Theory of Beams

  • David H. Allen


The development of a cogent model for predicting the mechanical response of beams must be regarded as one of the great achievements of humankind. As verification of this statement, the reader only need drive down the street a few blocks and notice the enormous number of structural components that are long and slender and subjected to lateral loads that produce bending. Indeed, this chapter may be regarded as the single most important chapter in this text for the beginning structural engineer. Building on the theoretical developments of Chaps. 2–4, the student will be introduced to the kinematic assumption that reduces the study of beams from a fully three-dimensional problem to one that, although nonetheless physically challenging, is mathematically one dimensional. When completely assimilated by the student, the resulting model is at once straightforward and powerful, having been shown by exhaustive experimentation to be quite accurate. Indeed, this model is now more than a quarter of a millenium old and is nevertheless today an essential underpinning of nearly all modern structures on earth.


Shear Stress Coordinate Direction Displacement Boundary Condition Kinematic Boundary Condition Free Body Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Allen D, Haisler W (1985) Introduction to aerospace structural analysis. Wiley, New YorkGoogle Scholar
  2. Euler L (1744) Method inveniendi lineas curvas. Opera Omnia, St. PetersburgGoogle Scholar
  3. Greenberg M (1978) Foundations of applied mathematics. Prentice-Hall, New JerseyGoogle Scholar
  4. Oden J, Ripperger E (1981) Mechanics of elastic structures. McGraw-Hill, New YorkGoogle Scholar
  5. Popov E (1998) Engineering mechanics of solids, Second edn. Prentice-Hall, New JerseyGoogle Scholar
  6. Roark R, Young W, Budynas R, Sadegh A (1975) Formulas for stress and strain, Eighth edn. McGraw-Hill, New YorkGoogle Scholar
  7. Wempner G (1995) Mechanics of solids. International Thomson Pub., BostonGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • David H. Allen
    • 1
  1. 1.College of Engineering and Computer ScienceUniversity of Texas-Pan AmericanEdinburgUSA

Personalised recommendations