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1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1 // Recitation: F3:00-4:30

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1.033/1.57: Mechanics of Material Systems Part II: Momentum Balance, Stresses and Stress States 3. Momentum Balance

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1.033/1.57: Mechanics of Material Systems Content 1.033/1.57 Part I. Deformation and Strain 1 Description of Finite Deformation 2 Infinitesimal Deformation Part II. Momentum Balance and Stresses 3 Momentum Balance 4 Stress States / Failure Criterion Part III. Elasticity and Elasticity Bounds 5 Thermoelasticity, 6 Variational Methods Part IV. Plasticity and Yield Design 7 1D-Plasticity – An Energy Approac 8 Plasticity Models 9 Limit Analysis and Yield Design

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1.033/1.57: Mechanics of Material Systems Body & Surface Forces

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1.033/1.57: Mechanics of Material Systems Hypothesis of local contact forces =Action-Reaction Law

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1.033/1.57: Mechanics of Material Systems Tetrahedron Lemma: Stress vector T(n)

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1.033/1.57: Mechanics of Material Systems Cauchy Stresses σ ij and Stress Vector T(n) Components of σ ij Stress Vector T j = σ ij n j

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1.033/1.57: Mechanics of Material Systems Exercise: Two-Layer Soil Substratum

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1.033/1.57: Mechanics of Material Systems Reduction Formulae Section =Relation between local stress and section forces and moments Oriented Surface Position Vector in Section Stress Vector

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1.033/1.57: Mechanics of Material Systems Momentum Balance and Symmetry of Stress Tensor Dynamic Moment TheoremDynamic Resultant Theorem

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1.033/1.57: Mechanics of Material Systems Training Set: Pressure Vessel Formula

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1.033/1.57: Mechanics of Material Systems Momentum Balance in Cylinder Radial Direction: Coordinates

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1.033/1.57: Mechanics of Material Systems Vessel Formula by Reduction Elements

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