M. Saje

University of Ljubljana, Faculty of Civil and Geodetic Engineering, Faculty Member

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Prof. Dr. Moustafa Moharam

Sohag University

Michele Brun

University of Cagliari

Benjamin Wilson

Aalto University

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ISET Nabeul

Viorel Chihaia

Institute of Physical Chemistry "Ilie Murgulescu"

Joel Taylor

Norwegian Institute for Cultural Heritage Research

Dr. James Doughari Hamuel

Federal University of Technology, Yola

Shayne Rivers

West Dean College

C. Vázquez

Universidad Complutense de Madrid

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Papers by M. Saje

Exact buckling load of a restrained RC column

Structural Engineering and Mechanics, Oct 20, 2007

Theoretical foundation for the buckling load determination in reinforced concrete columns is desc... more Theoretical foundation for the buckling load determination in reinforced concrete columns is described and analytical solutions for buckling loads of the Euler-type straight reinforced concrete columns given. The buckling analysis of the limited set of restrained reinforced concrete columns is also included, and some conclusions regarding effects of material non-linearity and restrain stiffhesses on the buckling loads and the buckling lengths are presented. It is shown that the material non-linearity has a substantial effect on the buckling load of the restrained reinforced concrete columns. By contrast, the steel/concrete area ratio and the layout of reinforcing bars are less important. The influence on the effective buckling length is small.

Inelastic buckling load of a locally weakened reinforced concrete column

Engineering Structures, 2012

This paper presents a mathematical model for investigating the buckling of geometrically perfect,... more This paper presents a mathematical model for investigating the buckling of geometrically perfect, materially and kinematically non-linear, locally weakened reinforced concrete columns. The present analytical model is based on the linearized stability theory and is capable of predicting exact buckling loads. Based on a systematic parametric analysis, the effects of the weakness location, its magnitude, the number of weaknesses and the material non-linearity of concrete and reinforcing steel on buckling loads have been investigated. The results are given in terms of graphs showing in detail that the material non-linearity of concrete and reinforcing steel and the local weaknesses have a significant influence on the buckling load.

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A note on relationship between fixed-pole and moving-pole approaches in static and dynamic analysis of non-linear spatial beam structures

Fixed-pole approach in the non-linear analysis of beam structures offers a different and promisin... more Fixed-pole approach in the non-linear analysis of beam structures offers a different and promising framework for development of new element types with particular potential in the area of conservative time integrators. The finite elements formulated using this approach, however, utilise non-standard degrees of freedom which makes them difficult to combine with standard finite elements in existing codes. A modified approach which combines the benefits of the fixed-pole approach with the use of standard kinematic unknowns from the existing (moving-pole) approaches is presented in this work along with a family of solution procedures for static analysis of geometrically non-linear spatial beam structures. Such a hybrid formulation opens a number of questions which are specifically addressed.

Numerical modelling of behaviour of reinforced concrete columns in fire and comparison with Eurocode 2

International Journal of Solids and Structures, 2005

The paper describes a two-step finite element formulation for the thermo-mechanical non-linear an... more The paper describes a two-step finite element formulation for the thermo-mechanical non-linear analysis of the behaviour of the reinforced concrete columns in fire. In the first step, the distributions of the temperature over the cross-section during fire are determined. In the next step, the mechanical analysis is made in which these distributions are used as the temperature loads. The analysis employs our new strain-based planar geometrically exact and materially non-linear beam finite elements to model the column. The results are compared with the measurements of the full-scale test on columns in fire and with the results of the European building code EC 2. The resistance times of the present method and the test were close. It is also noted that the building code EC 2 might be non-conservative in the estimation of the resistance time.

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Stability of C‐Shaped Spring

Journal of Engineering Mechanics, 1987

The C-shaped spring is a planar, very flexible elastic beam, the center axis of which is, in an u... more

On a virtual work consistent three-dimensional Reissner–Simo beam formulation using the quaternion algebra

Acta Mechanica, 2013

In the paper, we present the Reissner-Simo beam theory in which the rotations are represented by ... more In the paper, we present the Reissner-Simo beam theory in which the rotations are represented by quaternions. From the generalized virtual work principle, where the unity constraint of the rotational quaternion is properly considered and the consistent energy complements of the rotational quaternions are employed, we derive the weak kinematic equations in the quaternion-based description. These equations are then employed in the extended virtual work principle to obtain the consistent governing equations of the three-dimensional beam in terms of the quaternion algebra. The quaternion moment equilibrium equation is analyzed, discussed, and interpreted. In numerical implementation, the standard Galerkin discretization is used to obtain the quaternion-based finite-element formulation. Various examples prove the suitability of the formulation.

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The wavelet-based theory of spatial naturally curved and twisted linear beams

Computational Mechanics, 2008

DRUGG-Digitalni repozitorij UL FGG http://drugg.fgg.uni-lj.si/ Ta članek je avtorjeva zadnja rece... more

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The effects of different strain contributions on the response of RC beams in fire

Engineering Structures, 2007

A two-step formulation, consisting of separate thermal and mechanical analyses, is presented for ... more A two-step formulation, consisting of separate thermal and mechanical analyses, is presented for the thermo-mechanical analysis of reinforced concrete planar frames subject to fire conditions. The heating and the cooling phases are considered. Standard planar, four-node quadrilater finite elements are employed in the non-linear time-dependent thermal analysis of cross-sections, while the recently proposed strainbased planar beam finite elements are used in the non-linear mechanical analysis of the frame [Bratina S, Saje M, Planinc I. On materially and geometrically non-linear analysis of reinforced concrete planar frames. International Journal of Solids and Structures 2004;41:7181-7207]. The formulation includes both exact geometric and material non-linearities, and considers the temperature dependence of thermal and material parameters, the plastic, creep and thermal strains in concrete and steel, the transient strain in concrete, and the strain localization as a consequence of softening of material at high temperatures. A so called 'constant strain element' is introduced to resolve numerically the loss of uniqueness of strain measures at the point of localization. The formulation is validated by comparing some of the present numerically predicted results with the data, measured in experiments. Although the present model is essentially 1D stress-strain model, and is thus simple in terms of the number of degrees of freedom used and ignores transfer of water in concrete during heating, the comparisons with the measured data are found to be satisfactory. In particular, the agreement of the fire resistance times and critical deflections between the predicted and the experimental values was found very satisfactory. In contrast, a disagreement was found in distributions of temperature over the beam cross-sections. The results make it possible to draw several conclusions concerning behaviour of structures in fire. In particular, it is established that the consideration of creep and transient strains in concrete has little effect on the fire resistance time of statically determinate beams under bending or unconstrained centrically loaded columns; their effect on displacements is, however, remarkable.

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On convergence of nonconforming convex quadrilateral finite elements AGQ6

Computer Methods in Applied Mechanics and Engineering, 2010

The 4-node quadrilateral membrane elements AGQ6-I and II are two novel incompatible models formul... more The 4-node quadrilateral membrane elements AGQ6-I and II are two novel incompatible models formulated by the Quadrilateral Area Coordinate Method (QACM). In this paper, the sufficient conditions for their convergence are established. It is further shown theoretically that the convergence in the energy norm is linear, and the convergence in the L 2 norm is quadratic provided that certain geometric conditions are met requiring asymptotically parallelograms meshes to be used. The necessity of conditions is also discussed. The results of numerical examples completely confirm the theoretical findings.

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Integrating rotation from angular velocity

Advances in Engineering Software, 2011

The integration of the rotation from a given angular velocity is often required in practice. The ... more The integration of the rotation from a given angular velocity is often required in practice. The present paper explores how the choice of the parametrization of rotation, when employed in conjuction with different numerical time-integration schemes, effects the accuracy and the computational efficiency. Three rotation parametrizations-the rotational vector, the Argyris tangential vector and the rotational quaternion-are combined with three different numerical time-integration schemes, including classical explicit Runge-Kutta method and the novel midpoint rule proposed here. The key result of the study is the assessment of the integration errors of various parametrization-integration method combinations. In order to assess the errors, we choose a time-dependent function corresponding to a rotational vector, and derive the related exact time-dependent angular velocity. This is then employed in the numerical solution as the data. The resulting numerically integrated approximate rotations are compared with the analytical solution. A novel global solution error norm for discrete solutions given by a set of values at chosen time-points is employed. Several characteristic angular velocity functions, resulting in small, finite and fast oscillating rotations are studied.

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Exact buckling load of a restrained RC column

Structural Engineering and Mechanics, 2007

The Influence of Non-Linear Material Properties on the Global Convergence in the Finite-Element Analysis of Spatial Beams

Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing

Abstract This paper shows the influence of the manner the non-linear constitutive equations in th... more

A direct computation of critical points: the application of det KT

Zeitschrift für angewandte Mathematik und Mechanik, 1998

Résumé/Abstract The paper presents a quadratically convergent algorithm for the computation of st... more

Analytical solution of linear elastic beams cracked in flexure and strengthened with side plates

Journal of Composite Materials, 2012

ABSTRACT A new mathematical model and its analytical solution for the analysis of the stress-stra... more ABSTRACT A new mathematical model and its analytical solution for the analysis of the stress-strain state of a linear elastic beam cracked in flexure and strengthened with plates on its lateral sides is presented. Both the longitudinal and the transversal interactions at the side plate/beam interface are considered. Linear behaviour of the contact connection is assumed. The method is based upon the linearised planar beam theory of Reissner. The weakening of the beam induced by the flexural crack is modelled conventionally as a rotational spring. The suitability of the theory is demonstrated in a case presentation involving the comparison between analytical results of the present beam (one-dimensional) model, the experiments and the numerical results of a full three-dimensional solid model created in the LUSAS finite element analysis software. An excellent agreement between the results is observed and the proposed formulation is found to be accurate and reliable. Finally, the solution is employed in an engineering analysis, discussing the effects of the material and the geometric properties of selected characteristic cases of the observed beams on the static and kinematic quantities, including the boundary conditions of the side plates, the longitudinal and the transversal stiffness of the connection, the size of the cracks, the span of the beam, and the length and the stiffness of the side plates. For the cracked cantilever beam, a substantial effect of any of these parameters is found. In contrast, for the cracked two-span continuous beam, only the effect of the stiffness of the side plates and the effect of the length of the beam spans are noticeable.

Approximate directional derivatives and quadratically convergent algorithms

Zeitschrift für angewandte Mathematik und Mechanik, 2001

Résumé/Abstract The response curve of a structure in the load-displacement space exhibits stable ... more

Approximate directional derivatives and quadratically convergent algorithms

Zeitschrift für angewandte Mathematik und Mechanik, 2001

Résumé/Abstract The response curve of a structure in the load-displacement space exhibits stable ... more

Contributions to the Discussion on the Computation of Displacements, Consolidation and Earth Pressures of Soils Exhibiting Non-Linear and Viscous Deformability

Acta Geotechnica, 1974

The article contains contributions from four authors: Gaberc,A refers to a computer program for t... more The article contains contributions from four authors: Gaberc,A refers to a computer program for the analysis of the consolidation of non-linear and viscous layered soils in linear strain conditions and presents the results of an application of this program. Saje,M presents the fundamentals of numerical stress and strain computation by the finite element method in plane strain conditions for cases when the stress-strain relations can be expressed in terms of octahedral values; the experimentally obtained families of stress versus strain charts are approximated by spline functions. Majes,B presents the results of the application of such a computer program to the computation of stresses and displacements in a layer of limited thickness subjected to a surface load. Vidmar,S presents the results of a similar program which facilitates the analysis of the increase of passive earth pressures with increasing movements of a rigid retaining plate. The resulting earth pressures have been compar...

An out-of-plane mechanical response of a planar steel frame in fire

Contributions to the Discussion on the Computation of Displacements, Consolidation and Earth Pressures of Soils Exhibiting Non-Linear and Viscous Deformability

Acta Geotechnica, 1974

An out-of-plane mechanical response of a planar steel frame in fire

Exact buckling load of a restrained RC column

Structural Engineering and Mechanics, Oct 20, 2007

Inelastic buckling load of a locally weakened reinforced concrete column

Engineering Structures, 2012

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A note on relationship between fixed-pole and moving-pole approaches in static and dynamic analysis of non-linear spatial beam structures

Numerical modelling of behaviour of reinforced concrete columns in fire and comparison with Eurocode 2

International Journal of Solids and Structures, 2005

Download

Stability of C‐Shaped Spring

Journal of Engineering Mechanics, 1987

The C-shaped spring is a planar, very flexible elastic beam, the center axis of which is, in an u... more

On a virtual work consistent three-dimensional Reissner–Simo beam formulation using the quaternion algebra

Acta Mechanica, 2013

Download

The wavelet-based theory of spatial naturally curved and twisted linear beams

Computational Mechanics, 2008

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The effects of different strain contributions on the response of RC beams in fire

Engineering Structures, 2007

Download

On convergence of nonconforming convex quadrilateral finite elements AGQ6

Computer Methods in Applied Mechanics and Engineering, 2010

Download

Integrating rotation from angular velocity

Advances in Engineering Software, 2011

Download

Exact buckling load of a restrained RC column

Structural Engineering and Mechanics, 2007

The Influence of Non-Linear Material Properties on the Global Convergence in the Finite-Element Analysis of Spatial Beams

Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing

Abstract This paper shows the influence of the manner the non-linear constitutive equations in th... more

A direct computation of critical points: the application of det KT

Zeitschrift für angewandte Mathematik und Mechanik, 1998

Résumé/Abstract The paper presents a quadratically convergent algorithm for the computation of st... more

Analytical solution of linear elastic beams cracked in flexure and strengthened with side plates

Journal of Composite Materials, 2012

Approximate directional derivatives and quadratically convergent algorithms

Zeitschrift für angewandte Mathematik und Mechanik, 2001

Résumé/Abstract The response curve of a structure in the load-displacement space exhibits stable ... more

Approximate directional derivatives and quadratically convergent algorithms

Zeitschrift für angewandte Mathematik und Mechanik, 2001

Résumé/Abstract The response curve of a structure in the load-displacement space exhibits stable ... more

Contributions to the Discussion on the Computation of Displacements, Consolidation and Earth Pressures of Soils Exhibiting Non-Linear and Viscous Deformability

Acta Geotechnica, 1974

An out-of-plane mechanical response of a planar steel frame in fire

Contributions to the Discussion on the Computation of Displacements, Consolidation and Earth Pressures of Soils Exhibiting Non-Linear and Viscous Deformability

Acta Geotechnica, 1974

An out-of-plane mechanical response of a planar steel frame in fire

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