CON 124 Session 5: Examples of Concrete Proportioning O. Tavares

1. CON 124
Basic Concrete Mix Design Proportioning
Session 5
Examples of Concrete Proportioning

2. Examples of Proportioning Concrete
Mixtures
 Absolute volume method
 Trial mixture using the Water-Cement ratio
method

3. Proportioning Concrete Mixtures
Example 1
Using the Absolute Volume Method
Abs Vol Density = Weight/Volume
(no voids)
Specific Gravity =
Abs Vol Density / Density of Water
Vol

4. Proportioning Concrete Mixtures
Absolute Volume Method for Example 1 using
the equations below:
Abs Vol=Wt/(Specific Gravity x Density of Water)
Wt=Abs Vol x Specific Gravity x Density of Water
Density of Water = 62.4 lbs per cu ft ( @ 40C)
1 Cubic yard concrete = 27 cubic feet

5. Conditions for Example 1
 Concrete for a building foundation
 Specified Compressive Strength: f c= 3500 psi
 Type I cement; Relative Density = 3.15
 Design for minimum 3 in of concrete cover
 Minimum distance between reinforcement bars is 4 in;
 Only admixture allowed is air entrainment
 No statistical data on mixes available
 Coarse Aggregate: ¾ in gravel; OD Relative Density = 2.68;
Absorption = 0.5%; Oven dry density = 100 lbs/cuft; Moisture
= 2%
 Fine Aggregate: Natural sand; OD Relative Density = 2.64;
Absorption = 0.7%; Moisture = 6%; Fineness Modulus = 2.80

6. Specifications for Example 1
 Strength: No statistical data available; fcr =
fc + 1200; therefore, fcr = 3500 + 1200 = 4700
psi (Table 11 CON 124 Proportioning Methods)
 Water to Cement ratio: No required Max
(Table 1 CON Proportioning and Mix Design);
Recommended W/C ratio for fcr = 4700 psi
, 0.42 interpolated (Fig 1 or Table 3 CON 124
Proportioning and Mix Design)

7. Specifications for Example 1 (Cont)
 Coarse Aggregate Size: ¾ in nominal maximum
size adequate ¾ distance between reinforcing
bars also between reinforcing bars and forms
(cover)
 Air Content: Target air of 6% needed to improve
workability and reduced bleeding. Design 6% +/-
1%, Max of 7%
 Slump: Not specified, range 1 to 3 in adequate
(foundations, CON 124 Proportioning and Mix
Design)

8. Specifications for Example 1 (cont)
 Water Content: 3-in slump, air entrained
concrete, ¾ in nominal maximum size
aggregate; requires 305 lbs/cu yd (Fig 3 and
Table 5,CON 124 Proportioning and Mix
Design); Crushed gravel particles reduce water
by 35 lbs, Estimated water content of 270 lbs
 Cement Content: Based on max W/C ratio and
water content; 270 lbs/0.42 = 643 lbs

9. Specifications for Example 1 (cont)
 Coarse Aggregate Content: Bulk volume CA
recommended using a fine aggregate Fineness
Modulus of 2.80 is 0.62 (Fig 3 or Table 4, CON
Proportioning and Mix Design); CA (oven dry) weighs
100 lbs/cu ft, thus for a cubic yard of concrete(27 cu ft)
requires 100x27x0.62 = 1674 lbs/cu yd
 Admixture Content: 7% air, 0.9 fl oz/100 lbs of cement
 Fine Aggregate Content: Volume is determined by
subtracting absolute volumes of known ingredients
from 27 cu ft/ cu yd (see next slide), Absolute Volume =
27.0 – 19.50 = 7.50 cu ft; Weight of dry fine aggregate
= 7.50x2.64x62.4 = 1236 lbs

10. Absolute Volume Computation
for Fine Aggregate Content
Water = 270
1 • 62.4
= 4.33 ft3
Cement =
643
3.15 • 62.4
= 3.27 ft3
Air =
7.0 • 27
100
= 1.89 ft3
Coarse
aggregate =
1674
2.68 • 62.4
= 10.01 ft3
Subtotal = 19.50 ft3
Fine aggregate volume=27-19.50= 7.50 ft3
Fine aggregate mass =7.50 • 2.64 • 62.4 = 1236 lb

11. Mixture Design for Example
1 per Cubic Yard
 Water: 270 lbs
 Cement: 643 lbs
 Coarse Aggregate (dry): 1674 lbs
 Fine Aggregate (dry): 1236 lbs
 Total weight: 3823
 Air-entraining admixture: 5.8 fl oz
 Slump: 3-in (+/- ¾ in for trial batch)
 Air Content: 7%

12. Trial Batch Corrections for Moisture in
Aggregates
 Dry Batch Weights need correction for absorbed
and surface moisture (MC)
 Mixing water reduction due to amount of free
moisture contributed by aggregates
 Coarse Aggregate (CA) MC is 2%; Fine Aggregate
(FA) MC is 6%
 CA (2% MC) = 1674 lbs x 1.02 = 1707 lbs
 FA (6% MC) = 1236 lbs x 1.06 = 1310 lbs
 Estimated mix water: 270 lbs – (1674 x 0.015) –
(1236 x 0.053) = 179 lbs

13. Estimated Batch Weights for Aggregate
Moisture Content
 Water (to be added): 179 lbs
 Cement: 643 lbs
 CA (2% MC,wet) 1707 lbs
 FA (6% MC, wet) 1310 lbs
 Total Batch Weight: 3839 lbs/ 1 Cubic Yd

14. Laboratory Trial Batch
(2.0 cu ft; or 2/27 cu yd)
 Trial batch concrete needed for air, slump, and
casting of cylinders for strength
 Water: 179 lbs x 2/27 = 13.26 lb
 Cement: 643 lbs x 2/27 = 47.63 lb
 CA, wet: 1707 lbs x 2/27 = 126.44 lb
 FA, wet: 1310 lbs x 2/27 = 97.04 lb
 Total laboratory trial batch: 284.37 lbs
 Air Entraining admixture: 5.8 fl oz x 2/27 = 0.43

15. Laboratory Trial Batch Data
 Lab trial batch concrete testing:
 Measured Slump, 4-in
 Air Content, 8%
 Density (unit weight), 141.49 lbs
 Pre-measured water remained unused, original
amount of water was 13.26 lbs, only used 13.12 lbs
 Mixture Design: Water = 13.12 lbs, Cement =
47.63 lbs, CA (2% MC) = 126.44 lbs, FA (6%MC) =
97.04; Total trial batch = 284.23 lbs/ 2.0 cu ft

16. Yield of Laboratory Trial Batch
 Total laboratory batch weight : 284.23 lbs
 Laboratory density (unit weight): 141.49
lbs/cu ft
 Yield: 284.23lbs/141.49 lbs/cu ft = 2.009 cu ft

17. Mixing Water Content of Trial Batch for
1- cubic yard
 Water added: 13.12 lbs
 Free Water CA: 126.44/1.02 x 0.015 = 1.86 lbs
 Free Water FA: 97.04 /10.6 x 0.053 = 4.85 lbs
 Total Water: 19.83 lbs
 Mix water needed / cu yd for same slump:
19.83 lbs x 27.00 cu ft/cu yd/2.009 cu ft = 267
lbs

18. 1 yard Concrete Trial Batch
Adjustments
 Measured 4-in slump unacceptable more than 0.75 in above
designed 3-in max
 Trial yield slightly exceeds design
 Air content of 8% is unacceptable, more than 0.50% above designed
7% max
 Reestimate amount of air entraining admixture for a 7% max air
content, and adjust water to obtain 3-in slump
 Increase mixing water by 5 lbs for each 1%;reduce mixing water by
10 lbs for 1-in reduction in slump:
(5 x 1) – (10 x 1) + 267 lbs = 262 lbs/cu yd
 With less mixing water needed, less cement required for desired
water-cement ratio of 0.42:
262 lbs/cu yd/0.42 = 624 lbs/ cu yd

19. New Adjusted Concrete Batch Volumes
per Cubic Yard
 Water: 262/1 x 62.4 = 4.20 cu ft
 Cement: 624/3.15 x 62.4 = 3.17 cu ft
 CA: 1674/2.68 x 62.4 = 10.01 cu ft
 Air: 7.0/100 x 27.0 = 1.89 cu ft
 Total from above: 19.27 cu ft
 FA: 27.00 – 19.27 = 7.73 cu ft

20. Adjusted Dry Weights for 1 Cubic Yard
 FA (dry): 7.73 x 2.64 x 62.4 = 1273 lbs
 Air dosage; 0.8 fl oz/ 100 lbs of cement to achieve 7% air:
0.8 fl oz x 624/100 = 5.0 fl oz
 Designed Batch weights:
 Water = 262 lbs
 Cement = 624 lbs
 CA (dry) = 1674 lbs
 FA (dry) = 1273 lbs
 Total Batch = 3833 lbs
 Estimated Concrete Density (unit weight) at SSD
 (262 + 624 + (1674 x 1.005) + (1273 x 1.007)) divided by
27 = 142.60 lb/cu ft

21. Example 2 Proportioning by Trial
Mixtures Using W/C ratio
 Trial batching verifies that a concrete mixture meets
design requirements prior to use in construction.
 Trial mixtures should use the same materials proposed
for the work.
 Three mixtures with three different water-cementing
materials ratios or cementing materials contents
should be made.
 The trial mixtures should have a slump and air content
within ±20 mm (±0.75 in.) and ± 0.5%, respectively, of
the maximum permitted.
 Three cylinders for each water-cementing materials
ratio should be tested at 28 days.

22. Laboratory Trial Mixtures Using the
Water-Cement Ratio
 Conditions:
 Foundation wall requiring air-entrained concrete exposed to
moderate sulfate soils
 Compressive strength, fcr, 4000 psi @ 28 days, Type II cement
 Minimum thickness of wall is 10-in; concrete cover over ½-in
diameter reinforcing bars 3-in
 Specifications:
 Water-cement ratio vs compressive strength relationship based
on field and previous lab data
 Test records of materials used, std dev is 300 psi
 Max W/C ratio for the above conditions should be 0.50
 (Table 1 CON 124 Concrete Proportioning and Mix Design)

23. Concrete Trial Mixture Designed
Compressive Strengths
 Standard Deviation (S) of 300 psi
 fcr = fc + 1.34S = 4000 + 1.34 (300) = 4402 psi
 Or fcr = fc + 2.33S – 500 = 4000 + 2.33 (300) – 500
= 4199 psi
 Therefore fcr = 4400 psi
 W/C ratio for air-entrained concrete is 0.55 for an
fcr of 4400psi; Exposure Conditions requirements
govern; Thus W/C ratio of 0.50 used producing
higher strengths than needed to satisfy structural
needs

24. Relationship
between strength
and water to
cement ratio
based on field and
laboratory data for
specific concrete
ingredients.

25. Example 2 Concrete Trial Batch Mixture
Data
 Aggregate: 1½-in max size is satisfactory; less than
1/5 wall thickness; less than ¾ the clear distance
between reinforcing bars, as well as forms
 Air Content: Exposure conditions and workability
require moderate level, target concrete air with an
1½-in aggregate is 4.5%+/- 1%, aim for 5.5%+/- 0.5%
in trial batch
 Slump: 1-3-in for placing a reinforced concrete
foundation wall; trial batch for 3-in +/- 0.75 in

26. Relationship
between:
 Slump
 Agg. Size
 W/C
 Cement content
Example graphical relationship for a
particular aggregate source
demonstrating the relationship
between slump, aggregate size, water
to cement ratio, and cement content.

27. Example 2 Batch Quantities
 Batch size contains 20 lbs of cement
 Mixing Water: 20 lbs x 0.50 = 10 lbs (values
entered as initial weights, Col 2)
 FA & CA (SSD) proportions used from mixes used
to develop graph above
 Mixing continues until a workable concrete of 3-
in slump is reached
 Results of slump, air, unit weight, and description
and workability are noted on data sheet

28. Example 2 Trial Batch Data
 Workability: (from data sheet) The amounts
of FA & CA not used are recorded, Col
3, Masses of aggregates used (Col 2 minus Col
3) are recorded in Col 4
 Additional information on slump, water
required, cement quantities are recorded

29. Example 2 Mixture Proportions for 1
Cubic Yard
 From Col 5 of data sheet, use batch yield (volume) &
density (unit weight) for mixture proportions
 Example, Cement lbs/cu yd = 27 cuft//volume of
concrete in batch x lbs of cement in batch; % of FA is
calculated; cement content is 539 lbs/cu yd; FA
aggregate is 33.5% of total aggregate
 Air content and slump were acceptable; 28-day
compressive strengths were 4950 psi (greater than fcr )
 Mixture in Col 5, with slump and air content, 1-3-in and
3.5% to 5.5%,respectively, now ready for submission.

30. Example 2 Trial
Mixture Data
Sheet
Trial mixture data sheet (inch-
pound units).

31. Test Results of Laboratory Trial
Mixtures for Example 2 at a W/C Ratio
of 0.50, economy & workability
Batch
no.
Slump,
in.
Air
content
percent
Density
lb/ft3
Cement
content,
lb/yd3
Fine
aggregate,
percent of
total
aggregate
Worka-
bility
1 3 5.4 144 539 33.5 Good
2 2¾ 4.9 144 555 27.4 Harsh
3 2½ 5.1 144 549 35.5 Excellent
4 3 4.7 145 540 30.5 Excellent
Inch-Pound
Results of Laboratory Trial Mixtures
(Inch-Pound Units) for economy and
workability of mixture adjustments.

32. Common Mix Design Mistakes
 Not varying water-cement ratio (3 point curve)
 Not monitoring slump loss during mix design
to identify false setting tendency in cement
 Not monitoring early age concrete
temperatures to identify retardation effects of
water reducers

33. Proportioning Concrete Mixes
 Ordering Concrete by ASTM C94
 Option A -
 manufacturer assumes responsibility for
proportions
 purchaser specifies:
 strength requirements
 durability, placeability, density requirements

34. Proportioning Concrete Mixes
 Ordering Concrete by ASTM C94
 Option B -
 purchaser assumes responsibility for proportions
 purchaser specifies:
 cement content
 max allowable water content
 admixtures (type and dose)

35. Proportioning Concrete Mixes
 Ordering Concrete by ASTM C94
 Option C -
 manufacturer assumes responsibility for
proportions with minimum allowable cement
content specified by purchaser
 purchaser specifies:
 required compressive strength
 minimum cement content
 admixtures (type and dose)

36. Questions?
Email cemtek@netzero.net

37. Please return to Blackboard and watch
the following videos:
 Video 1: Concrete Sampling
 Video 2: Concrete Temperature
 Video 3: Density