ISYU TUNGKOL SA SEKSWLADIDA (ISSUE ABOUT SEXUALITY
Concrete Mix Design Proportioning Examples
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
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.
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)