Structural Health Monitoring (SHM) is a non-destructive evaluation tool that assesses the functionality of structural systems that are used in the civil, mechanical and aerospace engineering practices. A much desirable objective of a SHM system is to provide a continuous monitoring service at a minimal cost with ability to identify problems even in inaccessible structural components. In this dissertation, several such approaches that utilize the measured dynamic response of structural systems are presented to detect, locate, and quantify the damages that are likely to occur in structures. In this study, the structural damage is identified as a reduction in the stiffness characteristics of the structural elements. The primary focus of this study is on the utilization of measured dynamic strains for damage identification in the framed structures which are composed of interconnected beam elements. Although linear accelerations, being more convenient to measure, are commonly used in most SHM practices, herein the strains being more sensitive to elemental damage are considered. Two different approaches are investigated and proposed to identify the structural element stiffness properties. Both approaches are mode-based, requiring first the identification of system modes from the measured strain responses followed by the identification of the element stiffness coefficients. The first approach utilizes the Eigen equation of the finite element model of the structure, while the second approach utilizes the changes caused by the damage in the structural curvature flexibilities. To reduce size of the system which is primarily determined by the number of sensors deployed for the dynamic data collection, measurement sensitivity-based sensor selection criterion is observed to be effective and thus used. The mean square values of the measurements with respect to the stiffness coefficients of the structural elements are used as the effective measures of the measurement sensitivities at different sensor locations. Numerical simulations are used to evaluate the proposed identification approaches as well as to validate the sensitivity-based optimal sensor deployment approach.