Mechanics of Materials

An outline of Mechanics of Materials is located here.

The teachings of Vincent Lee at the University of Southern California were vital to the completion of this outline.

The textbook “Mechanics of Materials,” by Gere, is also highly recommended.

“Mechanics of Materials” is typically an engineering student’s first exposure to the
important concepts relating to material properties, such as material strength and material
stiffness. Material strength and stiffness are important for the analysis of structures, since
the equations of static equilibrium are not enough to determine the distribution of forces
within a complex structure. In addition, knowledge of material strength and stiffness is
vital for the design of structures, where the size (and corresponding cost) of a component
of a structure, such as a beam, depends on both its resistance to excessive deformation
(primarily a function of stiffness), and its ability to resist damage (primarily a function of
strength).

As we will see, beginning with this outline, two of the most important quantities in
structural engineering are “stress” and “strain.” The stress and strain of a material are
often linearly-related – a discovery that dates back to 1678, when Hooke famously stated
“ut tensio, sic vis,” meaning, “as the extension, so the force.” The larger this ratio, the
more stiff the material, and the greater its resistance to deformation. Keeping
deformations small is sometimes a constraint in the design of structures.

A constraint that is even more often present in engineering design is to ensure that the
material strength, which has units of stress, is not exceeded. Stress demands, unlike
strains, are not so easy to “see” or directly measure, but stress is a quantity that engineers
like to use for the purpose of comparing to material strength. Designing a structure so
that the stress demands in all of its structural components remain less than their
corresponding material strength values is one way that an engineer can ensure that the
structure is safe to perform its intended function.