Civil Engineering Reference
In-Depth Information
(b)
The second modification also refers to
factors. The Code specifies values of
0.65 and 0.70 for tied and spiral columns, respectively. Should a column have
quite a large moment and a very small axial load so that it falls on the lower part
of the curve between points
B
and
C
(see Figure 10.10), the use of these small
values may be a little unreasonable. For instance, for a member in pure bending
(point
C
on the same curve) the specified
is 0.90, but if the same member has a
very small axial load added,
would immediately fall to 0.65 or 0.70. Therefore,
the Code (9.3.2.2) states that when members subject to axial load and bending
have net tensile strains (
t
) between the limits for compression-controlled and
tensile-controlled sections, they fall in the transition zone for
. In this zone it is
permissible to increase
t
increases from
the compression-controlled limit to 0.005. In this regard, the reader is again re-
ferred to Figure R9.3.2 in the Code (it's Figure 3.5 in this text) where the transi-
tion zone and the variation of
linearly from 0.65 or 0.70 to 0.90 as
values are clearly shown. This topic is continued
in Section 10.9.
(c)
As described in Chapter 9, maximum permissible column loads were specified
for columns no matter how small their
e
values. As a result, the upper part of
each design interaction curve is shown as a horizontal line representing the ap-
propriate value of
c
(
A
g
A
st
)
f
y
A
st
]
P
u
P
n
max
for tied columns
0.80
[0.85
f
(ACI Equation 10-2)
c
(
A
g
A
st
)
f
y
A
st
]
P
u
P
n
max
for spiral columns
0.85
[0.85
f
(ACI Equation 10-1)
These formulas were developed to be approximately equivalent to loads applied with
eccentricities of 0.10
h
for tied columns and 0.05
h
for spiral columns.
Each of the three modifications described here is indicated on the design curve of
Figure 10.13, and the letter in parentheses corresponds to the letter used in describing the
modification in the preceding paragraphs.
Cut off because of
maximum
P
n
formulas (c)
φ
φ
P
n
P
n
(a)
φ
Figure 10.13
A column interaction
curve adjusted for the three
modifications described in this section
(10.5).
Break due to
modified values (b)
0.10
f
c
A
g
'
φ
M
n
φ
