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