This paper describes a new 2D flat shell element which deals with the nonlinear analysis of composite floor slabs, the main focus being the modelling of geometric orthotropy and material nonlinearities. In order to address geometric orthotropy, it has been necessary to modify the commonly applied Reissner-Mindlin hypothesis [1], such that different orientations are allowed for the slab normals in the cover and rib regions. This modification is incorporated in the proposed element through the use of additional hierarchic rib freedoms associated with relative extension and shear deformations at the bottom of the rib. Four variants of the proposed element are developed, each intended to represent a separate part of the composite slab. However, the details of only one variant element are presented, since it subsumes the other three variants.

The new shell element is formulated in such a manner that it can accommodate any number of steel and concrete material models of different levels of sophistication. A plasticity-based model for concrete cracking is developed in this work, the aim being to achieve reasonably realistic simulations whilst overcoming numerical problems often associated with the nonlinear concrete response. In this model, tensile cracking for a biaxial stress state is based on one of the principal stresses exceeding the tensile strength of concrete, subsequent to which softening behaviour is considered. The softening response is modelled by allowing incremental translation of the tensile `yield' surface according to a specified post- cracking softening modulus.

The developed method for composite floor slabs has been implemented in the nonlinear structural analysis program ADAPTIC [2]. Two example problems are analysed using ADAPTIC in order to illustrate the importance of the various parameters of the proposed flat shell formulation and the robustness of the developed concrete model.

The first example is concerned with a simply supported composite slab subjected to a central concentrated load, where the objective is to establish the importance of the additional rib freedoms. It is clearly shown that the incorporation of these additional freedoms, and hence the use of the proposed modification of the Reissner- Mindlin hypothesis [1], improves significantly the accuracy of modelling composite floor slabs with flat shell elements. In the example considered, errors of 15% and 30 original Reissner-Mindlin hypothesis is adopted instead of its proposed modification.

The second example illustrates the applicability of the proposed shell element not only to composite slabs but also to reinforced concrete (R/C) slabs. Furthermore, it demonstrates the numerical robustness of the developed nonlinear material model for concrete, investigating in the process the influence of a variation in the post- cracking modulus of concrete softening on the response of a R/C slab with two different reinforcement levels. Regardless of the reinforcement level, the overall response at large deformations is shown to be independent of the softening modulus, as long as a non-zero value for the modulus is employed. For a lightly reinforced slab, a considerable difference is found between predictions based on perfectly plastic and plastic softening behaviours for concrete, as expected. This emphasises the importance of accounting for the reduction in the concrete tensile strength subsequent to cracking. Furthermore, it is noted that, despite the considerable nonlinearity in the predicted response, convergence to the equilibrium solutions is achieved with a conventional incremental/iterative solution procedure based on the Newton-Raphson method, thus highlighting the robustness of the developed concrete model.

The proposed nonlinear structural analysis method for composite floor slabs is currently being developed, as part of an ongoing EPSRC research project (GR/L96523), to include the following enhancements:

• geometric nonlinearities including the effects of large displacements,
• nonlinear biaxial compressive response of concrete,
• elastic super-element for modelling the composite slab with a coarse mesh,
• practical nonlinear adaptivity, and
• effect of elevated temperatures on the nonlinear biaxial response of concrete.

Upon completion of the method development, it will provide a much needed tool for the assessment of composite floor slabs subject to fire and earthquake conditions.

1

Zienkiewicz, O.C., Taylor, R.L., "The Finite Element Method", 4th ed., Vol. 2, McGraw Hill, 1991.

2

Izzuddin, B.A., "Nonlinear Dynamic Analysis of Framed Structures", PhD thesis, Department of Civil Engineering, Imperial College, University of London, 1991.

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