Deflection calculations of reinforced concrete slabs

Regarding serviceability, a particular attention must be provided to ensure that non-structural elements are not damaged by the building deflections. The construction steps are analyzed in order to properly assess the total deflections of such non-structural elements after their installations. In GSE™ software, the construction steps are represented by load combinations for the dead weight, the sustained dead weight and the live loads. Other parameters, required by the various standards may be edited by the end user.

The deflections of concrete slabs are composed of: immediate deflections and time-dependent deflections. The immediate deflections are calculated for the selected load combinations. The shrinkage and creep phenomenon are time-dependent effects causing deflections over long periods of time. The overall deflections of the building is a combination of both the immediate and time-dependent deflections.

The immediate cracked deflection calculations require an iterative analysis procedure where the loads are applied progressively. The initial finite element stiffness is calculated using the concrete isotropic elastic properties. As the loading intensity increases, the flexural efforts in the slabs also increase. Thus, cracks may form near high flexural effort areas. At those locations, the slab sectional inertias change and the concept of effective inertia I_e is used. The effective inertia is calculated according to the uncracked inertia I_g and the fully cracked inertia I_cr. A well-known equation to calculate the effective inertia I_e is presented below:

The shell finite elements effective inertias Ie in both principal reinforcement directions (I_ex & I_ey) are calculated and the shell elements stiffness are modified, thus requiring an orthotropic shell finite element formulation.