Displacement Calculation for Service Loads of Reinforced Concrete Beams and Slabs Using Physically Non-Linear Analysis

Antonio Renato Bicelli, Pedro Cantor, Rafael Wong, Mário Rui Arruda

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This paper aims to use non-linear physical analysis to calculate the displacement of beams and slabs in a cracked state. This study uses the commercial software SAP2000 to perform a numerical analysis using the finite element formulation, applying the multi-layer method. Initially, a parametric study was carried out to evaluate the vertical displacement for service loads of reinforced concrete beams and slabs using different spans, support conditions and geometry. In order to validate the finite element model, the study compared displacement values for linear analysis using Bares tables. Subsequently, simplified methods of displacement calculation in the long term are applied, using an abacus from Comité Euro-International du Béton (CEB). These values are then compared with the physically non-linear analysis in the long-term cracked state with SAP2000. Two structural codes were used in the numerical and analytical methods, Regulamento de Estruturas de Betão Armado e Pré-Esforçado (REBAP) and Eurocode 2 (EC2), to evaluate their differences in deformation control. Therefore, the main goal is to establish comparisons between the two methods of analysis in order to show that non-linear finite element modelling provides values that are lower than the analytical calculation, thus allowing greater economy in the design of structural reinforced concrete elements. In addition, it can be noted that EC2 has some inconsistencies in the design of simply supported slabs, requiring a greater thickness than a flat square slab and that indirect deformation for REBAP is underestimated for beams and, in some cases, for slabs.

Original languageEnglish
Article number8307
Number of pages24
Issue number23
Publication statusPublished - Dec 2022


  • cracked state
  • displacement calculation
  • multi-layer method
  • physically non-linear analysis


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