Simplified Theories Stress Resultants

48 For many applications of continuum mechanics the problem of determining the three-dimensional stress distribution is too difficult to solve. However, in many (civil/mechanical)applications, one or more dimensions is/are small compared to the others and possess certain symmetries of geometrical shape and load distribution.

49 In those cases, we may apply "engineering theories" for shells, plates or beams. In those problems, instead of solving for the stress components throughout the body, we solve for certain stress resultants (normal, shear forces, and Moments and torsions) resulting from an integration over the body. We consider separately two of those three cases.

50 Alternatively, if a continuum solution is desired, and engineering theories prove to be either too restrictive or inapplicable, we can use numerical techniques (such as the Finite Element Method) to solve the problem.

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