models have been refined using data from concrete that is confined by FRP composite

materials that their amount and properties produce such behavior. Cases with lower grade

material or smaller amounts of FRP composites are scarce and have not been used to

demonstrate the applicability of the available models.

 Ductility Factors

 Two ductility factors are usually used to measure the ductility of structural

components. The displacement ductility factor (uj) is defined as the ratio of the ultimate

displacement (6,) over the displacement at first yield (6y).


 a (4-1)


 The second factor is the curvature ductility factor (up) defined as the ratio of the

ultimate curvature (0,) over the curvature at first yield (0y).


 / 0A Y (4-2)


 The definition of ultimate and yield displacements or curvatures is simple when the

behavior is elasto-plastic. Definition of these parameters is more complicated when the

behavior is not elasto-plastic. Usually the behavior of reinforced concrete is not perfectly

elasto-plastic. Therefore, the need for a consistent definition of the ultimate and yield

displacements or curvatures was realized. Researchers have proposed definitions of

ultimate and yield displacement and curvature as well as instructions on how to calculate

them.

 The ultimate displacement (or curvature) has been defined as the displacement (or

curvature) at which the lateral load in the descending portion of the load-displacement

curve is not less than 80% of the maximum load, P,, (Priestley and Park 1987; Zahn, et