This book provides a systematic and thorough overview of the
classical bending members based on the theory for thin beams
(shear-rigid) according to Euler-Bernoulli, and the theories for
thick beams (shear-flexible) according to Timoshenko and Levinson.
The understanding of basic, i.e., one-dimensional structural
members, is essential in applied mechanics. A systematic and
thorough introduction to the theoretical concepts for
one-dimensional members keeps the requirements on engineering
mathematics quite low, and allows for a simpler transfer to
higher-order structural members. The new approach in this textbook
is that it treats single-plane bending in the x-y plane as well in
the x-z plane equivalently and applies them to the case of
unsymmetrical bending. The fundamental understanding of these
one-dimensional members allows a simpler understanding of thin and
thick plate bending members. Partial differential equations lay the
foundation to mathematically describe the mechanical behavior of
all classical structural members known in engineering mechanics.
Based on the three basic equations of continuum mechanics, i.e.,
the kinematics relationship, the constitutive law, and the
equilibrium equation, these partial differential equations that
describe the physical problem can be derived. Nevertheless, the
fundamental knowledge from the first years of engineering
education, i.e., higher mathematics, physics, materials science,
applied mechanics, design, and programming skills, might be
required to master this topic.
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