Civil Engineering Reference
In-Depth Information
Figure 2.12
EXAMPLE 2.6
Determine
M
n
the nominal or theoretical ultimate moment strength of the beam section shown in
Figure 2.12 if
f
y
c
60,000 psi and
f
3000 psi.
SOLUTION
Computing Tensile and Compressive Forces
T
and
C
T
A
s
f
y
(3.00)(60)
180 k
c
ab
C
0.85
f
(0.85)(3)(
a
)(14)
35.7
a
Equating
T
and
C
and Solving for
a
T
C
for equilibrium
180
35.7
a
a
5.04 in.
a
2
Computing
d
and
M
n
d
a
2
21
5.04
18.48 in.
2
M
n
(180)(18.48)
3326.4 in.- k
277.2 ft- k
In Example 2.7, the nominal moment capacity of another beam is determined much
as it was for Example 2.6. The only difference is that the cross section of the compres-
sion area (
A
c
) stressed at is not rectangular. As a result, once this area is deter-
mined we need to locate i
t
s center of gravity. The c.g. for the beam of Figure 2.13 is
shown as being a distance
c
0.85
f
y
f
ro
m the top of the beam in Figure 2.14. Then the lever arm
from
C
to
T
is e
q
ual to
d
y
(which corresponds to
d
a
/2 in Example 2.6) and
M
n
equals
With this very simple procedure, values of
M
n
can be computed for tensilely rein-
forced beams of any cross section.
A
s
f
y
(
d
y
).
