Civil Engineering Reference
In-Depth Information
Section 8.5.1 of the ACI Code states that the following expression can be used for
calculating the modulus of elasticity of concretes weighing from 90 to 155 lb/ft
3
:
w
1.
c
33
c
E
c
f
In this expression,
E
c
is the modulus of elasticity in psi,
w
c
is the weight of the concrete in
pounds per cubic foot, and is its 28-day compressive strength in psi. This is actually a
secant modulus with the line (whose slope equals the modulus) drawn from the origin to a
point on the stress-strain curve corresponding approximately to the stress (0.45
c
f
c
f
) that
would occur under the estimated dead and live loads the structure must support.
For normal-weight concrete weighing approximately 145 lb/ft
3
, the ACI Code states
that the following simplified version of the previous expression may be used to determine
the modulus:
c
E
c
57,000
f
Table A.1 (see the Appendix at the end of the topic) shows values of
E
c
for different
strength concretes. These values were calculated with the first of the preceding formulas
assuming 145 lb/ft
3
concrete.
In SI units, with
w
c
varying from 1500 to 2500 kg/m
3
and
with in N/mm
2
or MPa (megapascals). Should normal crushed ston
e o
r gravel con-
crete (with a mass of approximately 2320 kg/m
3
) be used, . Table B.1 of
Appendix B of this text provides moduli values for several different strength concretes.
The term
unit weight
is constantly used by structural engineers working with U.S.
customary units. When using the SI system, however, this term should be replaced
w
1.
c
(0.043)
c
E
c
f
c
f
c
E
c
4700
f
Reinforced concrete bandshell in Portage, Michigan. (Courtesy of Veneklasen Concrete
Construction Co.)
