Key Concepts:  The study of solid mechanics includes the equilibrium of structural elements, the geometry of deformation of structures, and material behavior to applied loading.  See the chart below. In a Nut Shell – In solid mechanics you will analyze stresses, strains, and deflections that result from applied loads to the structure.  Common structures include frames, trusses, beams, bridges, pressure vessels, fuselages in aircraft, etc.  The governing principles used in solid mechanics include:   Equilibrium of the structural element – use to identify loads acting on the structure Geometry of deformation – extension, compression, shear, bending, torsion Material behavior – linear elastic, linear elastic-plastic

 Solid Mechanics

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 Equilibrium of     Structural  Element Geometry of Deformation Material Behavior Identify internal loads by construction of a Extension (or compression) of a rod from axial loading Wood, mild steel, concrete, and composites have very different material properties. Statically Determinate 2-D  Equilibrium  ΣFx = 0,  ΣFy = 0, ΣMz = 0 Sufficient to determine support Reactions Deflection of a beam from an external loading (bending) Relation between stress (force per unit area) and strain (deformation per unit length) Statically Indeterminate  ΣFx = 0,  ΣFy = 0, ΣMz = 0  Structure overconstrained  Need additional relations Twisting of a rod from external torques Hooke’s Law Stress is directly proportional to Strain The Free Body Diagram is of the undeformed structure except for buckling applications due to compression Idealized supports – include pins, clamps, rollers Connectivity of adjoining Members/Boundary Conditions Elastic-Plastic Model Sometimes used to represent “non-linear’ material behavior (Idealization)