**COMPUTATION METHOD OF CONCRETE
VOLUME CALCULATION**

The computation method of concrete volume calculation involves the use of a formula which specifies each constituent element. The formula for calculating concrete volume and materials required is given as

Vc = W + C + F_{a} + C_{a }

1000 1000S_{c} 1000S_{fa} 1000S_{ca}

Where Vc = Absolute volume of fully compacted fresh concrete

W =Mass of water

C = Mass of cement

Fa = Mass of fine aggregates

Ca = Mass of coarse aggregates

While Sc, Sfa, and Sca are the specific gravities of cement, fine aggregates, and coarse aggregates respectively. In this formula, the air content has been ignored

This method of calculating the concrete volume and quantities of materials takes into account the mix proportions from design mix or nominal mixes for structural strength and durability requirement.

## Calculation of materials Quantities per cubic meter concrete

Let us consider concrete with a mix ratio of 1:1.5:3 with water cement ratio of 0.45

**SOLUTION –** **COMPUTATION METHOD OF CONCRETE VOLUME **

From the question above, 1 represents part of cement, 1.5 represent parts of fine aggregates and 3 parts of coarse aggregates of a maximum size of 20mm.

Since volume has a close relationship with density, let us outline the density of the constituent of the concrete.

Cement = 1440 kg/m3, Sand = 1600 kg/m3, Coarse aggregates = 1600 kg/m3

**SPECIFIC GRAVITIES OF CONCRETE
MATERIALS ARE AS FOLLOWS**

Cement = 3.15, Sand = 2.6, Coarse aggregates = 2.6.

The percentage of entrained air is assumed to be 2%.

**DRY VOLUME OF MATERIALS
EXPRESSED IN TERMS OF MASSES**

Cement = 1 x 1440 = 1440

Sand = 1.5 x 1600 = 2400

Coarse aggregate = 3 x 1600 = 4950.

Therefore, the ratio of masses of these materials with respect to cement will be as follows

1440 : 2400 : 4950

1440 : 1440 : 1440

= 1: 1.7 : 3.4

The water cement ratio = 0.45

Now let us calculate the volume of concrete that can be produce with one bag of cement (i.e. 50 kg) using the formula.

The absolute volume of concrete that can be produce with 50 kg of cement is thus:

Vc = 0.45 x 50 + 1 x 50 + 1.7 x 50 + 3.4 x 50

1000 1000 x 3.15 1000 x 2.6 1000 x 2.6

Vc = 0.0225 + 0.0158 + 0.0326 + 0.0653= 0.136m^{3}

Thus, for the proportion
of mix considered, one bag of cement of 50 kg will produce a concrete of volume
0.1362m^{3}

We have considered an
entrained air of 2%. Therefore, the actual volume of concrete for 1 cubic meter
of compacted concrete for construction will be = 1 -0.02 = 0.98m^{3}.

Since the volume of concrete that be produce with one bag of
cement is 0.1362m^{3}, the quantity of cement required for 1 cubic
meter of concrete will be = 0.98/0.1362 = 7.19 approximately, 7 bags of cement.

**THE QUANTITIES OF MATERIALS FOR 1m ^{3} OF CONCRETE – COMPUTATION METHOD OF CONCRETE VOLUME**

The quantity of materials needed to produce 1m^{3} of concrete in term of weight can be calculated as follows:

The weight of cement required = 7.19 x 50 = 359.5 kg.

Weight of fine aggregate (sand) = 1.5 x 359.5 = 539.25 kg.

Weight of coarse aggregate = 3 x 359.5 = 1078.5 kg.