Generalized plasticity model for nonlinear space frame analysis

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..

Snabdevenost važnijih tipova zemljišta Srbije osnovnim alkalnim elementima Ca, Mg, K i Na

In this paper results are presented of agrochemical and mineralogical analyses of 14 types of important soils in Serbia (Vojvodina and Central Serbia) and total content and availability of base alkali elements (Ca, Mg Na, K) are determined. Total element content was as follows: Ca 2.22%; K 1.77%; Na 0.85% and Mg 0.61%. Total content of alkali metals in the soils investigated and their variations within and between the soil types, is in very good/close correlation with contents of primary and secondary minerals as well as their rates of weathering. Taking in account the average availabilities the most abundant is calcium with 947 mg/100 g, whilst the averages of the other elements (Mg, K and Na) are quite similar and are about of 40 mg/100 g of soil. The results obtained have shown that the soils investigated are well to moderate provided with K, Ca and Mg and that their deficit could not be expected in plant nutrition, apart for some plants/cultures in the case of magnesium due to occasionally higher Ca/Mg and K/Mg ratios.U ovom radu je ispitivano 100 reprezentativnih uzoraka 14 tipova zemljišta Srbije (Vojvodina, Šumadija i Severno Pomoravlje) u pogledu ukupnog i pristupačnog sadržaja osnovnih alkalnih metala (Ca, Mg, K i Na). Takođe je prikazan i prosečan mineraloški sastav ispitivanih zemljišta. Nađeni su sledeći srednji ukupni sadržaji ispitivanih elemenata: Ca - 2,25%; K - 1,77% Na - 0,85% i Mg - 0,61%. Ukupni sadržaji ispitivanih alkalnih metala u našim zemljištima i njihova vapipanja između i unutar zemljišnih tipova u uskoj su vezi sa zastupljenošću određenih primarnih i sekundarnih minerala i njihovom otpornošću na raspadanje. Prema srednjim vrednostima za pristupačne sadržaje najviše ima kalcijuma (947 mg/100 g), a srednji sadržaji za ostale baze (Mg K i Na) su vrlo slični i kreću ce oko 40 mg/100 g. Dobijeni rezultati pokazuju da su ispitivana zemljišta dobro i srednje obezbeđena K, Ca i Mg i da se ne mogu očekivati njihovi deficiti za ishranu biljaka, osim za neke kulture u slučaju magnezijuma, zbog ponekad suviše povišenih odnosa Ca/Mg i K/Mg

The availability of base elements (Ca, Mg, Na, K) in some important soil types in Serbia

In this paper results are presented of agrochemical and mineralogical analyses of 14 types of important soils in Serbia (Vojvodina and Central Serbia) and total content and availability of base alkali elements (Ca, Mg Na, K) are determined. Total element content was as follows: Ca 2.22%; K 1.77%; Na 0.85% and Mg 0.61%. Total content of alkali metals in the soils investigated and their variations within and between the soil types, is in very good/close correlation with contents of primary and secondary minerals as well as their rates of weathering. Taking in account the average availabilities the most abundant is calcium with 947 mg/100 g, whilst the averages of the other elements (Mg, K and Na) are quite similar and are about of 40 mg/100 g of soil. The results obtained have shown that the soils investigated are well to moderate provided with K, Ca and Mg and that their deficit could not be expected in plant nutrition, apart for some plants/cultures in the case of magnesium due to occasionally higher Ca/Mg and K/Mg ratios

Nosivost na savijanje spregnutih greda sa neduktilnim moždanicima

In this paper, the methods for determination of the bending resistance of composite beams with partial shear connection and nonductile shear connectors, according to Eurocode 4, are studied. The Eurocode 4 predicts the use of two calculation methods: the method based on the nonlinear theory and the simplified method that assume linear relation between elastic and plastic bending moment resistance. The algorithm for the nonlinear section analysis is explained in detail. Using the own computer program for nonlinear section analysis, for one composite beam cross section, the differences in results obtained by these two proposed methods are discussed.Zbornik radova Građevinskog fakultet

Comparison of different methods for viscoelastic analysis of composite beams

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

EXACT AND APPROXIMATE METHODS OF ANALYSIS OF STEEL-CONCRETE COMPOSITE BEAMS

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 compare

Formulacija fiber elementa prilikom nelinearne analize ramova

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

Continuous Composite Steel Concrete Beams with Partial Shear Connection

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

Fiber konačni element u nelinearnoj analizi kvadratnih spregnutih CFT stubova

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

Comparative analysis of reinforced concrete and CFT columns in buildings

Zbornik radova Građevinskog fakultet