Among different approaches developed for structural damage detection, changes in the measured static response have shown promise for locating structural damage. In this paper, an analytical study of the relationship between damage characteristics (location and severity) and changes in displacement curvatures is presented. Then a parametric study is carried out on using changes in displacement curvatures in structural damage detection. The influence of many parameters are investigated and applied numerically to two examples; an overhanging beam (statically determinate structure) and a two-span continuous beam (statically indeterminate structure) with different damage characteristics. The numerical results clarify that the displacement curvature, has the characteristic of localization at the damaged region. Also, the obtained results show that the displacement curvature, derived from static response only, can accurately locate single and multiple damages with different damage characteristics for specific load case. The merits as well as the disadvantages of using displacement curvature in structural damage detection are also discussed.