Experimental and theoretical investigation of crack width calculation methods for RC ties

Abstract

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.

Analytical Calculation Model for Predicting Cracking Behavior of Reinforced Concrete Ties

“…12. Comparison of crack widths predicted (in specimens with lengths similar to crack spacing predicted in Table 2) with crack widths reported in F12:2 experiments: (a) CEOS.fr (2016); and (b) Tan et al (2018a).…”

“…Nevertheless, the maximum crack spacing predictions were conservative, and the crack widths predicted show relatively good agreement with the maximum crack widths measured. Tan et al (2018a) conducted experiments on eight quadratic RC ties identified as X-ϕ-c, where X represents the loading regime the RC tie was exposed to, either at the crack formation stage (F) or the stabilized cracking stage (S), while ϕ and c represent the rebar diameter and cover respectively. The rebar diameter was either 20 or 32 mm, while the cover was either 40 or 90 mm.…”

“…This led to similar crack spacing predictions for RC ties with similar reinforcement ratios but different covers, which contradicts the experimental data in Table 2. It is well known that the cover has a significant influence on crack spacing, and therefore crack widths, as reported by Broms (1968), Gergely andLutz (1968), Caldentey et al (2013), and Tan et al (2018a). One approach to taking the cover into account could be to use the provisions in EC2 and MC2010…”

“…in N400 (NPRA 2015), which state that the crack width calculation 33 methods should be in accordance with the provisions in Eurocode 2 34 (EC2) (CEN 2004). However, Tan et al (2018a) showed that the 35 crack width formulas recommended by EC2 and the fib Model Code 2010 (MC2010) ( fib 2013) predict the cracking behavior of structural elements inconsistently, particularly in cases of large covers and bar diameters. The analytical calculation model presented in this paper was based on solving the second order differential equation (SODE) for the slip when applying a bond-slip law first proposed by Eligehausen et al (1983) and later adopted by MC2010.…”

Identification of the Influence of Concrete Cover Thickness and ∅/ρ Parameter on Crack Spacing.

“…Among them, it can be found various types of data to identify the crack width governing parameters. However, with the advancement of material and geometrical properties of concrete and reinforcement, the authors have selected two recent axial tensile experiments mentioned in (Tan et al, 2018;Tan et al,2019) and (Rimkus and Gribniak, 2017), to identify the crack spacing governing parameters. The selected experiments consist of the RC ties with multiple reinforcement bars, which are more similar to the RC members in practice.…”