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MAE 343 - Intermediate Mechanics of Materials Tuesday, Aug. 24, 2004

MAE 343 - Intermediate Mechanics of Materials Tuesday, Aug. 24, 2004. Textbook Sections 4.1 – 4.3 Forces, Equilibrium, Failure. 4.1 Loads and Geometry. Steps of machine design process (Table 1.1) Driven by functional performance specifications

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MAE 343 - Intermediate Mechanics of Materials Tuesday, Aug. 24, 2004

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  1. MAE 343 - Intermediate Mechanics of MaterialsTuesday, Aug. 24, 2004 Textbook Sections 4.1 – 4.3 Forces, Equilibrium, Failure

  2. 4.1 Loads and Geometry • Steps of machine design process (Table 1.1) • Driven by functional performance specifications • Yield “best” material and geometry for strength & life • Step VI – Global Force Analysis • Must be accurate, but difficult for new machines • Must include surface and body loads, moments, reaction forces • Surface forces may be concentrated or distributed in various patterns • Step VII-Iterative design of each part (Table 1.2) • Based on local forces and moments from global analysis • Local force analysis based on concepts & equations of equilibrium

  3. 4.2 Equilibrium Concepts and Free-Body Diagrams (FBD) • Six Equations of Static or Dynamic Equilibrium • Three force components along arbitrary x-y-z axes • Three moment components about arbitrary x-y-z axes • Free-Body Diagrams (Figs. 4.2 and 4.3) • Cutting Plane isolates selected portion from the rest • Internal Forces on cutting plane replaced by system of equivalent external forces for equilibrium of free body • Internal force per unit area of cut face is defined as stress

  4. 4.3 Force Analysis • Design based on physical model of a machine • Analytical simplifications for reasonable effort • Accurate analyses in local regions of contact • Basic factors to consider in force analysis • How forces and moments are applied on elements • How loads are transmitted through the structure and reacted • Likely failure modes and critical locations in the structure • “Force Flow” or “Line of Forces” • Visualize lines from applied forces to supports • Identify critical locations for preventing failure

  5. Example 4.1 –Force Flow through Pin and Clevis Joint • Lines of force flow for uniaxial tension • Free-Body Diagram (FBD) of the Pin • Distributed stresses along and around the bearing contact regions, C, D, and E • Depend on material, geometry, loading level • Potential Failure Modes • Elastic deformation between clevis and blade • Yielding and/or ductile rupture • Brittle fracture across shear planes A-A and B-B

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