BASIC STABILITY CALCULATION OF THIN-WALLED REINFORCED CONCRETE BEAMS

Abstract

This paper develops a physically grounded methodology for evaluating the lateral-torsional buckling stability of thin-walled reinforced concrete beams an energy-based approach to stiffness degradation. The relevance of this study is driven by the specific structural behavior of elements with high height-to-width ratios (h/b > 5), where conventional strength verification according proves insufficient due to the risk of sudden lateral-torsional instability occurring prior to the exhaustion of material load-bearing capacity. The authors propose an algorithm for determining the critical moment based on the Prandtl-Vlasov theory, adapted for reinforced concrete composites. A key feature of this methodology is the accounting for plastic flexural stiffness through the deformation parameters and effective torsional stiffness based on the energy invariant principle. For the first time within an engineering framework, the crack localization coefficient is calculated in detail considering the dowel action of the reinforcement. This allows for the inclusion of the longitudinal bars' contribution to the lateral stability of the element after the initiation of normal cracks. It was established that for ultra-slender sections (b = 30 mm), the introduction of a reduction factor kred»0.56 is critical to account integrally for concrete creep and inevitable initial geometric imperfections. Special attention is paid to the analysis of the energy balance in the vicinity of a normal crack, where the continuity of torque transfer is ensured through the dowel action of the reinforcement. It was found that the critical length of the stiffness degradation zone lcr is a function of the physico-mechanical properties of concrete and the geometric parameters of the reinforcement, allowing for a differentiated approach to evaluating the stability of beams with varying reinforcement ratios. The obtained results confirm that neglecting spatial deformability calculations can lead to non-conservative estimates of load-bearing capacity, particularly for elements with high compressive stresses in the concrete. Numerical case studies of cantilever beams confirmed a shift in the failure mode from material crushing to lateral instability as the reinforcement ratio increases. The proposed methodology provides engineers with a robust tool to establish the safe operational limits for thin-walled elements without the need for complex non-linear finite element analysis.