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. diameter, having a hemispherical tip.
4. Vibrator: 7000 vibrations per minute, 0.75 in. to 1.50 in. in diameter, at least 3 in. 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. thick, with a length and width at least 2 in. greater than the diameter of the measure. The edges of the plate shall be straight and smooth within tolerance of 1/16 in.
8. Rubber Mallet


Table 1  Dimensions of Measures 

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

Bottom 
Wall 







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 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: V_{m} = 15.57 / 62.274 = 0.250 ft^{3} ,
Where,
weight measure, plate, & water = 25.64 lbs
weight measure & plate = 10.07 lbs
weight water = 25.6410.07 = 15.57 lbs.
Density of Water @73.5 ºF = 62.274 lbs/ft^{3}
ºF 
lb./ft. ³ 
ºF 
lb./ft. ³ 
ºF 
lb./ft. ³ 
60.0 
62.366 
68.0 
62.315 
77.0 
62.243 
61.0 
62.361 
69.0 
62.309 
78.0 
62.234 
62.0 
62.355 
70.0 
62.301 
79.0 
62.225 
63.0 
62.349 
71.0 
62.294 
80.0 
62.216 
64.0 
62.343 
72.0 
62.286 
81.0 
62.206 
65.0 
62.336 
73.0 
62.278 
82.0 
62.197 
66.0 
62.330 
74.0 
62.270 
83.0 
62.187 
66.0 
62.330 
75.0 
62.261 
84.0 
62.177 
67.0 
62.323 
76.0 
62.252 
85.0 
62.166 
C. Testing Procedure
NOTE: There are two methods of consolidating the concrete – rodding and vibration. If the slump is greater than 3 in., consolidation is by rodding. When the slump is 1 to 3 in., 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., 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, W_{2,} from the gross weight of the measure plus the concrete, W_{1}. Calculate the density, ρ, by dividing the net weight, W_{3}, by the volume, V_{m}, of the measure as shown below.
W_{1  }W_{2 = }W_{3} Example: 42.8 – 7.6 = 35.2 lb.
ρ = W_{3 }/ V_{m}_{ }Example: ρ = 35.2 lb / 0.249 cu. ft. = 141.4 lbs/cu. ft.
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.
A = (T – ρ) X 100 / T
Example: A = (151.7 lbs/cu. ft. – 141.4 lbs/cu. ft.) X 100 = 6.8%
151.7 lbs/cu. ft.
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.
Y = (W_{t} ÷ 27) / ρ
Example: Y = (3842 lbs batched per cu. yd ÷ 27 lbs/cu. ft.) / 141.4 lb/cu. ft = 1.006
E. Density of Foamed Cellular Concrete
Foamed cellular concrete density may be determined as above using a smaller 1/10 cubic foot measure, or using a 400 ml cup and the following procedure.
1. Apparatus
a. Measure: A cylindrical measure meeting the requirements of ASTM C 185. Otherwise, any cylindrical container of a known volume, made of steel or other suitable metal container, not readily attacked by Portland cement.
b. Balance or scale: Accurate to 0.3 percent of the test load at any point within the range of use.
c. Scoop or spoon
d. A strike off bar
e. A metal or glass plate at least 1/4 in. thick, with a length and width at least 1 in. greater than the diameter of the measure.
2. Testing Procedure
a. Determine the weight of the dry measure. Include the glass plate when using the 400 ml cup
b. Obtain the sample of the foamed concrete. Testing shall begin within five minutes of obtaining the sample.
c. Dampen the inside of the measure.
d. Fill the measure in one layer, slightly overfilling the measure. Do not strike sides of measure. An excess of concrete protruding approximately 3 mm [^{1}/_{8} in.] above the top of the mold is optimum.
e. Strike off the surface of the concrete and finish it smoothly with a screening action of the strike off bar (sawing action of the strikeoff plate) using great care to leave the pot just full. The surface should be smooth and free of voids.
f. Press the glass plate down on the surface of the concrete to ensure the surface free of voids. Clean off all excess concrete from the exterior of the measure including the bottom of the plate. Determine and record the weight of the measure, plate, and concrete.
3. Calculations
Wt Cup + Plate + Conc. (gms)= 
1069.00 

Wt. Mortar Cup + Plate (gms)= 
741.50 

Weight of Concrete (gms)= 
327.50 

Volume of 400 ml container (l)= 
0.400 

Actual Unit Weight = 
327.50/0.400 
= 818.75 kg/m^{3} 



Convert kg/m^{3} to lb/ft^{3} 


818.75 kg/m^{3} / 16.0185 kg/m^{3} /lb/ft^{3} 

= 51.1 lb/ft^{3} 