1.050 Engineering Mechanics Lecture 6: Stresses and Equilibrium Application: Hoover Dam1.050 – 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 6 1. Review: 3-scale continuum model: Molecular scale, representative volume element (REV), macro-scale; stress vector and stress tensor 2. Implement dynamic resultant theorem for REV • Use Gauss theorem (divergence theorem) • Develop differential equilibrium: Partial differential equation 3. Application: Hoover Dam (hydrostatic problem)Photographs of Hoover Dam removed due to copyright restrictions. http://www.concreteresources.net/images/graphics/clip_image004.jpg http://www.sdsuniverse.info/Upload/hoover_dam.jpgEnergy Production ~ 4 billion kilowatt-hours a year ~ 1.3 million peopleForces that act on Hoover Dam ()nzpT −= )(nTForces that act on Hoover Dam Force reduction formula • Forces from stress vector • Force Equivalence ()nzpT −= ye xe xF yF yF−dydzdSx = Surface on which stress Hoover Dam: F ~ 16 billion Newtonx Vector acts (weight equivalence of 20 million people, or of the entire population of
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