Simplified Design for Columns - Simplified Design of Reinforced Concrete Buildings - page 158

(1) Point 1 (pure compression):

8.0
18

ρ g =

= 0.0247

× 18

φ P n(max) = (0.80 × 0.65 × 324)[(0.85 × 4) + 0.0247(60-(0.85 × 4))]

= 808 kips

18"

#3 tie

3-#9
A s3 = 3.0 in. 2

2-#9
A s2 = 2.0 in. 2

3-#9
A s1 = 3.0 in. 2

Figure 5-7 Column Cross-Section for Example Problem

(2) Point 2 (f s1 = 0):

Using Fig. 5-7 and Table 5-2:

C 2 d 1

Layer 1:

1 −

d 1 =

1 − 1 = 0

C 2 d 2

9.00
15.56

⎛
⎜

⎞

Layer 2:

1 −

d 1 =

1 − 1 ×

⎟ =

0.42

C 2 d 3

⎛
⎜

2.44
15.56

⎞

Layer 3:

1 −

d 1 =

1 − 1 ×

⎟ =

0.84 > 0.69

1- C 2 d 3 /d 1 being greater than 0.69 in layer 3 means that the steel in layer 3 has yielded; therefore, use
1- C 2 d 3 /d 1 = 0.69.