Tests of Hardened Concrete

Stress Balance for equilibrium  loads = external forces  internal forces = stress Axial tension

Strain deformation (elastic or permanent)  load  change in temperature  change in moisture unit deformation = strain Axial

Strain

Strength Envelope For Concrete

Effect of Confinement

Affect of Water Cement Ratio

Compressive Testing brittle stronger in compression cross-sectional area cylindrical, cube ends must be plane & parallel end restraint apparently higher strength

Loaded Compressive Specimen

Elastic Properties Linear Elastic Nonlinear Elastic Stress  Strain (  ) E 1 E = modulus of elasticity = Young’s modulus = slope Strain energy per unit volume = area

Elastic Properties Poisson’s ratio =- (radial strain/axial strain)

Poisson’s Ratio (  ratio of lateral strain to axial strain 0.15 to 0.50  steel 0.28  wood 0.16  granite 0.28  concrete 0.1 to 0.18  rubber 0.50 deformed axial

Flexure (Bending) Compression Tension Neutral Axis How would the cross-section deform?

Flexure (Bending) Compression Tension Neutral Axis

Laboratory Measuring Devices Dial 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 coil  Output voltage is measured in the secondary coil  Linear relationship between output voltage and displacement. Primary coil Secondary coil Secondary coil zero voltage Shell attached to point A Core attached to point B

LVDT Schematic Primary coil Secondary coil Secondary coil Positive voltage zero voltage Negative voltage

Longitudinal Displacement Gage length LVDT

Radial Displacement LVDT

Electrical Strain Gage Measure 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 Cell Electronic 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 gages

8 Channel LVDT Input Module 8 Channel Universal Strain/Bridge Module 2 Voltage Inputs from the controller (Stroke LVDT, and Load Cell) 6 strain Gauges Data Acquisition Setup

Strength

Tensile Testing Direct: ductile  cylindrical, prismatic  reduced center Test Parameters  surface imperfections  rate of loading  temperature (ductile)  specimen size Indirect: brittle  cylindrical  splitting tension / diametral compression tt cc

Flexure (Bending) Compression Tension Neutral Axis

Flexural Testing Three-point (center point)  smaller specimens  higher flexural strength (size effect)  shear may be a factor General  shear effects ignored as long as l/d > 5  apply load uniformly across width Four-point  constant moment, no shear in center  localized loading stresses (3 vs. 4 pt)  load symmetrically

Correlation of Concrete Strengths

Torsion torque pure shear strain (  ) cylindrical (radius r)  G=shear modulus  T = torque, twisting moment  J = polar moment of inertia   = angle of rotation  for isotropic materials    ss l

Standards & Standard Tests allow comparison ensure design = construction standard specifications for materials properties specified in design, measured with standard tests Standards Organizations  ASTM  AASHTO  ACI  State Agencies  Federal Agencies  Other

Scanning Electron Microscope

Impact Hammers

Ultrasonics

Pulse Velocity Testing ASTM C 597 Velocity of sound wave from transducer to receiver through concrete relates to concrete strength Develop correlation curve in lab Precision to baseline cylinders: ±10%

Pulse Velocity 12 Compressive Strength (MPa) Compressive Strength (psi) ,000 1,500 Pulse Velocity (1000 m/s) (1000 ft/s) Semi-direct mode

Concrete Strength Models Compressive Strength Modulus of Elasticity Tensile Strength

Hitting Target Strengths

Variability of Strength

VARIABILITY measured properties not exact always variability  material  sampling  testing probability of failure mean, standard deviation (s), coefficient of variation (COV)

DESIGN / SAFETY FACTORS design strength = f(material, construction variables) working stress = f(  y ) N = 1.2 to 4 = f(economics, experience, variability in inputs, consequences of failure)

Variability-Specification Using the normally distributed tensile test data for concrete, determine the mean and standard deviation for both  R & f t. In order to maintain a 1 in 15 chance that f t ≤ 320 psi, what average f t must be achieved? Specimen  R (psi) f t (psi)

Crack Growth

a Crack Tip x y Stress Distribution Stress Intensity Factor

Fracture Mechanics K I = stress intensity factor = F  (  C) 1/2  F is a geometry factor for specimens of finite size K I = K IC OR G I =G IC unstable fracture K IC = Critical Stress Intensity Factor = Fracture Toughness G I =strain energy release rate (G IC =critical)

Fracture Mechanics Three modes of crack opening Focus on Mode I for brittle materials

F Alpha 2 d 2 a KIKI cc Alpha = a/d

Failure Criterion

Linear Fracture Mechanics Non-Linear Fracture Mechanics

Crack d a cfcf KIKI Process Zone Alpha = a/d

Fracture specimens

Specimen Apparatus

Specimen Preparation

Test Specimens

Failure Criterion

Fracture Spread Sheet

Applications of Fracture Parameters Strength Determination - Beam

Applications of Fracture Parameters Strength Determination Size effect on strength (  0 = 0.2; B fu = 3.9 MPa = 566 psi; d a = 25.4 mm = 1 in) log (d/d a ) Specimen or structure sizelog (  N / B fu )  N d (mm or inch) (MPa or psi) or or or or or or 254

Durability