Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 199

e

Load Step ∆GP

Resultant Moment

FIGURE 7.20 Radial-loading concept.

4. Calculating the moment GM R about the geometric centroid.

GM
GP

R

e = and GM = × eGP (7.105)

R

(7.10 6)

GM = GM

R cos

α

x

GM = GM

x tan

α (7.10 7)

y

5. Transferring the moments to the inelastic centroid and calculating the new
transferred moments TM X and TM Y

)

(7.10 8)

TM = GM + GP YY ( −

x x Gc

TM = GM + GP XX ( − ) (7.10 9)

y y Gc

The advantage of transferring the moment to the position of the inelastic
centroid is to eliminate the coupling effect between the force and the two
moments, since EAM x = EAM y = 0 about the inelastic centroid (Figure 7.21).

EA 0 0 ε

φ
φ

GP
TM
TM

0

0
0

EI EI (7.110)

=

x xy

x x

EI EI

y

xy y y

6. Finding curvatures ϕ x and ϕ y by inverting Equation (7.110):

TM TM y

x

φ= β ×− β EI × EI

(7.111)

x y xy

2 2