Comparative Analysis of Grid Theory with Flexible Supports with Numerical Models in Building Slabs

There exist various methods for computing reactions in reinforced concrete slabs in buildings, but the most precise approaches involve solving differential equations that are challenging to apply, rendering their practical application infeasible. Consequently, practical methods adopt simplifications in the equations to ensure their practicality. The use of rigid supports is one of the commonly adopted simplifications in calculating displacements and support reactions. The grid theory assumes that the supports are rigid, which does not accurately represent reality in design practice since the beams supporting the slab deform, often causing considerable displacements in the calculation. In this study, a new extension to the grid theory is proposed, which considers the flexibility of slab supports in calculating displacements and support reactions. An analysis of bending moments and displacements of slabs was carried out on 20 numerical models with support flexibility and different boundary conditions. The analyzed loading was static and uniformly distributed, and the boundary conditions adopted in the analytical model included both simply supported and fixed slabs. The numerical analysis showed that the proposed model, which considers the flexibility of slab supports, produced results that were in good agreement with the numerical analysis.