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Shakedown analysis is a powerful and efficient tool for calculating the safety factors of structures under variable and repeated external quasi-static loads, that can prevent structures from incremental and alternative plasticity collapses. RC slabs in practical engineering applications are usually under long-tern variable and cyclic loads, but their fatigue behavior was rarely reported in the literature, particularly for those governed by the Nielsen yield condition. In this paper, dual static and kinematic shakedown formulations based on displacement-finite elements and conic programming are developed. The resulting optimization problems, characterized by a huge number of variables, are effectively solved. A wide range of practical RC slabs with diverse geometries, loading and boundary conditions are investigated, precisely capturing the collapse modes in terms localized plastic dissipation energy and presenting moment distribution at fatigue state. Strengthening strategies are performed in regions with localized plastic dissipation energy, showing that the load-bearing capacity of such slabs increases significantly while incremental and alternative collapse modes are prevented. • Dual shakedown analysis of reinforced concrete slabs is presented for the first time. • Finite element formulations for pseudo-static and kinematic shakedown analysis with conic programming are described. • Shakedown load factors and collapse modes of various practical RC slabs are reported. • Strengthening strategies are performed and optimal reinforcement layouts are obtained. [ABSTRACT FROM AUTHOR]

Highlights: [•] GBT formulation to perform first-order elastoplastic analyses of thin-walled members. [•] Applicable to members exhibiting arbitrary local/distortional/global deformation patterns. [•] Numerical results concerning the three steel beams presented and discussed in detail. [•] Mechanical insight and numerical efficiency provided by the GBT modal nature illustrated. [•] Accuracy of the GBT-based results assessed through comparisons with SFEA values. [ABSTRACT FROM AUTHOR]