Civil Engineering Reference
In-Depth Information
SOLUTION
When the beam has only four bars,
(4.00)(60)
(0.85)(3)(18)
a
5.23
27
5.23
2
M
n
(0.9)(4.00)(60)
5267 in.- k
439 ft- k
When the moment falls off to 439 ft-k, two of the six bars can theoretically be cut off.
When the beam has only two bars,
(2.00)(60)
(0.85)(3)(18)
2.61
a
27
2.61
2
M
n
(0.9)(2.00)(60)
2775 in.- k
231 ft- k
When the moment falls off to 231 ft-k, two more bars can theoretically be cut off leaving two bars
in the beam.
(Notice that
with 6 bars
0.0123, which is less than
max
0.013555 from Appen-
dix Table A.7. Also, this
is
min
of
0.00333.)
The moment at any section in the beam at a distance
x
from the left support is as follows, with
reference being made to Figure 7.3:
6.00
(18)(27)
200
60,000
x
2
M
84
x
(5.6
x
)
From this expression the location of the points in the beam where the moment is 439 ft-k and
231 ft-k can be determined. The results are shown in Figure 7.4.
Discussion
If the approximate procedure had been followed (where bars are cut off purely on the
basis of the ratio of the number of bars to the maximum moment, as was illustrated with the equa-
tions on page 181), the first two bars would have had lengths equal to 17.32 ft (as compared to the
theoretically correct value of 16.52 ft) and the second two bar lengths equal to 24.50 ft (as com-
pared to the theoretically correct value of 23.88 ft). It can then be seen that the approximate proce-
dure yields fairly reasonable results.
Figure 7.3
Figure 7.4
