Civil Engineering Reference
In-Depth Information
ally, the proportion of fine to coarse aggregate is kept con-
stant in adjusting the batch weights to maintain worka-
bility or other properties obtained in the first trial batch.
After adjustments to the cementitious materials, water,
and air content have been made, the volume remaining for
aggregate is appropriately proportioned between the fine
and coarse aggregates.
Additional trial concrete mixtures with water-cement
ratios above and below 0.31 should also be tested to
develop a strength to water-cement ratio relationship. From
that data, a new more economical mixture with a compres-
sive strength closer to Âand a lower cement content can be
proportioned and tested. The final mixture would probably
look similar to the above mixture with a slump range of
25 mm to 75 mm and an air content of 5% to 8%. The
amount of air-entraining admixture must be adjusted to
field conditions to maintain the specified air content.
Table 9-11 is equal to ˘ + 1200. Therefore, Â = 3500 + 1200
= 4700 psi.
Water to Cement Ratio.
Table 9-1 requires no maximum
water to cement ratio. The recommended water to cement
ratio for an  of 4700 psi is 0.42 interpolated from Fig. 9-2
or Table 9-3 [water to cement ratio = {(5000 - 4700)(0.48 -
0.40)/(5000 - 4000)} + 0.40 = 0.42].
Coarse-Aggregate Size.
From the specified information,
a
3
⁄
4
-in. nominal maximum-size aggregate is adequate as it
is less than
3
⁄
4
of the distance between reinforcing bars and
between the rebars and forms (cover).
Air Content.
A target air content of 6.0% is specified in this
instance not for exposure conditions but to improve work-
ability and reduce bleeding. Therefore, design the mix for
6% ±1.0% air and use 7% (or the maximum allowable) for
batch proportions. The trial batch air content must be
within ±0.5 percentage points of the maximum allowable
air content.
Slump.
As no slump was specified, a slump of 1 to 3 in.
would be adequate as indicated by Table 9-6. Use 3 in. for
proportioning purposes, the maximum recommended for
foundations.
Water Content.
Fig. 9-5 and Table 9-5 recommend that a
3-in. slump, air-entrained concrete made with
3
⁄
4
-in. nom-
inal maximum-size aggregate should have a water content
of about 305 lb per cu yd. However, gravel with some
crushed particles should reduce the water content of the
table value by about 35 lb. Therefore, the water content can
be estimated to be about 305 lb minus 35 lb, which is 270 lb.
Cement Content.
The cement content is based on the
maximum water-cement ratio and the water content.
Therefore, 270 lb of water divided by a water-cement ratio
of 0.42 requires a cement content of 643 lb.
Coarse-Aggregate Content.
The quantity of
3
⁄
4
-in. nom-
inal maximum-size coarse aggregate can be estimated
from Fig. 9-3 or Table 9-4. The bulk volume of coarse
aggregate recommended when using sand with a fineness
modulus of 2.80 is 0.62. Since it weighs 100 lb per cu ft, the
ovendry weight of coarse aggregate for a cubic yard of
concrete (27 cu ft) is
100 x 27 x 0.62 = 1674 lb per cu yd of concrete
Admixture Content.
For a 7% air content, the air-
entraining admixture manufacturer recommends a dosage
rate of 0.9 fl oz per 100 lb of cement. From this informa-
tion, the amount of air-entraining admixture is
Example 2. Absolute Volume Method
(Inch-Pound Units)
Conditions and Specifications.
Concrete is required for
a building foundation. A specified compressive strength,
˘, of 3500 psi is required at 28 days using a Type I cement.
The design calls for a minimum of 3 in. of concrete cover
over the reinforcing steel. The minimum distance between
reinforcing bars is 4 in. The only admixture allowed is for
air entrainment. No statistical data on previous mixes are
available. The materials available are as follows:
Cement:
Type I, ASTM C 150, with a relative
density of 3.15.
Coarse aggregate:
Well-graded
3
⁄
4
-in. maximum-size
gravel containing some crushed par-
ticles (ASTM C 33) with an ovendry
relative density (specific gravity) of
2.68, absorption of 0.5% (moisture
content at SSD condition) and oven-
dry rodded bulk density (unit weight)
of 100 lb per cu ft. The laboratory
sample for trial batching has a mois-
ture content of 2%.
Fine aggregate:
Natural sand (ASTM C 33) with an
ovendry relative density (specific
gravity) of 2.64 and absorption of
0.7%. The laboratory sample mois-
ture content is 6%. The fineness mod-
ulus is 2.80.
643
0.9 x
= 5.8 fl oz per cu yd
100
Fine-Aggregate Content.
At this point, the amount of all
ingredients except the fine aggregate are known. In the
absolute volume method, the volume of fine aggregate is
determined by subtracting the absolute volumes of the
known ingredients from 27 cu ft (1 cu yd). The absolute
volume of the water, cement, and coarse aggregate is cal-
Air-entraining
admixture: Wood-resin type, ASTM C 260.
From this information, the task is to proportion a trial mix-
ture that will meet the above conditions and specifications.
Strength.
Since no statistical data is available, Â (re-
quired compressive strength for proportioning) from
