Simplified approach to predict the flexural strength of self-centering masonry walls Reza Hassanli a , Mohamed A. ElGawady b,⇑ , Julie E. Mills c a School of Natural and Built Environments, University of South Australia, SA, Australia b Civil, Arch. and Environmental Eng. Dept., Missouri University S&T, Rolla, MO, United States c Head of School of Natural and Built Environments, University of South Australia, SA, Australia article info Article history: Received 26 November 2016 Revised 9 January 2017 Accepted 23 March 2017 Available online 11 April 2017 Keywords: Masonry MSJC 2013 Shear strength Flexural strength Unbonded In-plane Post-tensioned wall abstract This paper develops a simplified design approach to predict the flexural strength of unbonded post- tensioned masonry walls. The accuracy of different flexural expressions was investigated according to experimental and finite element modelling results. Using an analytical model and considering the stress-strain relationships for unconfined and confined masonry, force displacement curves were devel- oped for eleven tested walls, with and without confinement plates. The developed force–displacement procedure was able to predict the lateral strength, stiffness and post-peak degradation of the behavior of the tested walls. Using a similar analytical procedure, a parametric study was performed to obtain the force-displacement response of walls with different features and to investigate the effect of different parameters including axial stress ratio, length, height and thickness of the wall, on the compression zone length. Multivariate regression analysis was performed to develop an empirical equation to estimate the compression zone length in unbonded post-tensioned walls. According to the results, the wall length and axial stress ratio were found to be the most significant factors affecting the compression zone length. Depending on the configuration of the wall, the compression zone length varied between 6.7% to 28% of the wall length. The proposed equation for compression zone length was then incorporated into the flexural analysis of post-tensioned masonry walls and validated against experimental results and finite element results. Comparing the prediction from Masonry Standards Joint Committee, MSJC (2013), and the proposed method reveals that ignoring the elongation of PT bars in strength prediction resulted in a considerable underestimation of the strength. Using the non-iterative proposed approach significantly improved the prediction. Crown Copyright Ó 2017 Published by Elsevier Ltd. All rights reserved. 1. Introduction Recent research has demonstrated that unbonded post- tensioned structural elements including concrete walls, concrete columns, and masonry walls can display high displacement levels while withstanding high levels of seismic loads. When an unbonded masonry wall (PT-MW) is subjected to a lateral in- plane load and the cracking moment is exceeded at the base of the wall, a single horizontal crack forms at the wall-foundation interface. The restoring nature of the post-tensioning (PT) force returns the wall back to its original vertical position and minimizes the residual displacement. This behavior is specifically favorable for structures which are designed for immediate occupancy perfor- mance levels. The rocking mechanism of PT-MWs results in plastic deformation concentrated at the toe of the wall which can be repaired with minimal cost [1–5]. To determine the in-plane flexural strength of an unbonded PT- MW, the level of stress developed in PT bars corresponding to the wall peak strength needs to be calculated. The stress developed in a PT bar is a function of the bar strain and hence the elongation of the bars. In bonded PT-MWs, the strain compatibility concept can be considered to determine the stress in the bars. For unbonded PT-MWs, the strain in the PT bar remains approximately constant along the length of the bar. Therefore, instead of the conventional strain compatibility equations used for strain calculations in struc- tural elements having bonded reinforcement, displacement com- patibility criteria need to be considered, in which the stress in the PT bars is a function of wall rotation and compression zone length. While the current approach of the Masonry Standards Joint Committee (MSJC 2013) [6] considers the stress increase in PT bars http://dx.doi.org/10.1016/j.engstruct.2017.03.050 0141-0296/Crown Copyright Ó 2017 Published by Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: reza.hassanli@unisa.edu.au (R. Hassanli), elgawadym@mst. edu (M.A. ElGawady), Julie.Mills@unisa.edu.au (J.E. Mills). Engineering Structures 142 (2017) 255–271 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct