Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 180

7.3.2 i interaCtion D iagramS For C irCular C olumnS
u Sing kDot C olumn e xpert
As shown in the previous section, the effective confining pressure ( f l ) in the case of
the two eccentric points (Point B and Point C) is lower than that of pure axial com-
pression (Point A), where the section is fully confined. In KDOT Column Expert
software, this issue of partial confinement is modeled more consistently throughout
the range of eccentricities. While the case of pure axial compression has zero eccen-
tricity and full confinement, the pure bending case has infinite eccentricity and no
confinement at all. The confined strength in between the two extremes ( f cc and f c ) is
mapped gradually as a function of the eccentricity:

1 1

f = f + f

cc

e
D

cc

D
e

c

(7.47)

1 + 1 +

where f cc is the eccentric confined strength at eccentricity ( e / D ), and the equation
satisfies the two extremes ( f cc and f c ). Figure 7.6 illustrates three different sections
under concentric load, a combination of axial load and bending moment, and pure
bending moment: The highlighted fiber in the three cases has the same strain.
However, the size of the compression zone does play an important role in predicting
the stress, which is different in the three cases of Figure 7.6. Hence, it is more realis-
tic to relate the eccentric strength and ductility to the level of confinement utilization
and compression zone size represented in circular columns by the eccentricity, as
seen in Figure 7.7.

7.3.2.1 Eccentric Model Based on Lam and Teng Equ ati ons
The ultimate eccentric or partially confined strength f cc is determined from
Equation (7.47) and is paired with the ultimate eccentric or partially confined strain

FIGURE 7.6 Effect of compression zone size or eccentricity on concrete strength.