1026 / JOURNAL OF STRUCTURAL ENGINEERING / SEPTEMBER 2000 ANALYSIS AND DESIGN OF LOW-RISE MASONRY AND CONCRETE WALLS RETROFITTED USING STEEL STRIPS By Mustafa Taghdi, 1 Michel Bruneau, 2 and Murat Saatcioglu 3 ABSTRACT: Indeterminate truss models are proposed for the analysis of low-rise walls retrofitted using a special system of vertical and diagonal steel strips. An equilibrium diagram is also presented to calculate the ultimate strength of walls based on a lower bound theorem of plasticity. Step-by-step analyses were conducted to establish force-displacement relationships of walls that compared well with those obtained experimentally. A simple retrofit design procedure is formulated and illustrated using a numerical example. FIG. 1. Simplified Truss Model INTRODUCTION Experimental results presented in a companion paper (Taghdi et al. 2000) demonstrate that the seismic strength and ductility of low-rise walls can be significantly enhanced when retrofitted using a specially detailed system of vertical and di- agonal steel strips. This was shown to be equally true for un- reinforced masonry, reinforced masonry, and reinforced con- crete walls. The mechanism of load resistance in these retrofitted walls is illustrated in this paper through analyses, using simple models that are suitable for an office environment design. Truss models are developed to investigate the force-dis- placement relationship of walls retrofitted by steel strips. An equilibrium diagram is presented to calculate the ultimate strength of walls based on a lower bound approach of the theory of plasticity. All models presented here consider the walls to be subjected to an incrementally increasing static lat- eral loads. Although this approach does not recognize the po- tential stiffness and strength degradation that would arise un- der cyclic loading, it can be used to draw the envelope of maximum strengths reached at given displacements throughout the hysteretic response. This backbone of the hysteretic curve provides valuable information for design purposes. Analytical results obtained using the models presented in this paper compare well with those obtained experimentally. A retrofit design procedure is then formulated and illustrated using a numerical example. SIMPLE TRUSS MODEL The simplest model considered here consists of an indeter- minate truss having five members, as shown in Fig. 1. Based on the direction of loading shown in the figure, members can be labeled following a numbering scheme. Member 1 is a ten- sion steel member that consists of the vertical steel strip along one edge and the vertical reinforcing bars that may be present at the same location. The member in the plane of the floor or roof [or the top beam present in each of the wall specimens 1 Postdoctoral Res. Fellow, Ottawa Carleton Earthquake Engrg. Res. Ctr., Dept. of Civ. Engrg., Univ. of Ottawa, ON, Canada K1N 6N5. E-mail: mtaghdi@uottawa.ca 2 Deputy Dir., Multidisciplinary Ctr., Earthquake Engrg. Res., and Prof., 130 Ketter Hall, Dept. of Civ., Struct., and Envir. Engrg., State Univ. of New York, Buffalo, NY 14260. E-mail: bruneau@acsu.buffalo.edu 3 Prof., Ottawa Carleton Earthquake Engrg. Res. Ctr., Dept. of Civ. Engrg., Univ. of Ottawa, ON, Canada K1N 6N5. E-mail: murat@eng. uottawa.ca Note. Associate Editor: Walter H. Gerstle. Discussion open until Feb- ruary 1, 2001. Separate discussions should be submitted for the individual papers in this symposium. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on July 6, 1999. This paper is part of the Journal of Structural Engineering, Vol. 126, No. 9, September, 2000. ASCE, ISSN 0733-9445/00/0009- 1026–1032/$8.00 + $.50 per page. Paper No. 21326. tested by Taghdi et al. (2000)] is designated as Member 2. The vertical strut in compression, at the other end of the wall, is referred to as Member 3, and its stiffness and strength are defined by considering both the steel strips and a concrete/ masonry column of width taken as one-tenth of the wall length. The diagonal strips in tension and compression con- stitute Members 4 and 5, respectively. Member 5 consists of a concrete/masonry strut with an effective width equal to the diagonal steel strip width. Obviously, Members 1 and 2, as well as 4 and 5, would be respectively swapped if horizontal loading was considered to act in the reverse direction. A series of elastic push-over analyses is performed using the above truss model. The stiffness and strength of each mem- ber is reduced gradually, as appropriate in the step-by-step analysis, to account for degradation due to concrete crushing. The first analysis is conducted to determine all member forces (F 1 , F 2 , F 3 , F 4 , and F 5 ) and the corresponding lateral deflection  in terms of the total applied force V. The lateral load and the corresponding deflection at first yield are labeled as V y1 and  y1 , respectively. Usually, the com- pression capacity of Members 3 and 5 is sufficiently large to ensure that tension yielding of Members 1 and 4 occurs first. However, a number of factors must be considered to determine which of those two tension member yields first. These include the type of wall material (concrete or masonry), the area and yield strength of the steel strips, the wall reinforcement layout, and the lateral restraint provided to the longitudinal reinforcing bars by the bolts of the vertical steel strips. Note that, for Member 1, if the steel strip yield strength is different from that of the reinforcing bars, an additional anal- ysis step is warranted using the same statically indeterminate truss, but discounting those members that have already