### Calculating the quantity of cement, sand, & aggregates in M10 (1:3:6) grade PCC./Rate analysis of PCC.

Let us consider M10 grade PCC as shown in the below drawing for the calculation purpose.

Given data:

The grade of PCC = M10.

Length of the PCC bed = 4m.

Breadth of the PCC  = 2.5m.

The thickness of the PCC = 100mm. = 0.01m.

The volume of the PCC bed

= length × breadth × thickness

= 4m. × 2.5m. × 0.01m.

= 1 CUM.

Here,

Cement:sand: aggregates = 1:3:6 (a:b:c)

M10 grade means 👉  1:3:6 ratio.

Wet volume of PCC = 1 cum.

Now, dry volume of PCC

= 1.54 × 1 cum = 1.54 cum.

1. Volume of  cement required

= [{its ratio  ÷ (total ratio)} × dry volume of PCC.]

=[{ a ÷ (a + b + c)} × dry volume of PCC.]

= [{1÷ ( 1 + 3 +6 )} × 1.54]

= [{ 1 ÷ 10 } × 1.54]

= [0.1 × 1.54]

=  0.154 cum.

As you know, 1 bag of cement = 0.03472 cum.

So, the number of cement bags required

= 0.154 cum. ÷ 0.03472 cum.

= 4.435 bags

Weight of cement

= 4.435 bags × 50 kgs.

(1 bag of cement = 50 kgs.)

221.77 kgs.

2. Volume of sand required

= [{its ratio  ÷ (total ratio)} × dry volume of PCC.]

=[{ b ÷ (a + b + c)} × dry volume of PCC.]

= [{3÷ ( 1 + 3 +6 )} × 1.54]

= [{3 ÷ 10 } × 1.54]

= [0.3 × 1.54]

=  0.462 cum.

=  16.32 cu ft.

3. Volume of aggregates required

= [{its ratio  ÷ (total ratio)} × dry volume of PCC.]

=[{ c ÷ (a + b + c)} × dry volume of PCC.]

= [{6÷ ( 1 + 3 +6 )} × 1.54]

= [{ 6 ÷ 10 } × 1.54]

= [0.6 × 1.54]

=  0.924 cum.

= 32.63 cu ft.

4. Volume of water required.

Let us consider the w/c ratio for M10 grade concrete as 0.5.

i.e. wt. of cement / wt. of water = 0.5

So, the weight. of water

= 0.5 × wt. of cement

=0.5 × 221.77 kgs

= 110.89 kgs

= 110.89 liters

( 1kg= 1 liter)

Note: This w/c ratio holds good if you use plasticizers. Practically for good workability, the water we add for the concrete is 133 liters.

#### Alternate method:

1. Volume of cement ( from above) = 0.154 cum.

2. Volume of sand

= [volume of cement × b]

=   [0.154 cum × 3]

= 0.462 cum.

3.  Volume of aggregates

= [volume of cement × c]

= [ 0.154 cum × 6]

= 0.924 cum.

Now, let us put these material quantities in a table format for easy reference.
 Materials in 1CUM of M10 grade PCC. Sl. No. Item Unit In cum. In cu ft. 1. Cement bags 4.435 bags - 2. Sand - 0.462 16.32 3. Aggregates - 0.924 32.63 4. Water litres 110.89 -

Note: To calculate the quantity of materials in M7.5 & M15 grade PCC, you have to replace the mix ratio in the above calculation.