Tests of HardenedConcrete

StressBalance for equilibriumloads = external forces internal forces = stress

Straindeformation (elastic or permanent)loadchange in temperaturechange in moistureunit deformation = strainAxial

Strain

StrengthEnvelopeFor Concrete

Effect of Confinement

Affect of Water Cement Ratio

Compressive Testingbrittlestronger in compressioncross-sectional area cylindrical, cubeends must be plane & parallelend restraint apparently higher strength

Loaded Compressive Specimen

Elastic Properties

Linear Elastic

Nonlinear ElasticE = modulus of elasticity = Youngs modulus = slopeStrain energy per unit volume = area

Elastic PropertiesPoissons ratio =- (radial strain/axial strain)

Poissons Ratio (u)ratio of lateral strain to axial strain

0.15 to 0.50steel 0.28wood 0.16granite 0.28concrete 0.1 to 0.18rubber 0.50

Flexure (Bending)CompressionTensionNeutralAxisHow would the cross-section deform?

Flexure (Bending)CompressionTensionNeutralAxis

Laboratory Measuring DevicesDial gage:Measure relative deformation between two points.Two different pointers: one division of small pointer corresponds to one full rotation of the large pointer.

Laboratory Measuring Device Linear Variable Differential Transformer (LVDT)Electronic device for measuring small deformations.Input voltage through the primary coilOutput voltage is measured in the secondary coilLinear relationship between output voltage and displacement.Primary coilSecondarycoilSecondarycoilzero voltageShell attached to point ACore attached to point B

LVDT SchematicPrimary coilSecondarycoilSecondarycoilPositive voltagezero voltageNegative voltage

Longitudinal DisplacementGage lengthLVDT

Radial DisplacementLVDT

Electrical Strain GageMeasure small deformation within a certain gage length.A thin foil or wire bonded to a thin paper or plastic.The strain gage is bonded to the surface for which deformation needs to be measured.The resistance of the foil or wire changes as the surface and the strain gage are strained.The deformation is calculated as a function of resistance change.

Surface wire

Load CellElectronic force measuring device.Strain gages are attached to a member within the load cell.An electric voltage is input and output voltage is obtained.The force is determined from the output voltage.Strain gagesStrain gages

Data Acquisition Setup8 Channel LVDT Input Module8 Channel Universal Strain/Bridge Module2 Voltage Inputs from the controller (Stroke LVDT, and Load Cell)6 strain Gauges

Strength

Tensile TestingDirect: ductilecylindrical, prismaticreduced section @ center

Test Parameterssurface imperfectionsrate of loadingtemperature (ductile)specimen sizeIndirect: brittlecylindricalsplitting tension / diametral compression

Flexure (Bending)CompressionTensionNeutralAxis

Flexural TestingThree-point (center point)smaller specimenshigher flexural strength (size effect)shear may be a factorGeneralshear effects ignored as long as l/d > 5apply load uniformly across widthFour-pointconstant moment, no shear in center

localized loading stresses (3 vs. 4 pt)load symmetrically

Correlation of Concrete Strengths

Torsiontorque pure shear strain (g)cylindrical (radius r)

G=shear modulusT = torque, twisting momentJ = polar moment of inertiag = angle of rotation

for isotropic materials

ttgdsl

Standards & Standard Testsallow comparisonensure design = construction

standard specifications for materialsproperties specified in design, measured with standard testsStandards OrganizationsASTMAASHTOACIState AgenciesFederal AgenciesOther

Scanning Electron Microscope

Impact Hammers

Ultrasonics

Pulse Velocity TestingASTM C 597Velocity of sound wave from transducer to receiver through concrete relates to concrete strengthDevelop correlation curve in labPrecision to baseline cylinders: 10%

Pulse Velocity12Compressive Strength (MPa)Compressive Strength (psi)2468101214024681005001,0001,500Pulse Velocity (1000 m/s)01234(1000 ft/s)Semi-direct mode

Concrete Strength ModelsCompressive StrengthModulus of ElasticityTensile Strength

Hitting Target Strengths

Variability of Strength

VARIABILITYmeasured properties not exact

always variabilitymaterialsamplingtesting

probability of failure

mean, standard deviation (s), coefficientof variation (COV)

DESIGN / SAFETY FACTORS

design strength = f(material, construction variables)

working stress = f(sy)

N = 1.2 to 4 = f(economics, experience, variability in inputs, consequences of failure)

Variability-SpecificationUsing the normally distributed tensile test data for concrete, determine the mean and standard deviation for both MoR & ft. In order to maintain a 1 in 15 chance that ft 320 psi, what average ft must be achieved?SpecimenMoR (psi) ft(psi)1580319257832235883314588352

Crack Growth

aCrack TipxyStress DistributionStress Intensity Factor

Fracture MechanicsKI = stress intensity factor = Fs(pC)1/2 F is a geometry factor for specimens of finite sizeKI= KIC OR GI=GIC unstable fractureKIC= Critical Stress Intensity Factor= Fracture ToughnessGI=strain energy release rate (GIC=critical)

Fracture MechanicsThree modes of crack opening

Focus on Mode I for brittle materials

FAlpha2 d2 aKIccAlpha = a/d

Failure Criterion

Linear Fracture MechanicsNon-Linear Fracture Mechanics

CrackdacfKIProcess ZoneAlpha = a/d

Fracture specimens

Specimen Apparatus

Specimen Preparation

Test Specimens

Failure Criterion

Fracture Spread Sheet

Chart1

0

0

0

0

0

0

Regression

X

Y

Split Tension Test

Module1

specimenD (m)L (m)2ao (mm)holed (0 or 1)P (N)alpha0F0(alpha)F'0(alpha)g(alpha)g'(alpha)X (m)Y MPa.mNot

10.15240.15240011000000.964-0.02602.91947631360.000003.818E-1510

20.15240.15240011000000.964-0.02602.91947631360.000003.818E-1510

30.15240.152425.41700000.16666666670.99939814810.44383333330.0104505153.6023221190.000227.640E-1500.0000000489

40.15240.152425.41700000.16666666670.99939814810.44383333330.0104505153.6023221190.000227.640E-1500.0000000489

50.15240.1524101.61500000.66666666671.66833333330.2130.009627578310.23263975070.000075.272E-1500.0000000051

60.15240.1524101.61500000.66666666671.66833333330.2130.009627578310.23263975070.000075.272E-1500.0000000051

Kif =0.24MPa.m217.55psi.in

Cf =0.23mm0.009in.

Relative Probable Error of KIf =0.12%

Relative Probable Error of cf =0.00%

SUMMARY OUTPUT

Regression Statistics

Multiple R0.9811388937

R Square0.9626335288

Adjusted R Square0.953291911

Standard Error0

Observations6

ANOVA

dfSSMSFSignificance F

Regression100103.04783911290.0005302572

Residual400

Total50

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept003.23873748730.031711850800

X Variable 10010.15124815540.000530257200

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Module1

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Regression

X

Y

Split Tension Test

Fracture Spread Sheet

Spec

#

b

(in)

d

(in)

2a0

(in)

P

(lb)

a

1

3

6

0

13000

0

2

3

6

1

10000

0.167

3

3

6

4

3500

0.667

F()

g()

g'()

X (in)

(g/g') d

Y (psi.in1/2) 1/(g'2)

0.964

0.000

2.92

0.0000

1.620E-06

0.999

0.523

3.60

0.8711

2.219E-06

1.645

5.699

10.02

3.4125

6.512E-06

Fracture Spread Sheet

Split Tensile

Cn

Plain#

0.0

0.964

0.0

2.9195

Slotted#

0.1667

0.9994

0.5230

3.6023

Hole and Slot##

0.6667

1.6497

5.6997

10.0214

#

##

Beam###

Cn

###

_1138700812.unknown

_1138709138.unknown

_1138709307.unknown

_1138709733.unknown

_1138712390.unknown

_1138709696.unknown

_1138709284.unknown

_1138708715.unknown

_1138700714.unknown

_1138700731.unknown

_1138700692.unknown

Applications of Fracture Parameters Strength Determination - Beam

Chart2

3.82446206813.9017220928

3.82446206813.1440460849

02.5502810439

0.12.082793002

0.21.713575928

0.31.4211496778

0.41.1887416544

0.51.0031924834

0.60.8542139296

0.70.7338116828

a = a/d

sN (MPa)

split

(b)

split

3.82446206813.9017220928

3.82446206813.1440460849

02.5502810439

0.12.082793002

0.21.713575928

0.31.4211496778

0.41.1887416544

0.51.0031924834

0.60.8542139296

0.70.7338116828

a = a/d

sN (MPa)

size effect

(b)

size effect

-0.0662287473-0.34689160441.375

-0.1854952741-0.5166863503-0.014437236

-0.2620386717-0.6107960582-0.1647715037

-0.318520074-0.6762351209-0.2527568564

-0.3633014049-0.7264526431-0.31519608

-0.4004079218-0.7672103788-0.3636329977

-0.4320893939-0.8015136015-0.4032115607

-0.4597316541-0.8311298715-0.4366763408

-0.4842491616-0.8571873635-0.465665853

-0.5062771713-0.880450327-0.4912370886

-0.5262749698-0.901460525-0.5141118134

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alpha=0.2

alpha=0.6

LEFM

log(sN/Bfu)

log(d/da)

sawcut

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sawcut

0.59402260780.84007482830.59402260780.84007482830.36511156190.73022312370.26774847870.5354969574

0.25352917560.45505327080.15981162760.30530330090.36511156190.73022312370.26774847870.5354969574

0.19117596540.35798401560.11595042040.2261200036

0.16055399240.30677686350.09579936790.188418625

0.13952445640.26895288820.08269027130.163202843

0.12160620040.23451503260.07204716720.1422209298

15.24 cm

15.24 cm

45.72 cm

45.72 cm

dT = 5.56 C

dT = 11.11 C

dT = 5.56 C

dT = 11.11 C

6 hrs (15.24 cm)

12 hrs (15.24 cm)

6 hrs (45.72 cm)

12 hrs (45.72 cm)

a

sN (MPa)

4 aggs

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4 aggs

0.78586727170.3383520772

0.6721904308

0.5802433343

0.7761468745

0.971246283

1.6073201355

0.3383520772

X = d g/g' (m)

Y = cn2/g' s2 (MPa)

Waco

Sheet15

0.10922293490.2367755563

0.12277359990.1929205596

0.1181970323

0.1457857929

0.1670844254

0.2946898967

0.258439072

0.2367755563

0.1929205596

X = d g/g' (m)

Y = cn2/g' s2) (MPa)

El Paso

Sheet16

0.28607322370.1887027689

0.17824821730.5707283042

0.2064463085

0.1561430475

0.3170658673

0.7200774435

0.4621253079

0.1887027689

0.5707283042

X = d g/g' (m)

Y = cn2/g' s2 (MPa)

Blue Mound

0.29926220680.3710188314

0.37585696310.6036022889

0.3477741635

0.438266033

0.2819280559

0.4650815602

0.401020169

0.3710188314

0.6036022889

X = d g/g' (m)

Y = cn2/g' s2 (MPa)

Altair

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Applications of Fracture Parameters Strength DeterminationSize effect on strength( a0 = 0.2; Bfu = 3.9 MPa = 566 psi; da = 25.4 mm = 1 in)

log (d/da) Specimen or structure sizelog (sN / Bfu) sN d (mm or inch) (MPa or psi) 0.70127 or 5 - 0.182.57 or 373 1.00305 or 12 - 0.262.15 or 312

1.30507 or 20 - 0.351.75 or 254

Durability

1) Tensile stresses at the ends of the specimen may cause tensile splitting failure perpendicular to the direction of loading.

2) Barrelling effect changes the length/diameter ratio.The difference in 3 point bending and 4 point bending is 25%.

Shear effects tends to cause greater deflection and back-calculation of lower elastic modulus. (as would be the case in shorter beams).Concrete permeability, porosity, and density affect strength. Concrete is stronger in compression than in tension. Often used with reinforcing steel to carry the tensile load after cracking has occurred.

Concrete strength also depends on the w/c and the degree of hydration. The degree of hydration depends on temperature and moisture of the concrete.