Page 178 - Civil Engineering Formulas

CHAPTER 5
CONCRETE

FORMULAS

REINFORCED CONCRETE

When working with reinforced concrete and when designing reinforced con-
crete structures, the American Concrete Institute (ACI) Building Code Require-
ments for Reinforced Concrete, latest edition, is widely used. Future references
to this document are denoted as the ACI Code. Likewise, publications of the
Portland Cement Association (PCA) find extensive use in design and construc-
tion of reinforced concrete structures.
Formulas in this chapter cover the general principles of reinforced concrete
and its use in various structural applications. Where code requirements have to
be met, the reader must refer to the current edition of the ACI Code previously
mentioned. Likewise, the PCA publications should also be referred to for the lat-
est requirements and recommendations.

WATER/CEMENTITIOUS MATERIALS RATIO

The water/cementitious (w/c) ratio is used in both tensile and compressive
strength analyses of Portland concrete cement. This ratio is found from
w w m
(5.1)
c w c
where w weight of mixing water in batch, lb (kg); and w weight of
m c
cementitious materials in batch, lb (kg).
The ACI Code lists the typical relationship between the w/c ratio by weight
and the compressive strength of concrete. Ratios for non-air-entrained concrete
2
vary between 0.41 for a 28-day compressive strength of 6000 lb/in (41 MPa)
2
and 0.82 for 2000 lb/in (14 MPa). Air-entrained concrete w/c ratios vary from
2
2
0.40 to 0.74 for 5000 lb/in (34 MPa) and 2000 lb/in (14 MPa) compressive
strength, respectively. Be certain to refer to the ACI Code for the appropriate
w/c value when preparing designs or concrete analyses.
Further, the ACI Code also lists maximum w/c ratios when strength data
are not available. Absolute w/c ratios by weight vary from 0.67 to 0.38 for
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