Name: _ _ SOLUTION_ _ _ _ _ _ _ _
CE 441 Reinforced Concrete Design – Assignment 1
Due Thursday September 3, 2009
The stressstrain (
f

ε
) relationship for a certain concrete from a 28thday uniaxial compression test is determined to
be represented by the equation
f
(ksi)=4,000
ε
– 1.0x10
6
ε
2
as shown in the figure.
A beam of rectangular cross
section with height
h
=24 inches and width
b
=10 inches is made of this concrete with three #9 bars as tension
reinforcement (A
s
=3.0 in
2
from ACI31808 p 439), located at d=21.0 in. The modulus of elasticity of steel bars is
E=29,000 ksi and the yield strength is F
y
=60 ksi. Please answer the following questions and carry out the required
analysis:
(a) What is the 28day compressive strength f
c
' for this concrete?
(b) Assume that the tension steel A
s
will reach its yield strain
ε
y
before the concrete reaches its maximum strain of
0.003 (to be verified later in part (e)). Draw the linear strain diagram acting on the cross section for
ε
s
=
ε
y
and using
similar triangles write the strain
ε
at distance
y
(+
↑
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 Spring '09
 Tensile strength, Compressive stress, Compressive strength, linear strain diagram

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