Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 186

ε ec

TM

ε 0

P

H

P

GM

Y c

Y G

φ

cover

ε es

FIGURE 7.13 Transferring moment from geometric centroid to inelastic centroid.

7. Find the curvature ϕ:

TM
EI

φ= (7.68)

Strain at the inelastic centroid ε 0 , the extreme compression fiber strain
ε ec , and strain at the extreme level of steel in tension ε es are found as follows:

GP
EA

ε=

(7.69)

ε=ε+φ− ( HY ) (7.70)

ec 0 c

ε=ε−φ−

(7.71)

( Y cover)

es 0 c

where cover is up to the center of the bars.

8. Calculate strain ε ci and corresponding stress f ci in each layer of concrete
section by using the selected model from step 2:

ε=ε−φ Y (7.72)

ci ec i

9. Calculate strain ε si and corresponding stress f si in each bar in the given sec-
tion by using the steel model (elastic up to yield strength and then perfectly
plastic):

ε=ε−φ Y
si si

(7.73)

ec