This paper proposes a new simple derivation of bilateral bounds for the strain energy-based shear and torsion factors, χi, of an elastic beam together with some comments about the coherence of the current formulations. A rearrangement of the definition as a mean over the cross-section and an original decomposition of the shear stress in two parts — τeqv that is equivalent to the external force and a residual Δτ — allow (i) to interpret (χ-1) as the mean quadratic deviation of the shear field with respect to the distribution τeqv and (ii) to easily evaluate an upper bound, using minimal information about the stress field. In this formulation the lower bound becomes trivial. Several numerical examples illustrate the accuracy and suitability of the results obtained.
Bilateral bounds for the shear and torsion factors: comments on elementary derivations / Mentrasti, Lando. - In: ACTA MECHANICA. - ISSN 0001-5970. - (accepted Nov 10, 2011, published on line 20 december 2011 ):(2011), pp. (1)-(13). [10.1007/s00707-011-0584-x]
Bilateral bounds for the shear and torsion factors: comments on elementary derivations
MENTRASTI, LANDO
2011-01-01
Abstract
This paper proposes a new simple derivation of bilateral bounds for the strain energy-based shear and torsion factors, χi, of an elastic beam together with some comments about the coherence of the current formulations. A rearrangement of the definition as a mean over the cross-section and an original decomposition of the shear stress in two parts — τeqv that is equivalent to the external force and a residual Δτ — allow (i) to interpret (χ-1) as the mean quadratic deviation of the shear field with respect to the distribution τeqv and (ii) to easily evaluate an upper bound, using minimal information about the stress field. In this formulation the lower bound becomes trivial. Several numerical examples illustrate the accuracy and suitability of the results obtained.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.