1. 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

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

3. 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

4. 1.033/1.57: Mechanics of Material Systems
Body & Surface Forces
1.033/1.57: Mechanics of Material Systems

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

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

7. Cauchy Stresses σij and Stress Vector T(n)
Components of σij
Stress Vector Tj= σijnj
1.033/1.57: Mechanics of Material Systems

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

9. 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

10. Momentum Balance and Symmetry of Stress Tensor
Dynamic Resultant Theorem
Dynamic Moment Theorem
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11. Training Set: Pressure Vessel Formula
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12. Momentum Balance in Cylinder
Coordinates
Radial Direction:
1.033/1.57: Mechanics of Material Systems

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