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.