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1.033/1.57

1.033/1.57. 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. Part II: Momentum Balance, Stresses and Stress States. 4. Stress States / Failure Criteria.

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1.033/1.57

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  1. 1.033/1.57 • 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 4. Stress States / Failure Criteria 1.033/1.57 Mechanics of Material Systems

  3. 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. Stress Vector and Stress Components Stress components on a material surface oriented in the principal stress direction n = uI Stress components on a material surface oriented by unit normal n 1.033/1.57 Mechanics of Material Systems

  5. Stress Vector in the Principal Stress Space • (Illustration of Stress Invariants) • = Orientation of hydrostatic axis • T(−u3) • 1.033/1.57 Mechanics of Material Systems

  6. Stress Vector in the Mohr Plane 1.033/1.57 Mechanics of Material Systems

  7. Mohr Circles and The Mohr Circle The Mohr Circle 1.033/1.57 Mechanics of Material Systems

  8. Selected Stress States: Hydrostatic Pressure σ = −p1 Material Plane Mohr Stress Plane 1.033/1.57 Mechanics of Material Systems

  9. Selected Stress States: Uniaxial Tension • σ = σI ez⊗ez • Material Plane Mohr Stress Plane • 1.033/1.57 Mechanics of Material Systems

  10. Selected Stress States: Pure Shear • σ = τ (ex⊗ey+ ey⊗ex) • Material Plane Mohr Stress Plane • 1.033/1.57 Mechanics of Material Systems

  11. Selected Stress States: Plane Stress • T(n=ez) = σ ⋅ez = 0 • Material Plane Mohr Stress Plane • 1.033/1.57 Mechanics of Material Systems

  12. Tension Cut-Off Shear Direct Tension −τmax 1.033/1.57 Mechanics of Material Systems

  13. Tresca Criterion

  14. Tresca Criterion: Application 1.033/1.57 Mechanics of Material Systems

  15. Mohr- Coulomb 1.033/1.57 Mechanics of Material Systems

  16. Mohr- Coulomb Direct Tension Shear Uniaxial Compression 1.033/1.57 Mechanics of Material Systems

  17. Training Set: Excavation Set 1.033/1.57 Mechanics of Material Systems

  18. Max. Excavation Depth of Tresca Material 1.033/1.57 Mechanics of Material Systems

  19. Homework Set #2 • Part I: Triaxial Test Part II: Circular Foundation

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