Mix design M 40

Mix Design of M40 mix concrete by IS method:

(a) Design stipulations:

Characteristic compressive strength required in the field at 28 days.	40 MPa
Maximum size of aggregate	20 mm (angular)
Degree of quality control	Good
Type of Exposure	Mild

(b) Test data for Materials:

Specific gravity of cement	3.15
Compressive strength of cement at 7 days	Satisfies the requirement of IS: 269 – 1989
1. Specific gravity of coarse aggregates	2.60
2. Specific gravity of fine aggregates	2.60
Water absorption:
1. Coarse aggregate	1.0%
2. Fine aggregate	1.0%
Free (surface) moisture:
1. Coarse aggregate	Nil
2. Fine aggregate	2.0%

(c) Target mean strength of concrete:

The target mean compressive (f_t) strength at 28 days is given by

f_t = f_ck + 1.65 S

i.e. 40 + 1.65 x 5 = 48.25 MPa

(d) Selection of water-cement ratio:

The water-cement ratio required for the target mean strength of 48.25 MPa is 0.40. Adopt W/C ratio of 0.40.

(e) Selection of water and sand content:

For 20 mm maximum size aggregate, sand confirming to grading Zone II, water content per cubic metre of concrete = 180 kg and sand content as percentage of total aggregate by absolute volume = 25 per cent.

Required water content = 180 + 5.4 = 185.4/m³

(f) Determination of cement content:

Water-cement ratio = 0.40

Water = 185.4 litre

Cement by mass = Water content/Water cement ratio

Cement = 185.4/0.40 = 463.5 kg/m³

This cement content is adequate for ‘mild’ exposure condition.

(g) Determination of coarse and fine aggregate contents:

For the specified maximum size of aggregate of 20 mm, the amount of entrapped air in the wet concrete is 2 per cent. Taking this into account and applying equations.

Where V = absolute volume of concrete = gross volume (1m³) minus the volume of entrapped air

           S_c = specific gravity of cement

              W = Mass of water per cubic metre of concrete, kg

            C = mass of cement per cubic metre of concrete, kg

            p = ratio of fine aggregate to total aggregate by absolute volume

     f_a, C_a = total masses of fine and coarse aggregates, per cubic metre of concrete, respectively, kg, and

  S_fa, S_ca = specific gravities of saturated surface dry fine and coarse aggregates, respectively

f_a = 530.27 kg/m³, and

C_a = 1153.13 kg/m³.

The mix proportion then becomes:

Water	Cement	Fine aggregate	Coarse aggregate
185.4	463.5 kg	530.27 kg	1153.13 kg
0.40	1	1.14	2.49

(h) Actual quantities required for the mix per bag of cement:

The mix is 0.40: 1: 1.14: 2.49.

For 50 kg of cement, the quantities of materials are worked out as below:

                i.            Cement = 50 kg

              ii.            Sand = 57 kg

             iii.            Coarse aggregate = 124.5 kg                     

            iv.            Water:

a)      for w/c ratio of 0.40, quantity = 20 litres of water

b)      Extra quantity of water to be added for absorption in case of CA, at

0.5 per cent mass = 0.62 litres

c)      Quantity of water to be deducted for moisture present in sand, at

2 per cent by mass = 1.14 litres.

d)      Actual quantity of water required to be added = 20 + 0.62 – 1.14

                                                                                          = 19.48 litres

 Actual quantity of sand required after allowing for mass of free moisture = 57 + 1.14

                                                                                                               = 58.14 kg

Therefore, the actual quantities of different constituents required for one bag mix are:

Water          :         19.48 litres

Cement       :         50.00 kg

Sand           :          58.14 kg

Coarse Aggregates: 124.5 kg