Civil Engineering Reference
In-Depth Information
The failure of a column is generally a more severe matter than is the failure of a beam
because a column generally supports a larger part of a structure than does a beam. In other
words, if a column fails in a building, a larger part of the building will fall down than if a
beam fails. This is particularly true for a lower-level column in a multistory building. As a
result, lower
values are desirable for columns.
There are other reasons for using lower
values in columns. As an example, it is
more difficult to do as good a job in placing the concrete for a column than it is for a
beam. The reader can readily see the difficulty of getting concrete down into narrow col-
umn forms and between the longitudinal and lateral reinforcing. As a result, the quality of
the resulting concrete columns is probably not as good as that of beams and slabs.
The failure strength of a beam is normally dependent on the yield stress of the tensile
steel—a property that is quite accurately controlled in the steel mills. On the other hand,
the failure strength of a column is closely related to the concrete's ultimate strength, a
value that is quite variable. The length factors also drastically affect the strength of
columns and thus make the use of lower
factors necessary.
It seems impossible for a column to be perfectly axially loaded. Even if loads could
be perfectly centered at one time, they would not stay in place. Furthermore, columns
may be initially crooked or have other flaws, with the result that lateral bending will
occur. Wind and other lateral loads cause columns to bend, and the columns in rigid-
frame buildings are subjected to moments when the frame is supporting gravity loads
alone.
9.7
DESIGN FORMULAS
In the pages that follow, the letter
e
is used to represent the eccentricity of the load. The
reader may not understand this term because he or she has analyzed a structure and has
computed an axial load
P
u
and a bending moment
M
u
, but no specific eccentricity
e
for a
particular column. The term
e
represents the distance the axial load
P
u
would have to be
off center of the column to produce
M
u
. Thus
P
u
e
M
u
or
M
u
P
u
e
Nonetheless, there are many situations where there are no calculated moments for the
columns of a structure. For many years the Code specified that such columns had to be de-
signed for certain minimum moments even though no calculated moments were present.
This was accomplished by requiring designers to assume certain minimum eccentricities
for their column loads. These minimum values were 1 in. or 0.05
h
, whichever was larger,
for spiral columns and 1 in. or 0.10
h
for tied columns. (The term
h
represents the outside
diameter of round columns or the total depth of square or rectangular columns.) A mo-
ment equal to the axial load times the minimum eccentricity was used for design.
In today's Code, minimum eccentricities are not specified, but the same objective is
accomplished by requiring that theoretical axial load capacities be multiplied by a factor
sometimes called
, which is equal to 0.85 for spiral columns and 0.80 for tied columns.
