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 elasticplastic


Equilibrium of
Structural Element

Geometry of Deformation 
Material Behavior 
Identify
internal loads by construction of a
Free Body Diagram

Extension
(or compression) of
a rod from axial loading 
Wood,
mild steel, concrete,
and
composites have very
different
material properties.

Statically Determinate
2D Equilibrium
ΣF_{x} = 0, ΣF_{y}
= 0, ΣM_{z} = 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
ΣF_{x}
= 0, ΣF_{y}
= 0, ΣM_{z} = 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 
ElasticPlastic
Model
Sometimes
used to represent
“nonlinear’
material
behavior
(Idealization) 
