Page 189 - Civil Engineering Formulas

CONCRETE FORMULAS 125

earlier for spirally reinforced columns. The ratio p for a tied column should not be
g
less than 0.01 or more than 0.08. Longitudinal reinforcing should consist of at least
four bars; minimum size is No. 5.
Long Columns Allowable column loads where compression governs design
must be adjusted for column length as follows:
1. If the ends of the column are fixed so that a point of contraflexure occurs
between the ends, the applied axial load and moments should be divided by R
from (R cannot exceed 1.0)
0.006h
R 1.32 (5.17)
r
2. If the relative lateral displacement of the ends of the columns is prevented
and the member is bent in a single curvature, applied axial loads and
moments should be divided by R from (R cannot exceed 1.0)

0.008h
R 1.07 (5.18)
r
where h unsupported length of column, in (mm)
r radius of gyration of gross concrete area, in (mm)
0.30 times depth for rectangular column
0.25 times diameter for circular column
R long-column load reduction factor
Applied axial load and moment when tension governs design should be sim-
ilarly adjusted, except that R varies linearly with the axial load from the values
given at the balanced condition.
Combined Bending and Compression The strength of a symmetrical column is
controlled by compression if the equivalent axial load N has an eccentricity e in each
principal direction no greater than given by the two following equations and by tension
if e exceeds these values in either principal direction.
For spiral columns,
e b 0.43 p g mD s 0.14t (5.19)
For tied columns,
e b (0.67p g m 0.17)d (5.20)

where e eccentricity, in (mm)
e maximum permissible eccentricity, in (mm)
b
N eccentric load normal to cross section of column
p ratio of area of vertical reinforcement to gross concrete area
g
m f /0.85 f
y
c
D diameter of circle through centers of longitudinal reinforcement,
s
in (mm)