CEE 111 Design Exercise 6
Winter 2012
Due March 19, 2012
Work independently!!!
Consider the reinforced concrete beam shown below:
Beam CrossSection
The beam is to be designed to resist a maximum moment of
300Kft
D
M
at least cost.
For simplicity, total cost can be considered to be only the material cost of the concrete
and the steel reinforcing bars.
The reinforcing bars are to be made of A615 Grade 60
steel at $500/ton ($0.85/ft
2
per foot of beam) and 4,000 psi normal weight concrete at
$25/yd
3
($0.93/ft
2
per foot of beam).
Let
b
= the beam width in inches,
d
= depth of the
beam to the centroid of reinforcing steel, and
A
S
= the total crosssectional area of
reinforcing steel.
Based on these values, the total cost of the beam is given by:
2.5
$85
$95
12
12
S
db
CA
The resisting moment of the beam,
R
M
,
1.7
Sy
RS
y
C
Af
MA
f
d
f b
where
100 ft
50 ft
P = 6K
b
d
2.5 in
A
s
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View Full Documenta strength reduction factor that reduces the theoretical strength of the
beam to account for minor adverse field conditions, equal to 0.90 for bending.
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 Winter '12
 RECKER
 Rebar, American Concrete Institute, steel reinforcement, concrete beam

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