WEIGHT PER CUBIC FOOT, YIELD &
SCOPE
This procedure covers the determination of density, or unit weight of freshly mixed concrete. It also provides formulas for calculating the volume of concrete produced from a mixture of known quantities of component materials.
SIGNIFICANCE
The unit weight is a useful tool in determining the concrete batch yield and air content. Since air adds no weight to the concrete and only occupies a volume, the unit weight of the concrete gives a very good indication of the air content of the concrete. Normal weight concrete is in the range of 140  150 lbs./cu. ft. For normal weight concrete, a change in unit weight of 1.5 lbs./cu. ft. relates to approximately a 1 percent change in air content. Using the unit weight to indicate air content can also prevent any discrepancies between air meters.
PROCEDURE
A. Apparatus
1. Measure: May be the base of the air meter used for determining air content from IM 318. Otherwise, it shall be a metal container meeting the requirements of AASHTO T121. The capacity and dimensions of the measure shall conform to those specified in Table 1.
2. Balance or scale: Accurate to 0.3 percent of the test load at any point within the range of use.
3. Tamping Rod: 5/8 in. (16 mm) diameter, having a hemispherical tip.
4. Vibrator: 7000 vibrations per minute, 0.75 in. to 1.50 in. (19 mm to 38 mm) in diameter, at least 3 in. (75 mm) longer than the section being vibrated for use with low slump concrete.
5. Scoop
6. Strike off bar
7. A glass or acrylic strike off plate at least 1/2 in. (12 mm) thick, with a length and width at least 2 in. (50mm) greater than the diameter of the measure The edges of the plate shall be straight and smooth within tolerance of 1/16 in. (1.5mm).
8. Rubber Mallet
Table 1 

Dimensions of Measures 

Capacity M³ (ft. ³) 
Inside Diameter mm (in.) 
Inside Height mm (in.) 
Minimum Thickness mm (in.) 
Nominal Maximum Size of Coarse Aggr. mm (in.) 

Bottom 
Wall 

0.0071 
203 ± 2.54 
213 ± 2.54 
5.1 
3.0 
25 
(1/4) 
(8.0 ± 0.1) 
(8.4 ± 0.1) 
(0.20) 
(0.12) 
(1) 
Measure may be the base of the air meter used in IM 318.
B. Calibration of Measuring Bowl
1. Determine the weight of the dry measure and strikeoff plate.
2. Fill the measure with water at a temperature between 16ºC and 29ºC (60ºF and 85ºF) and cover with the strikeoff plate in such a way as to eliminate bubbles and excess water.
3. Wipe dry the measure and cover plate, being careful not to lose any water from the measure.
4. Determine the weight of the measure, strikeoff plate, and water in the measure.
5. Determine the weight of the water in the measure by subtracting the weight in Step 1 from the weight in Step 4.
6. Measure the temperature of the water and determine its density from Table 2, interpolating as necessary.
7. Calculate the volume of the measure, V_{m}, by dividing the weight of the water in the measure by the density of the water at the measured temperature, from Table 2.
Example: _{} _{}³
Table 2 

Unit Weight of Water 

15ºC to 30ºC 

ºC 
(ºF) 
kg/m³ 
(lb./ft. ³) 
ºC 
(ºF) 
kg/m³ 
(lb./ft. ³) 
15 
(59.0) 
999.10 
(62.372) 
23 
(73.4) 
997.54 
(62.274) 
15.6 
(60.0) 
999.01 
(62.366) 
23.9 
(75.0) 
997.32 
(62.261) 
16 
(60.8) 
998.94 
(62.361) 
24 
(75.2) 
997.29 
(62.259) 
17 
(62.6) 
998.77 
(62.350) 
25 
(77.0) 
997.03 
(62.243) 
18 
(64.4) 
998.60 
(62.340) 
26 
(78.8) 
996.77 
(62.227) 
18.3 
(65.0) 
998.54 
(62.336) 
26.7 
(80.0) 
996.59 
(62.216) 
19 
(66.2) 
998.40 
(62.328) 
27 
(80.6) 
996.50 
(62.209) 
20 
(68.0) 
998.20 
(62.315) 
28 
(82.4) 
996.23 
(62.192) 
21 
(69.8) 
997.99 
(62.302) 
29 
(84.2) 
995.95 
(62.175) 
21.1 
(70.0) 
997.97 
(62.301) 
29.4 
(85.0) 
995.83 
(62.166) 
22 
(71.6) 
997.77 
(62.288) 
30 
(86.0) 
998.65 
(62.156) 
C. Testing Procedure
NOTE: There are two methods of consolidating the concrete – rodding and vibration. If the slump is greater than 3 in. (75 mm), consolidation is by rodding. When the slump is 1 to 3 in. (25 to 75 mm), internal vibration or rodding can be used to consolidate the sample, but the method used must be that required by the agency in order to obtain consistent, comparable results. For slumps less than 1 in. (25 mm), the sample may be consolidated by internal vibration.
NOTE: The measure should be slightly over full, about 1/8 in. (3 mm) above the rim. If there is a great excess of concrete, remove a portion with the scoop. If the measure is under full, add a small quantity. This adjustment may be done only after consolidating the final layer and before striking off the surface of the concrete.
D. Calculations
Unit Weight (density) – Calculate the net weight, W_{3}, of the concrete in the measure by subtracting the weight of the measure, W2_{,} from the gross weight of the measure plus the concrete, W1. Calculate the density, ρ, by dividing the net weight, W_{3}, by the volume, V_{m}, of the measure as shown below.
_{} Example: 42.8 – 7.6 = 35.2 lb.
_{} Example: _{}
Theoretical unit weight (airfree basis) – The theoretical unit weight, T, is the total weight of materials batched divided by the absolute volume of materials batched on an airfree basis.
Using the actual batch weights and absolute volumes, sum the following:
Weight SpGr Abs. Vol. Example Abs. Vol. Calc.
Cement 477 3.14 0.090 = 477/(3.14 x 62.4 x 27)
Fly Ash 84 2.68 0.019
Total Water 220 1.00 0.131 (Plant, aggr., grade)
Fine 1246 2.65 0.279 Aggregate, SSD Dry Batch Weights
Intermediate 364 2.57 0.084
Coarse 1451 2.57 0.335
Total 3842 0.938
Theoretical unit weight (cu. Ft.) = Batch weight
Abs. Vol. x 27
= 3842
0.938 x 27
= 151.7 lbs./cu. ft.
Air Content – Air content is calculated by subtracting the unit weight, ρ, from the theoretical unit weight, T, divided by the theoretical unit weight, T, multiplied by 100 as shown below.
_{}
Example: _{}
Theoretical Unit Weight = 151.7 lbs./cu. ft.
The theoretical unit weight, T, is the total weight of materials batched divided by the absolute volume of materials batched on an air free basis.
Relative Batch Yield – Calculate the yield, Y, or volume of concrete produced per cubic yard, by dividing the total weight of the cubic yard batched, W_{t,} by 27, then dividing by the density, ρ, of the concrete as shown below.
_{}
Example: _{}