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