1.050 Engineering Mechanics Lecture 4: Stresses and Strength Stresses and Equilibrium Discrete Model1.050 – Content overview I. Dimensional analysis 1. On monsters, mice and mushrooms 2. Similarity relations: Important engineering tools II. Stresses and strength 2. Stresses and equilibrium 3. Strength models (how to design structures, foundations.. against mechanical failure) III. Deformation and strain 4. How strain gages work? 5. How to measure deformation in a 3D structure/material? IV. Elasticity 5. Elasticity model – link stresses and deformation 6. Variational methods in elasticity V. How things fail – and how to avoid it 7. Elastic instabilities 8. Plasticity (permanent deformation) 9. Fracture mechanics Lectures 1-3 Sept. Lectures 4-15 Sept./Oct. Lectures 16-19 Oct. Lectures 20-31 Nov. Lectures 32-37 Dec.1.050 – Content overview I. Dimensional analysis II. Stresses and strength Lecture 4: Newton’s laws, fall of the WTC towers Lecture 5: Stress vector and stress tensor Lecture 6: Hydrostatic problem ApplicationsLecture 7: Soil mechanics / geostatics problem Lecture 8: Beam stress model Lecture 9: Beam model II and summary Lecture 10: Strength models … III. Deformation and strain IV. Elasticity V. How things fail – and how to avoid itContent lecture 5 1. 3-scale continuum model: Molecular scale, representative volume element (REV), macro-scale 2. Stress vector, stress matrix and stress tensor • Definition of stress vector • Generalized expression as stress matrix • Definition of stress tensor 3. Implement dynamic resultant theorem for REV • Use Gauss theorem (divergence theorem) • Develop differential equilibrium: Partial differential
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