Page 190 - Civil Engineering Formulas

126 CHAPTER FIVE

t diameter of column or overall depth of column, in (mm)
d distance from extreme compression fiber to centroid of tension rein-
forcement, in (mm)
2
f yield point of reinforcement, lb/in (MPa)
v
Design of columns controlled by compression is based on the following
equation, except that the allowable load N may not exceed the allowable load P,
given earlier, permitted when the column supports axial load only:
f a f bx f by
1.0 (5.21)
F a F b F b
2
where f axial load divided by gross concrete area, lb/in (MPa)
a
f , f bending moment about x and y axes, divided by section modulus
by
bx
2
of corresponding transformed uncracked section, lb/in (MPa)
F allowable bending stress permitted for bending alone, lb/in 2
b
(MPa)
F 0.34(1 p m) f c
a
g
The allowable bending load on columns controlled by tension varies linearly
with the axial load from M when the section is in pure bending to M when the
b
0
axial load is N .
b
For spiral columns,
(5.22)
M 0 0.12A st f y D s
For tied columns,
M 0 0.40A s f y (d d ) (5.23)
2
2
where A total area of longitudinal reinforcement, in (mm )
st
f yield strength of reinforcement, lb/in (MPa)
2
v
D diameter of circle through centers of longitudinal reinforcement, in
s
(mm)
2
2
A area of tension reinforcement, in (mm )
s
d distance from extreme compression fiber to centroid of tension rein-
forcement, in (mm)
N and M are the axial load and moment at the balanced condition (i.e., when
b
b
the eccentricity e equals e as determined). At this condition, N and M should
b
b
b
be determined from
M b N b e b (5.24)
When bending is about two axes,
M x M y
1 (5.25)
M 0x M 0y