Tied RC Column φPn,max

ϕ P_{n, m a x} = 0.80 ϕ [0.85 f_{c}^{'} (A_{g} - A_{s t}) + F_{y} A_{s t}] (tied, ϕ = 0.65)

Maximum usable axial (small e) for a tied column. Spirals use 0.85 instead of 0.80 and φ=0.75. Accidental eccentricity is why the 0.80 exists. Interaction diagrams for e>0.

$A g$: Gross concrete area
$A s t$: Longitudinal steel
$φ$: 0.65 tied / 0.75 spiral

Step-by-step solved example

Tied 16 in square, f'c=4 ksi, Fy=60, Ast=4 in². φPn,max?

Tied RC column: 0.80 φ [0.85 f'c (Ag−Ast)+Fy Ast].

1. Pn,max core
0.85×4×(256−4)+60×4=0.85×4×252+240=857+240=1097 kip, ×0.80=878 kip.
2. φ
0.65×878=571 kip.

Answer: φPn,max ≈ 571 kip

10 practice questions

0/10 correct

1.Spiral φ is

2.The 0.80 (tied) accounts for

3.ρg = Ast/Ag is usually between

4.Ties (not spirals) typically

5.If e is large the column is

6.f'c=5 ksi, Ag=200, Ast=0: 0.85 f'c Ag =

7.φ=0.65 tied even for high steel because

8.Slenderness kLu/r of RC columns

9.Ast=6 in², Fy=60: steel force contribution is

10.Gross 18 in round Ag=