determine ductility factors without having to experimentally measure the slope. It should

also be noted that using the initial and secondary slopes of the displacement diagram is

not as simple as it might be at first though. Typically there are no distinct slopes which

mean that a decision on which slopes to use has to be made which is subjective and

dependent upon the person that makes the decision. This can generate inconsistent

results.

 The second method that has been proposed is a deformation based method. The

ductility factor, also referred to as J-factor, is the product of a strength factor and a

deformability factor. The strength factor takes into account the increase in the moment or

load capacity while the deformability factor takes into account the increase in either the

curvature or the displacement of the structure relative to a specific load level. This

specific load level has been defined as the load at which the concrete compressive strain

is equal to 0.001 (Fig. 2-4) (Theriault and Benmokrane 1998; Wang and Belarbi 2005) or

the cracking load (Zou 2003) or the service load (Newhook et al. 2002).

 Based on the diagram in Fig. 2-4 the load factor (LF) and deformability factor (DF)

are the following:

 Po
 LF = (2-3)
 P0 001

where P, is the ultimate load and Po.0oo is the load at a concrete compressive strain equal

to 0.001.


 DF = (2-4)
 0001

where 6, is the ultimate load and 60.00oo is the load at a concrete compressive strain equal

to 0.001.