Keywords: finite elements, flat slab, reinforced-concrete, shell element, moments, column.

The technique used to model the supporting columns in flat slabs was found to have a great impact on the negative design moments in the column region. One column modelling technique used by some designers is evaluated in this study. In this technique, the part of the slab inside the perimeter of the column section is stiffened to simulate the rigid behavior of this area and a vertical frame element is placed at the center of the column to simulate the axial and rotational stiffness of the column. This modelling technique was termed in this study as the stiffened slab model. The results were compared to values produced by a model representing columns as three-dimensional solid elements. Choosing the three-dimensional solid model as a basis for evaluation was validated using previous experimental results [1]. The finite element three-dimensional solid model produced negative moments in the slab very close to the experimental results when shear reinforcement was present. When no shear reinforcement was provided, the experimental results where about 25% lower than the finite elements model.

The ratio between the stiffness of the stiffened part to the stiffness of the slab (the stiffness ratio) was varied to study its effect on the results of the stiffened slab model. The stiffness ratio was varied from a minimum of 1 (i.e. un-stiffened) to a maximum of 1000. Modelling the column using a frame element located at the centre of the column without stiffening the slab (the un-stiffened model) produced average negative moments that reached a value 36% lower than those obtained using the three-dimensional solid model. The discrepancy between the un-stiffened model and the three-dimensional solid model was more pronounced at the edge column and in cases where adjacent spans were different in length or subjected to different load values. By increasing the stiffness ratio, the value of the average moment converged to a value that is in most cases closer to that obtained using the three-dimensional solid model. Based on this result, it is recommended that a stiffness ratio of 100 or higher is used for the stiffened slab model. Using the thick Mindlin-Reissner formulation [2] for the shell elements in the stiffened area produced a negative moment distribution that is closer to the three-dimensional solid model than the thin Kirchhoff formulation [2]. Therefore, it is recommended that shell elements based on the Mindlin-Reissner formulation be used for the stiffened part of the slab over the column section.

1

A.G. Sherif, "Behaviour of Reinforced Concrete Flat Slabs", Ph.D. Dissertation, The University of Calgary, Calgary, Alberta, Canada, 1996.

2

R.L. Taylor, J.C. Simo, "Bending and Membrane Elements for Analysis of Thick and Thin Shells", Proceedings of the NUMEETA Conference, Swansea, Wales, 1985.

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