An overview of some characteristic numerical models for concrete

On the basis of experimental testing of behaviour of concrete, reinforced concrete and prestressed concrete structures, various phenomena were observed; in the first place, highly non-linear and inelastic behaviour of concrete. Since it is hard to include all the phenomena and changes that occur in concrete, a large number of numerical models for concrete were developed to describe different states of the problem under consideration, with the tendency to include in these analyses the changes that are dominant in the observed problem. This paper will give a brief overview of some characteristic numerical models for concrete, developed so far, with a short overview of their advantages and disadvantages, i.e. possibilities and limitations. The models were classified depending on the formulation of the constitutive laws. Models were chosen to demonstrate the diversity of modelling and specifics of their application

Roger Owen – Eminent Scientist and Extraordinary Friend

With profound sadness we heard that Professor Roger Owen passed away on Monday 13th January 2020. He was eminent scientist, researcher, lecturer, teacher, mentor, engineer, and above all beloved husband and father, good man and reliable, altruistic, genial and extraordinary friend. With this review we want to describe, after conventional curriculum vitae, his connections with researchers and professors from the University of Split, Faculty of Civil Engineering, Architecture and Geodesy, as well as some common projects

EKSPERIMENTALNA ANALIZA ZAJEDNIČKOG DJELOVANJA SAVIJANJA, POSMIKA I TORZIJE DRVENIH NOSAČA

Wood is an anisotropic material, i.e., it is composed of fibres that correspond better to normal stresses in the longitudinal direction or in the direction of fibres and poorly to stresses perpendicular to the fibres and to the longitudinal shear stresses. In practical situations it is better to avoid these stresses, although that is often very difficult. Because of this, the analysis of different interactions between shear and normal stresses perpendicular to the fibres is necessary. In this paper an experimental analysis of interaction of stresses from torsion and bending caused by an eccentric shear force was performed. The results are compared in a simple and practical way with the calculated values and the values from a linear numerical model. The paper analysed shear stresses parallel to the fibres and normal stresses perpendicular to the fibres and the results are shown numerically and by a force/displacement diagrams.Drvo je anizotropan materijal, odnosno, sastoji se od skupa vlakana koja bolje podnose normalna naprezanja u svom uzdužnom pravcu ili pravcu vlakana, a slabije okomito na pravac vlakana te posmično u uzdužnom pravcu. U praktičnim slučajevima potrebno je izbjegavati pojavu ovih nepovoljnih naprezanja, iako je to u pravilu teško izvedivo. Iz tog razloga, neizbježne su analize interakcija između svih posmičnih te normalnih naprezanja. U radu je eksperimentalno analizirana interakcija naprezanja od torzije i savijanja kroz djelovanje ekscentričnom poprečnom silom, a rezultati su na jednostavan i praktičan način uspoređivani s računskim vrijednostima te vrijednostima dobivenim linearnim numeričkim modelom. Naglasak je stavljen na posmična naprezanja paralelno vlaknima i normalna naprezanja okomito na vlakna, a rezultati su prikazani tablicom i dijagramima sila/pomak

Dinamička analogija za dokazivanje konvergencije rubnih zadaća ploča

This paper describes a procedure for proving the convergence and for estimating the numerical solution error of boundary value problems . The procedure is based on the transformation of a discrete boundary value problem in to an equivalent discrete dynamic eigenproblem. Discrete dynamic eigenproblem has physical meaning in convergence analysis because a mass represents the measure of domain discretization. The convergence and accuracy of numerical solution of boundary value problem depend on the convergence of discrete dynamic eigenproblem spectrum. The developed procedure is relatively simple, easy to perform ; in this paper it is used to evaluate the convergence and accuracy of numerical solution of the thin plate bending problem. The plate is discretized with four-node finite elements. One translational and two rotational degrees of freedom , which are independent of each other, are associated to each node of the plate. The shape func tions satisfy a homogenous differential equation of plate bending . The developed procedure gives the greatest global error which can appear for a chosen discretization . The performance of the proposed method is illustrated by the solution procedure of two examples: a simply supported square thin plate and a cantilever square thin plate.U ovome radu se opisuje postupak dokazivanja konvergencije i ocjene točnosti numeričkog rješenja rubnih zadaća. Postupak se temelji na transformaciji diskretne rubne zadaće u ekvivalentnu diskretnu dinamičku vlastitu zadaću. Diskretna dinamička vlastita zadaća im a fizikalno značenje jer masa predstavlja mjeru diskretizacije područja. Konvergencija i točnost numeričkog rješenja rubne zadaće ovisi o konvergenciji diskretne dinamičke vlastite zadaće. Razvijeni postupak je relativno jednostavan i lako izvediv , a u ovome radu je upotrijebljen za analizu konvergenci je i točnosti numeričkog rješenja tankih ploča. Ploča je diskretizirana s četvero čvornim konačnim elementima. Svakom čvoru ploče su pridruženi jedan translacijski i dva rotacijska stupnja slobode koji su međusobno neovisni . Bazne funkcije zadovoljavaju homogenu diferencijalnu jednadžbu savijanja ploča. Razvijenim postupkom dobivamo najveću moguću pogrešku koja se može pojaviti kod određene diskretizacije. Učinkovitost predloženog postupka je pri kazana u postupku rješavanja dva primjera: slobodno oslonjene kvadratne tanke ploče i ukliještene kvadratne tanke ploče

Comparison of two-dimensional and threedimensional analysis of reinforced and prestressed concrete structures

This paper presents the comparison of two-dimensional and three-dimensional analysis of the reinforced and prestressed concrete structures. The curved prestressing tendons and reinforcing bars, which are modelled by onedimensional finite element, are embedded into adequate two-dimensional and three-dimensional finite elements. The influence of the prestressing tendons on the concrete is modelled by distributed normal and tangential forces along the tendons and two concentrated forces at the anchors. The computation of the post-tensioned prestressed structures is organized in three phases: before, during and after prestressing of the tendons. A few numerical examples are given to compare the results obtained by these two analyses

Wave properties of wind actions on structures

In this paper the wave properties of wind actions on structures analyzed on a single degree of freedom (SDOF) system are shown. The wave character of the action was examined by windows-wavelet analysis on several different measured data of wind actions. The constant and then the fluctuating action extracted from the wind force were analyzed by the wavelet transform. Fluctuating component of the wind action is represented by a harmonic function. The wavelet transform of wind action shows that the intensity of harmonic component decreases linearly with the number of cycles which implies that the resonance is not innate to wind action. All data of the wind action are obtained by measurements on SDOF oscillator. Time resolution varied from 0.01 to 0.00001 seconds. Significantly, the characteristics of wind action observed from the data on intensity of the averaging wind force are strongly connected with the length of the averaging wind force. The overall data of dynamic action show that the influence of wind is significantly higher for shorter periods of averaging. In this paper the term resonant spectra is used and the dynamic factor is based on them. The empirical relations for the value of the constant and the first harmonious component of the action are suggested. All results are compared with the classical spectra of the elastic force of SDOF system

Mathematical formulation of the space curvature of the tendon in the PC structures

This paper presents the mathematical formulation of the space curvature of the prestressing tendon in the nonlinear analysis of prestressed concrete (PC) structures. The nonlinear behaviour of prestressed tendons is described by the one dimensional elasto-viscoplastic model. The tendon element geometry is described by the second order space function which is determined by its projections. These elements make it possible to model arbitrarily curved prestressing tendons in space, thus they can be determined independently of the three-dimensional (3D) finite element mesh. This is very important in the case when the prestressing tendon can not be located in a plane. The transfer of prestressing force on the concrete was modelled numerically. The developed model makes it possible to compute prestressing structures in phases: before prestressing, during prestressing and after prestressing. The described models are implemented in the computer programme for a 3D analysis of the prestressed concrete structures where the structures are discretized by three-dimensional finite elements with an embedded one-dimensional element of prestressed tendons

Validation of the developed triaxial nonlinear material model for concrete

This paper presents a validation of newly developed material model for concrete. The model is based on a combination of elasto-fractureplastic formulation, considering all dominant influences in concrete: yielding in compression, fracture in tension, softening and hardening. The modified Mohr-Coulomb criterion for dominant compression stresses, the modified Rankine criterion for dominant tension stresses, exponential softening and the function for hardening are considered in this model. All constitutive equations are defined by elementary material parameters (Young’s modulus of elasticity, Poisson’s coefficient, maximal uniaxial tensile and compression stresses, the coefficient of tensile correction, maximal tensile and maximal compression strains). A multi-surface presentation of the model is implemented which permits the rapid convergence of the mathematical procedure. The model uses return-mapping algorithm for the integration of the constitutive equations with associated and non-associated flow rules. Considering triaxial stress state, the paper presents the structural validation of a developed numerical model, which is incorporated into computer programme PRECON3D, illustrated on four examples, both experimental and numerical, taken from the literature: (i) four point bending of normalstrength and high-strength reinforced concrete beams with four different constant-zone lengths and two different reinforcement ratios; (ii) three point bending of reinforced concrete beam; (iii) prestressed concrete beam; (iv) prestressed Π-beam

Numerical testing of prestressed reinforced concrete structures with PRECON3D material model

Some time ago, we have developed a computer programme called PRECON3D for a three-dimensional non-linear analysis of reinforced and prestressed concrete structures where the structures are discretized by three-dimensional finite elements with an embedded one-dimensional element of reinforcement and prestressed tendons. Non-linear triaxial behaviour of concrete is involved in the material model, including all dominant influences in concrete (yielding in compression, fracture in tension, softening and hardening). The non-linear behaviour of reinforcement and prestressed tendons is described by the one-dimensional elasto-viscoplastic model. The tendon element geometry is described by the second order space function which is determined by its projections. Programme PRECON3D can be used very simple because the material model is defined by elementary material parameters (Young’s modulus, Poisson’s coefficient, maximal uniaxial tensile and compression stresses, coefficient of tensile correction, maximal tensile and maximal compression strains). Furthermore, the developed model makes it possible to compute prestressing structures in phases including losses caused by friction and the losses which result from the concrete deformation. In the described analyses we have performed the numerical testing of the prestressed concrete girders from the engineering practice (prefabricated element), which were reinforced with various cross-sectional area of prestressed reinforcement and various tendons geometry. During analyses next parameters were observed: deflections of the girders, concrete stresses and strains at the top and bottom of the girders, compressive and tensile strains of the reinforcement. The paper presents the structural validation of developed numerical model, PRECON3D, on a few examples and the obtained results are compared with the known numerical and experimental ones. It is concluded that the presented programme and numerical model can be effectively used in nonlinear analysis of reinforced and prestressed concrete structures