CONCRETE MIX DESIGN STEP BY STEP FULL CALCULATION

                 

                  CONCRETE MIX DESIGN STEP BY STEP FULL CALCULATION

Concrete mix design is the process of detrmining right proportions of cement, sand and aggregates for concrete to achieve target strength of concrete.

The Advantages of concrete mix design is that it gives the right proportions of materials, thus making the concrete use economical in achieving required strength of structural members. As, the quantity of concrete required for huge, constructions are huge, economy in quantity of materials such as cement makes the project construction economical.

Concrete Mix design of M – 20, M – 25, M – 30 and higher grade of concrete can be calculated from following steps:

Concrete Mix Design:

Data Required for Mix Design of Concrete:

Concrete Mix Design Date:-

(a) Characteristic compressive strength of concrete required at end of 28 days  = M 25

(b) Nominal maximum size of aggregate used = 20 mm

(c) Shape of Coarse Aggregate = Angular

(d) Required workability at site = 50-75 mm (slump Value)

(e) Quality control is done by as per IS: 456

(f) Type of exposure Condition of concrete (as defined in IS: 456) = Mild

(g) Type of cement used = PSC conforming IS: 456 – 2000

(h) Method of placing Concrete on Site = pumpable concrete

(ii) Material testing data (determined in the laboratory):

(a) Specific gravity of cement =  3.15

(b) Specific gravity of FA = 2.64

(c) Specific gravity of CA = 2.84

(d) Aggregates are assumed to be having surface dry condition.

(e) Fine aggregates are confirm to Zone II of IS – 383

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Procedure for M – 25 Concrete Mix Design:

Step 1: Determining the Target Strength of concrete:-

Himsworth constant for 5% risk factor is 1.65 & standard deviation is taken from IS: 456 2000 for M – 25 Grade of concrete is  4.0.

ftarget = fck + 1.65 x S

= 25 + 1.65 x 4.0 = 31.6 N/mm2

Where,

S = standard deviation (N/mm2) = 4 (Refer: IS 10262- 2009 table -1)

Step 2 — Determining water / cement ratio:-

Refer:  IS 456, (page no 20) Table 5

Maximum water-cement ratio taken for Mild exposure condition = 0.55

Assume water-cement ratio as 0.50 for experiment base

0.5 < 0.55, hence it is OK.

Step 3 — Selection of Water Content for mix:

Refer:  IS 10262- 2009 Table 2

Maximum water content taken = 186 Kg (maximum size of aggregate = 20 mm)Correction in water content is

Estimated water content for mix = 186+ (3/100) x 186 = 191.6 kg /m3

Step 4 :  Selection of Cement Content for mix:

Water-cement ratio = 0.50

Corrected water content for mix = 191.6 kg /m3

Cement content =

Refer IS 456 – 2000, Table 5

Minimum cement Content required for mild exposure condition = 300 kg/m3

383.2 kg/m3 > 300 kg/m3, hence, OK.

This value is required to be checked for durability requirement from IS: 456 – 2000

In this example for mild exposure and for the reinforced concrete the minimum cement content is 300 kg/m3 which are less than 383.2 kg/m3. Hence cement content adopted = 383.2 kg/m3.

IS: 456: 2000, clause 8.2.4.2

Maximum cement content for mix = 450 kg/m3.

Read more : Cement, Sand and Aggregate calculator

Step 5: Estimation of Coarse Aggregate proportion for mix :-

Refer IS 10262- 2009, Table 3

For Nominal max. size of aggregate for mix = 20 mm,

Zone of fine aggregate = Zone II

And For w/c = 0.5

Volume of coarse aggregate per unit volume Concrete = 0.62

Table for correction in estimation of coarse aggregate proportion

(Note 1: For every ±0.05 increase or decrease change in w/c, the coarse aggregate proportion is to be changed by 0.01. If the w/c is less than 0.5, volume of coarse aggregate is required to be increased to reduce the fine aggregate content in mix. If water cement ratio is more than 0.5, volume of coarse aggregate is to be reduced to increase the fine aggregate content. If coarse aggregate is not of  angular shape, volume of coarse aggregate is required to be increased suitably, based on experience based)

(Note 2: For pump able concrete or congested reinforcement in structure the coarse aggregate proportion may be reduced up to 10%)

Hence,

Volume of coarse aggregate per unit volume of total Volume of concrete = 0.62 x 90% = 0.558

Volume of fine aggregate in mix = 1 – 0.558 = 0.442

Step 6: Estimation of the mix Materials:

a) Volume of concrete is taken = 1 m3

b) Volume of cement = (Weight of cement / Specific gravity of cement) x (1/100)

= (383.2/3.15) x (1/1000) = 0.122 m3

c) Volume of water = (Weight of water / Specific gravity of water) x (1/1000)

= (191.6/1) x (1/1000) = 0.1916 m3

d) Volume of aggregates = a – (b + c ) = 1 – (0.122 + 0.1916) = 0.6864 m3

e) Weight of coarse aggregates = 0.6864 x 0.558 x 2.84 x 1000 = 1087.75 kg/m3

f) Weight of fine aggregates = 0.6864 x 0.442 x 2.64 x 1000 = 800.94 kg/m3

Concrete Mix proportions for Concrete Trial Mix – 1

Cement = 383.2 kg/m3

Water = 191.6 kg/m3

Fine aggregates = 800.94 kg/m3

Coarse aggregate = 1087.75 kg/m3

W/c = 0.5

For trial -1 of concrete in lab & to check its properties.

It will satisfy durability & economy.

For making trial -1, mass of ingredients required will be calculated for 4 no’s cube assuming 25% wastage.

Volume of concrete required for Making 4 cubes = 4 x (0.153 x1.25) = 0.016878 m3

Wt. of Cement = (383.2 x 0.016878) kg/m3 = 6.47 kg

Wt. of Water = (191.6 x 0.016878) kg/m3 =3.23 kg

Wt. of Coarse aggregate = (1087.75 x 0.016878) kg/m3 =18.36 kg

Wt. of Fine aggregates = (800.94 x 0.016878) kg/m3 = 13.52 kg

Step 7: Correction for absorption / moisture of aggregate:-

As we assumed the aggregate is saturated surface dry condition, therefore no correction is required.

Step 8: Concrete Trial Mixes:-

Concrete Trial Mix 1:

The mix proportion determined in Step 6 Make trial mix -1 & with this proportion, concrete is manufactured and tested for fresh concrete properties requirement like workability, bleeding and finishing qualities.

In this Trial Mix,

Slump value = 25 mm

Compaction Factor = 0.844

From Mix Slum test, the concrete is  workable and had a true slump of about 25 mm and it is free from segregation and bleeding.

required slump = 50-75 mm

So modifications and changes are needed in trial mix 1 to get the desired workability.

Concrete Trial Mix 2:

To increase the workability of concrete mix from 25 mm to 50-75 mm an increase in water content by +3% is to be made.

The corrected water content for mix = 191.6 x 1.03 = 197.4 kg.

As mentioned earlier to adjust fresh concrete properties the water cement ratio should not be changed. Hence

Cement Content = (197.4/0.5) = 394.8 kg/m3

Which also need to satisfy durability requirement.

Volume of aggregate in Concrete = 1 – [{394.8/(3.15×1000)} + {197.4/(1 x 1000)}] = 0.6773 m3

Weight of coarse aggregate = 0.6773 x 0.558 x 2.84 x 1000 = 1073.33 kg/m3

Weight of fine aggregate = 0.6773 x 0.442 x 2.64 x 1000 = 790.3 kg/m3

Concrete Mix Proportions for Trial Mix 2

Weight of Cement = 384.8 kg/m3

Weight of  Water = 197.4 kg/m3

Weight of  Fine aggregate =790.3 kg/m3

Weight of Coarse aggregate = 1073.33 kg/m3

For making trial -2, Weight of material required will be calculated for 4 no’s cube assuming 25% wastage.

Volume of concrete required for 4 cubecasting = 4 x (0.153 x1.25) = 0.016878 m3

Weight of Cement = (384.8 x 0.016878) kg/m3 = 6.66 kg

Weight of Water = (197.4 x 0.016878) kg/m3 =3.33 kg

Weight of Coarse aggregate = (1073.33 x 0.016878) kg/m3 =18.11 kg

Weight of Fine aggregates = (790.3 x 0.016878) kg/m3 = 13.34 kg

In this trial Mix,

Slump value for mix = 60 mm

Compaction Factor for mix = 0.852

So, from results of slump of Mix , the concrete is workable and had a true slump of about 60 mm.

Required slump = 50-75 mm

So, it satisfied the desired workability by satisfying the requirement of 50-75 mm slump value.

Now, we have to go for trial mix-3

Concrete Trial Mix 3 :

In this trial mix water / cement ratio is to be decreased by 10% keeping water content constant.

Water cement ratio = 0.45

As reduction of 0.05 in w/c, we have to increase of coarse aggregate fraction by 0.01.

Coarse aggregate fraction in mix = 0.558 +0.01 =0.568

W/c = 0.45 and water content for mix = 197.4 kg/m3

Cement content for mix = (197.4/0.45) = 438.7 kg/m3

Volume aggregate in total volume of concrete = 1 – [{438.7/(3.15 x 1000)} + (197.4/1000)] = 0.664 m3

Weight of coarse aggregate = 0.664 x 0.568 x 2.84 x 1000 = 1071.11 kg/m3

Weight of fine aggregate = 0.664 x 0.432 x 2.64 x 1000 = 757.28 kg/m3

Recommended mix Weight of ingredients for grade of concrete M25:

For  Compressive Strength of concrete vs. C/W graph for target strength 31.6 MPa , we found

Water cement ratio = 0.44

Weight of water content = 197.4 kg/m3

Weight of Cement content = (197.4/0.44) = 448.6 kg/m3

Volume of aggregate in total volume of concrete = 1 – [{448.6/(3.15 x 1000)} + (197.4/1000)] = 0.660 m3

A reduction of 0.05 in w/c, we have to increase of coarse aggregate fraction by 0.01.

Coarse aggregate volume = 0.558 +0.01 =0.568

Volume of fine aggregate in mix = 1 – 0.568 = 0.432

Weight of coarse aggregate = 0.660 x 0.568 x 2.84 x 1000 = 1064.65 kg/m3

Weight of fine aggregate = 0.660 x 0.432 x 2.64 x 1000 = 752.71 kg/m3