Civil Engineering Reference
In-Depth Information
strength and ε
cu
is the maximum usable concrete compressive strain and is
assumed equal to 0.003.
For ultimate strength calculations controlled by concrete crushing,
ACI 318-11 [2] allows the approximation of the stress-strain curve to an
equivalent rectangular stress, or “stress block,” distribution as discussed
in Section 4.5. In the design examples discussed in the chapters of Part 3,
the stress-strain curve proposed by Todeschini et al. [3] is adopted when
concrete crushing does not control failure.
Modulus of elasticity.
The modulus of elasticity of concrete varies with
concrete compressive strength (
f
′
c
), concrete age, properties of cement and
aggregates, and rate of loading. Based on statistical analysis of experi-
mental data available for concrete with unit weights,
w
, varying between
90 and 155 pcf (1442 and 2483 kg/m
3
), ACI 318-11 [2] provides the follow-
ing empirical equation for computing the modulus of elasticity:
1.5
E
=⋅
33
wf
′
(4.4)
c
c
1.5
[or
E
=⋅
0.43
w
f
′
in SI units]
c
c
This equation is representative of the secant modulus for a compressive
stress at service load. The secant modulus of elasticity in tension is gener-
ally assumed to be the same as in compression for computing deflections
under service conditions.
For normal-weight concrete weighing 145 pcf (2323 kg/m
3
), the follow-
ing simplified equation is suggested by ACI 318-11:
E
=
57000
f
′
(4.5)
c
c
[or
E
=
4700
f
′
in SI units]
c
c
It must be noted that, generally, creep and shrinkage over time cause a
reduction of the secant modulus in compression inducing larger deflections.
These effects are not taken into consideration in either Equation (4.4)
or (4.5).
Tensile strength.
ACI 318-11 suggests the following equation to compute
the concrete tensile strength:
7.=λ′
(4.6)
f
f
ct
c
[or
f
0.=λ′
in SI units]
f
ct
c
where λ is a modification factor equal to 1.0 for normal-weight concrete or
0.75 for lightweight concrete.
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