capacity. Others have also used the energy method to determine ductility factors for FRP
reinforced concrete structures without having to measure the amount of inelastic energy.
They estimated the elastic energy as the area under a straight line drawn from the point
representing failure load and having a slope equal to the average of the initial and
secondary slopes of the load-displacement diagram of the structure (Alsayed and
Alhozaimy 1998; Vijay and GangaRao 2001; Li and Wang 2002).
p S=[P 1S1+(P2-P1)S2]/P2
S3
P3 --------- ------- ---------------- --.---
S2
P2 -------- -----
PI --- Inelastic Elastic
P1 Elastic
Inelastic
Energy Energy
Energy
0 8or
Figure 2-3. Schematic for energy method ductility factor
Grace et al. (1998) however discovered that the average slope used to estimate the
elastic energy was different that the one measured from their tests for a number of their
specimens and proposed the introduction of four more parameters to eliminate the
differences between the experimentally measured slopes and the average slope based on
the initial and secondary slopes. This made the process complicated and also raised
questions about the reliability of this particular method and whether it can be used to