56
Designing and Proportioning Normal Concrete Mixtures
Designing and Proportioning Normal Concrete Mixtures
Proportioning
Factors in the Proportioning of Quality Concrete Mixtures
■ Workability■ Durability■ Strength■ Appearance■ Economy
Proportioning
Materials
■ Cement■ Supplementary Cementing
Materials■ Water■ Aggregate■ Admixtures■ Fibers
Proportioning
Proportioning
Mix Characteristics
■ Strength■ Water-cementing materials ratio■ Aggregate size and volume■ Air content■ Slump and workability■ Water content■ Cementing materials content
and type■ Admixtures
Proportioning
Requirements for Exposure Conditions
35 (5000)0.40For corrosion protection for
reinforced concrete exposed to chlorides
31 (4500)0.45Concrete exposed to
freezing and thawing in a moist condition or deicers
28 (4000)0.50Concrete with low permea-bility; exposed to water
Select for structural
requirements
Select for strength, workability, and finishing needs
No freeze-thaw, deicers, aggressive substances
Exposure conditionMin. strength, f'c, MPa (psi)
Maximum w/c-ratio by mass
Proportioning
Requirement for Concrete Exposed to Sulfates
35 (5000)0.40V, HSOver 10,000
Over 2.00
Very severe
31 (4500)0.45V, HS1500 to 10,000
0.20 to 2.00Severe
28 (4000)0.50
II, MS, IP(MS), IS(MS), P(MS), I(PM)(MS), I(SM)(MS)
150 to 1500
0.10 to 0.20Moderate
——No special type required
Less than 150
Less than 0.10Negligible
Cement type
Sulfate (SO4) in water, ppm
Sulfate exposure
Maximum w/c-ratio, by mass
Sulfate (SO4) in soil, % by mass
Minimum strength, f'c, MPa (psi)
Proportioning
Relationship between W/C-Ratio and Strength
0.700.79150.600.69200.520.61250.450.54300.390.47350.340.42400.300.3845
Air-entrained concrete
Non-air-entrained concrete
Water-cementitious materials ratio by massCompressive
strength at 28 days, MPa
MetricMetric
Proportioning
Relationship between W/C-Ratio and Strength
0.740.8220000.590.6830000.480.5740000.400.4850000.320.416000—0.337000
Air-entrained concrete
Non-air-entrained concrete
Water-cementitious materials ratio by massCompressive
strength at 28 days, psi
InchInch--PoundPound
Proportioning
Compressive Strength Vs. W/C-Ratio
Proportioning
Bulk Volume of Coarse Aggregate
0.810.830.850.87(6)150 0.760.780.800.82(3)75 0.720.740.760.78(2)50 0.690.710.730.75(1 1/2)37.5 0.650.670.690.71(1)25 0.600.620.640.66(3/4)19 0.530.550.570.59(1/2)12.5 0.440.460.480.50(3/8)9.5
3.002.802.602.40
Fineness modulus of sandMaximum size of aggregate,
mm (in.)
Proportioning
Bulk Volume of Coarse Aggregate
Proportioning
Absolute Volume of Coarse Aggregate per m3 of Concrete
Given:0.46 m3 of coarse aggregateBulk density = 1567 kg/m3, roddedRelative density = 2.65Water = 1000 kg/m3
0.46 m3 • 1567 kg/m3 = 715.5 kg
Absolute volume = 715.5/(2.65 • 1000) = 0.27 m3
So the coarse aggregate is 27% of the absolute volume of the concrete
1 m3
0.46 m3
Proportioning
Absolute Volume of Coarse Aggregate per yd3 of Concrete
1 yd3
0.46 yd3
Given:0.46 yd3 of coarse aggregateBulk density = 98 lb/ft3, roddedRelative density = 2.65Water = 62.4 lb/ft3
0.46 • 27 = 12.4 ft312.4 • 98 = 1215 lbAbsolute volume = 1215/(2.65 • 62.4) = 7.357.35/27 = 0.27
So the coarse aggregate is 27% of the absolute volume of the concrete
Proportioning
Air Content and Aggregate Size
Proportioning
Water and Air Requirements for Different Slumps and
Sizes of Aggregate
0.20.30.511.522.53Approximate amount of entrapped air in non-air-entrained concrete, percent
—160178190202216228243150 to 17512414516918119320521622875 to 10011313015416617919019920725 to 50
150 mm
75 mm
50 mm
37.5 mm
25 mm
19 mm
12.5 mm
9.5 mmSlump, mm
Water, kilograms per cubic meter of concrete, for indicated sizes of aggregate
NonNon--airair--entrained concreteentrained concreteMetricMetric
Proportioning
Water and Air Requirements for DifferentSlumps and Sizes of Aggregate
1.01.52.02.53.03.54.04.5Mild exposure
3.03.54.04.54.55.05.56.0Moderate exposure
Recommended average total air content, percent, for level of exposure
4.04.55.05.56.06.07.07.5Severe exposure
-154166174184197205216150 to 17511913315716517518419320275 to 10010712214215016016817518125 to 50
150 mm
75 mm
50 mm
37.5 mm
25 mm
19 mm
12.5 mm
9.5 mmSlump, mm
Water, kilograms per cubic meter of concrete, for indicated sizes of aggregate
AirAir--entrained concreteentrained concreteMetricMetric
Proportioning
Water and Air Requirements for Different Slumps and Sizes of Aggregate
0.20.30.511.522.53Approximate amount of entrapped air in non-air-entrained concrete, percent
—2703003153403603854106 to 72102452853003253403653853 to 41902202602753003153353501 to 2
6 in.
3 in.2 in.1½in.
1 in.¾in.
½ in.3/8 in.Slump, in.
Water, pounds per cubic yard of concrete, for indicated sizes of aggregate
NonNon--airair--entrained concreteentrained concreteInchInch--PoundPound
Proportioning
Water and Air Requirements for DifferentSlumps and Sizes of Aggregate
1.01.52.02.53.03.54.04.5Mild exposure
3.03.54.04.54.55.05.56.0Moderate exposure
Recommended average total air content, percent, for level of exposure
4.04.55.05.56.06.07.07.5Severe exposure
—2602802903103253453656 to 72002252652752953053253403 to 41802052402502702802953051 to 2
6 in.
3 in.2 in.1½in.
1 in.¾in.
½ in.3/8 in.Slump, in.
Water, kilograms per cubic meter of concrete, for indicated sizes of aggregate
AirAir--entrained concreteentrained concreteInchInch--PoundPound
Proportioning
Slump Test
Proportioning
Recommended Slump Ranges
25 (1)75 (3)Mass concrete25 (1)75 (3)Pavements and slabs 25 (1)100 (4)Building columns 25 (1)100 (4)Beams and reinforced walls
25 (1)75 (3)Plain footings, caissons, and substructure walls
25 (1)75 (3)Reinforced foundation walls and footings
MinimumMaximumConcrete construction
Slump, mm (in.)
Proportioning
Approx. Water Requirements for Various Agg. Sizes and Slumps
Proportioning
Approx. Water Requirements for Various Agg. Sizes and Slumps
Proportioning
Minimum Cementing Materials Content for Flatwork
360 (610)(3/8)9.5
350 (590) (½)12.5
320 (540) (¾)19
310 (520) (1)25
280 (470) (1½)37.5
Cementing materials,
kg/m3 (lb/yd3)Nominal maximum size of aggregate, mm (in.)
Proportioning
Determination of Cement Content
Cement Content = Required Water Content
Water-Cement Ratio
Example: air-entrained concrete 25-mm max. size aggregate75-mm slump
175 kg/m3 Water 0.53 W/C-ratio
= 330 kg cement per m3 of concrete
Proportioning
Determination of Cement Content
Cement Content = Required Water Content
Water-Cement Ratio
Example air-entrained concrete 1-in. max. size aggregate 3-in. slump
295 lb/yd3 Water 0.53 W/C-ratio
= 557 lb. cement per yd3 of concrete
Proportioning
Cementitious Materials Requirements for Concrete Exposed to Deicing Chemicals
35Total of natural pozzolans and silica fume
50Total of fly ash, slag, silica fume and natural pozzolans
10Silica fume50Slag 25Fly ash and natural pozzolans
Cementitious materialsMaximum of cementi-tious materials, %
Proportioning
Maximum Chloride-Ion Content for Corrosion Protection
0.30Other reinforced concrete construction
1.00Reinforced concrete that will be dry or protected from moisture in service
0.15Reinforced concrete exposed to chloride in service
0.06Prestressed concreteType of member
Maximum chloride ion content in concrete, % by mass of cement
Proportioning
Methods for Proportioning Concrete Mixtures
■ Water-cement ratio method
■ Weight method
■ Absolute volume method
■ Field experience (statistical data)
■ Trial mixtures
Proportioning
Proportioning from Field Data
1.0030 or more1.03251.08201.1615
see next slideLess than 15Number of tests
Modification factor for standard deviation
Modification Factor for Standard Modification Factor for Standard Deviation (Deviation (≤≤ 30 Tests)30 Tests)
Proportioning
Required Strength When Data Are Required Strength When Data Are Available to Establish a Standard Available to Establish a Standard DeviationDeviation
MetricMetric
Proportioning from Field Data
f'cr = f'c+ 1.34sf'cr = 0.90f'c + 2.33s
Use larger valueOver 35
Use larger value
f'cr = f'c+ 1.34sf'cr = f'c + 2.33s – 3.45≤ 35
Specified compressive strength, f'c, MPa
Required average compressive strength, f'cr, MPa
Proportioning
Required Strength When Data Are Required Strength When Data Are Available to Establish a Standard Available to Establish a Standard DeviationDeviation
f'cr = f'c+ 1.34sf'cr = 0.90f'c + 2.33s
Use larger valueOver 5000
Use larger value
f'cr = f'c+ 1.34sf'cr = f'c + 2.33s - 500≤ 5000
Specified compressive strength, f'c, psi
Required average compressive strength, f'cr, psi
InchInch--PoundPound
Proportioning from Field Data
Proportioning
Required Strength When Data Are Required Strength When Data Are NotNot Available to Establish a Available to Establish a Standard DeviationStandard Deviation
1.10f'c + 5.0Over 35
f'c + 8.521 to 35
f'c + 7.0Less than 21
Specified compressive strength,
f'c, MPa
Required average compressive strength,
f'cr, MPa
MetricMetric
Proportioning from Field Data
Proportioning
Required Strength When Data Are Required Strength When Data Are NotNot Available to Establish a Available to Establish a Standard DeviationStandard Deviation
1.10f'c + 700Over 5000
f'c + 12003000 to 5000
f'c + 1000Less than 3000
Specified compressive strength,
f'c, psi
Required average compressive strength,
f'cr, psi
InchInch--PoundPound
Proportioning from Field Data
Proportioning
Proportioning by Trial Mixtures
Trial batching verifies that a concrete mixture meets design requirements prior to use in construction.
Proportioning
Density of Water Vs. Temperature
995.6130
996.2028
996.7526
997.2724
997.7522
998.1920
998.5818
998.93 16
Density, kg/m3Temperature, °C
CelsiusCelsius
Proportioning
Density of Water Vs. Temperature
62.16685
62.21680
62.26175
62.30270
62.33765
62.36860
Density, lb/ft3Temperature, °F
FahrenheitFahrenheit
Proportioning
Absolute Volume Computation for Fine Aggregate Content
Water = 135 1 • 1000
= 0.135 m3
Cement = 4353.0 • 1000
= 0.145 m3
Air = 8.0100
= 0.080 m3
Coarse aggregate = 1072
2.68 • 1000 = 0.400 m3
Subtotal = 0.760 m3
Fine aggregate volume = 1 - 0.76 = 0.24 m3
Fine aggregate mass = 0.24 • 2.64 • 1000 = 634 kg
Proportioning
Absolute Volume Computation for Fine Aggregate Content
Water = 270 1 • 62.4
= 4.33 ft3
Cement = 4353.15 • 62.4
= 3.27 ft3
Air = 7.0 • 27100
= 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
Proportioning
Proportioning
Result of Laboratory Trial Mixtures
MetricMetric
Good40.234823246.8364
Good38.034123137.5453
Fair33.333723326.2402
Harsh28.634623415.7501
Worka-bility
Slump, mm
Batch no.
Fine aggregate, percent of total
aggregate
Cement content,
kg/m3
Density,
kg/m3
Air content, percent
Water-Cement ratio was 0.45.
Proportioning
Result of Laboratory Trial Mixtures
InchInch--PoundPound
Excellent30.55401454.734
Excellent35.55491445.12½3
Harsh27.45551444.92¾2
Good33.55391445.431
Worka-bility
Slump, in.
Batch no.
Fine aggregate, percent of total
aggregate
Cement content,
lb/yd3
Density,
lb/ft3
Air content, percent
Water-Cement ratio was 0.50.
Proportioning
Proportioning
Proportioning
Example Trial Mixtures for Air-Entrained Concrete of 75-mm to 100-mm slump
122558332315158537.5107165438357178619.0750833534062027.59.50.50
125551829395158537.5107157735446178619.0750744505052027.59.50.40
Air,
%
Cement, kg/m3 of concrete
Water, kg/m3 of concrete
W/C-ratio,
kg per kg
Coarse aggre-gate,
kg/m3 of concrete
Fine aggre-gate,
kg/m3 of concrete
Fine aggregate
in % oftotal
aggregate
Nominal maximum
size of aggregate,
mm
With fine sand, FM = 2.50
Proportioning
Example Trial Mixtures for Air-Entrained Concrete of 3-in. to 4-in. slump
21109803253026551½18001100386003006¾12601400536803407.53/80.5021108702966526551½1800970357503006¾12601250508503407.53/80.40
Air,
%
Cement, lb/yd3 of concrete
Water, lb/yd3 of concrete
W/C-ratio, lb per
lb
Coarse aggre-gate,
lb/yd3 of concrete
Fine aggre-gate,
lb/yd3 of concrete
Fine aggregate
in % oftotal
aggregate
Nominal maximum
size of aggregate,
in.
With fine sand, FM = 2.50
Proportioning
Relationship between:
Slump
Agg. Size
W/C
Cement content
Proportioning
14120613737.515112623825.016104674019.01688744312.5167485469.5
Water,
kg
Cement,
kg
Wet coarse aggregate,
kg
Wet fine aggregate,
kg
AirAir--entrained concreteentrained concreteNominal maximum
size coarse aggregate,
mm
Proportions to Make 1/10 m3
of Concrete for Small Jobs
MetricMetric
Proportioning
14120693737.515112723825.016104754019.01888854312.5187494469.5
Water,
kg
Cement,
kg
Wet coarse aggregate,
kg
Wet fine aggregate,
kg
NonNon--airair--entrained concreteentrained concreteNominal maximum
size coarse aggregate,
mm
Proportions to Make 1/10 m3
of Concrete for Small Jobs
MetricMetric
Proportioning
97538231½97039241106542253/4105546271/2104653293/8
Water,
lb
Cement,
lb
Wet coarse aggregate,
lb
Wet fine aggregate,
lb
AirAir--entrained concreteentrained concreteNominal maximum
size coarse aggregate,
in.
Proportions to Make 1 ft3 of Concrete for Small Jobs
InchInch--PoundPound
Proportioning
97543231½107045241106547253/4115553271/2114659293/8
Water,
lb
Cement,
lb
Wet coarse aggregate,
lb
Wet fine aggregate,
lb
NonNon--airair--entrained concreteentrained concreteNominal maximum
size coarse aggregate,
in.
Proportions to Make 1 ft3 of Concrete for Small Jobs
InchInch--PoundPound
Proportioning
½32¼137.5 (1½)½2¾2¼125 (1)½2½2¼119.0 (3/4)½22¼112.5 (1/2)½1½2¼19.5 (3/8)
WaterCementWet coarse aggregate
Wet fine aggregate
AirAir--entrained concreteentrained concreteNominal maximum
size coarse aggregate,
mm (in.)
Proportions by Bulk Volume of Concrete for Small Jobs
Proportioning
½32½137.5 (1½)½2¾2½125 (1)½2½2½119.0 (3/4)½22½112.5 (1/2)½1½2½19.5 (3/8)
WaterCementWet coarse aggregate
Wet fine aggregate
NonNon--airair--entrained concreteentrained concreteNominal maximum
size coarse aggregate,
in.
Proportions by Bulk Volume of Concrete for Small Jobs
Proportioning
≥≥
Proportioning
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
Proportioning
Videos
Maximum Size AggregateNominal Max. Size Aggr.
