Outline_03

Outline_03 - 1.054/1.541 Mechanics and Design of Concrete...

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Unformatted text preview: 1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 3 1 / 1 4 Massachusetts Institute of Technology 1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 3 Failure Theories and Concrete Plasticity Failure of concrete o Concrete is a brittle material which fails through brittle cleavage (splitting) at the interfaces and in mortar except for high triaxial compression where shear slippage occurs resulting in a ductile behavior. Failure occurs by tensile splitting with the fractured surface orthogonal to the direction of the maximum tensile stress or strain. Prediction of multiaxial behavior o In general the material properties are known from simple tests such as uniaxial loadings giving ' c f and t f . Prediction involves strength calculation in multiaxial situations given the data from the uniaxial tests. o In the field of concrete research attempts have been made to apply some of the classical failure theories to concrete. These theories were altered to overcome some disadvantages or otherwise improve their agreement with the phenomenological behavior of concrete. New failure theories were therefore formed. Principal stresses: 3 2 3 1 1 3 2 2 1 1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 3 Some classical failure theories o Maximum principal stress theory o Maximum principal strain theory o Maximum shear stress theory o Internal friction theory o Maximum strain energy theory o Distortion energy theory o Fracture mechanics based theories stress intensity, toughness fracture energy release. These introduce either limitations or contradictions when applied to concrete. Modifications to concrete have resulted: o Internal friction-maximum stress theory o Octahedral shear-normal stress theory o Newmans two-part criterion o Local deformation theories, etc. Extensive research has been conducted to develop better theories: Elastic-plastic, plastic-fracturing, endochronic, bounding surface etc. approaches. Maximum principal stress theory (elastic behavior) o 1 2 3 > > o Failure occurs when: max 1 t = (Tensile strength) max ' 3 c c f = = (Compressive strength) It does not reflect splitting nature of failure. Maximum principal strain theory (elastic behavior) o Failure occurs when: max limit t = = 2 / 1 4 1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 3 Maximum shear stress theory o 1 2 3 > > o Failure occurs when: ( ) 1 3 1 3 2 s + + = where 1 3 = shear stress, ( 1 3 ) + = portion of the volumetric stress, s = a critical shear stress value (e.g. under pure shear) o For metals, . For brittle materials, ....
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Outline_03 - 1.054/1.541 Mechanics and Design of Concrete...

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