# stress - Overview of Topics Stress-Strain Behavior in...

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Stress-Strain Behavior in Concrete Dr. Kimberly Kurtis School of Civil Engineering Georgia Institute of Technology Atlanta, Georgia Overview of Topics EARLY AGE CONCRETE Plastic shrinkage – shrinkage strain associated with early moisture loss Thermal shrinkage – shrinkage strain associated with cooling LATER AGE CONCRETE Drying shrinkage -shrinkage strain associated with moisture loss in the hardened material Deformations occur under loading - Elastic - Viscoelastic Elastic Behavior Under loading, concrete deforms in a non-linear, inelastic manner However, an estimate of E is useful for determining stresses induced when strain is produced is very small (e.g., by environmental effects) Non-Linear Inelastic Behavior Elastic Modulus Initial Tangent Modulus/Dynamic Modulus - slope of the tangent to the curve at the origin (D) Tangent Modul us – slope of a line drawn tangent to curve at any point (T) Secant Modulus – slope of line drawn from the origin to a point on the curve, usually corresponding to 0.40 ultimate stress (S) Chord modulus – slope of the line drawn between 2 points, one of which corresponds to 50 microstrain and the other generally occurs at 0.40 ultimate stress (C) Stress Distribution Concrete is highly heterogeneous Localized stress/strain can be quite different from nominal applied stress/strain Largest strains often occur at the interface -> microcracking

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For E agg >E paste , (1) Tensile bond failure (2) Shear bond failure (3) Tensile matrix failure (4) Occasional aggregate failure Stress Distribution Paste shows more ductility Paste shows broader high stress region Due to stress concentrations and heterogeneity of concrete Elastic Modulus: Two Phase Models E c =E concrete E p =E cement paste E a =E agg V c =vol concrete V p =vol paste V a =vol agg K=bulk modulus G=shear modulus Elastic Modulus: Two Phase Models Hirsch, Counto, and H-S models give fairly good representations of E in most concrete Deviations from actual behavior are believed to be due to ITZ effects Elastic Modulus: Three Phase Models Elastic Modulus: Three Phase Models E c =E concrete E p =E cement paste E a =E agg E i =E ITZ V c =vol concrete V p =vol paste V a =vol agg V i =vol ITZ K=bulk modulus G=shear modulus
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stress - Overview of Topics Stress-Strain Behavior in...

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