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The paper compares the following methods for analysis of composite steel-concrete beams: the “exact” analysis method, simplified method, effective modulus method and the method proposed by Eurocode 4 design code. The exact analysis method is based on the application of linear integral operators. Simplified analysis is derived from the exact method and adopts the assumption that generalized displacements change linearly with the concrete creep function. Effective modulus method and the method proposed by the Eurocode 4 design code are algebraic methods, widely used in practice. The results obtained using the mentioned four methods are compared on one example.

The paper presents the calculation of continuous composite steel-concrete beams with a partial shear connection and ductile shear connectors. The algorithm for determining the ultimate load as a function of shear resistance capacity is explained. The calculation is applied to a numerical example. The obtained results are discussed. Guidelines for further research in this area are given.

The paper presents four different methods for viscoelastic analysis of steel-concrete composite structures: “exact” analysis method, simplified method, effective modulus method and method proposed by the European design code, Eurocode 4. The exact analysis method uses the mathematical theory of linear integral operators for presenting viscoelastic relations of the steel-concrete composite structures. The simplified analysis method is derived from the exact method. It adopts the assumption that generalized displacements change linearly with the concrete creep function. Due to this assumption, the problem equations transforms from nonhomogeneous integral equations to nonhomogeneous algebraic equations. The effective modulus method and the method proposed by the Eurocode 4 are algebraic methods where stress-strain relations for concrete are expressed through the effective modulus, which depend on time. On the numerical example of continuous steel-concrete beam, the results obtained using the mentioned approximate and the exact method are compared

The paper presents and compares four methods for visco-elastic analysis of steel-concrete composite beams. The method denoted as "exact" is based on the use of linear integro-differential operators and besides inevitable approximations of the rheological properties of constituent materials does not introduce other mathematical simplifications. The underlying assumption of the simplified method is that unknown deformations change linearly with the concrete creep function. In the paper, the results of the analysis of continuous composite beam obtained using the mentioned two methods are compared with results of widely used the Effective modulus method and its modified form proposed by Eurocode 4. Results have shown that the simplified method gives solutions closest to the “exact” analysis method.

Zbornik radova Građevinskog fakulteta

The paper presents nonlinear analysis of square CFT columns using distributed plasticity fiber elements. Behaviour of CFT columns is nonlinear and it is necessary to include different nonlinear effects into the numerical model in order to simulate their behaviour properly. Model proposed in this work considers: nonlinear behaviour of concrete and steel using nonlinear stress-strain models, confinement effect and geometrical nonlinearities. Tests exposed to static loading with different slenderness, different D/t ratio (where D is the total dimension of a cross section and t is the thickness of steel tube) and different loading conditions are analyzed. Stress-strain models that best approximate the behaviour of CFT columns are determined from a detailed parametric study. The proposed numerical model is validated by comparing numerical with experimental results available in the literature. U radu je prikazana nelinearna analiza kvadratnih CFT stubova, pomoću fiber konačnog elemenata raspodeljene plastičnosti. CFT stubove karakteriše nelinearno ponašanje, što je potrebno imati u vidu u numeričkom modelu. Model predložen u ovom radu uzima u obzir sledeće nelinearne uticaje: nelinearno ponašanje betona i čelika primenom odgovarajućih konstitutivnih relacija, efekat utezanja betona i geometrijske nelinearnosti. Analizirani su uzorci izloženi delovanju statičkog opterećenja koji imaju različitu vitkost, odnos D/t (odnos ukupne dimenzije čeličnog profila [D] i debljine čeličnog profila [t]), kao i uzorci izloženi različitim tipovima naprezanja. Na osnovu parametarske analize, određeni su modeli materijala za čelik i beton, kao i njihovi parametri koji najbolje aproksimiraju ponašanje CFT stubova. Tačnost modela proverena je zatim i upoređivanjem sa eksperimentalnim podacima dostupnim u literaturi.

The paper discusses two formulations for the fiber based distributed plasticity beam/column element. For force based and displacement based formulations, basic details and main differences are emphasized. The differences in results of analysis when elements with these two formulations are used are demonstrated on two numerical examples. The first example involves the nonlinear static pushover analysis of low-rise frame with distributed element loading. The second example is nonlinear time history analysis of two-story frame subjected to earthquake loading. The differences in global and local response depending on the used finite element discretization are shown. In conclusion, the advantages of force based formulation and directions for the use of the two elements are summarized. U radu su prikazane dve formulacije fiber konačnog elementa raspodeljene plastičnosti. Za metodu sila i metodu deformacija, ukazano je na osnovne razlike dve metode. Razlike u rezultatima analize koje se dobijaju primenom fiber elementa prema ove dve formulacije prikazane su putem dva numerička primera. Prvi primer obuhvata statičku pushover analizu rama s raspodeljenim opterećenjem duž greda. Drugi primer je nelinearna dinamička analiza dvospratnog rama izloženog zemljotresnom opterećenju. Prikazane su razlike kod dobijenog globalnog i lokalnog odgovora u zavisnosti od formulacije i diskretizacije rama. U zaključku, rezimirane su primene dve formulacije fiber elementa i date napomene u vezi s njihovim korišćenjem.

In the paper, a simplified method for design of circular composite CFT columns according to the European standard for deisgn of composite steel and concrete structures – Eurocode 4 is presented. Veri¬fication of the column section capacity under axial compression and bending is based on the concept of limit states and determination of the N-M interaction curve. For eight the most common in practice CFT columns, continuous N-M interaction curves are constructed. In addition, for these selected sections, the influence of the variation of the concrete and steel classes on the column cross-section capacity is analyzed. Given interaction curves simplify the design of composite columns and the choice of dimensions of CFT column and its steel and concrete classes. Zbornik radova Građevinskog fakulteta

Bending resistance of a composite steel and concrete section apart from shape and dimensions of a cross section and mechanical characteristics of materials, depends also on type of shear connection, i.e. connectors and shear steel-concrete interface. In the paper, ductile and nonductile headed studs are considered. Bending resistance of composite sections with partial shear connection, which is a connection where a number of shear studs is smaller than necessary for fully plastic bending resistance of a section to be achieved, is analysed. The reduced bending resistance is found. The calculaton in accordance with Eurocode 4 is presented. Nosivost na savijanje spregnutog preseka od čelika i betona pored oblika i dimenzija poprečnog preseka i mehaničkih karakteristika materijala, zavisi i od načina sprezanja, tj. tipova sredstava za sprezanja i oblikovanja kontaktnog (smičućeg) spoja između betona i čelika. U radu se koriste duktilni i neduktilni moždanici sa glavom. Određuje se nosivost na savijanje spregnutih preseka sa parcijalnim smičućim spojem u kome, za razliku od punog smičućeg spoja, broj moždanika nije dovoljan da se ostvari moment pune nosivosti, tako da se određuje redukovani moment nosivosti. Proračun se sprovodi prema Evrokodu 4.

Predmet disertacije je efikasna nelinearna analiza okvirnih konstrukcija grednim konačnim elementima sa težištem na modeliranju materijalnih nelinearnosti. Geometrijska nelinearnost se uzima u obzir poznatim metodama. U tezi su analizirana i unapređena dva gredna konačna elementa: fiber element i element koncentrisane plastičnosti i napisan je sopstveni kompjuterski program kojim su elementi implementirani u postojeći open-source program za analizu konstrukcija – FEDEASLab. Tokom rada na tezi, ostvareni su sledeći ciljevi. Izvršena je optimizacija integracije poprečnog preseka čeličnih i armirano-betonskih elemenata u cilju poboljšanja efikasnosti fiber elemenata kako pri cikličnom pseudo-statičkom opterećenju, tako i pri nelinearnoj dinamičkoj analizi pojedinih delova i čitave konstrukcije. Formulisana su praktična pravila i definisane jasne smernice za diskretizaciju poprečnog preseka čeličnog I profila i pravougaonog armiranobetonskog preseka, u zavisnosti od vrste analize koja se sprovodi i željene tačnosti. Razvijen je novi konačni elementa iz grupe elemenata koncentrisane plastičnosti koji prevazilazi ograničenja postojećeg elasto-plastičnog elementa kao što su nemogućnost opisivanja postepene plastifikacije poprečnog preseka i opisivanja ponašanja materijala sa ojačanjem. Pri tome, element je zadržao svoju veliku kompjutersku efikasnost koja je osnovna prednost elemenata koncentrisane plastičnosti. Za određivanje stanja elementa razvijena su dva algoritma prema “general closest point projection” i “convex cutting plane” return mapping algoritmima i analizirana je zavisnost konvergencije od implementiranog algoritma. Mogućnosti novog elementa za modeliranje okvirnih konstrukcija pri delovanju statičkog i dinamičkog opterećenja su potvrđene kroz niz numeričkih primera. Specijalna pažnja je posvećena primeni novog GP elementa za modeliranje CFT stubova spregnutih konstrukcija... The objective of this study is the efficient nonlinear analysis of space frames with beam/column finite elements considering material nonlinearity. Geometric nonlinearity is taken into account using known methods. Two different nonlinear beam/column elements are analyzed and improved: a fiber element and a concentrated plasticity element. Own computer code is written and implemented into the existing matlab toolbox for nonlinear structural analysis – FEDEASLab. During this study, the following objectives are achieved. By the optimization of the number and position of material integration points at monitored steel and reinforced concrete cross-sections, the significant improvement in efficiency of the fiber beam-column element under cyclic static and dynamic loading conditions is gained. The practical rules for an efficient discretization of steel wide-flange sections and rectangular reinforced-concrete sections are defined, depending on the desired level of accuracy and the type of analysis. In addition, the new three-dimensional nonlinear beam-column element is formulated. The element is of concentrated plasticity type and overcomes the common limitations of the existing elasto-plastic elements, such as the inability to describe gradual plastification of a cross-section and the hardening behavior. Also, the element keeps its high computational efficiency which is one benefit of concentrated plasticity elements. Two algorithms for element state determination are developed in accordance with the general closest point and convex cutting plane return mapping algorithms. Their influence on element convergation is studied. The ability of the element to simulate frame behavior is confirmed on a number of numerical examples. The special attention is devoted to model CFT composite column behavior...

In the paper, an efficient three-dimensional concentrated plasticity nonlinear beam-column element is used for the simulation of the response of square CFT columns. The element adopts the concept of the generalized plasticity material model for the section resultant - element deformation relation and has plastic hinges located at the ends of the element and described with yield and limit surfaces. Determination of the adequate element parameters which are essential for a successful description of the CFT member behavior is discussed. Among these parameters, most important are the stiffness and yield surface parameters.

Predmet disertacije je efikasna nelinearna analiza okvirnih konstrukcijagrednim konačnim elementima sa težištem na modeliranju materijalnihnelinearnosti. Geometrijska nelinearnost se uzima u obzir poznatim metodama.U tezi su analizirana i unapređena dva gredna konačna elementa: fiber elementi element koncentrisane plastičnosti i napisan je sopstveni kompjuterskiprogram kojim su elementi implementirani u postojeći open-source program zaanalizu konstrukcija – FEDEASLab.Tokom rada na tezi, ostvareni su sledeći ciljevi. Izvršena je optimizacijaintegracije poprečnog preseka čeličnih i armirano-betonskih elemenata u ciljupoboljšanja efikasnosti fiber elemenata kako pri cikličnom pseudo-statičkomopterećenju, tako i pri nelinearnoj dinamičkoj analizi pojedinih delova i čitavekonstrukcije. Formulisana su praktična pravila i definisane jasne smernice zadiskretizaciju poprečnog preseka čeličnog I profila i pravougaonog armiranobetonskogpreseka, u zavisnosti od vrste analize koja se sprovodi i željenetačnosti. Razvijen je novi konačni elementa iz grupe elemenata koncentrisaneplastičnosti koji prevazilazi ograničenja postojećeg elasto-plastičnog elementakao što su nemogućnost opisivanja postepene plastifikacije poprečnog preseka iopisivanja ponašanja materijala sa ojačanjem. Pri tome, element je zadržao svojuveliku kompjutersku efikasnost koja je osnovna prednost elemenatakoncentrisane plastičnosti. Za određivanje stanja elementa razvijena su dvaalgoritma prema “general closest point projection” i “convex cutting plane”return mapping algoritmima i analizirana je zavisnost konvergencije odimplementiranog algoritma. Mogućnosti novog elementa za modeliranjeokvirnih konstrukcija pri delovanju statičkog i dinamičkog opterećenja supotvrđene kroz niz numeričkih primera. Specijalna pažnja je posvećena primeninovog GP elementa za modeliranje CFT stubova spregnutih konstrukcija... The objective of this study is the efficient nonlinear analysis of space frameswith beam/column finite elements considering material nonlinearity.Geometric nonlinearity is taken into account using known methods. Twodifferent nonlinear beam/column elements are analyzed and improved: a fiberelement and a concentrated plasticity element. Own computer code is writtenand implemented into the existing matlab toolbox for nonlinear structuralanalysis – FEDEASLab.During this study, the following objectives are achieved. By the optimization ofthe number and position of material integration points at monitored steel andreinforced concrete cross-sections, the significant improvement in efficiency ofthe fiber beam-column element under cyclic static and dynamic loadingconditions is gained. The practical rules for an efficient discretization of steelwide-flange sections and rectangular reinforced-concrete sections are defined,depending on the desired level of accuracy and the type of analysis. In addition,the new three-dimensional nonlinear beam-column element is formulated. Theelement is of concentrated plasticity type and overcomes the commonlimitations of the existing elasto-plastic elements, such as the inability todescribe gradual plastification of a cross-section and the hardening behavior.Also, the element keeps its high computational efficiency which is one benefitof concentrated plasticity elements. Two algorithms for element statedetermination are developed in accordance with the general closest point andconvex cutting plane return mapping algorithms. Their influence on elementconvergation is studied. The ability of the element to simulate frame behavior isconfirmed on a number of numerical examples. The special attention is devotedto model CFT composite column behavior...

In the paper, design of composite steel-concrete column according to Eurocode 4 is illustrated on detailed numerical example. The theoretical foundations of the Eurocode 4 design procedure is explained before, in the paper of the same group of authors. The resistance of a composite column subjected to axial compression and biaxial bending is determined. Capacity and stability analysis of the individual composite column under axial compression is based on the use of European buckling curves. The verification of column bearing capacity is based on use of interaction diagram determined from capacity analysis of composite cross-section. Second order effects and effects of creep and shrinkage of concrete are taken into account. For the cross section of fully encased column with I steel section, the dependency of concrete class and reinforcement ratio on ultimate cross section capacity is studied. For this type of composite cross section and 6 different steel sections, the continuous interaction curves are constructed, for common concrete classes. These curves are very practical since simplify the design of composite columns and choice of dimensions of concrete section, steel section and concrete class. U radu se, na detaljnom brojnom primeru spregnutog stuba kod koga je čelični I profil potpuno obložen betonom, ilustruje proračun nosivosti spregnutih stubova prema važećem evropskom standardu za proračun spregnutih konstrukcija od čelika i betona - Evrokodu 4 koji je detaljno objašnjen u prethodnom radu iste grupe autora. Određena je nosivost spregnutog stuba izloženog samo aksijalnom pritisku i izloženog istovremenom uticaju aksijalnog pritiska i savijanja momentima. Analiza nosivosti, a time i stabilnosti pri aksijalnom pritisku izolovanog stuba bazira se na primeni Evropskih krivih izvijanja. Provera nosivosti pri kombinaciji aksijalnog pritiska i savijanja momentima zasniva se na interakcionoj krivoj koja se određuje pri analizi nosivosti poprečnog preseka posmatranog stuba. Uzeti su u obzir uticaji drugog reda kao i uticaji skupljanja i tečenja betona. Za poprečni presek spregnutog stuba kod koga je čelični I profil potpuno obložen betonom, prikazan je uticaj marke betona i procenta armiranja na graničnu nosivost poprečnog preseka. Za dati tip spregnutog poprečnog preseka i nekoliko valjanih čeličnih profila, konstruisane su kontinualne krive interakcije za uobičajene klase betona. Ove krive su vrlo pogodne za praktičnu primenu i olakšavaju dimenzionisanje spregnutih stubova, budući da pojednostavljuju izbor dimenzija betonskog dela preseka, čeličnog profila i klase betona.

The paper deals with the design of composite steelconcrete columns according to Eurocode 4. The simplified design method and limitations for its use are explained in details. A column is analysed as an individual member, subjected to lateral loadings over the column height and axial forces and bending moments at the element ends, determined from global analysis, i.e. from the analysis of the whole structure. The resistance of a composite column subjected to axial compression and biaxial bending is analysed. The verification of bending resistance of a composite steelconcrete column cross section is based on theory of plasticity, while resistance of individual column is based on the theory of elasticity, but include the second-order effects and imperfections. Capacity and stability analysis under axial compression is based on the use of European buckling curves. The verification of column bearing capacity is based on the use of interaction diagram determined from capacity analysis of composite cross-section. Since the Eurocodes are being accepted as our national standards, the main aim of this paper is to simplify the use of this standard in our ordinary engineering practice through the detailed explanations of the design procedure of composite steel-concrete columns. U radu se prikazuje proračun nosivosti spregnutih stubova prema važećem evropskom standardu za proračun spregnutih konstrukcija od čelika i betona - Evrokodu 4 (EC4). Daje se detaljni prikaz približne metode proračuna i uslovi za njenu primenu. Stub se posmatra kao izolovani element opterećen mogućim poprečnim opterećenjem i opterećen na krajevima aksijalnom silom pritiska i momentima određenim globalnom analizom tj. analizom konstrukcije kojoj pripada posmatrani stub. Analizira se nosivost spregnutog stuba izloženog samo aksijalnom pritisku i izloženog istovremenom uticaju aksijalnog pritiska i savijanja momentima. Provera nosivosti poprečnog preseka spregnutog stuba vrši se u okviru teorije plastičnosti, a analiza nosivosti izolovanog stuba u okviru teorije elastičnosti, vodeći računa o uticajima drugog reda i imperfekcijama stuba. Analiza nosivosti, a time i stabilnosti, pri aksijalnom pritisku izolovanog stuba bazira se na primeni Evropskih krivih izvijanja. Provera nosivosti pri kombinaciji aksijalnog pritiska i savijanja momentima zasniva se na interakcionom dijagramu koji se određuje pri analizi nosivosti poprečnog preseka posmatranog stuba. Kako je u toku usvajanje Evrokodova za konstrukcije kao naših zvaničnih standarda, cilj ovog rada je da detaljnim prikazom proračuna spregnutih stubova prema Evrokodu 4 olakša primenu ovog standarda u našoj inženjerskoj praksi.

A three-dimensional nonlinear beam-column element for the simulation of the global and local response of frames under monotonic and cyclic loading conditions is pre-sented. The element belongs to the group of concentrated plasticity models, with plastic hinges located at the ends of the element and described with yield and limit surfaces. The concept of generalized plasticity, originally developed for material plasticity, is extended to force resultants in the element formulation. The element takes into account the interaction of the axial force and the bending moments about the principal axes of the cross section and the hardening behavior. The gradual yielding of the cross section is described by the asymptoti-cal approaching of the limit surface.

Different analytical methods, with different levels of approximations and accuracy, are available for analysis of continuous composite steel-concrete beams. The Eurocode 4 recommends few simple methods for calculation of creep, shrinkage, cracking of concrete and shear lag effects that are explained in the paper. Through the numerical examples of four continuous composite steel-concrete beams, the proposed methods of analyses are evaluated and compared. Practical recommendations for analysis of this type of girders are formulated. Za analizu spregnutih kontinualnih nosača od čelika i betona postoje različite analitičke metode, različitog stepena tačnosti. Evrokod 4 dozvoljava i preporučuje nekoliko jednostavnih metoda kojima se u proračun uvode nelinearni efekti kao što su skupljanje i tečenje betona, ispicalost betonske ploče i shear-lag efekat, i one su objašnjene u radu. Kroz numeričku analizu četiri spregnuta kontinualna nosača ove metode su upoređene i date su praktične preporuke za analizu ove grupe nosača.

In this paper, the analysis of longitudinal shear in concrete slab, according to Eurocode 4 (EN 1994-1-1:2004), is shown. The potential surfaces of shear failure in solid and composite slab are analyzed. For each potential surface of shear failure, the corresponding length is defined. The transverse reinforcement should be determined from the condition that, for any potential surface of shear failure, the design longitudinal shear per unit length (shear flow) is not greater than the longitudinal shear resistance of the slab per unit length. The longitudinal shear resistance of concrete slab per unit length should be determined according to EN 1992-1-1. The rules for transverse reinforcement are based on a truss analogy, i.e. the concrete slab is considered as a truss system that has compressed concrete struts and tensioned reinforcement (chords).The failure occurs when either the reinforcement yields or the concrete struts fail in compression. The transverse reinforcement in the concrete slab transfers the shear stresses from studs (shear connectors) and ensures that the premature failure of the slab will not occur. U radu se prikazuje proračun podužnog smicanja u betonskoj ploči prema Evrokodu 4 (EN 1994-1-1:2004). Analiziraju se potencijalne površine loma usled podužnog smicanja, u punoj i spregnutoj betonskoj ploči. Za svaku potencijalnu površinu loma definiše se odgovarajuća dužina površine smicanja. Proračun nosivosti pri podužnom smicanju se zasniva na uslovu da proračunski podužni napon smicanja, bilo koje potencijalne površine loma usled podužnog smicanja u okviru ploče, ne bude veći od proračunske nosivosti pri podužnom smicanju. Proračunska nosivost pri podužnom smicanju betonske ploče se određuje u skladu sa EN 1992-1-1. Ovaj proračun se zasniva na modelu rešetke, tj. betonska ploča se posmatra kao sistem kosih (dijagonalnih) pritisnutih betonskih štapova kombinovan sa zategama koje predstavlja poprečna zategnuta armatura. Gubitak nosivosti (lom) betonske ploče nastaje ako dođe do tečenja (loma) u armaturi ili ako dođe do drobljenja betona u pritisnutim štapovima. U betonskoj ploči se obezbeđuje adekvatna površina poprečne armature koja će da prenese smičuće napone iz moždanika i obezbedi da ne dođe do prevremenog loma u betonu.