Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 179

It is important to mention here that f cc and ε′ ccu for points B and C are deter-
mined from Equations (7.6), (7.8), and (7.9) by computing f l in Equation (7.7) using
ε fe = 0.004 instead of κ ε ε fu used for pure axial compression.

7.3.1.2 Contribution of Steel
The following computation steps are taken in general:

1. The angle between each two consecutive bars is

360
No.ofbars

θ=
bar

(7.41)

2. The radius of bars is

D d

bar

R =− − clear cover d − (7.42)

bar spiral

2 2

3. The depth of each bar measured from the top extreme fiber is

D

d =+ −×θ R cos( j 1) (7.43)

_ barj bar bar

2

Note that the first bar is placed on the vertical axis on the tension side of the sec-
tion (bottom side).

4. The strain and stress in the steel bar is

ε= −

cd
c

_ barj

ε

sj ccu

(7.4 4)

f =ε≤ E f

sj s j y

and f cj from Equation (7.3) by substituting ε sj for ε c .

5. The axial force ( P sn ) and the bending moment ( M sn ) contribution of steel are

∑

P = ( f − f ) × A

sn sj cj s bar ,

j

D

∑

M = ( f − f ) × A × − d

(7.45)

sn sj cj s bar , _ barj

2

j

The axial force and bending moment capacity of the section is the simple sum of
the contribution of concrete and steel:

PP P =+

n c n s n

(7.4 6)

MM M =+

n c n s n