CIVIL ENGINEERING FORMULAS

CONCRETE FORMULAS 125

earlier for spirally reinforced columns. The ratio pgfor a tied column should not be
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 (Rcannot exceed 1.0)

(5.17)

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 Rfrom (Rcannot exceed 1.0)

(5.18)

where hunsupported length of column, in (mm)
rradius of gyration of gross concrete area, in (mm)
0.30 times depth for rectangular column
0.25 times diameter for circular column
Rlong-column load reduction factor

Applied axial load and moment when tension governs design should be sim-
ilarly adjusted, except that Rvaries 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 Nhas an eccentricity ein each
principal direction no greater than given by the two following equations and by tension
ifeexceeds these values in either principal direction.

For spiral columns,

(5.19)

For tied columns,

(5.20)

where eeccentricity, in (mm)
ebmaximum permissible eccentricity, in (mm)
Neccentric load normal to cross section of column
pgratio of area of vertical reinforcement to gross concrete area
m fy/0.85fc
Dsdiameter of circle through centers of longitudinal reinforcement,
in (mm)

eb(0.67pgm0.17)d

eb0.43pgmDs0.14t

R1.07

0.008h

r

R1.32

0.006h

r