what is the basic formula to calculate the mix design propertion
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Step By Step Procedure For Concrete Mix Design Of M30 Grade Concrete
Step 1 — Determining The Target Strength For Mix Proportioning
F’ck = fck + 1.65 x S
Where,
F’ck = Target average compressive strength at 28 days
Fck = Characteristic compressive strength at 28 days
S = Assumed standard deviation in N/mm2 = 5 (as per table -1 of IS 10262- 2009)
= 30 + 1.65 x 5.0 = 38.25 N/mm2
Note : Under control conditions if Target average compressive strength is achieved then at field the probability of getting compressive strength of 30 MPa is very high
Step 2 — Selection Of Water-Cement Ratio:-
From Table 5 of IS 456, Maximum water-cement ratio = 0.50
Note : Do not start with w/c ratio above 0.50,even though the other desired results like Strength, workability could be achieved.
Step 3 — Selection Of Water Content
Maximum water content for 20 mm aggregate = 186 Kg (for 25 to 50 slump)
We are targeting a slump of 100mm, we need to increase water content by 3% for every 25mm above 50 mm i.e. increase 6% for 100mm slump
i.e. Estimated water content for 100 Slump = 186+(6/100) X 186 = 197 litre
Water content = 197 liters
Step 4 – Calculation Of Cement Content
Water-Cement Ratio = 0.50
Water content from Step – 3 i.e. 197 liters
Cement Content = Water content / “w-c ratio” = (197/0.50) = 394 kgs
From Table 5 of IS 456,
Minimum cement Content for moderate exposure condition = 300 kg/m3
394 kg/m3 > 300 kg/m3, hence, OK.
As per clause 8.2.4.2 of IS: 456
Maximum cement content = 450 kg/m3, hence ok too.
Step 5: Proportion Of Volume Of Coarse Aggregate And Fine Aggregate Content
From Table 3 of IS 10262- 2009, Volume of coarse aggregate corresponding to 20 mm size and fine aggregate (Zone I) = 0.60
Note 1: In the present case water-cement ratio is 0.5.So there will be no change in coarse agreegate volume i.e. 0.60 .
Note 2: Incase the coarse aggregate is not angular one, then also volume of coarse aggregate may be required to be increased suitably based on experience.
Step 6: Estimation Of Concrete Mix Calculations
The mix calculations per unit volume of concrete shall be as follows:
Volume of concrete = 1 m3
Volume of cement = (Mass of cement / Specific gravity of cement) x (1/100) = (39/3.15) x (1/1000) = 0.125 m3
Volume of water = (Mass of water / Specific gravity of water) x (1/1000) = (197/1) x (1/1000) = 0.197 m3
Total Volume of Aggregates = 1- (b+c) =1- (0.125+0.197) = 0.678 m3
Mass of coarse aggregates = d X Volume of Coarse Aggregate X Specific Gravity of Coarse Aggregate X 1000 = 0.678 X 0.60 X 2.80 X 1000 = 1139 kgs/m3
Mass of fine aggregates = d X Volume of Fine Aggregate X Specific Gravity of Coarse Aggregate X 1000 = 0.678 X 0.40 X 2.70 X 1000 = 732 kgs/m3
Step-7: Concrete Mix Proportions For Trial Number 1
Cement = 394 kg/m3
Water = 197 kg/m3
Fine aggregates = 732 kg/m3
Coarse aggregate = 1139 kg/m3
Water-cement ratio = 0.50
Note-1: Aggregates should be used in saturated surface dry condition. If otherwise, when computing the requirement of water, allowance shall be made for the free (surface) moisture contributed by coarse aggregate and fine aggregate. On the other hand, if the aggregates are already dry , the amount of water mixed should be increased by an amount equal to the moisture likely to be absorbed by the aggregates. Necessary adjustments are also required to be made in the mass of the aggregates. The surface water and percenetage water abosorption shall be determined according to IS 2386.
Correction in water content due to absorption or moist aggregates
The slump shall be measured and the water content and shall be adjusted for achieving the required slump based on trial, if required. The mix proportions shall be reworked for the actual water content and checked for durability requirements.
Two more trials having variation of +/- 10% of water cement ratio shall be carried out and a graph between three water-cement ratios and their corresponding strength shall be plotted to work out the mix proportions for the given target strength for field trials. However, durability requirement shall be met.
Step 1 — Determining The Target Strength For Mix Proportioning
F’ck = fck + 1.65 x S
Where,
F’ck = Target average compressive strength at 28 days
Fck = Characteristic compressive strength at 28 days
S = Assumed standard deviation in N/mm2 = 5 (as per table -1 of IS 10262- 2009)
= 30 + 1.65 x 5.0 = 38.25 N/mm2
Note : Under control conditions if Target average compressive strength is achieved then at field the probability of getting compressive strength of 30 MPa is very high
Step 2 — Selection Of Water-Cement Ratio:-
From Table 5 of IS 456, Maximum water-cement ratio = 0.50
Note : Do not start with w/c ratio above 0.50,even though the other desired results like Strength, workability could be achieved.
Step 3 — Selection Of Water Content
Maximum water content for 20 mm aggregate = 186 Kg (for 25 to 50 slump)
We are targeting a slump of 100mm, we need to increase water content by 3% for every 25mm above 50 mm i.e. increase 6% for 100mm slump
i.e. Estimated water content for 100 Slump = 186+(6/100) X 186 = 197 litre
Water content = 197 liters
Step 4 – Calculation Of Cement Content
Water-Cement Ratio = 0.50
Water content from Step – 3 i.e. 197 liters
Cement Content = Water content / “w-c ratio” = (197/0.50) = 394 kgs
From Table 5 of IS 456,
Minimum cement Content for moderate exposure condition = 300 kg/m3
394 kg/m3 > 300 kg/m3, hence, OK.
As per clause 8.2.4.2 of IS: 456
Maximum cement content = 450 kg/m3, hence ok too.
Step 5: Proportion Of Volume Of Coarse Aggregate And Fine Aggregate Content
From Table 3 of IS 10262- 2009, Volume of coarse aggregate corresponding to 20 mm size and fine aggregate (Zone I) = 0.60
Note 1: In the present case water-cement ratio is 0.5.So there will be no change in coarse agreegate volume i.e. 0.60 .
Note 2: Incase the coarse aggregate is not angular one, then also volume of coarse aggregate may be required to be increased suitably based on experience.
Step 6: Estimation Of Concrete Mix Calculations
The mix calculations per unit volume of concrete shall be as follows:
Volume of concrete = 1 m3
Volume of cement = (Mass of cement / Specific gravity of cement) x (1/100) = (39/3.15) x (1/1000) = 0.125 m3
Volume of water = (Mass of water / Specific gravity of water) x (1/1000) = (197/1) x (1/1000) = 0.197 m3
Total Volume of Aggregates = 1- (b+c) =1- (0.125+0.197) = 0.678 m3
Mass of coarse aggregates = d X Volume of Coarse Aggregate X Specific Gravity of Coarse Aggregate X 1000 = 0.678 X 0.60 X 2.80 X 1000 = 1139 kgs/m3
Mass of fine aggregates = d X Volume of Fine Aggregate X Specific Gravity of Coarse Aggregate X 1000 = 0.678 X 0.40 X 2.70 X 1000 = 732 kgs/m3
Step-7: Concrete Mix Proportions For Trial Number 1
Cement = 394 kg/m3
Water = 197 kg/m3
Fine aggregates = 732 kg/m3
Coarse aggregate = 1139 kg/m3
Water-cement ratio = 0.50
Note-1: Aggregates should be used in saturated surface dry condition. If otherwise, when computing the requirement of water, allowance shall be made for the free (surface) moisture contributed by coarse aggregate and fine aggregate. On the other hand, if the aggregates are already dry , the amount of water mixed should be increased by an amount equal to the moisture likely to be absorbed by the aggregates. Necessary adjustments are also required to be made in the mass of the aggregates. The surface water and percenetage water abosorption shall be determined according to IS 2386.
Correction in water content due to absorption or moist aggregates
The slump shall be measured and the water content and shall be adjusted for achieving the required slump based on trial, if required. The mix proportions shall be reworked for the actual water content and checked for durability requirements.
Two more trials having variation of +/- 10% of water cement ratio shall be carried out and a graph between three water-cement ratios and their corresponding strength shall be plotted to work out the mix proportions for the given target strength for field trials. However, durability requirement shall be met.
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