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PCE219
Fall 2007
The Necessary Categories of Equations for the Mathematical
Description of Problems in Mechanics.
Equilibrium
:
In classical mechanics these are equations that are used to satisfy Newton’s
Laws of Motion, especially the 2
nd
law that the net force = mass x acceleration (F=ma).
In
addition, equilibrium equations can be used to satisfy Newton’s 3
rd
law that for every action there
is an equal and opposite reaction.
Forces are often written in terms of the second order tensor,
stress, which is the intensity of the force at a point with in a body. (force per unit area).
We
typically discuss stresses with regard to a surface or plane.
In any given plane, there can be a
normal stresses that is perpendicular to the plane and two shear stress components that lie in the
plane.
For many problems, one can express internal forces by integrating the stresses over the
surface that they act.
They we talk about the normal and shear forces in a member of a structure.
Free body diagrams are useful in developing equilibrium equations.
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 Spring '09
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