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CivilComp Proceedings
ISSN 17593433 CCP: 86
PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 163
Analysis of ThreeDimensional Reinforced Concrete Beams with Hybrid Geometry L. Svoboda and D. Rypl
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic L. Svoboda, D. Rypl, "Analysis of ThreeDimensional Reinforced Concrete Beams with Hybrid Geometry", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 163, 2007. doi:10.4203/ccp.86.163
Keywords: reinforced concrete beam, eightnode solid element, rigid arm, hanging node, slave degree of freedom, dynamic relaxation.
Summary
In this paper the use of the microplane model in an analysis of reinforced concrete beams is
discussed. The microplane model [1], is generally
a constitutive, fully threedimensional model
capable of describing concrete in its very complex behaviour. Thanks to its qualities, the
microplane model is convenient for the simulation of experimental results and
a comprehensive analysis of various concrete structures. In particular, the authors have
focused on reinforced concrete (RC) frames and have proposed an adaptive analysis of RC frames with
microplane joints.
It is based on a geometrical model of frame compound of onedimensional beams and threedimensional elements (bricks). The
microplane model is applied only on bricks, that will be used for segments of the frame with
significant nonlinear strains. The rest of the frame will be modelled using beam elements with
fibered crosssections, which partly allows simulation of nonlinear behaviour of material.
To obtain an appropriate model of the threedimensional segment of a RC beam the authors implemented into a finite element code a linear eightnode solid element with rotational degrees of freedom [2]. This element has an advantage over a common linear eightnode solid element in that it has six degrees of freedom per node. So it can be combined with both truss elements (three DOFs per node) and beam elements (six DOFs per node). Because the solution time of a commonly used nonlinear static analysis is rather large the authors also employed explicit dynamic relaxation analysis. The adaptive analysis employes drefinement which combines a onedimensional and threedimensional geometrical model of RC beams. This approach leads to a complicated finite element mesh consisting of onedimensional (beam and truss) and threedimensional (brick) elements and brings two problems  generation of the mesh and connection of all finite elements into one compact unit. To satisfy the first one it was necessary to develop a special preprocessor capable to generate such a composite finite element mesh. In order to achieve a true response it was necessary to provide a suitable connection of onedimensional and threedimensional elements. There are two types of this connection. The first connection is between onedimensional and threedimensional models of the RC beam (segment). The second one is realized inside a threedimensional segment between onedimensional elements (representing bars of reinforcement) and threedimensional elements (representing concrete). To provide these connections the rigid arm node and hanging nodes was implemented in the finite element code. Both nodes were based on a socalled slave degree of freedom. All above mentioned elements and computational tools and schemes was tested for a fixedended beam loaded with a midspan point load. References
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