The first method is an energy based method in which the ratio of total energy of the

structural system to the elastic energy is used to calculate an energy ductility factor (see

Fig 2-3). This was first introduced by Jeong (1994) that proposed the following

expression for determining the energy ductility factor (uE):


 PE = 0.5 Etot +1 (2-2)
 Eela )

where Etot is the total energy under the load-displacement curve and Eea is the portion of

the total energy which is considered elastic.

 PI

 Pu -------------- --- -----------------
 Pi ------------ ---------------- --------
 0.8 Pu -----------

 0.75 Pi -------- ---










 0 6y or 6c du 6


Figure 2-2. Schematic for ductility factor component definitions

 Many researchers have used this method to characterize the ductility of FRP

reinforced concrete structures. Grace and Sayed (1998) tested bridge models prestressed

with CFRP tendons and used the energy method to determine ductility. However, they

had to measure the amount of inelastic energy of their bridge models. They did that by

subjecting their bridge models to loading and unloading cycles near 90% of their ultimate