Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 200

TM x

GP ε 0

GM x

GP

Y C

Y G

φ x

X c

X G

φ y ε 0

GP GP

TM y

GM y

FIGURE 7.21 Moment transferring from geometric centroid to inelastic centroid.

TM

TM y

x

φ= β ×− β EI × EI (7.112)

y x xy

2 2

2 2

β= EI EI − EI (7.113)

x y xy

7. 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:

ε= GP
EA

(7.114)

0

ε=ε+φ−+φ ( HY ) ( BX − ) (7.115)

ec 0 x c y c

ε=ε−φ− −φ ( Y over) ( X − over) (7.116)

es 0 xc y c

where the cover is up to the center of the bars

8. Calculating strain ε ci and corresponding stress f ci in each filament of con-
crete section by using the Lam and Teng or the Mander model.

( ) ( )

GP
EA

TM HY Y −−

β

TM BX X −−

β

x c i y c i

ε= + EI + EI

ci y x

2 2

( )

( )

TM BX X −−

β

TM HY Y −−

β

x c i y c i

− EI − EI (7.117)

xy xy

2 2