Page 155 - Civil Engineering Formulas

COLUMN FORMULAS 93

be at least 4 percent of the total composite area. The concrete should be rein-
forced with longitudinal load-carrying bars, continuous at framed levels, and
lateral ties and other longitudinal bars to restrain the concrete; all should have
1 in (38.1 mm) of clear concrete cover. The cross-sectional area of
at least 1 2
transverse and longitudinal reinforcement should be at least 0.007 in 2
2
(4.5 mm ) per in (mm) of bar spacing. Spacing of ties should not exceed two-
thirds of the smallest dimension of the composite section. Strength of the con-
should be between 3 and 8 ksi (20.7 and 55.2 MPa) for normal-weight
crete f c
concrete and at least 4 ksi (27.6 MPa) for lightweight concrete. Specified mini-
mum yield stress F y of steel core and reinforcement should not exceed 60 ksi
(414 MPa). Wall thickness of steel pipe or tubing filled with concrete should
be at least bwF y /3E or DwF y /8E , where b is the width of the face of a rectangular
section, D is the outside diameter of a circular section, and E is the elastic mod-
ulus of the steel.
The AISC LRFD specification gives the design strength of an axially loaded
composite column as P n , where 0.85 and P n is determined from

(3.22)
P n 0.85A s F cr
For c 1.5
2
F cr 0.658l c F my (3.23)

For c 1.5
0.877
F cr F my (3.24)
2
c
where c (KL/r m
)wF my /E m
KL effective length of column, in (mm)
2
2
A s gross area of steel core, in (mm )
F my F y c 1 F yr (A r /A s ) c 2 f c (A c /A s )
E m E c 3 E c (A c /A s )
r m radius of gyration of steel core, in 0.3 of the overall thickness of the
composite cross section in the plane of buckling for steel shapes
2
2
A c cross-sectional area of concrete, in (mm )
2
2
A r area of longitudinal reinforcement, in (mm )
E c elastic modulus of concrete, ksi (MPa)
F yr specified minimum yield stress of longitudinal reinforcement, ksi
(MPa)
For concrete-filled pipe and tubing, c 1 1.0, c 2 0.85, and c 3 0.4. For
concrete-encased shapes, c 1 0.7, c 2 0.6, and c 3 0.2.
When the steel core consists of two or more steel shapes, they should be tied
together with lacing, tie plates, or batten plates to prevent buckling of individ-
.
ual shapes before the concrete attains 0.75 f c