Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 202

where
E ci = secant modulus of elasticity of the concrete filament = ε

f ci

f si

ci

E si = secant modulus of elasticity of the steel bar = ε

si

11. Transferring back the internal moment about the geometric centroid

GM =− − M PY ( Y ) (7.128)

0 x 0 x Gc

GM =− − M PX ( X ) (7.129)

0 y 0 y Gc

12. Checking the convergence of the inelastic centroid

)

(7.130)

TOL = EAM /( EA × Y

x x c

TOL = EAM /( EA × X ) (7.131)

y y c

13. Comparing the internal force to applied force and the internal moments to
applied moments, and making sure the inelastic centroid converges:

− 5

GP −≤× F z 110 (7.132)

− 5 − 5

GM − GM ≤ × 110 nd GM − GM ≤× 110 (7.133)

x 0 x y 0 y

− 5 − 5

TOL ≤× 110 nd TOL ≤× 110 (7.134)

x y

If Equations (7.132), (7.133), and (7.134) are not satisfied, the location of the inelas-
tic centroid is updated by EAM x / EA and EAM y / EA , and steps 5 to 12 are repeated
until Equations (7.132), (7.133), and (7.134) are satisfied.

YY EAM
EA

x

=+ (7.135)

c c

new old

XX EAM
EA

y

=+ (7.136)

c c

new old

Once equilibrium is reached, the algorithm checks for ultimate strain in concrete
ε ec and steel ε es not to exceed ε ccu and 0.05, respectively, and then it increases the
loading by Δ GP and runs the analysis f or t he new load level using the latest sec-
tion properties. Otherwise, if ε ec equals ε ccu or ε es equals 0.05, the target force and
resultant moment are reached as a point on the interaction diagram for the amount
of eccentricity, and angle α used.