Civil Engineering Reference
In-Depth Information
Figure 3.23
Bending-axial load interaction curve
2. Any radial line, such as OA, has a slope whose reciprocal represents the eccentric-
ity
e
=
M
n
/
N
n
. A vertical slope has an eccentricity of 0 and the horizontal slope
infinity.
3. In the compression zone the moment
M
n
decreases
with increasing load
N
n
, while in
the tension zone the moment
M
n
increases
with increasing load
N
n
. This characteristic
can be explained as follows. First, in the compression failure zone, failure is caused
by the overstraining of concrete in compression (
003). Since axial compression
increases the compression strain, it decreases the capacity of the concrete to resist flexural
compression. Second, in the tension failure zone, failure is caused by yielding of the steel
in tension. Since axial compression decreases the tensile strain in the steel, it increases the
capacity of the steel to resist flexural tension.
4. The balanced point B in Figure 3.23 corresponds to the case of balanced percentage
ε
u
=
0
.
ρ
b
in Figure 3.10(e). In the region of compression failure (Figure 3.23), a column should be
designed using a reduction factor
ϕ
=
0
.
7 (tied columns) and
ϕ
=
0
.
65 (spiral columns)
as indicated in the region to the left of
ρ
b
(Figure 3.10e). In the region of tension failure
(Figure 3.23), however, we should use a reduction factor
ϕ
that is a linear function of tensile
strain
ε
t
, as given to the right of
ρ
b
.
3.3.6 Moment-Axial Load-Curvature (M
) Relationship
The interaction of bending and axial load is shown in Figure 3.24(a) for a column with 2%
of tension steel and 1% of compression steel. All the steel bars are located at a distance
0
−
N
−
φ
0.004,
f
c
=
.
1
d
from the surfaces. The material properties are:
ε
u
=
27.6 MPa (4000 psi),
