Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 176

( )

2 2 2

(7.29)

DCT = 4 − cos θ

τ=τ f

c

(7.30)

oct oct

7. Recalculating ( f cce ) using the following equation (same as Equation [7.23],
but solving for σ 3 ):

σ= σ+σ −τ

( )

2

1 2 2

4.5 − σ−σ 0.75 (7.31)

3 oct 1 2

2

8. If the value from Equation (7.31) matches that of the assumed initial value,
then convergence is achieved. Otherwise, the value from Equation (7.31) is
set as the initial value and steps 4 through 8 are repeated until convergence
is accomplished.

An Excel spreadsheet program automating this procedure may be obtained
electronically from the author.

7.3 ENHANCEMENT UNDER COMBINED AXIAL
COMPRESSION AND BENDING MOMENT
It has been shown by experiments (Chaallal and Shahawy 2000; Memon and Sheikh
2005; Darby et al. 2011) and by computations (ACI 440.2R-08) that the use of FRP
wrapping of circular, square, and slightly rectangular columns provides strength
improvement under the effect of axial compression and bending moment. To estab-
lish a procedure accounting for FRP confinement effects on the strength improve-
ment in wrapped columns, ACI 440.2R-08 takes the following considerations in
constructing the P-M interaction diagram:

1. The equations of Section 7.2.1 and 7.2.2 are applicable to finding the pure
compression point (Point A), see Figure 7.5.

2. The effective hoop FRP strain in the jacket for diagram points other than pure
axial compression needs to assume a value of 0.004 in the compression-con-
trolled region of the curve to ensure shear integrity of confined concrete. The
ACI 440.2R-08 guide allows finding two more points to draw the compres-
sion-controlled region when establishing the interaction diagram, as seen in
Figure 7.5:

a. Point B with a strain distribution corresponding to a compressive strain

of ε′ ccu at the extreme compression fiber and zero strain at the extreme
layer of tensile steel reinforcement

b. Point C with a strain distribution corresponding to a compressive strain

of ε′ ccu at the extreme compression fiber and yielding tensile strain ε sy at
the extreme layer of tensile steel reinforcement (balanced failure)

c. Connecting Points A, B, and C with straight lines to construct the
enhanced compression-controlled region.