Concrete Construction

1.
Using the DOE mix design tables and charts, calculate the weights of all materials that you
would use for the first trial mix on a concrete mix required to achieve a compressive strength
of 30 MPa at 28 days.
Cement type: 42.5N
Max. aggregate size: 30 mm
Aggregate type: Crushed
Rel. density of combined aggregate at SSD: 2.65
Fine aggregate grading: Zone 3
Required slump: 80 mm
Minimum cement content: 380 kg/m3
Max free w/c ratio: 0.65
Plant S.D. Unknown
Solution
Step 1: Calculation of Target Mean Strength
Find the target mean strength from the specified characteristic strength
Target mean strength = specified characteristic strength + Standard deviation * risk factor
fm = fc +M
Where fm = the target mean strength
fc = the specified characteristic strength
M = s*k - the margin
s = the standard deviation, and
k = a constant
✓ Characteristic strength (fc)= 30 MPa
✓ Standard deviation (s) = Since number of results are unknown it is better to use the maximum
value of standard deviation of 8 N/mm2 for characteristic strength of 30 MPa. (fig.3)
✓ Risk factor (k) is corresponding to on the assumption that 5 percent of defective results are
allowed to fall less than the specified characteristic strength. k = 1.64
Therefore, 𝑓𝑚= 30 + 8 𝑥1.64 = 43.12N/mm2 ≈ 44N/mm2
✓ Cement strength class
Cement type=42.5N
✓ Aggregate type
Crushed
✓ Free-Water/cement ratio
From table 2 below, approximate compressive strength is 49 N/mm2 corresponding to W/C
ratio of 0.5.
Find an intersection point for 49MPa and 0.5 W/C ratio. Draw a curve line parallel to the
neighboring curve as shown below in fig.4. From this curve read off the W/C ratio for a
target mean strength of 44MPa. The Water/cement ratio is = 0.55
1
The max free w/c ratio specified is 0.65. Therefore, we take the lower value i.e 0.55.
Step 2: Determination of free Water Content

✓ Slump or Vebe time
Given slump=80mm
✓ Maximum Aggregate Size
Max. Aggregate size = 30mm
✓ Free-Water Content
From table 3 below, the approximate free-water content (kg/m3) corresponding to slump 80mm,
max. Aggregate size 30mm and for crushed aggregate by interpolation is 215kg/m3.
Y = Y1 + (Y2 – Y1)/ (X2 -X1) * (X - X1)
Y = 225 + (205-225)/ (40-20) * (30-20) = 215kg/m3.
Step 3: Calculation of cement content

✓ Cement content
𝐶𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 = free-water content/(free-water/ cement 𝑟𝑎𝑡𝑖𝑜)
𝐶𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 = 215/0.55
=390.9 Kg/m3 ≈ 391Kg /m3
✓ Maximum cement content:
Not specified
✓ Minimum cement content:

The minimum cement content specified is 380kg/m3. The cement content attained is 391kg/m3.
Therefore, minimum cement requirement is satisfied.
✓ Modified free-water/ cement ratio:

The calculated cement content is greater than the minimum. Hence, no need to calculate
modified free-water/cement ratio.
2
Step 4: Calculation of Weight of total aggregate content
From fig. 5 below, the average wet density of concrete corresponding to free-water of
215kg/m3 and Relative density of aggregate (SSD) = 2.65 can be calculated as follows.
✓ Wet density of concrete = 2320 (corresponding to Relative density of aggregate (SSD) = 2.6)
✓ Wet density of concrete = (2320+2380)/2 = 2350 (corresponding to Relative density of
aggregate (SSD) = 2.65)
Therefore, Average Wet Density of Concrete = 2350kg/m3
✓ Total Aggregate Content (kg/m3):

Total aggregate content (kg/m3) = D - C - W = (2350-391-215) kg/m3
Where D = the wet density of concrete (kg/m3)
C = the cement content (kg/m3)
W = the free-water content (kg/m3)
Total Aggregate Content =1,744kg/m3
3
Step 5: Calculation of fine and coarse aggregate contents
✓ Grading of fine Aggregate
__________________________________________________________________________
4
From the graphs attached above, the grading lies in Zone-3.
Proportion of fine Aggregate corresponding to the percentage passing 600μm sieve (60%) = 38%
Therefore, the proportion of fine Aggregate average of the two = (38%+32%)/2 = 35%
✓ Fine Aggregate content
Fine Aggregate Content = 35% * Total Aggregate Content
Fine Aggregate Content = 35% * 1744 = 610.40 kg/m3
Fine Aggregate Content =610.40kg/m3
✓ Coarse Aggregate content
Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate
Coarse Aggregate Content = (1744 – 610.40) kg = 1133.60 kg
Coarse Aggregate Content = 1133.60 Kg
Summary of Materials quantity per m3 of Concrete
REFERENCE OR
STEPS ITEMS VALUES
CALCULATIONS
Characteristic strength Specified 30 MPa at 28 days
Proportion defective 5%
Standard deviation Fig 3 No data 8 N/mm2
Risk Factor Specified Strength 1.64
Margin Specified M=1.64*8= 14 N/mm2
Target mean strength C2 30+14= 44 N/mm2
1
Cement strength class Specified 42.5N
Aggregate type: coarse Specified Crushed
Aggregate type: fine Specified Crushed
Free-water/ cement ratio Table 2, fig 4 0.55 use the lower value 0.55
Maximum free- water/
Specified 0.65
cement ratio
Slump or vebe time Specified 80mm or vebe time …. in sec
2 Maximum aggregate size Specified 30 mm
Free water content Table 3 215 kg/m3
5
Cement content C3 215/0.55= 391 kg/m3
Maximum cement
Specified No
content
3
Minimum cement content Specified 380 kg/m3
Modified free- water/
………
cement ratio
Relative density of
Specified 2.65
aggregate (SSD)
4 Concrete density Fig 5 2350 kg/m3
Total aggregate content C4 2350- 391 – 215 =1744 kg/m3

Percentage passing
Grading of fine aggregate Zone 3
600mm sieve
Proportion of fine
Fig 6 Taking average = 35%
5 aggregate
Fine aggregate content 1744*35% = 610.40 kg/m3
Coarse aggregate content 1744-610.40 = 1133.60 kg/m3
Cement Water Fine Aggregate Coarse Aggregate (kg) Remark

Quantities
(kg) (kg) (kg) 10mm 30mm 40mm
3
Per m (to the
391 215 610.40 1133.60
nearest 5kg)
6
2. Using the DOE mix design tables and charts, calculate the wights of materials required to
produce the four trial mixes which the information is given below. Calculate also the adjusted
batch weights that would be suitable for use on site by taking into account the expected free
moisture contents of the aggregates.
Mix no.
1 2 3 4
Characteristic strength, N/mm2 20 30 50 40
Age (days) 28 7 28 7
Cement type PPC SRPC OPC PPC
Aggregate type Uncrushed Crushed Uncrushed Crushed
Maximum aggregate size 20 30 20 30
Relative density of combined aggregate 2.55 2.60 2.70 2.60
Fine aggregate grading Zone 1 Zone 3 Zone 3 Zone 2
Required slump (mm) 70 100 80 50
Minimum cement content (kg/m3) 290 320 - 340
Maximum cement content (kg/m3) - 380 450 -
Maximum free w/c 0.50 0.45 0.60 0.60
Allowable failure rate 4.5% 1.5% 2.5% 3%
Plant S.D. (N/mm2) 7 5 Unknown 3
Free moisture content of sand 2.8 1.4 1.2 3.8
Solution
For all Mix
Step 1
✓ Characteristic Strength
The 7 days characteristic strength is approximately 65% and the 28 days strength is approximately
99% of the final characteristic strength. Hence, to get the 28 days characteristic strength from 7
days characteristic strength, we can calculate the factor i.e 99/65 = 1.523. Let us take conversion
factor = 1.5. For mix-2 and mix-4 we can obtain by multiplying the 7days strength with a
conversion factor of 1.5.
Mix-No
Mix-1 Mix-2 Mix-3 Mix-4
Characteristic Strength
20 30 50 40
(N/mm2)
28th day Characteristic Strength 20 45 50 60
(N/mm2)
7
✓ Standard deviation (s) and Risk factor (k)
A Constant (k)
Mix-No
Allowable Failure Rate 4.5% 1.5% 2.5% 3%
Corresponding Constant, 1.704 2.207 1.96 1.896
K
The corresponding k-values for 4.5%, 1.5% and 3% allowable failure rate are obtained by
interpolation.
Standard Deviation (s)
Mix-No
Plant S.D. (N/mm2) 7 5 Unknown 3
The Standard deviation (s) for Mix-3 is unknown. Since the no of test results are unknown, it is
better to use the maximum value of standard deviation (s) for Mix-3.
For Mix-3, s = 8 N/mm2
✓ Margin (M)
Mix-No
Corresponding Constant, k 1.704 2.207 1.96 1.896
Plant S.D. (N/mm2), s 4.5 1.5 2.5 3
Margin (M) = k*s 7.668≈ 8 3.3105≈ 4 4.9≈ 5 5.688≈ 6
✓ Target Mean Strength (TMS)

Target Mean Strength fm = fc + M
Mix-No
Characteristic Strength 20 45 50 60
(N/mm2)
Margin (M) = k*s 8 4 5 6
Target Mean Strength (TMS) 28 49 55 66
= (Fck + M)
8
✓ Cement Strength Class
Cement Strength class of 42.5 is assumed for all cement types.
Mix-No
Cement type PPC SRPC OPC PPC
Cement Class 42.5 42.5 42.5 42.5
PFA 30% - - 30%
✓ Aggregate type
Mix-No
Aggregate type Uncrushed Crushed Uncrushed Crushed
✓ Free-Water/Cement Ratio
For Mix-1
From the table below, 42 N/mm2 is the strength corresponding to W/(C+0.3F) ratio of 0.5 with
target mean strength of 28N/mm2
Find an intersection point for 42 N/mm2 and 0.5 W/C ratio. Draw a curve line parallel to the
neighboring curve as shown below in fig.4. From this curve read off the W/(C+0.3F): ratio for a
target mean strength of 28 N/mm2. The Water/cement ratio is = 0.64. But the specified maximum
Water/cement ratio is = 0.5. Therefore, we should take the minimum of the two i.e Water/cement
ratio is = 0.5
9
For Mix-2
From the table below, 49 N/mm2 is the strength corresponding to W/C ratio of 0.5 with target mean
strength of 49 N/mm2. The Water/cement ratio is = 0.5. But the specified maximum Water/cement
ratio is = 0.45. Therefore, we should take the minimum of the two i.e Water/cement ratio is = 0.45
10
For Mix-3
strength of 55N/mm2
neighboring curve as shown below in fig.4. From this curve read off the W/C ratio for a target
mean strength of 55 N/mm2. The Water/cement ratio is = 0.4
For Mix-4
From the table below, 49 N/mm2 is the strength corresponding to W/(C+0.3F) ratio of 0.5 with
target mean strength of 66N/mm2
Find an intersection point for 49 N/mm2 and 0.5 W/C ratio. Draw a curve line parallel to the
neighboring curve as shown below in fig.4. From this curve read off the W/C ratio for a target
mean strength of 66 N/mm2. The Water/cement ratio is = 0.38
11
Water to Cement ratio for each corresponding mix:
Mix-No
Target Mean Strength (TMS) 48 37.5 74 37.5
= (Fck + M)
W/C ratio calculated 0.64 0.5 0.4 0.38
✓ Maximum Free-Water/ Cement Ratio

Mix-No
Maximum W/C ratio 0.50 0.45 0.60 0.60
W/C ratio calculated 0.64 0.5 0.4 0.38

W/C ratio taken 0.5 0.45 0.4 0.38
12
Step 2
Mix-No
Required Slump (mm) 70 100 80 50
Specified

Mix-No
Maximum Aggregate Size 20 30 20 30
(mm)
For Mix-1
As shown on table 9 Part A, the approximate free-water content (kg/m3) corresponding to slump
(70mm), max. Aggregate size (20mm) and for uncrushed aggregate:
Free Water content = 195 kg/m3 and from Part B, water reduction is 20 kg/m3.
Therefore, the optimum free water content (for Mix-1) = 195 kg/m3 – 20 kg/m3 =175 kg/m3
For Mix-2
Y = Y1 + (Y2 – Y1)/ (X2 -X1) * (X - X1)
Y = 225 + (205-225)/ (40-20) * (30-20) = 215kg/m3.
13
For Mix-3
As shown on table 3, the approximate free-water content (kg/m3) corresponding to slump (80mm),
max. Aggregate size (20mm) and for uncrushed aggregate:
Free Water content = 195 kg/m3
For Mix-4
As shown on table 9 Part A, the approximate free-water content (kg/m3) corresponding to slump 50mm,
max. Aggregate size 30mm and for crushed aggregate by interpolation is 200kg/m3 and from Part B,
water reduction is 20 kg/m3.
Therefore, the optimum free water content (for Mix-4) = 200 kg/m3 – 20 kg/m3 =180 kg/m3
Y = Y1 + (Y2 – Y1)/ (X2 -X1) * (X - X1)
Y = 210 + (190-210)/ (40-20) * (30-20) = 200kg/m3.
14
Mix-No
Free Water Content (Kg/m3) 175 215 195 180
Step-3
✓ Cement content:
For Mix-1
From the quantity of free-water content and free-water/ cement/pfa ratio, the quantity of cement
can be obtained as follows:
Portland Cement Content = (100 – 30) *175/ [(100-0.7*30) *0.5]

Portland Cement Content = 310.13 kg/m3 ≈ 310kg/m3
Therefore, Cement content = 310 kg/m3
The pfa content of the mix can be obtained as follows:
pfa Content = (30*310)/ (100-30) = 132.86 kg/m3 ≈ 133 kg/m3

Therefore, pfa content = 133 kg/m3
The combined Portland cement content and pfa content, ie 310 + 133 = 443 kg/m3
15
Having determined both C and F the value of the ratio
can be determined and compared with the maximum free-water/cement ratio specified.
Therefore, 175/(310+30) = 0.51. The maximum W/C specified is 0.5 which is approximately
equal.
For Mix-2
Cement content = free-water content/ (free-water/cement 𝑟𝑎𝑡𝑖𝑜)
Cement content = 215/ 0.45
= 477.78 ≈ 478 kg/m3
For Mix-3
= 487.5 ≈ 488 kg/m3
For Mix-4
From the quantity of free-water content and free-water/ cement/pfa ratio, the quantity of cement
can be obtained as follows:
Portland Cement Content = (100 – 30) *180/ [(100-0.7*30) *0.38]

Portland Cement Content = 419.72 kg/m3 ≈ 420 kg/m3
Therefore, Cement content = 420 kg/m3
The pfa content of the mix can be obtained as follows:
pfa Content = (30*420)/ (100-30) = 180 kg/m3

Therefore, pfa content = 180 kg/m3
The combined Portland cement content and pfa content, ie 420 + 180 = 600 kg/m3
Having determined both C and F the value of the ratio
can be determined and compared with the maximum free-water/cement ratio specified.
Therefore, 180/(420+30) = 0.4. The maximum W/C specified is 0.6 which is greater than 0.4.
Therefore, the mix design is safe.
16
Selected quantities of cement content
Mix-No
Maximum Cement Content (kg/m ) 3 - 380 450 -
Minimum Cement Content (kg/m3) 290 320 - 340
Calculated Quantities of Cement (kg/m3) 443 478 488 600
Selected Quantities of Cement (kg/m3) 443 380 450 600
✓ Modified free-water/ cement ratio

For Mix-2
Cement content = 380 kg/m3
Free-water content = 215 kg/m3
Free-water content/ Cement content = 215/380 = 0.57 but maximum w/c given is 0.45.
For Mix-3
Free-water content = 195 kg/m3
Free-water content/ Cement content = 195/450 = 0.43
Modified Free-water content / Cement ratio = 0.43
Mix-No
Modified W/C ratio 0.5 0.45 0.43 0.38
Step-4
✓ Relative density of combined Aggregate (on saturated and surface dry basis)
Mix-No
Relative Density of combined
2.55 2.60 2.70 2.60
Aggregate (on SSD)
✓ Determination wet density of concrete mix (kg/m3)

For Mix-1
Wet density of concrete = 2320 (corresponding to Relative density of aggregate (SSD) = 2.5).
Wet density of concrete = 2380 (corresponding to Relative density of aggregate (SSD) = 2.6).
Average Wet Density of Concrete = 2350 kg/m3
17
For Mix-2
Wet density of concrete = 2330 kg/m3 (corresponding to Relative density of aggregate (SSD) =
2.6).
For Mix-3
2.7).
18
For Mix-4
2.6).
✓ Total Aggregate Content (Kg/m3):

For Mix-1
Aggregate Content (kg/m3) = Wet Concrete Content - Free Water Content - (Cement content +
pfa content)
Aggregate Content (kg/m3) = (2350 – 175 – (310 + 133)) kg/m3 = 1732 kg/m3
Aggregate Content (kg/m3) = 1732 kg/m3
19
For Mix-2
Aggregate Content (kg/m3) = Wet Concrete Content – Free Water Content – Cement Content
Aggregate Content (kg/m3) = (2330 – 215 – 380) kg/m3 = 1735 kg/m3
For Mix-3
For Mix-4
Aggregate Content (kg/m3) = Wet Concrete Content - Free Water Content - (Cement content +
pfa content)
Aggregate Content (kg/m3) = (2380 – 180 – (420 + 180)) kg/m3 = 1600 kg/m3
Step-4

Mix-No
Fine aggregate grading Zone 1 Zone 3 Zone 3 Zone 2
✓ Proportion of fine aggregate

Mix-No
Required Slump (mm) Specified 70 100 80 50
W/C ratio taken 0.5 0.45 0.43 0.38
20
For Mix-1
For Maximum Aggregate Size = 20mm, Slump 70mm and W/C ratio = 0.5
From the graph attached, the grading lies in Zone-1 (Percentage by weight passing 15-34).
• Proportion of fine Aggregate corresponding to the percentage passing 600μm sieve (30%)
= 48%
For Mix-2
• Proportion of fine Aggregate (20mm) corresponding to the percentage passing 600μm sieve
(70%) = 33%
(70%) = 29%
• Therefore, the proportion of fine Aggregate average of the two = (33%+29%)/2 = 31%
21
For Mix-3
= 32%
= 28%
22
For Mix-4
= 33%
23
Mix-No
Proportion Fine Aggregate
48 31 30 33
(%)
✓ Fine aggregate content

Fine aggregate content = total aggregate content x proportion of fine aggregate
For Mix-1 =1732 kg/m3 x 48%
=831.36 kg/m3
For Mix-2 =1,735 kg/m3 x 31%
=537.85 kg/m3
For Mix-3 =1,775 kg/m3 x 30%
=532.5 kg/m3
For Mix-4 =1,600 kg/m3 x 33%
=528 kg/m3
✓ Coarse aggregate content
Coarse Aggregate Content = Total Aggregate Content - Fine Aggregate
For Mix-1 = (1732 – 831.36) kg/m3
= 900.66 kg/m3
For Mix-2 = (1735 - 537.85) kg/m3
= 1,197.15 kg/m3
24
For Mix-3 = (1775 - 532.5) kg/m3
= 1,280.20 kg/m3
For Mix-4 = (1600 - 528) kg/m3
= 1,072 kg/m3
✓ Free moisture content of coarse and fine aggregate
Assume the following values of free moisture content for the coarse aggregate: 30mm 1.5% and
20mm 2.0%.
Mix-No
Fine Aggregate Content (kg/m3) 831.36 537.85 532.5 528
Free Moisture Content of Sand (%) 2.8 1.4 1.2 3.8
Free Water Content (kg) 23.28 7.53 6.39 20.06

Coarse Aggregate Content (kg/m3) 900.66 1197.15 1280.2 1072
Free Moisture Content of Coarse
2 1.5 2 1.5
Aggregate (%)
Free Water Content (kg) 18.01 17.95 25.6 16.08
Free Water Content in Coarse and
41.29 25.48 31.99 36.14
Fine Aggregate (kg)
✓ Free Water Content

Mix-No
Free Water Content (Kg/m3) 175 215 195 180
Free Water Content in Coarse
41.29 25.48 31.99 36.14
and Fine Aggregate (kg)
Free Water Content (Kg/m3) 133.71 189.52 163.01 143.66
✓ Quantity of Materials per m3 of Concrete

Fine
Cement Water Coarse Aggregate (kg) Remark
Quantities Aggregat
(kg) (kg)
e (kg) 20mm 30mm 40mm
Mix-1 443 133.71 831.36 900.66
Mix-2 380 189.52 537.85 1197.15
Mix-3 450 163.01 532.5 1280.2
Mix-4 600 143.66 528 1072
25
3. Repeat question 1 using the ACI mix design method and assuming the following:
Fineness modulus = 2.88
Air content = 2.50 %
SG of coarse and fine aggregates = 2.9
Bulk density of aggregate = 1767 kg/m3
Solution
Step-1: Choice of Slump

✓ The required Slump of the mix = 80mm
Step- 2: Choice of Maximum Size of Aggregate
✓ The Maximum Size of Aggregate = 30mm
Step- 3: Estimation of mixing water and air content
✓ Air content determination = 2.5%.
✓ Water content determination

From the figure below, the target water content for non-air entrained concrete and 30mm
Nominal Maximum Aggregate Size is = 185 kg/m3.
26
Step- 4: Selection of water/cement ratio
✓ The W/C ratio is obtained from the table = 0.54
Step 5: Calculation of Cement Content:
✓ Water Content = 185kg/m3

✓ The W/C ratio = 0.54
✓ Cement Content = Water Content / (W/C Ratio)
✓ Cement Content = 185/0.54 = 342.6 kg/m3
But the specified minimum cement content is 380 kg/m3. Therefore, Cement
Content = 380 kg/m3
Step 6: Estimation of coarse aggregate content
From table 9-4 below, the bulk volume of coarse aggregate recommended for fineness modulus
of 2.88 (using interpolation):
✓ The bulk volume of coarse aggregate (for fineness modulus of 2.88) = 0.678
✓ The bulk density of aggregate = 1767 kg/m3
✓ The oven dry mass of coarse aggregate = 0.678*1767 kg/m3 = 1198.03 kg/m3
Therefore, the oven dry mass of coarse aggregate = 1198 kg/m3
27
Step- 7: Estimation of Fine Aggregate Content:
To determine the fine aggregate content, convert the quantities of the ingredients into volume
and deduct the quantities from 1m3 of the volume of the mix. Assuming specific gravity of
cement=3.15
• Volume of water = 185kg/(1000kg/m3) = 0.185m3
• Volume of cement = 380kg/(3.15*1000kg/m3) = 0.121m3
• Volume of air = 2.5/100 = 0.025 m3
• Volume of coarse aggregate = 1198 kg / (2.9*1000kg /m3) = 0.413m3
• Volume of fine aggregate = (1 – 0.185 – 0.121 – 0.025 – 0.413) m3 = 0.256m3
• The dry mass of fine aggregate = 0.256m3*2.9*1000kg/m3 = 742.4 kg
Therefore, the dry mass of fine aggregate = 742 kg/m3
Summary of quantity of Materials per m3 of Concrete

Fine Coarse Aggregate (kg) Remark
Cement Water
Quantities Aggregate
(kg) (kg) 20mm 30mm 40mm
(kg)
Mix-1 380 185 742 1198
4. Repeat question 1 again using both DOE and ACI methods assuming there are no restrictions
on cement content and w/c
Solution
DoE Method
Step 1: Calculation of Target Mean Strength
Find the target mean strength from the specified characteristic strength
Target mean strength = specified characteristic strength + Standard deviation * risk factor
fm = fc +M
Where fm = the target mean strength
fc = the specified characteristic strength
M = s*k - the margin
s = the standard deviation, and
k = a constant
✓ Characteristic strength (fc)= 30 MPa
✓ Standard deviation (s) = Since number of results are unknown it is better to use the maximum
value of standard deviation of 8 N/mm2 for characteristic strength of 30 MPa. (fig.3)
28
✓ Risk factor (k) is corresponding to on the assumption that 5 percent of defective results are
allowed to fall less than the specified characteristic strength. k = 1.64
Therefore, 𝑓𝑚= 30 + 8 𝑥1.64 = 43.12N/mm2 ≈ 44N/mm2
✓ Cement strength class
Cement type=42.5N
✓ Aggregate type
Crushed
✓ Free-Water/cement ratio
From table 2 below, approximate compressive strength is 49 N/mm2 corresponding to W/C
ratio of 0.5.
neighboring curve as shown below in fig.4. From this curve read off the W/C ratio for a
target mean strength of 44MPa. The Water/cement ratio is = 0.55
29
The max free w/c ratio specified is not restricted.
Step 2: Determination of free Water Content

Given slump=80mm
Y = Y1 + (Y2 – Y1)/ (X2 -X1) * (X - X1)
Y = 225 + (205-225)/ (40-20) * (30-20) = 215kg/m3.
30
Step 3: Calculation of cement content
✓ Cement content
𝐶𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 = free-water content/(free-water/ cement 𝑟𝑎𝑡𝑖𝑜)
𝐶𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑛𝑡𝑒𝑛𝑡 = 215/0.55
=390.9 Kg/m3 ≈ 391Kg /m3
Not restricted
Not restricted
Step 4: Calculation of Weight of total aggregate content
From fig. 5 below, the average wet density of concrete corresponding to free-water of
215kg/m3 and Relative density of aggregate (SSD) = 2.65 can be calculated as follows.
✓ Wet density of concrete = (2320+2380)/2 = 2350 (corresponding to Relative density of
aggregate (SSD) = 2.65)
Therefore, Average Wet Density of Concrete = 2350kg/m3
31
✓ Total Aggregate Content (kg/m3):
Total aggregate content (kg/m3) = D - C - W = (2350-391-215) kg/m3
Where D = the wet density of concrete (kg/m3)
C = the cement content (kg/m3)
W = the free-water content (kg/m3)
Total Aggregate Content =1,744kg/m3
Step 5: Calculation of fine and coarse aggregate contents
From the graphs attached above, the grading lies in Zone-3.

Therefore, the proportion of fine Aggregate average of the two = (38%+32%)/2 = 35%
__________________________________________________________________________
32
Fine Aggregate Content = 35% * Total Aggregate Content
Fine Aggregate Content = 35% * 1744 = 610.40 kg/m3
Fine Aggregate Content =610.40kg/m3
Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate
Coarse Aggregate Content = (1744 – 610.40) kg = 1133.60 kg
Coarse Aggregate Content = 1133.60 Kg
Summary of Materials quantity per m3 of Concrete
REFERENCE OR
STEPS ITEMS VALUES
CALCULATIONS
Characteristic strength Specified 30 MPa at 28 days
Proportion defective 5%
Standard deviation Fig 3 No data 8 N/mm2
Risk Factor Specified Strength 1.64
Margin Specified M=1.64*8= 14 N/mm2
Target mean strength C2 30+14= 44 N/mm2
1
Cement strength class Specified 42.5N
Aggregate type: coarse Specified Crushed
Aggregate type: fine Specified Crushed
Free-water/ cement ratio Table 2, fig 4 0.55
Maximum free- water/
Specified Not restricted
cement ratio
Slump or vebe time Specified 80mm or vebe time …. in sec
2 Maximum aggregate size Specified 30 mm
Free water content Table 3 215 kg/m3
Cement content C3 215/0.55= 391 kg/m3
Maximum cement
Specified Not restricted
content
3
Minimum cement content Specified Not restricted
Modified free- water/
………
cement ratio
33
Relative density of
Specified 2.65
aggregate (SSD)
4 Concrete density Fig 5 2350 kg/m3
Total aggregate content C4 2350- 391 – 215 =1744 kg/m3

Percentage passing
Grading of fine aggregate Zone 3
600mm sieve
Proportion of fine
Fig 6 Taking average = 35%
5 aggregate
Fine aggregate content 1744*35% = 610.40 kg/m3
Coarse aggregate content 1744-610.40 = 1133.60 kg/m3
Cement Water Fine Aggregate Coarse Aggregate (kg) Remark

Quantities
(kg) (kg) (kg) 10mm 30mm 40mm
Per m3 (to the
391 215 610.40 1133.60
nearest 5kg)
Solution
ACI Method

✓ Air content determination = 2.5%.
34

35

Therefore, Cement Content = 343 kg/m3
cement=3.15
• Volume of air = 2.5/100 = 0.025 m3
36
Cement Water
(kg)
Mix-1 343 185 777 1198
5. Repeat question 2(1) using the ACI mix design method assuming the following:
Finess modulus = 2.85
Air content = 3%
SG of coarse and fine aggregates = 2.65
Strength development of SRPC = OPC
Solution

✓ Air content determination = 3%.
37

✓ Cement Content = 200/0.69 = 289.86 kg/m3 ≈ 290 kg/m3
The specified minimum cement content is 290 kg/m3. Therefore, Cement
Content is satisfied.
38
cement=3.15
• Volume of air = 3/100 = 0.03 m3
• The dry mass of fine aggregate = 0.299m3*2.65*1000kg/m3 = 792.35 kg ≈ 792kg

Cement Water
(kg)
Mix-1 290 200 792 1099
39
6. Repeat 2(2) using the DOE and ACI methods assuming there are no restrictions on cement
content and w/c
Solution
Using DoE Method
Step 1
✓ Characteristic Strength
The 7 days characteristic strength is approximately 65% and the 28 days strength is approximately
99% of the final characteristic strength. Hence, to get the 28 days characteristic strength from 7
days characteristic strength, we can calculate the factor i.e 99/65 = 1.523. Let us take conversion
factor = 1.5. For mix-2 we can obtain by multiplying the 7days strength with a conversion factor
of 1.5. Therefore, 1.5*30 = 45 N/mm2.
✓ Standard deviation (s) and Risk factor (k)
A Constant (k)
The corresponding k-values for 1.5% allowable failure rate are obtained by interpolation = 2.207
Standard Deviation (s)
For Mix-2, s = 5 N/mm2
✓ Margin (M) = 2.207*1.5 =3.3105 ≈ 4

Target Mean Strength fm = fc + M = 45+4 = 49 N/mm2
✓ Cement Strength Class
Cement Strength class of 42.5 is assumed for SRPC cement type.
✓ Aggregate type
Crushed
✓ Free-Water/Cement Ratio
strength of 49 N/mm2. Therefore, the Water/cement ratio is = 0.5.
40
Step 2
✓ Slump or Vebe time = 100mm

✓ Maximum Aggregate Size = 30mm
Y = Y1 + (Y2 – Y1)/ (X2 -X1) * (X - X1)
Y = 225 + (205-225)/ (40-20) * (30-20) = 215kg/m3.
41
Step-3
✓ Cement content:
= 430 kg/m3
Minimum & maximum cement content is not restricted.
Step-4
✓ Relative density of combined Aggregate (on saturated and surface dry basis)
Relative Density of combined Aggregate (on SSD) = 2.60
✓ Determination wet density of concrete mix (kg/m3)
2.6).

42
Step-4

Zone 3
✓ Proportion of fine aggregate
(70%) = 34%
(70%) = 30%
43
✓ Fine aggregate content
Fine aggregate content = total aggregate content x proportion of fine aggregate
=1,685 kg/m3 x 32% = 539.2 kg/m3
✓ Coarse aggregate content
Coarse Aggregate Content = Total Aggregate Content - Fine Aggregate
= (1,685 – 539.2) kg/m3 = 1,145.8 kg/m3
✓ Free moisture content of coarse and fine aggregate
Assume the following values of free moisture content for the coarse aggregate: 30mm 1.5%.
Mix-2
Fine Aggregate Content (kg/m3) 539.2
Free Moisture Content of Sand (%) 1.4
Free Water Content (kg) 7.55

Coarse Aggregate Content (kg/m3) 1145.8
1.5
Aggregate (%)
24.74
Fine Aggregate (kg)
44
Mix-2
Free Water Content (Kg/m3) 215
24.74
Free Water Content (Kg/m3) 190.26
✓ Quantity of Materials per m3 of Concrete
Fine
Quantities Aggregat
(kg) (kg)
e (kg) 20mm 30mm 40mm
Mix-2 430 190.26 539.2 1145.8
Using ACI Method

Step- 3: Estimation of mixing water and air content for non-air entrained concrete
45

Therefore, the oven dry mass of coarse aggregate = 1225.8 kg/m3
46
cement=3.15
• Volume of air = 3/100 = 0.03 m3
• Volume of coarse aggregate = 1225.8 kg / (2.65*1000kg /m3) = 0.463m3
Therefore, the dry mass of fine aggregate = 492.9 kg/m3

Cement Water
(kg)
Mix-1 461 175 492.9 1225.8
7. Repeat 2(3) using the ACI mix design method assuming the following:
Air content = 3%
SG of coarse and fine aggregate = 2.70
Characteristic strength = 50 N/mm2
Age (days) 28 days
Aggregate type Crushed
Max. aggregate size 20 mm
Rel density of combined aggregate 2.65
Fine aggregate grading Zone 2
Required slump (mm) 50
Min cement content (kg/m3) -
Max cement content (kg/m3) 450
Max free w/c ratio 0.60
Allowable failure rate 3%
Plant S.D (N/mm2) ---
Free moisture content of sand (%) = 4%
Assume the following values of free moisture content for the coarse aggregate: 30 mm
1.5%, 20 mm 2.5% and 10 mm 3.5%
47
Solution


50MPa=7251 psi W/c=0.32 from the table below
Max free w/c ratio=0.6 hence take the minimum i.e = 0.32

✓ Cement Content = 183/0.32 = 571.9 kg/m3 ≈ 572 kg/m3
The specified maximum cement content is 450 kg/m3. Therefore, Cement
Content is 450 kg/m3.
48
cement=3.15
• Volume of air = 3/100 = 0.03 m3
• The dry mass of fine aggregate = 0.269m3*2.7*1000kg/m3 = 726.3 kg ≈ 726kg
Free moisture content of coarse and fine aggregate.
Free moisture content of sand (%) = 4%
Assume the following values of free moisture content for the coarse aggregate: 20 mm 2.5%.
Fine Aggregate Content (kg/m3) 726

Free Moisture Content of Sand (%) 4

Coarse Aggregate Content (kg/m3) 1008
49
2.5
Aggregate (%)
54.24
Fine Aggregate (kg)
Free Water Content (Kg/m3) 183

54.24
Free Water Content (Kg/m3) 128.76

Cement Water
(kg)
Mix-1 450 128.76 726 1008
8. Calculate the weights of all material required for the first trial mix on the air entrained concrete
details of which are given below: Use both DOI and ACI methods:
Characteristic strength at 28 days = 40 N/mm2
Plant S.D = 4.0 N/mm2
Allowable failure rate =5.0%
Cement type OPC
Coarse aggregate
Max size 20
Type = crushed
Rodded bulk density = 1600 kg/m3
Rel density = 2.60
Fine aggregate
Type = uncrushed
Zone 3
Rel. density = 2.50
Air content = 5%
Slump = 80 mm
50
Solution
DOE Mix Design Methods
Step- 1
✓ Characteristic strength = 40MPa
✓ Standard deviation (s) and a constant (k)
A constant (k) corresponding to allowable failure rate of 5% = 1.64
k = 1.96
Standard deviation (s) =4 N/mm2
✓ Margin (M)
M = k*s = 1.64*4 = 6.56 N/mm2 ≈ 7 N/mm2
where fc = specified characteristic strength

M = the margin (see 4.4)
a = percentage by volume of air entrained
TMS (fm) = (40+7)/(1-0.055*5) = 64.83 ≈ 65
✓ Cement Strength Class:
The cement type OPC with an assumed strength class of 42.5.
✓ Aggregate type:
The coarse aggregate = crushed
Fine aggregate = Uncrushed
✓ Free-Water/Cement Ratio:
From the table below, 49 N/mm2 is the strength corresponding to W/C ratio of 0.5.
From the graph attached below, the W/C ratio corresponding to compressive strength of 65
N/mm2 is 0.39.
Free-Water/Cement Ratio (W/C) = 0.38
51
✓ Maximum Free-Water/ Cement Ratio: Not specified
Step- 2
The slump (specified) = 80mm
As seen from the table below, the approximate free-water content (kg/m3) corresponding to
slump (80mm), max. Aggregate size (20mm) and for crushed aggregate is obtained by the
following formula.
Water Content = 2/3Wf + 1/3Wc
Wf = 195 and Wc = 225
Water Content = 2/3*195 + 1/3*225 = 205 kg/m3
52
Step- 3
✓ Cement content:
From the quantity of free-water content and free-water/ cement ratio, the quantity of cement can
be obtained as follows:
• Free-water content/ cement content = 0.36
• Cement content = Free-water content/(W/C) = (205 kg/m3)/ 0.38 = 539.47kg/m3
Not specified
Not specified
Step- 4
✓ Relative density of combined Aggregate (on saturated and surface dry basis):
• The relative density of coarse Aggregate = 2.6
• The relative density of fine Aggregate = 2.5
• The relative density of combined Aggregate = 2.55
✓ Determination wet density of concrete mix (kg/m3):
• Wet density of concrete = 2350 (corresponding to Relative density of aggregate
(SSD) = 2.6).
(SSD) = 2.5).
(SSD) = 2.55) by interpolation.
• Average Wet Density of Concrete = 2315 kg/m3
The correct value of the wet density of air-entrained concrete is obtained by subtracting from the
wet density obtained above, an amount:
• Average Wet Density of Concrete = 2315 kg/m3

• Deduction = 10*5*2.55 kg/m3 = 127.5 kg/m3
• The net wet density of concrete modified for air entrainment = 2315 – 127=2188
The net wet density of concrete modified for air entrainment = 2188 kg/m3
53
• Wet Concrete Content = Free Water Content + Cement Content + Aggregate Content
• Aggregate Content (kg/m3) = Wet Concrete Content – Free Water Content – Cement
Content
• Aggregate Content (kg/m3) = (2188 – 205 – 540) kg/m3 = 1443 kg/m3
Step- 5
• From the graph attached the grading lies are in Zone-3.
= 28%
Therefore, the proportion of fine Aggregate =28%
54
• Fine Aggregate Content = 28% * Total Aggregate Content
• Fine Aggregate Content = 28% * 1443 = 404 kg/m3
Fine Aggregate Content =404 kg/m3
• Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate
• Coarse Aggregate Content = (1443 – 404) kg = 1039 kg
Coarse Aggregate Content = 1039 kg
Quantity of Materials per m3 of Concrete
Fine
(kg) (kg)
(kg) 10mm 20mm 40mm
Per m3 (to the
540 205 404 1039
nearest 5kg)
Using ACI Method

From the figure below, the target water content for air entrained concrete and 20mm Nominal
Maximum Aggregate Size is = 180 kg/m3.
55

56
To determine the fine aggregate content, convert the quantities of the ingredients into volume and
deduct the quantities from 1m3 of the volume of the mix. Assuming specific gravity of
cement=3.15
• Volume of cement = 530kg/(3.15*1000kg/m3) = 0.168 m3
• Volume of air = 5/100 = 0.05 m3
• The dry mass of fine aggregate = 0.215m3*2.5*1000kg/m3 = 537.5kg

Cement Water
(kg)
Mix-1 530 180 537 1005
9. Read the following specification taken from actual project documents and comment
on their completeness and suggest ways of improving the specifications
9.1 “…Reinforced concrete C25 (use OPC having 360 kg/m3) filled into form and
vibrated around reinforced bars, mix ratio should be 1:2:3…”
The given specification provides some information regarding the type of concrete and the mix ratio
to be used for a project. However, it lacks certain details that would be necessary for a complete
and comprehensive specification. Here are some suggestions to improve the specification:
➢ The required slump or workability of the concrete, which would affect the ease of placement
and consolidation.
➢ The specification should clearly state the required strength of the concrete. This information is
crucial for selecting the appropriate concrete mix design. In the given specification, only the
grade of concrete (C-25) is mentioned, which indicates a characteristic compressive strength
of 25 Megapascals (MPa) at 28 days. However, it's important to confirm if this strength
requirement is suitable for the intended use of the concrete.
➢ The specification mentions the use of reinforced bars but does not provide specific details
about the reinforcement type, size, or spacing. It is essential to include this information to
ensure proper coordination between the concrete mix and the reinforcement design.
➢ The specification does not mention the water-cement ratio, which is a critical factor in
determining the workability and strength of the concrete. Including the maximum allowable
57
water-cement ratio or a target range will help ensure consistency and quality in the concrete
mix.
➢ Curing is a crucial step in concrete construction to promote hydration and achieve the desired
strength and durability. The specification should include details about the curing methods,
duration, and any specific curing compounds or procedures to be followed.
➢ The maximum aggregate size, which could affect the workability and durability of the
concrete.
➢ Depending on the project location and environmental conditions, additional specifications may
be necessary. For example, in corrosive environments or areas prone to freeze-thaw cycles,
additional measures like specifying appropriate concrete additives or reinforcement coatings
may be required.
9.2 ”…25 mm thick cement plaster (1:3) with water proofing compound…”
The given specification provides some information about the thickness of the cement plaster and
the mix ratio, as well as the inclusion of a water proofing compound. However, there are some
areas where the specification could be improved for clarity and completeness. Here are some
suggestions:
➢ It is important to specify the type of surface or base material (e.g., concrete, masonry, metal)
and any surface preparation required before applying the plaster.
➢ The specification mentions the mix ratio of 1:3, but it does not specify the type of cement to
be used.
➢ The specification mentions the inclusion of a water proofing compound, but it does not provide
specific details about the type or brand of compound to be used. It is important to specify the
required properties of the water proofing compound and any specific standards or certifications
it should meet.
➢ The specification should provide details on the method of applying the cement plaster. This
may include information on surface preparation, mixing procedures, application techniques
(such as hand troweling or spray application), and any specific requirements for achieving the
desired thickness and finish.
➢ Cement plaster requires adequate curing to develop strength and durability. The specification
should include details on the curing methods, duration, and any specific curing compounds or
procedures to be followed.
➢ To ensure the quality of the cement plaster, it is important to include provisions for quality
control and testing. Specify any required tests, such as adhesion tests, thickness measurements,
or surface finish inspections.
➢ Depending on the project location and environmental conditions, additional specifications may
be necessary. For example, if the plaster will be exposed to severe weather conditions or high
humidity, additional measures like reinforcing mesh or surface treatments may be required.
58
9.3 “…120 mm thick lean concrete in C-10 with minimum cement content of 160 kg/m3 of
concrete under footing…
The given specification provides information about the thickness and concrete grade for a lean
concrete layer under a footing. However, it lacks some essential details and could be improved for
better clarity and completeness.
➢ Clearly state the purpose and function of the lean concrete layer. Specify why the lean concrete
layer is required under the footing. This information will help ensure that the specification
aligns with the project's design intent.
➢ Provide more information about the footing. It would be helpful to include details about the
type, dimensions, and load requirements of the footing.
➢ Include information about reinforcement, if applicable. If the lean concrete layer requires
reinforcement, specify the type, size, and spacing of reinforcement bars or fibers.
➢ Provide guidance on compaction and curing. Specify the compaction requirements for the lean
concrete layer, such as compaction method, equipment, and compaction density. Additionally,
provide instructions for proper curing methods and duration to ensure the concrete develops
adequate strength and durability.
➢ Include any relevant testing requirements. Specify any required tests or inspections to ensure
the quality of the lean concrete layer. This may include slump tests, compressive strength tests,
or any other tests deemed necessary based on project requirements.
10. Compare and contrast ACI mix design and DOE mix design guidelines’ steps and results.
Comparison of ACI mix design and BOE mix design guidelines’ steps and results
Similarities
1. Both methods are applicable for design of concrete mixes using different types of hydraulic
cements, blended cements and with or without other supplementary cementitious materials
and chemical admixtures.
2. Both methods give guidelines for design of concrete mixes using normal and heavy weight
aggregates.
3. The water-cement ratio of the mix governs the compressive strength of concrete. Selection
of water-cement ratio is primarily based on generalized relationship between compressive
strength of concrete and water-cement ratio, though some minor variations exist in the
process of selection in both methods.
4. Both methods specify different exposure conditions to meet the durability requirements.
5. Selection of water-Content is based on workability of the mix desired.
6. Cement content is estimated by dividing the free water-content by the free water-cement
ratio in both methods and checked against minimum cement requirements for durability.
7. Both methods are based on the absolute volume concept for calculation of required
proportion of materials.
59
8. The final mix proportion for the first trial mix is obtained by making suitable adjustments
for water absorption and surface moisture carried by the aggregates.
9. Cement Content: The computation of cement content in both methods is identical and
obtained by dividing the free water-content with the free water-cement ratio.
10. The adjustments for determining free water content taking in to account the aggregate
surface moisture and water absorption and first mix proportions are identical in both
methods.
Differences
1. Applicability
➢ ACI method: This method is applicable for design of normal and /or heavy concrete, and
mass concrete mixes. This standard is not applicable for Light weight aggregate concrete
and for special admixtures for concrete products manufacture. This method is also not
applicable for using condensed Silica fume. The ACI method of mix proportioning is
applicable for normal and heavy weight concrete having 28-days cylinder compressive
strength of 45 MPa and slump ranges of 25 to 100 mm.
➢ BS method: This method is applicable for design of normal concrete mixes having 28-days
compressive strength up to 75 MPa. This standard also gives guidelines for design of light
weight and heavy weight concrete. The compressive strength of hardened concrete is to be
specified on the basis of 150 mm cube test determined at 28 days (fck, cube), in N/mm2 or
150 mm diameter by 300 mm cylinder tests, determined at 28 days (fck, cyl), in N/mm2.
2. Type and shape of aggregates
➢ ACI method: This method takes in to account the nominal maximum size of aggregate, but
it does not differentiate between crushed and uncrushed or rounded aggregate and flakiness
and elongation in computation of water content.
➢ BS method: This method takes in to account the type of aggregates as crushed and
uncrushed only and upper size of coarse aggregate in computation of water content for the
desired workability.
3. Air content
✓ ACI method: In this method, the air content percentage in concrete is estimated depending
upon the type of concrete, whether air entrained or non-air entrained, exposure conditions
and the nominal maximum size of aggregate.
✓ BS method: For non-air entrained concrete, air content is not specified. For air-entrained
concrete, it specifies minimum total air content with a maximum total air content being 4%
higher than the specified minimum.
4. Exposure conditions and durability requirements
ACI method: This Standard recommends use of special ingredients such as low alkali
cement, pozzolanas, GGBS, silica fume, or aggregate selected to prevent harmful
expansion to the alkali-aggregate reaction. Entrained air is to be used in all exposed
concrete in climates where freezing occurs.
60
BS method: In this method exposure classes are classified as no risk of corrosion,
Carbonation-induced corrosion, Chloride-induced corrosion-Sea water and Chloride other
than from sea water, Freeze/thaw attack and Aggressive chemical environments, and
specifies maximum water cement ratio, minimum cement content and minimum strength
classes for different exposure classes.
5. Water - cement ratio
❖ ACI method: This standard specifies to have or to develop the relationship between
strength and water-cement ratio for the materials actually to be used. In the absence of such
data, approximate values for concrete containing type- I Portland cement can be taken from
Table A1.5.3.4(a) of ACI 211.1, based on compressive strength.
❖ BS method: This method considers the influence of cement, type of aggregate and target
mean strength in computation of water-cement ratio, which is selected from the table and
curve specified in this standard.
6. Workability
• ACI method: In This method Table A1. 5.3.1 of ACI 211.1 recommends different values
of maximum slump ranging from 50 to 100 mm for various types of construction with a
minimum slump value of 25 mm.
• BS method: In this method different Consistence classes are specified which covers the
workability of concrete, and either a class or target value can be used to specify consistence.
• The workability is specified in terms of slump, Vebe time or compacting factor is different
in both methods.
7. Water-content
➢ ACI method: In this method table A1 5.3.3 of ACI 211.1 specifies water requirements for
different slump values for different nominal maximum sizes of aggregates for air-entrained
concrete for “moderate exposure”, for reasonably well-shaped angular aggregates graded
within limits of accepted specifications. Rounded coarse aggregate will generally require
18 kg less water for non-air-entrained and 15 kg less for air-entrained concretes. The use
of water-reducing chemical admixtures (ASTM C 494), may also reduce mixing water by
5 percent or more.
➢ BS method: In this method water content is selected from the table specified in this standard
for different consistence classes and different sizes of aggregates and type of aggregate –
crushed or uncrushed. Reduction in water content is also specified when additives are used
in combination with cement. In this method, when the coarse and fine aggregates used are
of different types, the water content is estimated by the following expression:
W = (2/3*Wf) + (1/3*Wc)
Where, Wf = water content appropriate to type of fine aggregate
Wc = water content appropriate to type of coarse aggregate
8. Estimation of coarse and fine aggregate contents
✓ ACI method: This method assumes that the optimum ratio of bulk volume of coarse
aggregate to the total volume of concrete depends only on maximum size of coarse
61
aggregate and on the grading (fineness modulus) of fine aggregate. The volume of coarse
aggregate, on an oven-dry rodded basis, per unit volume of concrete is specified in table
A1 5.3.6 of ACI 211.1 for different nominal maximum size of aggregate and fineness
modulus of fine aggregate. The dry mass of coarse aggregate is obtained by multiplying
the value from table A1.5.3.6 by the dry-rodded unit mass of the aggregate. The volume of
fine aggregate is determined by subtracting the absolute volume of all other ingredients
from the unit volume of fresh concrete.
✓ BS method: In this method the total aggregate content is computed from the wet density of
concrete obtained from the figure specified in this standard. The wet density of concrete
depends on the specific gravity of overall aggregates in the saturated surface dry condition.
If no information is available, specific gravity may be taken 2.60 for uncrushed aggregate
and 2.70 for crushed aggregate. The percentage of fine aggregate is either specified or
obtained from the figures given in this standard expressed as a percentage of total aggregate
that will provide the target consistence of the fresh concrete to be made with the given
grading of fine aggregate, the nominal upper size of coarse aggregate and the free water-
cement ratio. From the percentages of fine and coarse aggregate in total aggregate content,
the quantities of fine and coarse aggregates are determined.
Result
Generally, it could be seen that ACI method gives the higher strength as compared to DOE method.
References
1. Design of normal concrete mixes (DOE mix Design manual), Second edition.
2. Standard Practice for Selecting Proportions for Normal, Heavyweight, and Mass Concrete
(ACI 211.1-91), Reported by ACI Committee 211.
3. Satya Prakash Mishra, “Comparison of IS, BS and ACI Methods of Concrete Mix Design
and Proposing Function Equations Based Design”, January 2012.
62

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1.

Step 1: Calculation of Target Mean Strength

Step 2: Determination of free Water Content

Step 3: Calculation of cement content

✓ Minimum cement content:

✓ Modified free-water/ cement ratio:

✓ Total Aggregate Content (kg/m3):

✓ Grading of fine Aggregate

✓ Fine Aggregate content

Fine Aggregate Content = 35% * Total Aggregate Content

Fine Aggregate Content = 35% * 1744 = 610.40 kg/m3

Fine Aggregate Content =610.40kg/m3

✓ Coarse Aggregate content

Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate

Coarse Aggregate Content = (1744 – 610.40) kg = 1133.60 kg

Coarse Aggregate Content = 1133.60 Kg

Summary of Materials quantity per m3 of Concrete

Total aggregate content C4 2350- 391 – 215 =1744 kg/m3

Cement Water Fine Aggregate Coarse Aggregate (kg) Remark

✓ Target Mean Strength (TMS)

Cement Class 42.5 42.5 42.5 42.5

PFA 30% - - 30%

✓ Maximum Free-Water/ Cement Ratio

W/C ratio calculated 0.64 0.5 0.4 0.38

✓ Maximum Aggregate Size

Portland Cement Content = (100 – 30) *175/ [(100-0.7*30) *0.5]

pfa Content = (30*310)/ (100-30) = 132.86 kg/m3 ≈ 133 kg/m3

Portland Cement Content = (100 – 30) *180/ [(100-0.7*30) *0.38]

pfa Content = (30*420)/ (100-30) = 180 kg/m3

Having determined both C and F the value of the ratio

✓ Modified free-water/ cement ratio

✓ Determination wet density of concrete mix (kg/m3)

✓ Total Aggregate Content (Kg/m3):

✓ Grading of fine Aggregate

✓ Proportion of fine aggregate

✓ Fine aggregate content

Free Water Content (kg) 23.28 7.53 6.39 20.06

✓ Free Water Content

✓ Quantity of Materials per m3 of Concrete

Step-1: Choice of Slump

✓ Water content determination

Step 5: Calculation of Cement Content:

✓ Water Content = 185kg/m3

Summary of quantity of Materials per m3 of Concrete

Step 1: Calculation of Target Mean Strength

Step 2: Determination of free Water Content

✓ Slump or Vebe time

Step 5: Calculation of fine and coarse aggregate contents

✓ Grading of fine Aggregate

From the graphs attached above, the grading lies in Zone-3.

Fine Aggregate Content = 35% * Total Aggregate Content

Fine Aggregate Content = 35% * 1744 = 610.40 kg/m3

Fine Aggregate Content =610.40kg/m3

✓ Coarse Aggregate content

Coarse Aggregate Content = Total Aggregate Content – Fine Aggregate

Coarse Aggregate Content = (1744 – 610.40) kg = 1133.60 kg

Coarse Aggregate Content = 1133.60 Kg

Summary of Materials quantity per m3 of Concrete

Total aggregate content C4 2350- 391 – 215 =1744 kg/m3

Cement Water Fine Aggregate Coarse Aggregate (kg) Remark

Portland Cement Content = (100 – 30) 175/ [(100-0.730) *0.5]

Portland Cement Content = (100 – 30) 180/ [(100-0.730) *0.38]