2. The Euler–Bernoulli and Timoshenko Theories

  1. Erasmo Carrera1,
  2. Gaetano Giunta2 and
  3. Marco Petrolo1

Published Online: 11 AUG 2011

DOI: 10.1002/9781119978565.ch2

Beam Structures: Classical and Advanced Theories

Beam Structures: Classical and Advanced Theories

How to Cite

Carrera, E., Giunta, G. and Petrolo, M. (2011) The Euler–Bernoulli and Timoshenko Theories, in Beam Structures: Classical and Advanced Theories, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119978565.ch2

Author Information

  1. 1

    Politecnico di Torino, Italy

  2. 2

    Centre de Recherche Public Henri Tudor, Luxembourg

Publication History

  1. Published Online: 11 AUG 2011
  2. Published Print: 16 SEP 2011

ISBN Information

Print ISBN: 9780470972007

Online ISBN: 9781119978565



  • Euler–Bernoulli and Timoshenko theories;
  • beam geometry, displacements, strains and stresses;
  • Euler–Bernoulli model, EBBT - beam reference coordinate frame;
  • bending of beam, and Euler–Bernoulli kinematic hypotheses;
  • cross-section reference systems - and centroidal reference system;
  • Navier equation - for longitudinal stress;
  • Timoshenko model in TBT - and Timoshenko's kinematic hypotheses;
  • cantilever beam bending - EBBT and TBT solutions


This chapter contains sections titled:

  • The Euler–Bernoulli model

  • The Timoshenko model

  • Bending of a cantilever beam: EBBT and TBT solutions

  • References