Civil Engineering Reference
In-Depth Information
EXAMPLE 10.2
It is assumed that the column of Figure 10.4 has a strain on its compression edge equal to
0.00300
and has a tensile strain of
0.00200 on its other edge. Determine the values of
P
n
and
M
n
that cause
this strain distribution if
f
y
60 ksi and
c
f
4 ksi.
s
,
SOLUTION
Determine the values of
c
and of the steel strains
and
s
by proportions with reference to the
strain diagram shown in Figure 10.5.
0.00300
0.00300
0.00200
c
(24)
14.40 in.
11.90
14.40
s
(0.00300)
0.00248
0.00207
yields
7.10
9.60
s
(0.00200)
0.00148
C
s
In the following calculations,
C
c
is the total compression in the concrete, is the total com-
pression in the compression steel, and
T
s
is the total tension in the tensile steel. Each of these values
is computed below. The reader should note that
C
s
c
A
s
is reduced by
0.85
f
to account for holes in the
concrete.
a
(0.85)(14.40)
12.24 in.
C
c
(0.85)(12.24)(14)(4.0)
582.62 k
C
s
(60)(3.0)
(0.85)(3.0)(4.0)
169.8 k
T
s
(0.00148)(29,000)(3.0)
128.76 k
By statics,
P
n
and
M
n
are determined with reference made to Figure 10.6, where the values of
C
s
,
C
c
,
and
T
s
are shown.
V
0
P
n
169.8
582.62
128.76
0
P
n
623.7 k
Figure 10.4
Figure 10.5
