Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 197

It is important to note here that the eccentrically confined or partially confined
Lam and Teng as well as Mander models follow the same formats described for cir-
cular columns in Sections 7.3.2.1 and 7.3.2.2.

7.3.4.1 Numerical Procedure
The column cross section is divided into a finite number of thin filaments, as seen in
Figure 7.19a. The force and moment of each filament is calculated and stored. The bars
are treated as discrete objects in their actual locations (Figure 7.19b). The advantage
of that is to precisely calculate the internal forces induced by steel bars and concrete
filaments in the column cross section. The cross section analyzed is loaded incremen-
tally by maintaining a certain eccentricity between the axial force P and the resultant
moment M R . Since increasing the load and resultant moment causes the neutral axis and
centroid to vary nonlinearly, the generalized moment-of-area theorem is devised. The
method is developed using an incremental iterative analysis algorithm, a secant stiffness
approach, and proportional or radial loading. It is explained in the following steps:

1. Calculating the initial section properties:
Elastic axial rigidity EA :

∑ ∑

( )

EA = Ewt + E − EA (7.96)

ci i s c si

i i

where

E c = initial modulus of elasticity of the concrete
E s = initial modulus of elasticity of the steel bar

The depth of the elastic centroid position from the bottom fiber of the section
Y c and from the left side of the section X c

(a) (b)

FIGURE 7.19 Geometric properties of concrete filaments and steel rebars.