate to the recommendations for the geometric characteristics of shear walls, and they were applied on two types of existing masonry buildings in Niš. On the basis of the performed analyses, conclusions were drawn regarding the methodological approach of the assessment of the condition of the structure, its seismic resistance and decision-making on remediation and/or strengthening measures.

Comparative non-linear static (NSA) and non-linear dynamic analyses (NDA) of 2D frames (as parts of skeletal 3D structures) of RC buildings founded on piles are presented in this paper. In order to produce a more realistic presentation of behaviour of a frame structure, the analysis involves a structure-foundation-soil interaction. Also, the model involves a linear-non-linear dynamic pile-soil interaction, using link elements. The foundation consists of drilled piles having 60 cm in diameter. The soil is modelled using Multi-linear plastic link elements, as well as with p-y curves, on both sides of the pile, assuming that p-y curves transfer only compression (p-y curves are experimentally determined non-linear relationships of displacement/pressure in soil, along the depth of a pile). The analysis shows the problems which accompany extraction of a 2D frame, as a representative of a regular 3D space frame. The impact of onset and location of individual plastic hinges on seismic performances of the analyzed structural system are investigated, and relative floor drifts are analyzed. It was concluded that the analysis of 2D frame, in the interaction with the foundation and soil, may provide sufficiently accurate results of behaviour and assessments of seismic performances of skeletal RC multi-storey building. It is important, because introduction of a spatial structure in such analyses is very complex and challenging.

This paper presents the use of a numerical model based on layered finite elements in the analysis of stress and strain due to creep and shrinkage of concrete and relaxation of prestressing steel in statically indeterminate composite structures. The calculation algorithm allows significant changes in the structure through characteristic time intervals, in accordance with technological procedures used during realisation of works. The corresponding computer program adapted to daily practical engineering design is also developed.

This paper involves the analytical and numerical calculations of the the largest pre-stressed concrete free-standing structure in the world – the Dome of the “Hall 1 of the Belgrade Fair”, designed by a well-known Serbian scientist and engineer Branko Žeželj, one of the founders of the Institute for testing of materials IMS in Belgrade, conveniently positioned just across the street, best known for coming up with a concrete pre-stressing system, which is still widely used today. As a part of this research, this large and unique structure will be analyzed from point of view of structural integrity, including numerical simulation of crack growth in one of its support columns. Presented analyses also include the calculation of forces and moments in the structure as a whole, while also taking into account foundation displacements in the columns.

The authors of the paper, on the basis of the analysis of a large number of scientific papers, presented their original systematization of seismic analyses of structures, where a large number of them were developed during the last twenty years. Seismic analyses are generally classified into two (four) groups: Linear Static Analyses (LSA) and Nonlinear Static Analyses (NSA), and Linear Dynamic Analyses (LDA) and Nonlinear Dynamic Analyses (NDA). The analyses of nonlinear seismic structural response were classified separately from the Target Displacement Analyses (TDA) which defines the relationship of the seismic demand and seismic response. On the other hand, classification was also conducted depending on whether a nonlinear response of the system is obtained by the implementation of incremental-iterative procedures or by implementation of semi-iterative and/or semi-incremental procedures. NDA were classified according to the concept of mathematical formulation, i.e. whether they are based on only one dynamic analysis, several dynamic analyses or they are solved in combination with other methods. By implementing the conducted systematization of seismic analyses, one can efficiently consider which type of analysis is optimal for structural analysis and which type of analysis should be taken into account in the phase of preliminary and final analyses in the course of scientific research and professional projects. This paper also presents the aspects of damping modelling in structural analysis through the systematization of damping types and flowcharts, depending on the type of analysis applied: linear and nonlinear, static and dynamic. Damping has been systematized based on the way it was introduced into calculations, i.e. over material damping, link element damping and damping directly introduced into the analyses which are conducted in capacitive, time and frequency domains. In the process of creating numerical structural models, the type of damping and the way of its introduction into structural analysis can be very efficiently selected by applying the flow charts developed. By applying the developed flowcharts, alternative approaches to the introduction of damping into structural analysis can also be defined.

On the territory of Montenegro, road straight and curved bridges with middle range spans are often frame structures with multi column bent type and a capping beam. This paper presents the response of tree RC bridges: two curved bridges (with radius R=250 m i R=150 m) and one straight bridge. Bridges under consideration are frame structures with multi column bent (two circular columns) and capping beam integrated into the deck. Skewness of the bridge bent is also considered in this paper. Tree angles of skew are analyzed: 0˚, 20˚ and 30˚. Significant mode shapes are obtained through modal analysis. Comparative analysis of modal responses is carried out and conclusions about the influence of skewness and horizontal curve on modal shapes and periods of vibrations are made. Static-nonlinear analysis was performed for all nine bridge prototypes. The obtained results were compared and conclusions about influence of considered geometric parameters were made.

This paper presents the case study of the authors&rsquo, design of the earth-sheltered house in Village Dobraca near Kragujevac, Serbia, in the context of development and some thermal properties of the underground housing. The historical insight, in brief, provides a better understanding of the reasons for their modern use as energy efficient and sustainable structures. It shows that underground houses even today are more thermally efficient than above ground houses since, besides earth, there is no need for new additional thermal layers. The article also includes a review of the representative physical forms of the underground housing through different periods, with the result of measurement of their main properties. The study of the underground housing structures provides an insight of the relation between the location and typology of underground homes in a contest of climate zones. These structures have an almost constant temperature, which provides the primary &ldquo, comfort&rdquo, condition in which the man is determined to live in. The results on property-based monitoring data showed that the earth-sheltered house could provide the thermal comfort that is close to the ideal human needs temperature. Today, the new materials and especially the solar, geothermal, and wind accessories, enables the maximum sustainability of these specific building structures and provides them with an even better energy efficiency.

U radu je analiziran utjecaj momenta koji se prenosi spojem unutrašnjeg stupa i ploče, te utjecaj čvrstoće betona na nosivost ravne ploče na proboj. Sedam uzoraka u punoj veličini ispitano je eksperimentalno i numerički. Rezultati su prikazani u obliku krivulje opterećenje-rotacija ploče i uspoređeni s kriterijima loma prema teoriji kritične posmične pukotine (CSCT), kao i s približnim izrazima. Provedena je nelinearna analiza MKE uz kalibraciju modela s eksperimentalnim podacima radi boljega poklapanja numerički dobivenog odnosa opterećenje-rotacija s eksperimentalnim rezultatima., The effects of moment transfer at the flat-slab-inner-column connection, and the influence of concrete strength on the punching resistance of slabs, are analysed in the paper. Seven full scale specimens are investigated experimentally and numerically. The results are presented as load-rotation curves and compared with the critical shear crack theory (CSCT) failure criterion, and with other comparable expressions. A detailed nonlinear FEM analysis, involving calibration of model with experimental data, is conducted to ensure better correspondence of numerically obtained load-rotation relationship with experimental results.

Almost to the end of the twentieth century durability was treated implicitly and its service life (SL) was not defined in technical regulations (codes) for the design of concrete structures (CS) which have been applied. Over time this approach has proved to be insufficient, especially in intensive growth environment pollution. In the current codes for the design of CS (e.g. EN, i.e. Eurocode - EC), durability is treated implicitly and most do not contain quantified guidance for the design of CS SL longer than 50 years. The SL is implicitly defined with no clear meaning, what is the end SL? It was considered that application of the provisions of these codes result in permanent CS service, and that they will achieve the required SL, which is often not the case. Experiences show that this approach fails to meet the requirements of durability, especially when the requested SL is significantly longer than 50 years (100 or more). Modern approach to the design of reliable CS is based on performance and behaviour during SL. Probabilistic approach (based on probability and reliability) design enables a more accurate forecast of the behaviour of CS during SL, but it is complex and the possibility of its wider practical application is in the developmental stage. Based on a review of literature and contemporary codes, the paper analyzed some models and approaches to the design of CS, according to durability. The emphasis is on the design of the performance, based on the indicators of durability of concrete, with current proposals for a revision of EN 1992 and EN 206, based on the experience gained and the latest research in this field.

The paper deals with methodology developed and presented for analyzing the damage on structures exposed to accidental and seismic actions. The procedure is based on non-linear numerical analysis, taking into account the principles of Performance-Based Seismic Design (PBSD). The stiffness matrix of the effects of vertical action is used as the initial stiffness matrix in non-linear analysis which simulates the collapse of individual ground-floor columns, forming thereby a number of possible scenarios. By the end of the analysis that simulates the collapse of individual columns, the stiffness matrix is used as the initial stiffness matrix for Non-linear Static Pushover Analysis (NSPA) of bi-directional seismic action (X and Y directions). Target displacement analyses were conducted using the Capacity Spectrum Method (CSM). The structure's conditions/state was assessed based on the calculated global and inter-storey drifts and the damage coefficient developed. The damage level to the building was established using an integrated approach based on global and inter-storey drifts, so that, depending on the level of displacements for which the drifts are identified, a more reliable answer can be obtained. Applying the damage coefficient, a prompt, reliable and accurate indication can be obtained on the damage level to the entire structure in the capacitive domain, from elastic and non-linear to collapse state.

century, at the time of intense urban development and migration into urban areas in Europe. These buildings need retrofitting to comply with contemporary demands of building performances. The directive [1], among other requirements for the planned maintenance of essential properties during the service life, sets for thermal comfort and energy savings. During RB service life, it is necessary to monitor the structure's performance through regular inspection of deterioration and other defects, investigate and detect the emerging problems and control the appropriate maintenance works [2]. The service life depends on the physical deterioration of materials and limitation of applied solutions, as well. The energy efficiency, especially thermal protection of buildings is a problem whose solution may also include the issues of technological, economic, social, legal, and moral obsolescence [3] of the existing residential buildings that were built in an industrial manner. Therefore, it has to be primary assessed so the energy rehabilitation measures could be set as compatible to the other building renewal activities.

This paper presents the comparative analyses of experimental and numerical research results of RC connections between the precast slab and monolithic wall (Type 1), and both monolithic slab and wall elements (Type 2). Type 1 was applied in prefabricated building system developed in Tuzla, Bosnia and Herzegovina, as the most sensitive part of the structure. In order to provide a favourable response of the bearing structure connections under seismic load (Type 1) it is dislocated in the span. In order to compare the behaviour of listed structure connection types, three specimens made of precast slabs and monolithic wall as well as three specimens made of monolithic slabs and walls were tested under quasi-static load. Thus, the mathematical models are proposed in order to analyse both types of connection, based on the exact method of displacement and FEM. Furthermore, the stiffness matrix is modified by introducing the stiffness parameter (semi-rigid) connection. The approximate Strut and Tie model is proposed according to the stress field analysis obtained by FEM.

Within the context of two case studies of complex industrial structures located in an aggressive environment, the issue of durability of reinforced concrete (RC) has been considered. Recommendations and guidelines of the International Association as well as some code provisions with regard to durability of RC structures were analyzed. Structures of the cooling tower (both of the shell and sprinkler) and the structure of Salt factory are presented briefly. The results of visual inspection of combined non-destructive and destructive investigation methodology of the concrete’s physical and mechanical properties as well as chemical measurements are presented. Parameters of the structures’ condition rating according to CEB (BI 243:1998) and a parameter recently introduced in fib (TG 5.3:2008) performance index are analyzed. These evaluations are valuable for condition assessment and taking decision about the level of repair of the heavily corroded structure. Conclusions are drawn up due to the analysis of the obtained results and on comparative analyses, and they relate directly to the state of the art system in this field. Clear recommendations in regard to RC structure durability analysis are considered by means of verification the limit state of depassivation and the reinforcement corrosion induced by chloride ingress.

This paper is a sequel to [19] where the theoretical foundations were given for the analysis of durability of concrete structures. An overview of some approaches to modeling the durability of RC structures is given in the paper. Experiences resulting from experimental and numerical research of some influential parameters leading to corrosion of the reinforcement, cracks and delaminating of the surrounding concrete, which leads to the decrease of service life of the RC structure's elements, are described in details. Methodologies of structure evaluation presented in this paper are based on assessment of critical influential parameters and represent a methodology of reasonable maintenance of an engineering construction, i.e. reasonable service life of the structure. The methods are based on analysis of conditions and performance (Condition Rating Method and Performance Rating Method). The results of ratings of concrete structures in the industrial zone of the city of Tuzla are presented in the final part of the paper.

This paper analyzes application of modern reinforcement methods for reinforced concrete (RC) beams using fiber-reinforced polymer (FRP) materials. Basic characteristics of FRP materials and the method of mounting the FRP bars within concrete, that is, near the surface of the beams (NSM method) are presented. The properties of this method and its advantages in comparison to externally bonded reinforcement laminate method (EBR) have been analyzed. The results of measured deflections and width of the cracks of the beams reinforced by FRP bars, depending on the load are presented and discussed, in comparison to the results obtained from the non-reinforced beams. The experimental research was published at the Faculty of Civil Engineering and Architecture of Nis in 2009.

Concrete structures (CS) are designed so that they can satisfy requirements regarding safety, serviceability, durability and aesthetics throughout their design service life. Present design procedures regarding CS required by national or international codes and standards such as Model Code Euro International Committee of Concrete (1993) now Federation Internationale du Beton (FIB), Eurocodes, ACI, RILEM, etc. are predominantly based on strength principles and limit state formulation. The durability aspect is a natural extension of the classical resistance verification where deterioration effects are normally neglected. The reliability is assessed through the given performance that must be delivered within the design service life, the so-called performance-based design. This approach can be adopted for a performance based on service life design. In the recent years design is related to durability through the analysis of carbonation, resistance to chloride ingress, improved freezing and thawing resistance, etc. The review of literature and some recommendations are presented referring to the design of structures aiming to attain greater durability of CS. The accent is put on the theory of reliability, failure probability and service life probability. The basics of this analysis are given through the principles of performances and service life, and deterministic and scholastic methods using the lifetime safety factor.

Experimental research of precast plate-monolithic wall connection within specific system developed in Tuzla, Bosnia and Herzegovina, in 80’s named “MMS” building system, is presented. System MMS is precast — monolithic building system specially adapted for high building constructions with characteristics of repetition of specific number of similar floors. The connections of monolithic wall and precast plate are executed with a dislocation potential joints opening which provided the structure displacement under seismic load. In this way joints become available for inspection and possible reparation/rehabilitation. The aim of presented researches is to determine the degree of connection loosening (yielding). The results of experimental tests will be used for numerical modeling of connections, which will be presented in forthcoming paper.

The paper provides an overview of ambient vibration tests and numerical analysis performed in the framework of Project NATO SfP 983828. The aim of the research is the definition of the dynamic characteristics of bridges on the examples. The paper considers three case studies: two older existing bridges and one newly constructed bridge. A comparative analysis of natural frequencies and mode shapes, obtained by ambient vibration measurements (AVM) and mathematical models (AMs), was carried with the aim to demonstrate the usefulness of ambient vibration tests for identification of the modal parameters of the tested bridge structure. Agreement between AVM and AMs results is very good. The mode shapes are very similar. Some differences between computed and measured frequencies were obtained, which can be attributed to the real nature of the boundary conditions, the uncertainty in the material properties of structure elements, and the mathematical models assumptions.

U radu je dan pregled istraživanja provedenih u okviru NATO projekta SfP 983828. Predmet istraživanja je identifikacija parametara koji utječu na dinamički odziv postojećih armiranobetonskih grednih mostova, utemeljena na mjerenjima ambijentalnih vibracija i numeričkim simulacijama uporabom modela na bazi konačnih elemenata (MKE). U tu je svrhu instrumentaliziran most preko rijeke Bosne u blizini Sarajeva. Urađena su ispitivanja ambijentalnih vibracija i geofizička istraživanja. Rezultati su analizirani i urađen je poboljšani trodimenzijski numerički model koji uzima u obzir interakciju tla i konstrukcije, kao i interakciju gornjeg i donjeg stroja mosta. Razvijeni su modeli s projektnim parametrima i parametrima dobivenim mjerenjem. Urađena je komparativna ocjena razvijenih modela i verificiran model koji je imao vrijednosti dinamičkih karakteristika konstrukcije podudarne mjerenim vrijednostima. Rezultati analize pokazuju da je odgovarajuće određivanje krutosti stupova, kolovozne ploče i ležajeva ključni parametar za pouzdanu identifikaciju sustava., An overview of research performed in the framework of the NATO Project SfP 983828 is given in the paper. The scope of the research was to identify the parameters affecting the dynamic response of an existing R/C girder bridge, based on ambient vibration measurements and numerical simulations using finite element models (FEM). For this purpose, the bridge across the river Bosnia near Sarajevo and the soil surrounding the bridge were instrumented. Ambient vibration tests and geophysical investigations were performed. The results are studied and a refined three-dimensional (3D) FEM is developed that takes into consideration the soil-structure interaction and superstructure-substructure interaction. The FEM’s with designed parameters and parameters obtained by measurements were developed. The developed FEM models are comparatively assessed and FEM model with congruence between the measured and computationally predicted dynamic characteristics of the structure was defined. The results of the analysis show that the adequate determination of the pier, deck and bearings stiffness is the key parameter for reliable system identification.

U članku je proučen utjecaj bimomenta na stabilnost tankostjenog štapa s otvorenim poprečnim presjekom uslijed vanjskog aksijalnog opterećenja. Primjenom principa virtualnih pomjeranja izvedene su diferencijalne jednadžbe deformiranog tankostjenog elementa u skladu s klasičnim pretpostavkama Vlasova. Pokazano je da kod poprečnih presjeka koji nemaju os simetrije bimomenat može značajno utjecati na uvojnu kritičnu silu. Dobiveni rezultati su provjereni primjenom programa ANSYS., In this paper the influence of the bimoment induced by external axial loads on the elastic torsional buckling of thin-walled beams with open cross-section is studied. The governing differential equations of a deformed thin-walled beam consistent with Vlasov’s classical assumptions are derived applying the principle of virtual displacements. It is shown that in the cross sections with lack of symmetry the bimoment can considerably affect the torsional buckling load. The obtained results are verified using ANSYS finite element software.

U radu je proučen utjecaj promjene parametara umjetnih akcelerograma na seizmičke karakteristike konstrukcija. Pri tome su analizirani seizmički odziv i seizmičko oštećenje. Nelinearni odziv sustava je određivan inkrementalnom dinamičkom analizom (IDA), dok je analiza oštećenja sustava razmatrana na osnovi indeksa oštećenja. Istraživanjem je utvrđeno da je za kreiranje umjetnih akcelerograma potreban znatan broj ciklusa kojim se poboljšava usklađenost spektra odziva zapisa u odnosu na spektar odziva prema EN 1998-1, a što je mjereno na osnovi odstupanja krivulja spektralnih ubrzanja u funkciji duktilnosti sustava., The impact of changes to artificial-accelerogram parameters on the seismic performance of structures is examined in this paper. The seismic response and seismic damage are analysed in this respect. Nonlinear response of the system is determined by the incremental dynamic analysis (IDA), while the damage analysis of the system is considered using the damage index. The study has shown that generation of artificial accelerograms requires a considerable number of cycles, which improves the correspondence between the range of recorded response spectra and the range of the response spectra according to EN 1998-1, which is measured based on deviation of spectral acceleration curves as a function of the ductility of the system.

U radu je razvijen postupak i prikazana aproksimativna analiza za procjenu vlastitih frekvencija i oblika vibracija tankostjene grede s proizvoljnim poprečnim presjekom, izrađene od laminata simetričnih u odnosu na srednju plohu. Teorija kompozitnih takostjenih greda zasniva se na pretpostavkama suglasnim Vlasovljevoj teoriji greda i klasičnoj teoriji laminata. Jednadžbe gibanja za spregnute savojno-uvojne vibracije izvedene su iz principa virtualnih pomjeranja. Za prosto oslonjenu tankostjenu gredu jednadžba frekvencije, dana u obliku determinante, proširena je u eksplicitni analitički oblik za određivanje vlastitih frekvencija slobodnih harmonijskih vibracija. Radi potvrde predloženog modela, uspoređeni su analitički rezultati drugih autora i FEM metoda uporabom programa ANSYS, s rezultatima dobivenim u ovom radu., The purpose of this paper is to develop and present an approximate analysis procedure to estimate the natural frequencies and mode shapes of thin-walled beams with arbitrary open cross-section, made of laminates with mid-plane symmetry. Theory of thin-walled composite beams is based on assumptions consistent with the Vlasov's beam theory and classical lamination theory. The equations of motion for coupled bending-torsional vibrations are derived from the principle of virtual displacements. In the case of simply supported thin-walled beam the frequency equation, given in determinant form, is expanded in an explicit analytical form, which gives the natural frequencies of free harmonic vibrations. For verification, the analytical study by other researchers and the FEM analysis using ANSYS are compared with the current results.