Civil Engineering Reference
In-Depth Information
the concrete. Development lengths are discussed in detail in Chapter 7. There we will
learn that required development lengths for reinforcing bars vary appreciably with their
spacings and their cover.
As a result, it is sometimes wise to use greater cover and larger
bar spacings than the specified minimum values in order to reduce development lengths.
When selecting the actual bar spacing, the designer will comply with the preceding
code requirements and, in addition, will give spacings and other dimensions in inches and
fractions, not in decimals. The workers in the field are accustomed to working with frac-
tions and would be confused by a spacing of bars such as 3 at 1.45 in. The designer should
always strive for simple spacings, for such dimensions will lead to better economy.
Each time a beam is designed, it is necessary to select the spacing and arrangement of
the bars. To simplify these calculations, Appendix Table A.5 is given. Corresponding infor-
mation is provided in SI units in Appendix Table B.5. These tables show the minimum beam
widths required for different numbers of bars. The values given are based on the assumptions
that stirrups and cover are required except for #18 bars where the stirrup diame-
ter is in. If three #10 bars are required, it can be seen from the table that a minimum beam
width of 10.4 in. (say 11 in.) is required. This value can be checked as follows, noting that 2
d
s
is the radius of bend of the bar and the minimum clear spacing between bars in this case is
d
b
:
3
8
-in.
1
2
-in.
1
2
d
b
d
b
Min. Beam width
cover
d
s
2
d
s
2
d
b
d
b
d
b
2
2
d
s
cover
3
3
8
1.27
2
1.27
2
3
8
3
1.50
8
(2)
(3)(1.27)
(2)
8
1.50
10.33 in. rounded to 10.4 in.
4.3
BEAM DESIGN EXAMPLES
Example 4.2 illustrates the design of a simple span rectangular beam. For this introduc-
tory example, approximate dimensions are assumed for the beam cross section. The depth
h
is assumed to equal about one-tenth of the beam span, while its width
b
is assumed to
equal about 1/2
h
. Next the percentage of reinforcing needed is determined with the equa-
tion derived in Section 3.4, and reinforcing bars are selected to satisfy that percentage. Fi-
nally,
M
n
is calculated for the final design.
EXAMPLE 4.2
Design a rectangular beam for a 22-ft simple span if a dead load of 1 k/ft (not including the beam
weight) and a live load of 2 k/ft are to be supported. Use
c
f
4000 psi and
f
y
60,000 psi.
SOLUTION
Estimating Beam Dimensions and Weight
Assume
h
(0.10)(22)
2.2 ft
Say 27 in.
(
d
24.5 in.)
Assume
b
1
2
h
24.5
Say 12 in.
2
Beam
wt
(12)(27)
144
(150)
337.5 lb/ft
