Size Effect of Slender and Thick Reinforced Concrete Members Without Transverse Reinforcement Failing in Shear
Parameter Analyses and Code Predictions
Gabriel Ferreira Girotto (São Paulo State University)
Ana Laura Shiraga Araújo (São Paulo State University)
Lisiane Pereira Prado (São Paulo State University)
Eva Olivia Leontien Lantsoght (Luleå University of Technology, TU Delft - Civil Engineering & Geosciences, Universidad San Francisco de Quito)
Eloi Figueiredo (Lusofona University, Lisbon, Universidade de Lisboa)
Alex Micael Dantas de Sousa (São Paulo State University)
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Abstract
The shear strength of reinforced concrete members without transverse reinforcement remains a critical design issue, particularly for thick and slender structural members where pronounced size effects may significantly reduce the nominal shear strength. This study investigates the combined influence of member depth, concrete compressive strength, and longitudinal reinforcement ratio on the shear capacity of beams without stirrups through nonlinear finite element analyses (NLFEA). Beam depths ranging from 1000 mm to 4000 mm and concrete strengths between 30 MPa and 50 MPa were considered, together with variations in different longitudinal reinforcement ratios. The numerical results confirmed a clear deterministic size effect, with nominal shear stresses decreasing systematically as the effective depth increased, while the influence of compressive strength was found to be secondary. The depth-dependent response was successfully represented using Bažant’s energetic Size Effect Law (SEL Type II), and the calibrated parameters provided an excellent fit to the numerical database. Furthermore, the numerical predictions of shear capacity were compared with major design provisions, including ACI 318 (2014 and 2019), Eurocode 2 (EN 1992-1-1:2005 and EN 1992-1-1:2023), and fib Model Code approaches with levels of approximation (LoA) 1 and 2. The results highlight that older formulations such as ACI 318-2014 and EN 1992-1-1:2005 tend to be unconservative for deep members, whereas EN 1992-1-1:2023 offers significantly improved agreement with reduced scatter. Among the evaluated expressions, fib Model Code LoA1 was the most conservative, while LoA2 provided the most accurate overall predictions. The findings emphasize the importance of incorporating size-effect considerations in modern shear design models, particularly for large reinforced concrete structures such as bridge decks, thick slabs, and dam walls.
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