The Threshold for Under-Reinforced Concrete Sections Proposed by ACI 318, EC 2 and BS 8110

Abstract

The ductile behavior of reinforced concrete (RC) cross-sections has always been desirable for building codes and standards. However, the threshold to distinguish ductile and brittle behavior of RC cross-sections proposed by building codes has yet to be evaluated [1-4]. This behavior mainly depends on the type of RC cross-section whether it is under- or over-reinforced. While there is not much research conducted on general comparison of the three codes of ACI 318-19, BS 8110 and Eurocode 2 (EC2) regarding design and analysis of RC structural elements, the specific detailed investigation on the threshold for under- and over-reinforced RC cross-sections has yet to be conducted. This article aims to determine the most accurate threshold used to distinguish under- and over-reinforced RC cross-sections amongst the three aforesaid codes by scrutinizing fundamentals and assumptions. A RC cross-section with strain distribution diagram over the section for the three statuses of under-reinforced, balanced, and over-reinforced cross-section is discussed in this research. A theoretical approach is adopted to compare the threshold through the depth of neutral axis of balanced steel concrete cross-sections. The method of calculation is associated with the maximum tensile strain of longitudinal steel bars at the cross-section. The depth of neutral axis is considered to be equal to effective depth of the cross-section multiple by a coefficient. This coefficient is the focus of the comparison. The coefficient is directly given as a number by BS 8110 and EC2. In ACI 318-19 there is no direct value given for the threshold, which leaves no choice other than the accurate calculation of depth of neutral axis for the balanced reinforcement which is in form of an equation. The article concludes that ACI 318-19 provides the most accurate threshold to classify under- and over-reinforced RC cross-sections while EC2 provides the least accurate threshold. The accuracy of threshold proposed by BS 8110 is between those of ACI318-19 and EC2. The scope of this research is confined to singly- and doubly-reinforced concrete cross-sections with any shape using ordinary concrete.