Simplified Design for Columns - Simplified Design of Reinforced Concrete Buildings - page 155

All bars in compression

*

1

0 ≤ f s ≤ 0.5f y
on tension face

2

3

Zone 1

Zone 2

Axial Load

f s ≥ 0.5f y
on tension face

4

Zone 3

f c

*0.65[0.85

ʹ

(A g - A st ) + f y A st ]

5
Bending Moment

b

d n 0.003

Compression face

ε sn

Layer n, A sn

c

d i

d 1 h

Layer i, A si
Layer 1, A s1

ε si
ε s1
Strain diagram Tension face

Figure 5-4 Transition Stages on Interaction Diagram

f c ʹ

For columns with square sections and concrete strength = 4 ksi, the above equations further simplify

as follows;

(1) Point 1 (see Fig. 5-2):

f c ʹ φ P n(max) = 0.80 φ [0.85 (A g - A st ) + f y A st ] ACI Eq. (10-2)

f c ʹ f c ʹ = 0.80 φ A g [0.85 + ρ g (f y - 0.85 )]

(2) Points 2-4 (see Fig. 5-4):

⎡ ⎤

⎛
⎜

C 2 d i
d 1

⎞
⎟

n
∑

φ P n =φ C 1 hd 1 + 87 A si 1 −

(5-1)

⎢ ⎥

⎣ ⎦

i = 1

⎡ ⎤

⎛
⎜

⎞
⎟

) + 87 A si 1 − C 2 d i
d 1

n
∑

h
2

⎛
⎜

⎞

(

φ M n =φ 0.5C 1 hd 1 h − C 3 d 1

⎟ −

d i /12

(5-2)

⎢ ⎥

⎣ ⎦

i = 1