Tests of Hardened Concrete
description
Transcript of Tests of Hardened Concrete
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Tests of HardenedConcrete
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StressBalance for equilibriumloads = external forces internal forces = stress
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Straindeformation (elastic or permanent)loadchange in temperaturechange in moistureunit deformation = strainAxial
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Strain
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StrengthEnvelopeFor Concrete
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Effect of Confinement
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Affect of Water Cement Ratio
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Compressive Testingbrittlestronger in compressioncross-sectional area cylindrical, cubeends must be plane & parallelend restraint apparently higher strength
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Loaded Compressive Specimen
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Elastic Properties
Linear Elastic
Nonlinear ElasticE = modulus of elasticity = Youngs modulus = slopeStrain energy per unit volume = area
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Elastic PropertiesPoissons ratio =- (radial strain/axial strain)
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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
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Flexure (Bending)CompressionTensionNeutralAxisHow would the cross-section deform?
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Flexure (Bending)CompressionTensionNeutralAxis
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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.
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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
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LVDT SchematicPrimary coilSecondarycoilSecondarycoilPositive voltagezero voltageNegative voltage
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Longitudinal DisplacementGage lengthLVDT
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Radial DisplacementLVDT
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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
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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
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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
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Strength
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Tensile TestingDirect: ductilecylindrical, prismaticreduced section @ center
Test Parameterssurface imperfectionsrate of loadingtemperature (ductile)specimen sizeIndirect: brittlecylindricalsplitting tension / diametral compression
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Flexure (Bending)CompressionTensionNeutralAxis
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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
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Correlation of Concrete Strengths
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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
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Standards & Standard Testsallow comparisonensure design = construction
standard specifications for materialsproperties specified in design, measured with standard testsStandards OrganizationsASTMAASHTOACIState AgenciesFederal AgenciesOther
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Scanning Electron Microscope
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Impact Hammers
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Ultrasonics
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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%
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Pulse Velocity12Compressive Strength (MPa)Compressive Strength (psi)2468101214024681005001,0001,500Pulse Velocity (1000 m/s)01234(1000 ft/s)Semi-direct mode
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Concrete Strength ModelsCompressive StrengthModulus of ElasticityTensile Strength
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Hitting Target Strengths
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Variability of Strength
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VARIABILITYmeasured properties not exact
always variabilitymaterialsamplingtesting
probability of failure
mean, standard deviation (s), coefficientof variation (COV)
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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)
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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
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Crack Growth
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aCrack TipxyStress DistributionStress Intensity Factor
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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)
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Fracture MechanicsThree modes of crack opening
Focus on Mode I for brittle materials
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FAlpha2 d2 aKIccAlpha = a/d
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Failure Criterion
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Linear Fracture MechanicsNon-Linear Fracture Mechanics
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CrackdacfKIProcess ZoneAlpha = a/d
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Fracture specimens
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Specimen Apparatus
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Specimen Preparation
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Test Specimens
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Failure Criterion
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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
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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
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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
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Beam###
Cn
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_1138700812.unknown
_1138709138.unknown
_1138709307.unknown
_1138709733.unknown
_1138712390.unknown
_1138709696.unknown
_1138709284.unknown
_1138708715.unknown
_1138700714.unknown
_1138700731.unknown
_1138700692.unknown
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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
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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.