Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach


Autoria(s): BECK, Andre Teofilo; SILVA JR., Claudio R. A. da
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

18/10/2012

18/10/2012

2011

Resumo

The selection criteria for Euler-Bernoulli or Timoshenko beam theories are generally given by means of some deterministic rule involving beam dimensions. The Euler-Bernoulli beam theory is used to model the behavior of flexure-dominated (or ""long"") beams. The Timoshenko theory applies for shear-dominated (or ""short"") beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two beam models is radically different in terms of uncertainty propagation. In the paper, some beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo-Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko beams than for Euler-Bernoulli beams. On the other hand, propagation of the uncertainty for random beam height is much larger for Euler beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities. (C) 2010 Elsevier Ltd. All rights reserved.

Sao Paulo State Foundation for Research - FAPESP[2008/10366-4]

National Council for Research and Development - CNPq[305120/2006-9]

Identificador

STRUCTURAL SAFETY, v.33, n.1, p.19-25, 2011

0167-4730

http://producao.usp.br/handle/BDPI/17844

10.1016/j.strusafe.2010.04.006

http://dx.doi.org/10.1016/j.strusafe.2010.04.006

Idioma(s)

eng

Publicador

ELSEVIER SCIENCE BV

Relação

Structural Safety

Direitos

closedAccess

Copyright ELSEVIER SCIENCE BV

Palavras-Chave #Euler-Bernoulli beam #Timoshenko beam #Uncertainty propagation #Parameterized stochastic processes #Monte Carlo simulation #Galerkin method #Engineering, Civil
Tipo

article

original article

publishedVersion