Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 211

Solution:

There are three points to determine for the compression-controlled interaction
diagram:

1. Point A: Pure compression

P = 0.85 ( f AA Af − ) + = ×× −× 0.85 6.0 480 10 1.27) nA cg st st y

+× ×=
φ= ×× =

10 1.27 60 3145.23 k

P 0.65 0.8 3145.23 1635.52 k

nA

2. Point B: Compression + bending when the extreme steel layer has a zero
strain (Figure 7.29)

P = 0.85 f ba + Af + Af + Af

n c sy 1 ss 2 2 ss 3 3

P nB = 0.85 × ×× ×+× 6.0200.752231.27 × +× × 60 21.2729,000 × 0.00182

+× × 21.2729,000 × 0.000909 = 2112.62

cd == 22"

0.05 6000
1000

ac =β = 1.05 − ×= ×= 22 0.75 22" 16.5"

1

φ= × P n 0.65 2112.62 = 1373.2k

B

a 2

3

( ) ( )

Pe ×= −+ −+ − 0.85 fbad Af dd Af dd n c sy 1 ss 2 2

2

dd −

+ Af ss 33

3

16.5
2

Pe n ×= ××× 0.85 6.020 16.522 − +×× 3.81 60 20 B

2
3

+ 2.54 × 29,000 × 0.00182 × × 20

20
3

+ 2.54 × 29,000 × 0.000909 × = 29,947.11 k-in.

20 in

0.003

e´

0.00273

e

0.00182

22 in

24 in

20 in

0.000909

FIGURE 7.29 Determination of Point B on the unconfined interaction diagram.