Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 188

If Equations (7.81), (7.82), and (7.83) are not satisfied, the location of the
inelastic centroid is updated by EAM/EA , and steps 5 to 11 are repeated
until Equations (7.81), (7.82), and (7.83) are satisfied.

YY EAM
EA

ol =+

(7.8 4)

c c

new

Once equilibrium is reached, the alg ori thm checks for ultimate strain in
concrete ε ec and steel ε es not to exceed ε cu and 0.05, respectively, and then
it increases the loading by ΔGP and runs the analysis for th e n ew load level
using the latest section properties. Otherwise, if ε ec equals ε cu 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 used. For more details
about this procedure, check the work of Rasheed and Dinno (1994) and Abd
El Fattah, Rasheed, and Esmaeily (2011).

Example 7.1: Analysis

One of the columns that were tested by Eid, Roy, and Paultre (2009) is investigated
in this example. The following are the properties of the column:

Diameter 11.9 in. 303 mm

Clear cover 1 in. 25 mm

f c 4.59 ksi 31.7 MPa

n × t f 2 × 0.015 in. 2 × 0.381 mm

E f 11, 30 6 k si 78,000 MPa

ε fu 0.013 0.013

f yt 66.1 k si 456 MPa

Hoop spacing 3.94 in. 100 mm

Hoop diameter #3 9.5 mm

Longitudinal bars 6 #5 6 ϕ 15.9 mm

f y 61.3 k si 423 MPa

Draw the interaction diagram per ACI 440.2R-08 then use KDOT Column
Expert.

Solution:

Using Equation (7.7):

2 nt E

D

ε

= ×× ×

2 20.015 11306 × 0.586 × 0.013

fffe

f = = 0.4343ksi l

11.9

f
f

0.4343
4.59

l

= = 0.095 > 0.08, stress-strain curve is ascending

c