Civil Engineering Reference
In-Depth Information
, determined in Example 4.2 by substituting into that long and tedious
equation, can be directly selected from Appendix Table A.13. We enter that table with the
The value of
M
u
value previously calculated in the example, and we read a value of
equal to 0.00982.
bd
2
was specified in the problem statement,
and the long equation was used to determine the required dimensions of the structure as
represented by
bd
2
. Again it is much easier to use the appropriate appendix table to deter-
mine this value. In nearly every other case herein in this textbook the tables are used for
design or analysis purposes.
Once
bd
2
is determined, the author takes what seem to him to be reasonable values
for
b
(in this case 12, 14, and 16 in.) and computes the required
d
for each width so that
the required
bd
2
is satisfied. Finally, a section is selected in which
b
is roughly to of
d
.
(For long spans
d
may be
In Example 4.3, which follows, a value of
1
2
2
3
2
2
,
or 3 or more times
b
for economical reasons.)
EXAMPLE 4.3
c
A beam is to be selected with
0.0120,
M
u
600 ft-k,
f
y
60,000 psi and
f
4000 psi.
SOLUTION
Assuming
0.90 and substituting into the following equation from Section 3.4:
1.7
f
y
M
u
bd
2
1
f
y
1
c
f
(12)(600,000)
(0.9)(
bd
2
)
(0.0120)(60,000)
4000
1
1.7
(0.0120)(60,000)
1
b
12
14
16
d
32.18
29.79
27.87
This one seems
pretty reasonable
to the authors.
bd
2
12,427
k
M
u
Note:
Upon entering Appendix Table A.13, we find
643.5 when
0.0120.
bd
2
M
u
bd
2
(12)(600,000)
bd
2
(0.90)(643.5)
12,432
OK
Try 14
33 (
d
30.00 in.)
A
s
bd
(0.0120)(14)(30)
5.04 in.
2
use 4 #10 (
A
s
5.06 in.
2
)
Checking Solution
A
s
5.06
(14)(30)
bd
0.01205
min
0.0033
max
0.0181 from Appendix Table A.7
M
u
bd
2
from Appendix Table A.13 equals 645.85.
with
0.01205
M
n
645.85
bd
2
(645.85)(0.9)(14)(30)
2
7,323,939 in. lb
610.3 ft- k
600 ft- k
