Issue 39

J. Navrátil et alii, Frattura ed Integrità Strutturale, 39 (2017) 72-87; DOI: 10.3221/IGF-ESIS.39.09 73 This situation resulted in a collaboration of F.J. Aschwanden, Swiss prefab company with high technological competence and innovation, and IDEA RS, Czech software company, which develops software for structural analysis and design of civil engineering structures and their members. The objective of common development project was to develop a software program for the calculation of reinforced concrete, concrete/concrete and steel/concrete composite columns subjected to various loadings and exposed to normal temperature or to fire conditions. Graphical user interface was developed by F.J. Aschwanden together with HOST module, which controls the sequence of individual analyses, and which mediates data transfer between the input and calculation cores for thermal analysis (TA) and for geometrical and material non-linearity (NLA). Both calculation cores are part of IDEA StatiCa software and were developed by IDEA RS. IDEA Open Model (IOM) has been created as an open interface to guarantee an effective interaction between HOST and IDEA StatiCa. T HERMAL ANALYSIS onlinear 2-dimensional steady state and transient analysis for heat transfer across column cross-section has been developed. Quadrilateral and triangular finite elements are used. Each finite element may have different nonlinear material properties dependent on the temperature. Initial temperature is defined in each node of mesh. Ambient temperature is given as the function of the time on boundary of cross-section. Convection and radiation coefficients are constant. No humidity transfer is taken into account, and no spalling of the surface is considered. The results are the temperatures across cross-section (in nodes of mesh) in selected time steps. G EOMETRICAL AND MATERIAL NON - LINEARITY rismatic beam element with general eccentricity is used - Euler formulation (without shear deformations included). The load can be applied in nodes or may be uniformly distributed. Cross section of general shape can have material nonlinear properties dependent on current temperature in each point. Initial strain is considered across the cross-section for any beam element (strain, curvature). Nonlinear stress across the element is solved in two Gauss integration points. Reinforcement bars are modeled as the points for stress analysis, therefore different mesh appears for TA and NLA. Corotational beam formulation is used. Deformation of beam element is split into the local deformation of beam and global deformation beam as rigid body. Multi load step iteration solver uses Finite Element Analysis in combination with Newton iteration, which can determine load carrying capacity without the possibility of post-critical behavior. This is not detrimental to the main objective – the column resistance. V ERIFICATION he methods used for both TA and NLA have been verified in a number of benchmarks. Selected benchmark examples are analyzed and documented in this report. Reinforced concrete column First example is reinforced concrete column according to [2], which was also chosen by the RILEM Technical Committee TC 114 as one of the benchmark problems for testing the computational models and computer programs for reinforced concrete structures. The column of rectangular cross-section 150 mm × 200 mm and length 2.25 m is loaded by eccentric compressive axial force, see Fig. 1. The eccentricity of axial force F is e = 15 mm, reinforcement 4 × ϕ 12 mm (A s = 4 × 113 mm 2 ). Position of bars (measured from the centre) x i = ± 55 mm, y i = ± 80 mm. Material properties of concrete is described by the stress-strain relationship for non-linear analysis given by EN 1992-1-1 [4], provision 3.1.5 with following parameters: f cm = 38.3 MPa, E cm = 33.6 GPa, ߝ c1 = 2.3 ‰, ߝ cu1 = 3.5 ‰. Resulting stress-strain diagram for concrete used for the analysis is illustrated in Fig. 2. It is worth noticing that horizontal branches are added to code stress-strain diagrams in order to maintain numerical stability of the calculation in IDEA software. N P T