Transcript MAE 343 - Intermediate Mechanics of Materials

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
– 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
4.2 Equilibrium Concepts and FreeBody 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
4.3 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
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