Page 164 - Civil Engineering Formulas

COLUMN FORMULAS 101

When P u is greater than P b , or e is less than e b , compression governs. In that case,
the ultimate strength is approximately

M u
P u P o (P o P b ) (3.41)
M b
P o
P u (3.42)
1 (P o /P b 1)(e/e b )
where M u is the moment capacity under combined axial load and bending, in
kip (kNm) and P o is the axial-load capacity, kip (N), of member when concen-
trically loaded, as given.
For symmetrical reinforcement in single layers, the ultimate strength when
compression governs in a column with depth, h, may be computed from
A s f y bhf c
P u e/d d 0.5 3he/d 1.18 (3.43)
2

Circular Columns

Ultimate strength of short, circular members with bars in a circle may be deter-
mined from the following equations:
When tension controls,

0.85e 2 mD s 0.85e
2
P u 0.85 f c D B D 0.38 2.5D D 0.38
1
(3.44)
where D overall diameter of section, in (mm)
D s diameter of circle through reinforcement, in (mm)
t A st /A g
When compression governs,
A st f v A g f c
P u 3e/D s 1 9.6D e /(0.8D 0.67D s ) 1.18 (3.45)
2

The eccentricity for the balanced condition is given approximately by
e b (0.24 0.39 t m)D (3.46)

Short Columns
Ultimate strength of short, square members with depth, h, and with bars in a
circle may be computed from the following equations: