Materials of Construction and Testing

Introduction Need for Materials with Various

Qualities Selecting Materials Sources of Information Inspection and Testing

Inspection – means examining a product or observing an operation to determine whether or not it is satisfactory.

Test – consists of applying some measurable influence to the material and measuring the effect on the material.

Standards

Testing method – is a specification explaining how to perform a test and how to measure the results.

Inspection and Test Category

1. Quality assurance or acceptance – inspection and tests performed to determine whether or not a material or product meets specific requirements in order to decide whether or not to accept or reject the material or product.

2. Quality control – inspection and tests performed periodically on selected samples to ensure that the product is acceptable.

3. Research and development – inspection and tests performed to determine the characteristics of new products and also to determine the usefulness of particular inspection procedures and tests to judge characteristics or predict behaviour of materials.

Aggregates

Aggregates – generally refers to mineral particles which have rock as their origin unless otherwise specified.

- Particles of random shape. Rock – includes any large solid mass

of mineral matter which is part of the earth’s crust.

Types of Rock

1. Igneous Rock – was at one time molten and cooled to its present form.

2. Sedimentary Rock – was at one time consisted of particles deposited as sediment by water, wind or glacier.

3. Metamorphic Rock – is either igneous or sedimentary rock that has been changed in texture, structure and mineral composition

or in or two of these characteristics, by intense geologic heat or pressure or both.

Definition of Terms (ASTM C125)

1. Coarse aggregate – (1) aggregate predominantly retained on the No. 4 (4.76-mm) sieve; or (2) that portion of an aggregate retained on the No. 4 (4.76-mm) sieve.

2. Fine aggregate – aggregate passing the 3/8-in. sieve and almost entirely passing the no. 4 (4.76-mm) sieve and predominantly retained on the No. 200 (74-micron) sieve; or (2) that portion of an aggregate passing the No. 4 (4.76-mm) sieve and retained on the No. 200 (74-micron) sieve.

3. Gravel – (1) granular material predominantly retained on the No. 4 (4.76-

mm) sieve and resulting from natural disintegration and abrasion of rock or processing of weakly bound conglomerate; or (2) that portion of an aggregate retained on the No. 4 (4.76-mm) sieve and resulting from natural disintegration and abrasion of rock or processing of weakly bound conglomerate.

4. Sand – (1) granular material passing the 3/8-in. sieve and almost entirely passing the No. 4 (4.76-mm) sieve and predominantly retained on the No. 200 (74-micron) sieve, and resulting from natural disintegration and abrasion of rock or processing of completely friable sandstone; or (2) that portion of an aggregate passing the No. 4 (4.76-mm) sieve and predominantly retained on the No. 200 (74-micron) sieve, and resulting from natural disintegration and abrasion of rock or processing of completely friable sandstone.

5. Bank gravel – gravel found in natural deposits, usually more or less intermixed with fine material, such as sand or clay, or combination thereof; gravelly clay, gravelly sand, clayey gravel, and sandy gravel indicate the varying proportions of the materials in the mixture.

6. Crushed gravel – the product resulting from the artificial crushing of gravel with substantially all fragments having at least one face resulting from fracture.

7. Crushesd stone – the product resulting from the artificial crushing of rocks, boulders, or large cobblestones, substantially all faces of which have resulted from the crushing operation.

8. Crushed rock – the product resulting from the artificial crushing of all rock, all faces of

which have resulted from the crushing operation or from blasting.

9. Blast-furnace slag – the non-metallic product, consisting essentially of silicates and aluminosilicates of lime and of other bases, which is developed in a molten condition simultaneously with iron in a blast furnace.

Properties and Uses

1. Weight.

2. Strength of the particles to resist weathering, especially repetitive freezing and thawing.

3. Strength as demonstrated by the ability of the mass to transmit a compressive force.

4. Strength as demonstrated by the ability of the individual particles to resist being broken, crushed, or pulled apart.

5. Strength of the particles to resist wear by rubbing or abrasion.

6. Adhesion or the ability to stick to a cementing agent.

7. Permeability of the mass, or the ability to allow water to flow through, without the loss of strength or the displacement of particles.

Tests for Aggregates

1. Size and Gradation

Range of sizes – smallest and largest particles.

Gradation – distribution of sizes within the range covered.

2. Surface Area

Surface area = 4 π r2

Volume = 4 π r3

3

Ratio = SurfaceareaVolume

= 4 π r2

4 π r3

3

=3r

Gradation Chart

Gradation Chart – a graph of percent by weight versus sieve sizes.

Effective Size (D10 ) - used to designate size of aggregate to be used as a filter for sewage or drinking water, is that diameter or size on the graph which has 10 percent of the total finer than its size.

Maximum Size of Aggregate – when used in the design of Portland cement concrete mixes, is taken for that purpose to be the size

of the sieve next above the largest sieve that has 15 percent of the total sample coarser than it (cumulative percentage retained).

Fineness Modulus – is a value used in the design of Portland cement concrete mixes to indicate the average size of fine aggregate.

Uniformity Coefficient (D60

D10) - is a mathematical

indication of how uniform the aggregate is.

3. Weight-Volume Relationships

Bulk Volume – is the volume of aggregate that may include solid matter, plus pores in the particles, plus voids.

Saturated Surface – Dry Volume – is the volume that may include solid matter, plus pores in the particles but not voids.

Solid Volume – is the volume that may include solid matter only, not pores or voids.

Wet Weight – is the weight that may include solid matter, plus enough water to fill the pores, plus free water on the particles surface.

Saturated Surface – Dry Weight – is the weight that may include solid matter, plus enough water to fill the pores.

Oven – Dry Weight – is the weight that may include solid matter only.

Example Problem:

Calculate the solid volume and percent of voids in a fine aggregate if it has a specific gravity of 2.65 and a bulk unit weight of 111.3 pef (1782.85 kg/m3).

Example Problem:

Calculate γ dry if an aggregate weighs 47.72 lb, has a moisture content of 6.3 %, and occupies a volume of 0.4987 cu. Ft.

4. Specific Gravity

Specific Gravity of Coarse Aggregate

Bulk SG= ODWeightSSDWeight−SubmergedWeight

Apparent SG= ODWeightODWeight−SubmergedWeight

% Absorption=SSDWeight−ODWeightODWeight

x 100

Example Problem:

Given: SSD weight in air = 5480 g

Submerged weight = 3450 g

OD Weight = 5290 g

Specific Gravity of Fine Aggregate

Bulk SG= ODWeight

[ (Flask+Water )+(ODWt ) ]−[Flask+Water+FA ]

Apparent SG= ODWeight

[ (Flask+Water )+(ODWt ) ]− [Flask+WAter+FA ]

% Absorption=SSDWeight−ODWeightODWeight

x 100

Example Problem:

Given: SSD weight = 500 g

OD weight = 492.6 g

Flask + Water Weight = 537.6 g

Flask + Water + fine aggregate weight = 846.2g

5. Deleterious Matter

a. Friable particles – are those which are easily crumbled, such as clay lumps, weak sandstone, or oxidized ores.

b. Material finer than No. 200 sieve – is that material which passes through the No. 200

sieve in a washed sieve analysis performed according to ASTM C117.

c. Soft particles – are those that are marked with a groove after being scratched on a freshly broken surface by a pointed brass rod under a force of 2 lb in accordance with ASTM C235, Test for Scratch Hardness of Coarse Aggregate Particles.

d. Lightweight pieces – are particles in coarse or fine aggregate that have an SG substantially less than that of the aggregate as a whole.

e. Organic impurities – are non-mineral material of an organic type, mainly tannic acid, sometimes found in fine aggregate.

f. Reactive aggregates – are those which contain minerals which react with alkalis in

Portland cement, causing excessive expansion of mortar or concrete.

6. Miscellaneous Properties

a. Toughness – means resistance to abrasion and impact.

b. Soundness – of aggregates means resistance to disintegration under weathering including alternate heating and cooling, wetting and drying, and freezing and thawing.

c. Hydrophilic – aggregates does not maintain adhesion to asphalt when it becomes wet.

Aggregate and Strength

Example Problem:

A wheel load (force) of 3000 lb is applied directly to a crushed rock base 8 in. deep.

Compute the pressure transmitted to the soil if the base material is of high quality, and angle θ can be considered to be 45°.

Example Problem:

A column load (force) of 33 kips acts on a 3 ft x 3ft spread footing. Calculate the pressure on the soil if the depth of aggregate base is 8 in., ad determine what depth of base is needed to reduce the pressure on the soil to 1.0 kip per sq ft. Assume angle θ is 40°. What is the maximum pressure on the aggregate?

Cubic meter compacted per hour = WxSxLp

Where: W = compacted width per pass as recommended by the equipment manufacturer (meters, m)

S = average speed (kilometres per hour, kph)

L = thickness of compacted lift (millimetres, mm)

P = number of passes required to meet specification requirements

Compaction

Compaction – is the densification of a material resulting in an increase in weight per unit volume.

Cubic yards compacted per hour = WxSxL x16.3P

Where: W = compacted width per pass as recommended by the equipment manufacturer (ft)

S = speed (mph)

L = thickness of compacted lift (in.)

P = number of passes required to meet specification requirements

16.3 = constant which converts mixed units.

Example Problems

Calculate the compacted cubic yards per hour, if a compactor with a 6-ft drum width travels at 7 miles per hour (mph) over an 8in. lift of aggregate base and the test strip indicates four passes will be required to meet the density requirement of the specification.

Calculate the compact cubic meters per hour, if a compactor with a 1.270 meter drum travels at an average speed of 6.5 kph over a 150-mm-thick fill and test strip data indicate that three passes will be required to meet specification requirements.

Permeability in Aggregates

Permeability – is a measure of the ease with which a fluid, most commonly water, will flow through a material.

k ≅ (D10)2

Where: k = coefficient of permeability (cm/s)

D10 = effective size based on gradation curve (mm).

Determine k for clean sand that has an effective size D10 of 0.5 mm.

Portland Cement Concrete Introduction

ACI 211.1 states: “Concrete is composed principally of aggregates, Portland cement, and water, and many contain other cementitious materials and/or chemical admixtures. It will

contain some amount of entrapped air and may also contain purposely entrained air obtained by use of admixture or air-entraining cement. Chemical admixtures are frequently used to accelerate, retard, improve workability, reduce mixing water requirements, increase strength, or alter other properties of the concrete. The selection of concrete proportions involves a balance between economy and requirements of placeability, strength, durability, density and appearance.”

Basic Relationship

ACI 21’1.1 states: “Concrete proportions must be selected to provide workability, consistency, density, strength and durability for the particular application.

Workability: The property of the concrete that determines its capacity to be placed and consolidated property and be finished without harmful segregation.

Consistency: It is the relative mobility of the concrete mixture, and measured in terms of the slump; the greater the slump value the more mobile the mixture.

Stregnth: The capacity of the concrete to resist compression at the age of 28 days.

Water-cement (w/c) or water-cementitious (w/(c+p)) ratio: Defined as the ratio of weight of water to the weight of cement, or the ratio of weight of water to the weight of cement plus added pozzolan. Either of these ratios is used in mix design and considerably controls concrete strength.

Durability: Concrete must be able to endure severe weather conditions such as freezing and thawing, wetting and drying, heating and cooling, chemicals, deicing agents and the like. An increase of concrete durability will enhance concrete resistance to severe weather conditions.

Density: For certain applications concrete may be used primarily for its weight characteristics. Examples are counterweights, weights for sinking pipelines under water, shielding from radiation and insulation from sound.

Generation of heat: If the temperature rise of the concrete mass is not held to a minimum and the heat is allowed to dissipate at a reasonable rate, or if the concrete is subjected to severe differential or thermal gradient, cracking is likely to occur.”

Effects of Chemical Admixtures on Concrete Proportions

ACI 211.1 states: “Chemical admixtures, pozzolanic and other materials can be added to concrete mix to alter some properties or to produce desired characteristics. Additives are used to affect the workability, consistency, density, strength and durability of the concrete.”

Background Data

ACI 211.1 states: “To the extent possible, selection of concrete proportions should be based on test data or experience with the materials actually to be used: The following information for available materials will be useful:

Sieve analyses of fine and course aggregates.

Unit weight of coarse aggregates. Bulk specific gravities and absorption

of aggregates. Mixing-water requirements of

concrete developed from experience with available aggregates.

Relationship between strength and water-cement ratio or ratio of water-to-cement plus other cementitious materials, if used.

Optimum combination of coarse aggregates to meet the maximum density grading for mass concrete.

Estimate of proportions of mix for preliminary design.”

Concrete Ingredients

1. Portland cement – the fundamental ingredient in concrete.

Types of Portland Cement: (ASTM Specification C-150)

Type I – is a normal, general-purpose cement suitable for all uses.

Type IA – is similar to Type I with the addition of air-entraining properties.

Type II – generates less heat at a slower rate and has a moderate resistance to sulfate attack.

Type IIA – is similar to Type II and produces air-entrained concrete.

Type III – is a high-early strength cement and causes concrete to set and gain strength rapidly.

Type IIIA – is an air-entraining, high-early strength cement.

Type IV – has a low heat of hydration and develops strength at a slower rate than other cement types.

Type V – is used only in concrete structures that will be exposed to severe sulfate action principally where concrete is exposed to soil and groundwater with a high sulfate sontent.

2. Aggregates

Properties considered in selecting aggregates for concrete:

Grading Durability Particle shape and surface texture Abrasion and skid resistance Unit weights and voids Absorption and surface moisture

3. Water

4. Chemical Admixtures – are the ingredients in concrete other than Portland cement, water, and aggregate that are added to the mix immediately before or during mixing used primarily to reduce the cost of concrete construction; to modify the properties of hardened concrete; to ensure the quality of concrete during mixing, transporting, placing and curing; and to overcome certain emergencies during concrete operations.

Classes of Chemical Admixtures:

Air-entraining – are used to purposely place microscopic bubbles into the concrete.

Water-reducing – reduce the required water content for a concrete mixture by about 5-10 percent.

Retarding – slow the setting rate of concrete.

Accelerating – increase the rate of early strength development, reduce the time required for proper curing and protection and speed up the start of finishing operations.

Plasticizers (superplasticizers) – or high-range water reducers, reduce water content by 12 to 30 percent and can be added to concrete with low-to-normal slump and water-cement ratio to make high-slump flowing concrete.

Physical Properties of Portland Cement

Fineness Soundness

Water-Cement Reaction

Hydration – is the chemical reaction that takes place when Portland cement and water are mixed together.

Setting – the hardening of a fluid paste (cement mixed with water).

False Set – is a stiffening of a concrete mixture with little evidence of significant heat generation.Heat o Hydration – is the heat generated when water and cement chemically react.

Maximum Size of Aggreagates based from ACI Recommendations:

1. One-fifth the minimum dimension of nonreinforced members.

2. Three-fourths the clear spacing between reinforcing bars or between reinforcing bars and forms.3. One-third the depth of nonreinforced slabs on grade.

Aggregate Moisture Conditions

TotalMoisture (% )=wet weight−ovendry weightovendry weight

x100

Absorbed Moisture (%)= saturated surface dry weight−oven dry weightovendry weight

x100

Free Moisture (% )=TotalMoisture (% )−Absorbed Moisture (% )

Example Problem:

Calculate the percentage of free moisture on a fine aggregate based on the given data.

Percent absorption = 1.7

Wet weight = 503.7 g

Oven – dry weight = 480.2 g

Concrete Estimating

Determining concrete quantities for a construction project requires volumetric calculations, because concrete is estimated an purchased by the cubic yard or cubic meter.

Waste Factors: Typical waste factors for concrete construction range from 3 to 8 percent, with lower values used for formed placements and higher values used for slab on grade projects.

Example Problem:

Calculate the concrete required to cast a 40 ft x 60 ft by 5 in. thick slab on a prepared sub-grade (1 cu yd = 27 cu ft). If the subgrade for this slab has not been fine graded accurately,

a waste factor of 7 percent might be appropriate.

Example Problem:

Calculate the concrete required to cast a wall 3 meters high, 20 meters long and 250 millimeters thick.

Proportioning Concrete Ingredients

Common Methods of Proportioning Concrete

a. Simple 1:2:3 Formula

b. ACI 211.1 (Recommended Practice for Designing Normal and Heavyweight Concrete)

Procedure for ACI 211.1:

Step 1: Choice of slump

Step 2: Choice of maximum size of aggregate

Step 3: Estimation of mixing water and air content

Step 4: Selection of water-cement or water-cementitious materials ratio

Step 5: Calculation of cement content

Step 6: Estimation of coarse aggregate content

Step 7: Estimation of fine aggregate content

Step 8: Adjustments for aggregate moisture

Step 9: Trial batch adjustments

Sample Computation (English Units):

Concrete is required for a portion of a structure that will be below ground level in a location where it will not be exposed to severe weathering or sulfate attack. Structural considerations require it to have an average 28-day compressive strength of 3500 psi. It is determined that under the conditions of placement to employed, a slump of 3 to 4 in. should be used and that the available No. 4 to 1 12-in. coarse aggregate will be suitable. The dry-rodded weight of coarse aggregate is found to be 100 lbft3 .

Type I non-air-entraining cement will be used and its specific gravity is assumed to be 3.15.

Coarse and fine aggregates in each case are of satisfactory quality and are graded within limits of generally accepted specifications.

The coarse aggregate has a bulk specific gravity of 2.68 and an absorption of 0.5 percent

The fine aggregate has a bulk specific gravity of 2.64, an absorption of 0.7 percent and a fineness modulus of 2.8.

Tests indicate total moisture of 2 percent in the coarse aggregate and 6 percent in the fine aggregate.

Sample Computation (SI Units):

Concrete is required for a portion of a structure that will be below ground level in a location where it will not be exposed to severe weathering or sulfate attack. Structural considerations require it to have an average 28-day compressive strength of 24 MPa. It is determined that under the

conditions of placement to be employed, a slump of 75 to 100 mm. The coarse aggregate has a nominal maximum size of 37.5 mm and dry-rodded mass of 1600 kgm3

Type I non-air-entraining cement will be used and its specific gravity is assumed to be 3.15.

Coarse and fine aggregates in each case are of satisfactory quality and are graded within limits of generally accepted specifications.

The coarse aggregate has a bulk specific gravity of 2.68 and an absorption of 0.5 percent.

The fine aggregate has a bulk specific gravity of 2.64, an absorption of 0.7 percent and a fineness modulus of 2.8.

Tests indicate total moisture of 2 percent in the coarse aggregate and 6 percent in the fine aggregate.

Water-Cement Ratio (w/c) and Water-Cement + Pozzolanic Materials (w/c+p)

1. Weight Equivalencywc+ p

=wc

Where:wc+ p

=weight of water divided by weight of cement+ pozzolanicmaterials

wc=target water−cement ratio by weight

Fw=p

c+ p

Where:

Fw = pozzolanic materials percentage by weight, expressed as a decimal factor

p = weight of pozzolanic materials

c = weight of cement

If only the desired pozzolanic materials percentage factor by absolute volume F v is known, it can be converted to Fw as follows:

Fw=1

1+( 3.15G p)( 1Fv

−1)Where:

F v = pozzolanic materials percentage by absolute volume of the total absolute volume of cement plus pozzolanic materials expressed as a decimal factor

G p = specific gravity of pozzolanic materials

3.15 = specific gravity of Portland cement (use actual value if known to be different)

Sample Problem: (Weight Equivalency)

If a water-cement ratio of 0.60 is required and a fly ash pozzolan is to be used as 20 percent of the cementitious material in the mixture by weight (

Fw=0.20), determine the required weight of cement and weight of fly ash. The estimated mixing-water requirement is 270 lbyd3.

If instead of 20 percent fly ash by weight, 20 percent by absolute volume of cement plus pozzolan was specified (F v=0.20¿, determine the required weight of cement and weight of fly ash. The specific gravity of fly ash is 2.40.

2. Absolute Volume Equivalency

wc+ p

=3.15

wc

3.15 (1−Fv )+G p (Fv )

If only the desired pozzolan percentage by weight Fw is known, it can be converted to F v as follows:

F v=1

1+( G p

3.15 )( 1Fw

−1)

Example Problem: Absolute Volume Equivalency

If a water-cement ratio of 0.60 is required and a fly ash pozzolan is to be used as 20 percent of the cementitious material in the mixture by volume (F v=0.20), determine the required weight of cement and weight of fly ash. The estimated mixing-water requirement is 270 lb

yd3.

If instead of 20 percent fly ash by volume, 20 percent by weight of cement plus pozzolan was specified (Fw=0.20), determine the required weight of cement and weight of fly ash. The specific gravity of fly ash is 2.40.

Mix Proportions

Mix proportions may be specified either by weight or by volume in terms of the ratios of fine aggregate and coarse aggregate to cement.

Example:

1:3:5 by volumetric ratio.

1:3:5 by weight ratio.

Water-cement ratio = weight of water/weight of cement or gallons of water per sack of cement.

One sack of cement = 1 cu. Ft. = 94 lbs.

One gallon of water = 8.34 lbs.

One cu. ft of water = 7.48 gallons.

The free moisture (m) content of the aggregate is expressed as a percentage of the SSD weight:

m=γ−γ sγ s

x100

Where: γ = wet bulk density

= total weight of the constituent including contained water, divided by the bulk volume.

γ s = saturated surface-dry bulk density.

= total weight of the saturated surface-dry constituent divided by the bulk volume.

γ=γ s(1+ m100 )

Yield of a mix = is the volume of concrete produced from one sack of cement.

The ratio of entrained air to the total volume of air plus solids is:

e=V e−V s

V e

Where: V s = volume of all solids.

V e = total volume of solids plus entrained air.

Also,

V e=V s

1−e

The yield of a mix without voids (i.e., the solid volume) is given by the absolute, or solid, volume method as:

V s=∑ ( γ sVGγw )Where: V = bulk volume of the saturated surface-dry constituent.

γ sV = total weight of the saturated surface-dry constituent.

G = specific gravity, or relative density of the constituent.

γwG = solid density.

The yield of a mix with entrained air is given by:

V e=V s

1−e

Where: e = ratio of entrained air to the total yield of the mix.

The cement factor is defined as the number of sacks of cement required to produce one cubic yard of concrete.

Example Problem: (Yield of a mix proportioned by weight)

The required proportion of a concrete mix are 1:2.5:3.5 by weight with 5.5 gallons of water per sack and 5 percent air entrainment. The sand contains 4 percent excess moisture and the stone 2 percent deficiency. Using the specific gravities given in the table, determine the yield of the mix, the cement factor and the quantities of water and aggregate required to provide one cubic yard of concrete.

Example Problem: (Yield of a mix proportioned by volume)

The required proportions of a concrete mix are 1:2:3 by volume with 5 gallons of water per sack. Using the specific gravities given in the table, determine the yield of the mix, the cement factor, and the quantities of water and aggregate required to provide one cubic yard of concrete.

Mix Design

Control of Concrete Quality:

A works strength test, in accordance with ACI Section 5.6.1.4, consists of the average of the strengths of two cylinders made from the sample of concrete and tested at 28 days.

ACI Section 5.6.1.1 requires the minimum sampling frequency for each class of concrete to be not less than

Once each day

Once for each 150 cubic yards of concrete placed each day.

Once for each 5000 square feet of slab or wall surface area placed each day.

A minimum of five samples from five randomly selected batches is desirable, or samples should be taken from each batch if fewer than five batches are made.

The concrete strength is considered satisfactory provided that:

The average of three consecutive strength tests is not less than the specified design strength.

No individual strength test falls below the specified design strength by more than 500 punds per square inch.

Mix Design Based on Statistical Data:

Standard deviation, s

s=[∑ (xi−x )2

(n−1 ) ]12

Where: x i=¿an individual test result (the average of two cylinder tests)

N = the number of consecutive tests (minimum of 30 cylinder tests) x=themean of n results

f cr' =f c

' +1.34 s

f cr' =f c

' +2.33 s−5.00

Where: f cr' = required target mean strength

f cr' = specified compressive strength.

S = standard deviation of the strength tests.

1.34s = required margin.

Testing Concrete

Slump Test – test for consistency of concrete.

Air Content Determination

Unit Weight Determination

Yield Determiniation

Determine the yield of a concrete batch with concrete unit weight of γ conc=149.2 pcf .

Batch Weights:

Water 265 lb

Cement 510 lb

CA 1917 lb

FA 1350 lb

Compressive Strength Tests

Compressive strength = PA

Determine the compressive strength of a 6-in.-diameter concrete cylinder that failed at a test load of 115 000lb.

A splitting tensile test was performed on a standard 6-by-12 in. – cylinder, the cylinder fractured at 49800lb. Calculate the splitting tensile strength and the approximate direct tensile strength of the concrete.

Flexural Strength TestsModulus of Rupture, R=K √ f c ' = 3PL

2b d2

K = constant value between 8 and 10.

Determine the approximate modulus of rupture of a concrete with a compressive strength of 4100 psi. Assume K = 9.

Non-destructive Tests

1. The rebound hammer

2. The penetration probe

3. Pullouts

4. Ultrasound

Coefficient of Variation, V=σxx100

Mean, x=∑ x

n

Standard deviation, σ=√∑ (x− x )2

n−1

Calculate the mean, standard deviation and coefficient of variation for the following test data:

3700 psi 2920 psi

4310 psi 3680 psi

3890 psi 4010 psi

4100 psi 3980 psi

Tensile Strength Tests

Spliting Tensile Strength, f t= 2Pπld

Approximations:

Tensile Strength = 4.5 √ f c '

Splitting Tensile Strength = 6.5√ f c '

Required Compressive Strength (f cr '): ACI 318

Where: f cr' =¿required strength for mix design

S = standard deviation

f c' =¿specified strength

f cr' =f c

' +1.34 S ( psi )∨(MPa)

f cr' =f c

' +2.33 S−500( psi)

f cr' =f c

' +2 .33S−3.45(MPa)

Example Problem:

Calculate the f cr' for a concrete mix that has a specified 400 psi strength requirement if previous data indicates a standard deviation of 325 psi based on 20 tests for a similar concrete mix.