Introduction to Solid Mechanics            Click here for Symbolic Solutons



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:


  1. Equilibrium of the structural element – use to identify loads acting on the structure
  2. Geometry of deformation – extension, compression, shear, bending, torsion
  3. Material behavior – linear elastic, linear elastic-plastic




    Solid Mechanics




        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

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



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)



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Copyright © 2019 Richard C. Coddington
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