Estimating fixed-end rotations of reinforced concrete members at yielding and ultimate

Strain penetration of the longitudinal reinforcement in reinforced concrete (RC) members at the joints and/or footings results in fixed-end rotations at the member ends. Several experimental studies have shown that fixed-end rotations caused by strain penetration contribute significantly (up to 50 %) to the total displacement capacity of RC members. Hence, accurate determination of these fixed-end rotations at yielding and ultimate limit states is of primary importance when defining the structural response of RC members. The purpose of this study is to present the theoretical background to and the assumptions made for the most common relationships found in the literature for determining strain penetration-induced fixed-end rotations at yielding and ultimate. Furthermore, new simple relationships are proposed on the basis of realistic and mechanically based assumptions. Comparisons between the existing and proposed relationships demonstrate the limitations of the former. Finally, the proposed relationships are calibrated against experimental measurements of RC column specimens subjected to cyclic loading with recorded fixed-end rotations due to strain penetration in the adjacent joints and/or footings.