Concrete design mix (ss)

1
Concrete Mix Design
By K.Shah
B.E.(Civil Engg) NIT Rourkela,India
M.Sc. (Environment), University of Leeds, UK
Ex-GM(Civil & Environment) – MNC
Currently Guest faculty-College of Technology &
Engineering

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Concrete Mix Design
Mix design is defined as the process of
selecting suitable ingredients of concrete
and determine their relative proportions
with the object of producing concrete of
certain minimum strength and durability as
economically as possible.

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• Variables in Proportioning :4 varaible
factors to be considered:
1. Water – cement Ratio
2. Cement –aggregate ratio
3. Gradation of the aggregates
4. Consistency

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• In design mix ,generally 2-3 factors are specified
& others are adjusted.
• To use minimum amount of cement paste that
can lubricate the mass and will bind the
aggregates together and fill the space between
them.
• Excess paste involves more cost, shrinkage,
impermeability etc.
• Good gradation of aggregates to minimize voids.

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Methods of Proportioning
1. Indian Standards Recommended method IS 10262-82
2. American Concrete Institute Method of Mix Design (ACI 211)
3. DOE method
4. Mix design for pumpable concrete
5. Indian Road Congress , IRC 44 method
6. Road note no.4 (Grading curve method)
7. Mix design based on flexural strength
8. Arbitrary proportion
9. Fineness modulus methods
10. Maximum density method
11. Surface area method

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American Concrete Institute
Method of Mix Design (ACI)
Data to be collected:
a) Fineness modulus of fine aggregates
b) Sp gravity of coarse & fine aggregates
c) Absorption characteristics of coarse &
fine aggregates
d) Sp gravity of cement

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STEPS IN ACI METHOD
1. From minimum strength specified, estimate average design
strength using standard deviation method
2. Find w/c ratio from table 2. Find water cement ratio for durability
from table 3. adopt lower value.
3. Decide maximum size of aggregate (generally 20 mm for RCC)
4. Decide workability in terms of slump for the type of job in hand.
Table 4.
5. Total water in kg/m3 is read from table 5 entering the table with
selected slump & selected maximum size of aggregate.
6. Cement content is computed by dividing total water content by w/c
ratio.

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7. From table 4 the bulk volume of dry rodded coarse aggregate / unit
volume of concrete is selected, for particular maximum size of
coarse aggregate & fineness modulus of fine aggregate.
8. The weight of CA /M3 of concrete is calculated by multiplying the
bulk volume with bulk density.
9. The solid volume of coarse aggregate in one M3 of concrete is
calculated by knowing the sp. Gravity of CA
10. Solid volume of cement, water & volume of air is calculated in one
m3 of concrete
11. Solid volume of sand is calculated by substracting soild volume of
cement, CA,water, & air from total volume of concrete.
12. Weight of fine aggregate is calculated by multiplying the solid
volume of fine aggregate by sp gr of FA.

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(1) Dry Bulk Volume of coarse aggregate/ unit volume of
concrete as per ACI 211.1-91
Maximum
size of
aggregate
Bulk volume of dry rodded CA /unit volume of concrete for
fineness modulus of sand of
FM 2.4 2.6 2.8 3.OO
10 0.5 0.48 0.46 0.44
12.5, 0.59 0.57 0.55 0.53
20
(25,40,50,70)
0.66 0.64 0.62 0.60
150 .87 0.85 0.83 0.81

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(2) Relation between water/cement ratio & average
compressive strength of concrete, as per ACI211.1-91
Average compressive
strength at 28 days
Effective water/cement ratio (by mass)
MPa Non air entrained
concrete
Air entrained concrete
45 0.38 -
40 0.43 -
35 (30,25,20) 0.48 0.4
15 0.8 0.71

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(3) Requirements of ACI-318-89 for w/c ratio &
strength for special exposure conditions
Exposure condition Maximum w/c ratio,
normal density
aggregate concrete
Minimum design
strength, low density
aggregate concrete
MPa
Concrete intended to be
watertight
(a) Exposed to fresh water
(b) Exposed to sea water
0.5
0.45
25
30
Concrete exposed to
freezing in a moist condition
0.45 30
For corrosion protection of
reinforced concrete exposed
to de icing salts, sea water
0.4 33

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(4) Recommended value of slump for various
types of construction as per ACI 211.1-91
Type of construction Range of slump (mm)
Reinforces foundation walls & footings 20-80
Plain footings,substructure wall 20-80
Beams & reinforced walls 20-100
Building columns 20-100
Pavements & slabs 20-80
Mass concrete 20-80

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(5) Approximate requirements for mixing water & air content for
different workabilities & nominal maximum size of aggregates as per
ACI211.1-91
Non air entrained concrete
Workability
or air
content
(Slump)
Water content, kg/m3 of concrete for indicted maximum
aggregate size
10 mm 12.5 mm 20 mm 150 mm
( 25, 40,50,70)
30 -50 mm 205 200 185 125
80-100 mm 225 215 200 140
150-180 mm 240 230 210 -
Approx
entrapped
air (%)
3 2.5 2 0.2

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(6) First estimate of density of fresh concrete as
per ACI 211.1-91
Maximum size of
aggregate (mm)
First estimate of density of fresh concrete
Non air entrained kg/m3 Air entrained kg/m3
10 2285 2190
12.5 (20,25,40,50) 2315 2235
20 2355 2280
150 2505 2435

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(7) Required increase in strength (mean strength) for
specified design strength when no tests records are
available as per ACI 318-89
Specified design
strength (MPa)
Required increase in
strength (MPa)
Less than 21 7
21-35 8.5
35 or more 10

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Example –ACI method
Design a concrete mix for construction of elevated water tank.
a) Specified design strength = 30 MPa
b) Standard deviation = 4 MPa
c) Sp gr. FA & CA = 2.65 & 2.7
d) Dry rodded bulk density of CA = 1600 kg/m3
e) FM of FA = 2.8
f) Slump = 50 mm
g) CA is absorptive up to = 1 %
h) Free surface moisture in sand = 2 %

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Calculation
• Mean Strength fm = fmin+ks (k =1.64)
• fm = 30+1.64x4 = 36.56 say 36.5
• From table 2 w/c = 0.47
• From exposure condition w/c = .5
• Minimum of 0.47 & 0.5 = 0.47
• From table 5 for slump 50 mm, 20 mm maximum aggregate & non air
entrained condition Mixing water is 185 kg/m3
• Required cement content = 185/0.47 = 394 kg/m3
• From table 1, for 20 mm CA, FA 2.8, the dry rodded bulk vol of CA = 0.62
• Weight of CA = 0.62x1600 = 992 kg/m3
• From table 6,the first estimate of density of fresh concrete for 20 mm CA &
non air entrained concrete is 2355 kg/m3
•

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• Weight of all ingredient :
• Weight of water = 185 kg/m3
• Weight of cement =394 kg/m3
• Weight of CA = 992 kg/m3
• Weight of sand = 2355 –(185+394+992) = 784 kg/m3

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ingredients Weight kg/m3 Absolute volume cm3
cement 394 394/3.15x103 = 125x 103
Water 185 185/1 x103 = 185x 103
CA 992 992/2.7 x103 = 367 x 103
air 2/100 x103 = 20 x 103
Total abs vol 697 x 103 cm3

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• Therefore absolute vol of FA =(1000 -697) X 103 = 303 103 cm3
• Weight of FA = 303 x 2.65 = 803 kg/m3
• Estimated qty of ingredients;
a) Weight of water = 185 kg/m3
b) Weight of cement =394 kg/m3
c) Weight of CA = 992 kg/m3
d) Weight of sand = 803 kg/m3
• Proportion
• C : FA : CA ; WATER
• 394: 803 : 992 : 185
• 1 : 2.04 : 2.52 : 0.47
• For one bag of cement 50 kg Ratio in kg is = 50:102:126:23.5

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Indian Standard Method of
Concrete Mix-IS 10262-1982
STEPS

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IS Method - Step 1
Target mean strength of concrete
fck =fck1+tS
Refer table 1 & 2 for t & S
 fck = strength at 28 days
 fck1 = characteristics strength at 28 days
 t = 1.65 = statistical value; (depends on
expected proportion of low results( risk factor)
 S = standard deviation

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IS Method – Step 2
Selection of water cement ratio:
• From graph 1 ,w/c ration corresponding to
target strength is determined.

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• If 28 days strength of cement is known
then w/c ratio can also be calculated from
graph 2.

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Estimation of entrapped air:
• Air content is estimated from table 3 for
maximum size of CA

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Selection of water content & Fine to Total
aggregate ratio:
a) water content & % of sand in total aggregate is
determined from table 4 & 5
b) w/c ratio in table 4 is 0.6 & in table 5 it is 0.35
c) For any departure from above values,
corrections are made as per table 6 for w/c
ratio & sand in total aggregate.

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Calculation of cement content:
Cement content = water content from step
5 divided by w/c ratio
Cement content = Water content /w/c

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Calculation of aggregate content:
1. V = [ W+C/Sc + Fa/PSfa] x 1/1000
0.98 = [191.6 + 383/3.15 + Fa/ 0.315 x2.6]/1000 Fa = 546 kg/m3
1. Ca = (1-P)/P X fa x Sca/Sfa = (1-0.315)/0.315 x 546 x2.6/2.6 = 1188
kg/m3
V = absolute volume =gross vol – entrapped air
W = mass of water (kg)/m3 of concrete
C= mass of cement (kg)/m3 of concrete
Sc= sp gr of cement
P= ratio of FA to total aggregate by absolute volume
Fa, Ca Total masses of FA & CA kg/m3 of concrete
Sca , Sfa Sp Gr of saturated, surface dry FA & CA

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Example – IS method
Given:
a) Characteristic compressive strength : 20 Mpa
b) Maximum size aggregate : 20 mm (angular)
c) Degree of workability : 0.9 compacting factor
d) Degree of quality control : good
e) Type of exposure : mild
Test data for materials :
a) Sp gr of cement : 3.15
b) Comp strength of cement at 7 days : satisfies requirement of IS 269
c) Sp gr of CA : 2.6
d) Sp gr of FA : 2.6
e) Water absorption CA ; 0.5 %
f) Water absorption FA : 1.0 %
g) Free moisture CA : nil
h) Free moisture CA : 2 %

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sieve analysis-CA
• IS
Sieve
size
Analysis of CA
fractions(%
passing)
I II
Analysis of CA fractions(%
passing)
I II combined
60% 40% 100%
remark
20 100 100 60 40 10 Conform
ing to
table 2
of IS 383
10 0 71.2 0 28.5 28.5
4.75 9.4 3.7 3.7
2.36 - - - -

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sieve analysis -FA
• IS Sieve size Fine aggregate (% passing) remark
4.75 mm 100 Conforming to
grading zone III of
table 4 IS 385-1970
2.36 mm 100
1.18 mm 93
600 μ 60
300 μ 12
150 μ 2

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Answer –IS Method
step 1
Target mean strength of concrete
fck =fck1+tS = 20+1.65x4=26.6 MPa
Refer table 1 & 2 for t & S
 fck = strength at 28 days
 fck1 = characteristics strength at 28 days
 t = 1.65 = statistical value; (depends on
expected proportion of low results( risk factor)
 S = standard deviation

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Table 1-Values of tolerance factor(f)(risk factor)
Toleran
ce level
No. of
sample
s
1 in 10 1 in 15 1 in 20 1 in 40 1 in
100
10 1.37 1.65 1.81 2.23 2.76
20 1.32 1.58 1.72 2.09 2.53
30 1.31 1.54 1.7 2.04 2.46
Infinite 1.28 1.5 1.64 1.96 2.33

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Table 2- assumed standard deviation as per IS
456-2000
Grade of concrete Assumed standard deviation N/mm2
M 10
M 15 3.5
M 20
M 25 4
M 30
M 35
M40 5
M45
M50

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Step 2
• Selection of w/c ratio
• From graph 1, w/c ratio for target mean
strength 26.6 MPa is 0.50
• Refer table 4 of IS 456: maxmimum w/c
ratio for “Mild exposure” is 0.55.
• Adopt lower value from above 2 options i.e
0.50

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Table 3 – approximate entrapped air content
Maximum size of aggregate (mm) Entrapped air, as % of volume of
concrete
10 3
20 2
30 1

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Table 4- approx sand,watercontent / m3 of conc. ;
w/c=0.6, workability 0.8 C.F.(slump 30 mm approx)
(Applicable for grade up to M 35)
Max size
aggregate(mm)
Water content/ m3 of
conc. (kg)
Sand as % of total
aggregate by absolute
volume
10 200 40
20 186 35
40 165 30

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STEP 3
Selection of water & sand content:
 From table 4, for 20 mm maximum size aggregate,
sand conforming to grading zone II, water content kg/ M3
of concrete = 186 kg & sand as % of total aggregate by
absolute volume = 35 %.

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Step 3
Change in condition (see table ) % adjustment required
water content sand in total
aggregate
For decrease in
water –cement ratio by (0.60 – 0.50) i.e. 0.10
0 - 2.0
For increase in compacting factor (0.9-0.8) , i.e.
0.10
+3 0
For sand conforming to zone III of table 4 , IS
383
0 - 1.5
Total + 3 - 3.5
From Table 6 For change in value in water in w/c ratio, compaction factor, for
sand belonging to zone III, following adjustment is required :
Therefore required sand content as % of total aggregate by absolute volume
= 35 – 3.5 = 31.5 %
Required water content = 186 + 5.58 = 191.6 kg/m3

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Table 6- Adjustment of values in water content & sand % for other
conditions
Change in conditions
stipulated for tables
Adjustment required in
Water content % sand in total
aggregate
Sand conforming to
grading zone III or IV of
table IS 383-1979
0 +1.5 % for zone I
-1.5 % for zone III
-3% for zone IV
Increase or decrease in
value of compacting
factor by 0.1
+/- 3% O
Each 0.05 increase or
decrease in water
cement ratio
0 +/- 1 %
For rounded aggregate -15 kg -7 %

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Table 5- approx sand,watercontent / m3 of conc. ;
w/c=0.35, workability 0.8 C.F.(slump 30 mm approx)
(Applicable for grade above M 35)
Max size
aggregate(mm)
Water content/ m3 of
conc. (kg)
Sand as % of total
aggregate by absolute
volume
10 200 28
20 180 25

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Step 4
Determination of cement content :
w/c ratio = 0.5
Water = 191.6
Cement = 191.6/0.5 = 383 kg/m3

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Step 5
Determination of CA & FA :
From table 3, for 20 mm CA, amount of entrapped air is 2 %. Taking this into account &
applying equations 1 & 2 we get:
I. V = [ W+C/Sc + Fa/PSfa] x 1/1000
II. 0.98 = [191.6 + 383/3.15 + Fa/ 0.315 x2.6]/1000 Fa = 546 kg/m3
III. Ca = (1-P)/P X fa x Sca/Sfa = (1-0.315)/0.315 x 546 x2.6/2.6 = 1188 kg/m3
V = absolute volume =gross vol – entrapped air = 100-2=98 %
W = mass of water (kg)/m3 of concrete = (191.6 from step 3)
C= mass of cement (kg)/m3 of concrete
Sc= sp gr of cement =3.15 (given in question)
P= ratio of FA to total aggregate by absolute volume = (31.5% from step 3.)
Fa, Ca Total masses of FA & CA kg/m3 of concrete =546 calculated above @ II
Sca , Sfa Sp Gr of saturated, surface dry FA & CA = 2.6 (given in question)

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RESULT
• Estimated qty of ingredients;
a) Weight of water = 191.6 kg/m3
b) Weight of cement =383 kg/m3
c) Weight of CA = 1188 kg/m3
d) Weight of sand = 546 kg/m3
• Proportion
• 383: 546 : 1188 : 191.6
• 1 : 1.425 : 3.1 : 0.5
• For one bag of cement 50 kg Ratio in kg is =
50:71:155:25

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• Extra qty of water for absorption in CA = 0.5 % by mass = 0.77 liters
• Qty of water to be deducted for 2 % moisture in sand =1.42 liters
• Actual qty of water required = 25+.77-1.42 =24.35 liters
• Actual qty of sand = 71+1.42 =72.42
• CA : fraction I =93-0.46=92.54 kg
• Fraction II : 62-0.31=61.69 kg
• Actual qty :
• 50: 72.42 : 92.54 & 61.69 : 24.35

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