An example illustrating the mix proportioning for a concrete of M 40 grade is given in A-1 to A-11.

A-1 Stipulations For Proportioning

a) Grade designation $\quad:$ $\quad$ M40

b) Type of cement $\quad:$ $\quad$ OPC 43 grade conforming to IS 8112

c) Maximum nominal size of aggregate $\quad:$ $\quad$ 20 mm

d) Minimum Cement Content $\quad:$ $\quad$ 320 $kg/m^3$

e) Maximum water-cement ratio $\quad:$ $\quad$ 0.45

f) Workability $\quad:$ $\quad$ 100mm (Slump)

g) Exposure condition $\quad:$ $\quad$ Severe (for reinforced concrete)

h) Method of concrete placing $\quad:$ $\quad$ Pumping

i) Degree of supervision $\quad:$ $\quad$ Good

j) Type of aggregate $\quad:$ $\quad$ Crushed angular aggregate

k) Maximum cement content $\quad:$ $\quad$ 450 $kg/m^3$

l) Chemical admixture type $\quad:$ $\quad$ Superplasticizer

A-2 Test Data for Materials

a) Cement used $\quad :$ OPC 43 grade conforming to IS 8112

b) Specific gravity of cement $\quad :$ 3.15

c) Chemical admixture $\quad :$ Superplasticizer conforming to IS 9103

d) Specific gravity of $\quad :$
Coarse aggregate$\quad :$ 2.74

e) Free (surface) moisture

1) Coarse aggregate $\quad :$ Nil (absorbed moisture also nil)

2) Fine aggregate $\quad :$ Nil

f) Sieve analysis $\quad :$

1) Coarse aggregate $\quad:$

2) Fine aggregate $\quad:$ Conforming to grading Zone I of Table 4 of IS 383

A- 3 Target Strength for Mix Proportioning.

$$ f_{c k}^{\prime}=f_{c k}+1.65 s $$

$\dot{\mathrm{f}}_{\mathrm{ck}}^{\prime}=$ target average compressive strength at 28 days,

$\mathrm{f}_{\mathrm{ck}}=$ characteristic compressive strength at 28 days and

$\mathrm{S}=$ standard deviation.

From Table 1

Standard deviation, $\quad s = 5N/mm^2$

Therefore, $\cdot$ target strength $=40+1.65 \times 5=48.25 \mathrm{N} / \mathrm{mm}^{2}$

A-4 Selection of Water Cement Ratio

From Table 5 of IS 456, maximum water cement ratio = 0.45

Based on experience, adopt water cement ration is 0.40

$0.40 \lt 0.45$ hence OK

A-5 Selection of Water Content

From table 2 of IS 10262 maximum water content for 20 mm aggregate = 186 litre (For 25 to 50 mm Slump range)

Estimated water content for 100 mm slump =$186+\frac{6}{100} \times 186 \\= 197 \ litre$

A-6 Calculation of Cement Content

$\begin{aligned} \text { Water-cement ratio } &=0.40 \\ \text { Cement content } &=\frac{140}{0.40}=350 \mathrm{kg} / \mathrm{m}^{3} \end{aligned}$

From Table 5 of IS 456 , minimum cement content for 'severe' exposure condition $=320 \mathrm{kg} / \mathrm{m}^{3}$

$350 \mathrm{kg}\mathrm{m}^{3}\gt320 \mathrm{kg} / \mathrm{m}^{3}$ , hence, O.K.

A- 7 Proportion of Volume of Coarse Aggregate and Fine Aggregate Content

From Table 3 of IS $10262,$ volume of coarse aggregate corresponding to 20 $\mathrm{mm}$ size aggregate and fine aggregate (Zone I) for water-cement ratio of $0.50=0.60 .$

In the present case water-cement ratio is $0.40 .$ Therefore, volume of coarse aggregate is required to be increased to decrease the fine aggregate content. As the water-cement ratio is lower by $0.10,$ the proportion of volume of coarse aggregate is increased by 0.02 (at the rate- $-/+0.01$ for every $\pm 0.05$ change in water-cement ratio). Therefore, corrected proportion of volume of coarse aggregate for the water-cement ratio of $0.40=0.62 .$

For pumpable concrete these values should be reduced by 10 percent.

Therefore, volume of coarse aggregate $=0.62 \times 0.9=0.56$

Volume of fine aggregate content $=1-0.56=0.44$

A-8 Mix Calculations

The mix calculations per unit volume of concrete shall be as follows:

a) Volume of concrete $=1 \mathrm{m}^{3}$

b) $\quad$ Volume of cement $=\frac{\text { Mass of cement }}{\text { Specific gravity of cement }} \times \frac{1}{1000}$

$$ \begin{aligned} &=\frac{350}{3.15} \times \frac{1}{1000} \\ &=0.111 \mathrm{m}^{3} \end{aligned} $$

$\begin{aligned} \text { c) } & \text { Volume of water }=\frac{\text { Mass of water }}{\text { Specific gravity of water }} \times \frac{1}{100} \\ &=\frac{140}{1} \times \frac{1}{1000} \\ &=0.140 \mathrm{m}^{3} \end{aligned}$

d) Volume of chemical admixture (superplasticizer) (@ 2.0 percent by mass of cementitious material)

$$ \begin{array}{l}{=\frac{\text { Mass of chemical admixture }}{\text { Specific gravity of admixture }} \times \frac{1}{1000}} \\ {=\frac{7}{1.145} \times \frac{1}{1000}=0.006 \mathrm{m}^{3}}\end{array} $$

e) Volume of all in aggregate $=[a-(b+c+d)] \\ =1-(0.111+0.140+0.006)=0.743 m^3$

f) Mass of coarse aggregate = e $\times$ Volume of coarse aggregate $\times$Specific gravity of coarse aggregate $\times$ 1000

$ = 0.743 \times 0.56 \times 2.74 \times 1000=1140kg$

g) Mass of coarse aggregate = e $\times$ Volume of fine aggregate $\times$Specific gravity of fine aggregate $\times$ 1000

$ = 0.743 \times 0.44 \times 2.74 \times 1000=896kg$

A- 9 Mix Proportions for Trial Number 1

$\begin{aligned} \text { Cement } &=350 \mathrm{kg} / \mathrm{m}^{3} \\ \text { Water } &=140 \mathrm{kg} / \mathrm{m}^{3} \\ \text { Fine aggregate } &=896 \mathrm{kg} / \mathrm{m}^{3} \\ \text { Coarse aggregate } &=1140 . \mathrm{kg} / \mathrm{m}^{3} \\ \text { Chemical admixture } &=7 \mathrm{kg} / \mathrm{m}^{3} \\ \text { Water-cement ratio } &=0.4 \end{aligned}$

A-10 The slump shall be measured and the water content and dosage of admixture shall be adjusted for achieving required slump based on trial, if required. The mix proportions shall be reworked for the actual water content and checked for durability requirements.

A-11 Two more trials having variation of $\pm 10$ percent of water cement ratio in A-10 shall be carried out and a graph between three water cement ratios and their corresponding strengths shall be plotted to work out the mix proportions for the given target strength for field trials.However durability requirement shall be met.