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**Franz-Josef Ulm Lecture: MWF1 // Recitation: F3:00-4:30**

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

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**Part II: Momentum Balance, Stresses and Stress States **

1.033/1.57: Mechanics of Material Systems

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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 1.033/1.57: Mechanics of Material Systems

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**1.033/1.57: Mechanics of Material Systems**

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

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**Hypothesis of local contact forces =Action-Reaction ‘Law’**

1.033/1.57: Mechanics of Material Systems

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**Tetrahedron Lemma: Stress vector T(n)**

1.033/1.57: Mechanics of Material Systems

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**Cauchy Stresses σij and Stress Vector T(n)**

Components of σij Stress Vector Tj= σijnj 1.033/1.57: Mechanics of Material Systems

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**Exercise: Two-Layer Soil Substratum**

1.033/1.57: Mechanics of Material Systems

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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 1.033/1.57: Mechanics of Material Systems

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**Momentum Balance and Symmetry of Stress Tensor**

Dynamic Resultant Theorem Dynamic Moment Theorem 1.033/1.57: Mechanics of Material Systems

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**Training Set: Pressure Vessel Formula**

1.033/1.57: Mechanics of Material Systems

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**Momentum Balance in Cylinder**

Coordinates Radial Direction: 1.033/1.57: Mechanics of Material Systems

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**Vessel Formula by Reduction Elements**

1.033/1.57: Mechanics of Material Systems

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Geology 5640/6640 Introduction to Seismology 28 Jan 2015 © A.R. Lowry 2015 Read for Fri 30 Jan: S&W 29-52 (§2.1-2.3) Last time: The Strain Tensor Stress.

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