Strengthening of Columns for Confinement - Strengthening Design of Reinforced Concrete with FRP - page 207

Point A:

( )

2

ρ= ×π

440.98
11.81

= 0.0216 s

× 11.81

b
h

h
b

( )

2

( )

2

hr − 2 + br − 2

c c

1 − −ρ s

A

A
A

3
1

g

e
c

=

−ρ

s

2

[2 × (11.8121.57) ]

3

− ×

1 − − 0.0216

× 11.81 × 11.81

= = 0.633

10.0216 −

2

A
A

b
h

e

κ= = 0.633

a

c

0.5

A
A

h
b

e
c

κ= = 0.633

b

According to Equation (7.6),

f cc = 3.625 + ×× × 0.95 3.30.633 0.796 = 5.2ksi

0.45

0.586 0.0145
0.002

×

ε= ×+× 0.002 1.5120.633 × 0.219 × = 0.00938 ccu

Following Equation (7.2) with and without ϕ factors,

× −× π × + ×× π ×

2 2

P n = 0.85 × 5.2 11.81 × 11.81 4 0.98 ) 79.75 4 0.98 = 843.8kips

4 4

φ= ×× = P n 0.65 0.8 1141.87 438.76 kips

Point B:

2 nt E

D

ε

= ×× ×

2 40.0063 31,030 × 0.004

fffe

f = = 0.375 ksi

fl

2 2

11.81 + 11.81

This f fl will not be used to determine whether the stress-strain curve is
ascending or descending, since it is computed for eccentric points.

f cc = 3.625 + ×× × 0.95 3.30.633 0.375 = 4.368 ksi

E = 3431.85 ksi, E = 144.49 ksi, ε= 0.002205 c 2 t

0.45

0.375
3.625

0.004
0.002

ε= ×+× 0.002 1.5120.633 × × = 0.005147

ccu

P = 522.45 kips, M = 95.93 kip-ft

nB , nB ,

Point C:

P = 259.97 kips, M = 148.96 kip-ft nC , nC ,