Civil Engineering Reference
In-Depth Information
5.2.3
Column Economics
Concrete is more cost effective than reinforcement for carrying compressive axial load; thus, it is more
economical to use larger column sizes with lesser amounts of reinforcement. Also, columns with a smaller
number of larger bars are usually more economical than columns with a larger number of smaller bars.
Reuse of column forms from story level to story level results in significant savings. It is economically unsound
to vary column size to suit the load on each story level. It is much more economical to use the same column
size for the entire building height, and to vary only the longitudinal reinforcement as required. In taller
buildings, the concrete strength is usually varied along the building height as well.
5.3
DESIGN STRENGTH FOR COLUMNS
For columns subjected to axial loads only (with no or negligible bending moment) the code provides the
following equations for the design axial strength
φ
P
n
:
For columns with spiral reinforcement conforming to Section 10.9.3
φ
φ
P
n, max
= 0.85
[0.85
f
c
ʹ
(A
g
-A
st
) + f
y
A
st
] ACI Eq. (10-1)
For columns with tie reinforcement conforming to Section 7.10.5
φ
φ
P
n, max
= 0.80
[0.85
f
c
ʹ
(A
g
-A
st
) + f
y
A
st
] ACI Eq. (10-2)
Were A
g
and A
st
are the gross area of the column cross section and reinforcement area respectively.
φ
The strength reduction factor
is taken as 0.75 for columns with spiral reinforcement and 0.65 for with
tie reinforcement.
In general columns are subjected to combined axial load and bending moment, P
u
and M
u
. The design strength
for a column cross section in this case is expressed by interaction diagram representing all possible
combinations of the design strengths
φ
φ
M
n
for a specific cross section. To develop an interaction
diagram two conditions must be satisfied: static equilibrium and compatibility of strain. Different strain
profiles are assumed, each strain profile is associated with one point on the interaction diagram. For each strain
profile the internal forces acting on the cross section are calculated using the assumptions introduced in Chapter
3 (See Figure 3-2). Figure 5-1, illustrates the development of interaction diagram for nominal strength P
n
and
M
n
. To develop the interaction diagram for design strength (
P
n
and
φ
φ
P
n
and
M
n
), the nominal strength is multiplied
φ
φ
by the strength reduction factor
depends on whether the column cross section is tension
controlled, compression controlled or in transition between these two limits. The definition of tension and
compression controlled section depend on the magnitude of the net tensile strain at the extreme layer of
longitudinal tension steel at nominal strength. The strength reduction
. The value of
φ
is calculated as follows:
ε
t
≤
0.002)
φ
1. For compression controlled section (
= 0.65 for columns with tie reinforcement and
φ
= 0.75 for columns with spiral reinforcement
ε
t
φ
2. For tension controlled section (
≥
0.005)
= 0.9
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