The introduction of an eccentricity in this system results in a geometric nonlinearity behavior. The midpoint of the diagonal member is connected to the corner joint using a brace member with a relatively low stiffness, thus forming a three-member bracing system in each braced panel. An iterative method of analysis has been developed to study the nonlinear load-deflection behavior of ODBS. The results indicate that the load-deflection behavior of this system follows a nonlinear stiffness-hardening pattern with two yielding points, which reflect the tensile failure of different bracings; the present study aims to investigate the efficiency of applying off-diagonal steel braces to reinforced concrete frames. To achieve this, three types of 2-story, 6-story, and 15-story structures without and with X-bracing and off-center bracing systems were modeled using SAP2000 software, and for micromodeling ANSYS software was used to achieve finite element results for an exact comparison between various retrofitting systems. The results showed that the structures strengthened by toggle bracing system revealed better behavior for low oscillation periods. Moreover, this type of bracing system is quite suitable for 10-story structures but not for higher ones. Its main problem, which requires special contrivances to solve, is the existence of a soft ground floor. 1. Introduction The earthquake catastrophe is one of the primary reasons for destruction of buildings, engineering infrastructures, and social systems [1]. Earthquake is known as the most common natural disaster since a large number of earthquakes of various magnitudes, which have caused serious damages, have been recorded in historical documents. According to these recorded earthquakes, the death toll is estimated to be around 800,000 people thus far [2]. Iran is located on the largest fold of earth surface which spreads throughout Saudi Arabia-Eurasia region with a surface area of 3,000,000？km2. Therefore, located on Alp-Himalaya chain, Iran is one of the most seismically active regions for which a lot of destructive earthquakes have been recorded thus far [3]. For example, a magnitude 6.6 earthquake hit southeast Iran on December 26, 2003, resulting in thousands of casualties and total destruction of Bam city. The total number of killed people was estimated to be 80,000. Such catastrophes happen not only because of the large magnitude of earthquakes but also as a result of nonstandard structures and weak buildings. However, reconstruction cost more than 10 billion dollars [4]. Appropriate design of structures
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