Civil Engineering Reference
In-Depth Information
larger the percentage of dead loads and the longer they are applied, the greater the creep
in the concrete and the larger the percentage of load carried by the reinforcement.
Though stresses cannot be predicted in columns in the elastic range with any de-
gree of accuracy, several decades of testing have shown that the ultimate strength of
columns can be estimated very well. Furthermore, it has been shown that the propor-
tions of live and dead loads, the length of loading, and other such items have little ef-
fect on the ultimate strength. It does not even matter whether the concrete or the steel
approaches its ultimate strength first. If one of the two materials is stressed close to its
ultimate strength, its large deformations will cause the stress to increase quicker in the
other material.
For these reasons, only the ultimate strength of columns is considered here. At fail-
ure, the theoretical ultimate strength or nominal strength of a short axially loaded column
is quite accurately determined by the expression that follows, in which
A
g
is the gross
concrete area and
A
st
is the total cross-sectional area of longitudinal reinforcement, in-
cluding bars and steel shapes:
c
(
A
g
A
st
)
f
y
A
st
P
n
0.85
f
9.4
FAILURE OF TIED AND SPIRAL COLUMNS
Should a short, tied column be loaded until it fails, parts of the shell or covering concrete
will spall off and, unless the ties are quite closely spaced, the longitudinal bars will buckle
almost immediately, as their lateral support (the covering concrete) is gone. Such failures
may often be quite sudden, and apparently they have occurred rather frequently in struc-
tures subjected to earthquake loadings.
When spiral columns are loaded to failure, the situation is quite different. The cover-
ing concrete or shell will spall off, but the core will continue to stand, and if the spiral is
closely spaced, the core will be able to resist an appreciable amount of additional load be-
yond the load that causes spalling. The closely spaced loops of the spiral together with the
longitudinal bars form a cage that very effectively confines the concrete. As a result, the
spalling off of the shell of a spiral column provides a warning that failure is going to
occur if the load is further increased.
American practice is to neglect any excess capacity after the shell spalls off since it
is felt that once the spalling occurs the column will no longer be useful—at least from
the viewpoint of the occupants of the building. For this reason the spiral is designed so
that it is just a little stronger than the shell that is assumed to spall off. The spalling
gives a warning of impending failure, and then the column will take a little more load
before it fails. Designing the spiral so that it is just a little stronger than the shell does
not increase the column's ultimate strength much, but it does result in a more gradual or
ductile failure.
The strength of the shell is given by the following expression, where
A
c
is the area of
the core, which is considered to have a diameter that extends from out to out of the spiral:
c
(
A
g
A
c
)
Shell strength
0.85
f
By considering the estimated hoop tension that is produced in spirals due to the lat-
eral pressure from the core and by tests, it can be shown that spiral steel is at least twice as
