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Abstract: Failure of concrete under compression results in a localized region of softened material subject to high strain. The paper attempts to find out the error of the numerical method for the mechanical analysis of planar reinforced-concrete beams subject to temperature increase simulating typical fire conditions at high temperatures, if the strain softening in concrete is considered, while employing continuous finite elements. The results are confronted with the formulation using constant-strain crack band elements in the localized regions combined with the continuous elements everywhere else. The width of the crack band is, in principle, temperature and stress–state dependent. In the paper we assume the crack band elements of constant width throughout the analysis, which may be a valid assumption at high temperatures, as indicated by some data given in literature. Results of the analyses of a two-story, two-bay reinforced concrete frame, designed strictly in accordance with the European standards, and subject to self weight, dead and service loads and, additionally, to the increasing fire-like thermal load are presented. The use of solely continuous finite elements, yet accounting for strain softening of material wherever it occurs, yields spatially oscillating results for strains around the localized region. This sometimes yields a totally false result or loss of convergence of the global Newton method. The width of the localized band tends to zero with the growing density of the finite-element mesh, with the results being highly mesh sensitive. The finite-element meshes where constant-strain crack band elements in the localized regions are combined with the continuous elements everywhere else yield, on the other hand, a computationally stable and accurate post-instability response for a wide range of crack-band element widths. Its critical point is, however, obtaining a reliable estimate of the width of the crack band element at high temperatures. This requires extensive experimental testing with hot concrete in compression. [Copyright &y& Elsevier]

Abstract: We have derived a one-dimensional mathematical model and a numerical procedure for the non-linear static analysis of pre-tensioned concrete planar beams, which intends to describe quantitatively the global behaviour as well as some local phenomena in the beam, such as the tangential slip and the traction between the tendon and concrete, with accuracy sufficient for engineering design. The advantage of such a model is its extreme computational efficiency compared to the two- and three-dimensional formulations. A shear-stiff, kinematically exact planar beam theory is used to model each component of the beam. The bending moment in the tendon is neglected. Cracking of concrete is accounted for using the smeared crack concept. Softening of material, and the related localisation of deformations, is in the numerical solution resolved by the combined use of the arc-length method and the constant strain crack band element, whose dimension is related to the fracture energy of concrete in tension. The tangential slip between the tendon and concrete is fully accounted for, yet the normal separation is not allowed. The model enables us to analyse the variation of slip and the tangential traction on tendons as well as softening of concrete in both tension and compression along the beam axis and in time. The validity of the present one-dimensional model is verified on two pre-stressed simply supported beams previously experimentally and computationally studied in literature (Rabczuk and Eibl, 2004 [2]; Rabczuk et al., 2005 [18]; Rabczuk and Belytschko, 2006 [20]). It is found out that the results of the present one-dimensional model are well in keeping with the experimental and numerical results from literature. Recalling the extreme computational efficiency of the present formulation compared to the 2D and 3D formulations it is concluded that the proposed method of analysis could be very convenient for engineering design. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

A new finite element model for the analysis of the restrained curved reinforced-concrete (RC) beams simultaneously exposed to mechanical and extreme fire-like thermal loading is presented. The moisture and heat transfer through concrete is considered to be uncoupled with the deformation and the shape change of the beam. The hygro–thermo-mechanical analysis is performed in two separate steps, the first one starting with the coupled moisture and heat transfer analysis, and the next one continuing with the mechanical stress–strain analysis. A novel, strain-based finite element formulation of the curved planar beam has been developed for the mechanical part of the fire analysis. The unilateral soil–concrete beam contact is modelled with the set of discrete non-linear springs situated at nodes of the finite element mesh at the soil–beam contact. The model is verified by the numerical results of a full three-dimensional solid finite element model created in the LUSAS finite element analysis software and they are in good agreement with the present solution. In the subsequent parametric studies, the effects of material parameters of soil dictating the unilateral restraining forces to the beam, the load magnitude and the boundary conditions on the behaviour of the curved reinforced-concrete RC beam exposed to fire are investigated. [ABSTRACT FROM AUTHOR]