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Computational elastoplastic Limit Analysis of the Paderno d’Adda bridge (Italy, 1889)

Ferrari R., Cocchetti G., Rizzi E.

Archives of Civil and Mechanical Engineering

2018

Vol. 18, no. 1

291--310

The Paderno d’Adda bridge is a historical iron arch bridge built in 1889 for connecting the provinces of Lecco and Bergamo across the Adda river, in northern Italy. The bridge was designed through the so-called Theory of the Ellipse of Elasticity. Its use is two-fold: a railway track lays within the inner deck of its upper continuous beam; automotive traffic runs on top. Today, after 128 years of continuous duty, the viaduct keeps in service, with trains crossing at slow speed and alternated one-way road traffic with no heavy-weight vehicles. Starting from a computational formulation for the elastoplastic Limit Analysis of 3D truss-frame systems, apt to provide the exact limit load multiplier and attached collapse mechanism, the full evolutive piece-wise-linear response of the bridge is derived, for different try-out loading configurations. The structural analysis, wholly original in its computational implementation, aims at outlining a survey on the potential plastic collapse characteristics of the bridge. Results reveal possible structural deficiencies for the upper continuous beam, where main plasticizations appeared. Instead, elements of the piers plasticized only for tests with loading much un-symmetrically located to the crown of the arch and the slender doubly built-in parabolic arch rarely showed some plasticization. This evidences the arch as a robust characteristic beautiful feature of the bridge. Moreover, analyses pointed out that the effect of the normal forces on the elastoplastic response of the bridge shall not be considered as negligible, as instead it may be often considered in the Limit Analysis of frames.

Secant stress/strain relations of orthotropic elastic damage with dual properties

Rizzi E., Carol I.

Archives of Mechanics

2007

Vol. 59, nr 2

133-171

A constitutive framework of orthotropic elastic damage in initially-isotropic materials is presented. The constitutive equations are developed within the phenomenological approach of Continuum Damage Mechanics. Focus is made on secant stress/strain relations that can be derived by the application of the so-called damage-effect tensors, namely the fourth-order operators that define the linear transformations between nominal and effective stress and strain quantities. In the attempt to provide selected forms of anisotropic damage approaching general orthotropy, several proposals of damage-effect tensors are formulated. Such fourth-order operators are obtained from the complete orthotropic representations as particular instances that satisfy a duality requirement between compliance- and stiffness-based derivations. A complete family of solutions based on a specific non-singular tensor generator is derived in fuli invariant form.