This paper theoretically and experimentally investigates the semi‐empirical formulas recommended by Eurocode 2 (EC2), fib Model Code 2010 (MC2010), and Eurocode 2 with the German National Annex (DIN) for calculating crack widths in reinforced concrete. It is shown that the formulas can be derived from the principles for the idealized behavior of RC ties. However, instead of explicitly solving the resulting differential equations, the use of simplifications leads to inconsistent formulas. An experimental study was carried out involving the testing of eight RC ties to discover the modeling uncertainty of the formulas. It was found that EC2 substantially overestimated the crack widths for the RC ties. MC2010 and DIN seemed to predict the crack widths better, but gave rather a large number of nonconservative crack width predictions. These experimental results, combined with the theoretical study, suggest that a more consistent calculation model should be formulated by explicitly solving the resulting differential equation.

This paper formulates an analytical calculation model for predicting the cracking behavior of reinforced concrete ties to provide 6 more consistent crack width calculation methods for large-scale concrete structures in which large bar diameters and covers are used. The 7 calculation model was derived based on the physical behavior of reinforced concrete ties reported from experiments and finite-element 8 analyses in the literature. The derivations led to a second order differential equation for the slip that accounts for the three-dimensional 9 effects of internal cracking by using a proper bond-slip law. The second order differential equation for the slip was solved completely ana-10 lytically, resulting in a closed-form solution in the case of lightly loaded members and in a non-closed-form solution in the case of heavily 11 loaded members. Finally, the paper provides a solution strategy to facilitate a practical and applicable method for predicting the complete 12 cracking response. Comparison with experimental and finite-element results in the literature demonstrated the ability of the calculation model 13 to predict crack widths and crack spacing consistently and on the conservative side regardless of the bar diameter and cover.

The cracking behaviour of reinforced concrete (RC) ties are investigated by conducting virtual experiments using nonlinear finite element analysis (NLFEA). The assumptions in the model are verified by benchmarking the classical experiments of Bresler and Bertero (1968) and Yannopoulos (1989), which shows good agreement in comparison of steel strains, development of crack widths and crack spacing. Furthermore, virtual experiments on four difference RC ties show that the size of the cover and not the bar diameter governs the crack spacing and thus implicitly the crack width. An increase of the bar diameter has a beneficial effect in reducing the steel stress and the associated steel strains, which in turn reduces the crack width. Finally, a single bond-slip curve is sufficient in describing the average bond transfer of an arbitrary RC tie.

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