Keywords: equivalent flat plates, periodically variable sections, stress transmission, composite floors, equivalent uniform beams.

This paper studies models of composite floors consisting of a steel sheet and a concrete slab on top of the sheet which have a profiled section in one of the two main directions. One challenge in the analysis, either static or dynamic, of such floors is to deal with the variable cross-sections. A full three-dimensional model of a real composite floor can be too time consuming and may not be necessary if an equivalent flat floor model can be used.

A method is proposed to establish the equivalence between a uniform beam and a beam with variable sections. An equivalent uniform beam and a beam with variable sections are considered to experience the same rotational deformation when they are subjected to the same pair of bending moments at their two ends. This leads to the expressions of the equivalent second moment of area of a uniform beam to that of a beam with discretely varying sections or a continuously varying sections respectively

To examine the stress variation between two different and adjacent cross-sections, a concave and convex unit is modelled for a detailed stress analysis. The comparison of the maximum displacements and the fundamental natural frequencies of a beam with periodically variable sections and its equivalent uniform beam shows very good agreement under different loading and boundary conditions.

Then the equivalence is applied to the modelling of a profiled plate and a profiled plate with steel sheeting. A three-dimensional solid model and its equivalent flat plate model of the profiled plates produce similar results.

As an application, the equivalent flat plate model is used to represent a multi-panel composite floor (45m x 21m) in a steel framed building as constructed in the Cardington Laboratory. The predicted natural frequencies and static stiffness compare reasonably well with the available frequency and stiffness measurements while the analysis becomes simple and effective.

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