How to calculate cement sand and aggregate quantity in concrete
The absolute volume method is used to work out the necessary quantities of materials for developing the desired quantity of concrete based on the specified mix ratios. This method follows the principle that the volume of fully compacted concrete is equivalent to the absolute volume of all the materials of concrete like cement, sand, course aggregates and water.
The materials are measured for the necessary volume of concrete with the following formula :-
- Here, VC denotes absolute volume of fully compacted fresh concrete
- W denotes mass of water
- C denotes mass of cement
- Fa denotes mass of fine aggregates
- Ca denotes mass of coarse aggregates
- SC, Sfa, Sca belong to the specific gravities of cement, fine aggregates and coarse aggregates simultaneously.
The calculation method considers the mix ratios from design mix or nominal mixes for structural stability and longevity requirement.
Given below, the process for material calculation :-
Assume mix ratios of concrete as 1: 1.5:3 where, 1 is for cement, 1.5 is for fine aggregates and 3 is for coarse aggregates of highest size of 20 mm.
The necessary water cement ratio for mixing of concrete is chosen as 0.45
Suppose, bulk densities of materials is given as follow :-
Cement = 1500 kg/m3
Sand = 1700 kg/m3
Course aggregates = 1650 kg/m3
Cement = 3.15
Sand = 2.6
Course aggregates = 2.6
The percentage of entrained air is taken as 2%
The mix ratios of 1:1.5:3 by dry volume of materials is represented in respect of masses as follow :-
Cement = 1 x 1500 = 1500
Sand = 1.5 x 1700 = 2550
Coarse aggregate = 3 x 1650 = 4950
So, the ratio of masses of these materials w.r.t. cement will be as follow :-
1 : 2550/1500 : 4950/1500 = 1: 1.7 : 3.3
The water cement ratio = 0.45
Now, the volume of concrete will be measured that can be formed with one bag of cement (50 kg of cement) for the mass ratios of concrete materials.
So, the absolute volume of concrete for 50 kg of cement will be as follow :-
Therefore, for the ratio of mix considered , with one bag of cement of 50 kg, 0.1345 m3 concrete will be formed.
Here, entrained air is taken as 2%. So, the actual volume of concrete for 1 cubic meter of compacted concrete construction should be = 1 - 0.02 = 0.98 m3
Therefore, the necessary quantity of cement for 1 cubic meter of concrete = 0.98 / 0.1345 = 7.29 bags of cement.
The quantities of materials for 1 m3 of concrete should be measured as follow :-
The necessary weight of cement = 7.29 x 50 = 364.5 kg.
The weight of fine aggregate (sand) = 1.5 x 364.5 = 546.75 kg.
The weight of coarse aggregate = 3 x 364.5 = 1093.5 kg.