Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 177

ε ccu

d

ε ccu

A

ε ccu

c = d

B

0.75A

0.75B

Eq. 7.1

ε ccu

c

Circular Column

d

0.75 C C

ε sy

0.003

d

D

0.9D

M n / D A g f ´ c

ε s > ε sy

FIGURE 7.5 Simplified interaction diagrams for FRP-confined concrete circular column.

d. Connecting Point C and the pure bending point with a straight line
indicating no strength enhancement in the tension-controlled region.

3. Drawing the interaction diagram reduced by the relevant resistance (ϕ) fac-
tors per ACI 318-11 (2011) for circular and rectangular cross sections.

4. Using Equations (7.1) and (7.2) to cap the reduced interaction diagram when
the eccentricity is less than or equal to 0.1 h.

7.3.1 i nteraCtion D iagramS For C irCular C olumnS
Since the derivation of the force and moment equations for points B and C requires
the integration of some involved integrands with trigonometric functions due to the
continuous variation of the section width, these expressions will be evaluated numer-
ically by dividing the cross section into 100 layers parallel to the centroidal x -axis.
The addition of the longitudinal steel bar contribution will have to be accounted for
numerically anyway. Accordingly, the formulation of this procedure is incorporated
into an Excel spreadsheet as follows.

7.3.1.1 Contribution of Concrete
The following computation steps are taken in general:

1. The thickness of each layer is

D

t =

(7.32)

lr

100