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An elastoplastic finite element formulation for the structural analysis of Truss frames with application to ha historical iron arch bridge
Full text linkThis doctoral thesis presents a structural analysis of the Paderno d’Adda Bridge, an impressive iron arch viaduct built in 1889 and located in Lombardia region (Italy).
The thesis falls in the context of a research activity started at University of Bergamo since 2005, that is still ongoing and aims to perform an evaluation of the present state of conservation of the bridge. In fact, the bridge is currently still in service and its important position in the context of transport network will soon lead to questions about its future destination, with particular attention to the evaluation of the residual performance capacity.
To this end, an inelastic structural analysis of the Paderno d’Adda bridge has been performed, up to failure. This analysis has been conducted through an autonomous computer code of a 3D frame structure that runs in the MATLAB environment and has been developed within the classical frame of Limit Analysis and Theory of Plasticity.
The algorithm has been developed applying the “exact” and stepwise holonomic step-by-step analysis method. It has shown very much able to track the limit structural behaviour of the bridge, by reaching convergence with smooth runs up to the true limit load and corresponding collapse displacements.
The main characteristic ingredients of its elastoplastic FEM formulation are: beam finite elements; perfectly plastic joints (as an extension of classical plastic hinges); piece-wise linear yield domains; “exact” time integration.
In the algorithm, the following original features have been implemented: treatment of mutual connections by static condensation and Gaussian elimination; determination of the tangent stiffness formulation through Gaussian elimination. These peculiar contributions are presented in detail in this thesis
Analisi strutturale del ponte in ferro di Paderno d’Adda (1889)
No full textIl ponte in ferro di Paderno d’Adda rappresenta un reperto di archeologia industriale del XIX secolo di indiscusso valore storico, ingegneristico ed architettonico. Costruito dalla Società Nazionale delle Officine di Savigliano (SNOS) tra il 1887 ed il 1889, esso offre un collegamento ferroviario e stradale tra le province di Lecco e Bergamo, poco a nord-ovest di Milano, scavalcando il fiume Adda tra i comuni di Paderno d’Adda e Calusco d’Adda, ad una quota di circa 85 m sul livello delle piene. L’interesse degli Autori verso questo affascinante viadotto li conduce, a partire dal 2005, ad intraprendere presso l’Università di Bergamo uno studio di ricerca approfondito sull’opera. Tale studio si è prima focalizzato sulla concezione architettonica e strutturale del ponte, secondo la teoria dell’ellisse di elasticità, intendendo riscoprire la filosofia ispiratrice alla base della progettazione della struttura portante del ponte; quindi, l’indagine si è orientata verso la formulazione di un modello strutturale ad elementi finiti dell’intera opera. La costituzione di quest’ultimo ha permesso di ottenere alcuni confronti qualitativi e quantitativi su specifici aspetti della risposta strutturale del ponte, riportati nella relazione tecnica originaria della SNOS. Queste validazioni si sono mostrate assai confortanti in merito alla rappresentatività del modello ad elementi finiti costituito. Infatti, i risultati ottenuti mediante le simulazioni numeriche secondo varie condizioni di carico statico hanno di fatto validato gli esiti dei calcoli eseguiti dalla SNOS in sede di progetto. Una volta costituito il modello ad elementi finiti del ponte, sono state inoltre avviate delle analisi di tipo dinamico, in merito all’individuazione delle caratteristiche dinamiche essenziali dell’opera, quali in primis le frequenze naturali di vibrazione e le corrispondenti forme modali. I risultati ottenuti sono stati confrontati con valori riportati recentemente in letteratura, documentanti la rilevazione sperimentale in situ delle caratteristiche dinamiche del ponte. Il presente lavoro formula una sintesi di alcuni degli aspetti sviluppati durante la prima fase della ricerca condotta sul ponte. Il rapporto tecnico intende presentare le caratteristiche fondamentali del modello ad elementi finiti assemblato, riportando nello specifico tutte le considerazioni effettuate in fase di modellazione, dalle semplificazioni attuate per costituire la morfologia del modello, alla descrizione delle caratteristiche geometriche di ogni sezione considerata. Esso mira a fornire una raccolta di informazioni sull’opera, prettamente di natura tecnica ma eventualmente utile anche a chi intendesse intraprendere studi con finalità financo distinte da quelle qui perseguite
FEM modelling of the Paderno d’Adda bridge (Italy, 1889)
No full textThe Paderno d’Adda bridge, also called San Michele bridge, is a marvellous arch iron bridge built in 1889 that allows to connect the two provinces of Lecco and Bergamo across the Adda river, between Paderno d’Adda and Calusco d’Adda. Despite its nearly 122 years of age, the bridge is still in service, allowing for alternated single-way transit of trains and vehicles. However, its present state of conservation seems rather poor and questions arise about its current health conditions. In light of this, an assessment of its present structural performance appears to be necessary. Towards this goal, the assembly of a complete FEM model of the bridge seems crucial for enquiring various aspects of mechanical response, specifically referring to both static and dynamic behaviours. Following recent previous work on this, with reference to conditions at the original design stage, the present paper attempts a first contribution to the modelling of the dynamic behaviour of the bridge, by investigating the different modal properties of the structure arising from the assembled FEM model
Structural modelling of the piers of the Paderno d’Adda Bridge (1889, Italy)
No full textThis note focuses on a specific aspect of the structural modelling of the Paderno d’Adda Bridge, a marvellous Italian historic wrought iron bridge with riveted connections that was completed in 1889 and opened to both railway and road traffics [1-2]. Within the current attempt of building a full 3D FEM model of the structure [3-7], the metallic piers of the bridge are considered [5-6], specifically the pier on the arch. The morphology of the piers has been reconstructed from the inspection of the original design drawings and implemented into a FEM model. Then, a structural analysis has been performed in the elastic range, by considering loading distributions that were conceived at design stage and also conditions that are nearer to present-state railway standards
On the denoising of structural vibration response records from low-cost sensors: a critical comparison and assessment
Full text linkDue to the increasing quest of adopting low-cost sensors in structural health monitoring (SHM) processes, which may lead to detecting signals contaminated by significant levels of noise, the need to devise appropriate and effective denoising strategies, at the post-processing stage, is becoming more and more essential. Among several approaches proposed in the literature, it has been demonstrated that the employment of discrete wavelet transform (DWT) as a multi-rate filter bank, as well as the use of singular value decomposition (SVD), may result to be quite effective in signal denoising within various research fields, as biological, acoustic and mechanical. Here, DWT- and SVD-based denoising techniques are first independently reconsidered and reimplemented, aiming at exploring their optimal calibration in purifying noise-corrupted vibration response signals encountered in civil engineering applications. Then, a systematic performance evaluation is provided within a comparative framework, developed at an increasing level of noise affecting the measurements, in terms of noise-to-signal (N/S) ratio. In the study, two specific classes of synthetic response signals are first considered, namely earthquake and ambient vibration signals, since they may be assumed as representative of more general non-stationary and stationary signal typologies, respectively. To achieve a complete description of the clarified signal, strengths and weaknesses of the two denoising approaches are explored, in both time and frequency domains. The results prove the effectiveness of the analyzed implementations, especially in purifying seismic response signals, while some limitations may arise concerning the treatment of ambient vibration signals, in particular for the DWT-based denoising technique. Finally, a real case study is analyzed, where both denoising approaches are adapted and employed for clarifying acceleration signals detected on a modern short-span railway bridge, with rather satisfactory results, for both techniques
On the theory of the ellipse of elasticity as a natural discretisation method in the design of Paderno d’Adda Bridge (Italy)
No full textThe Paderno d’Adda Bridge, Lombardia, northern Italy, is one of the very first great iron constructions designed through the practical application of the theory of the ellipse of elasticity, a graphical-analytical method of structural analysis that was developed in the 19th century. It embeds a natural discretisation of the structure into a series of elastic elements, treated then with standard tools of geometry of masses. In this work, the application of such theory to the calculation of the parabolic arch of the bridge is inquired, attempting to breathe, at the same time, the beauty of the architectonic and structural conception directly linked to that; later, results are compared with much modern approaches that also consider now-available numerical discretisation methods.A further, definite aim of this work is also that of trying to promote interest on the bridge, on its actual state of conservation and future destinations. Not only it represents a true industrial monument and a living testimony of the scientific and technological developments of the time but also a beautiful, effective achievement of architecture and engineering through the methods of Strength of Materials
New computational Limit Analysis approaches for structural optimization problems
No full textIn this paper, two recently developed algorithms for the computational Limit Analysis of large-scale 3D truss-frame structures are outlined as useful tools for structural design and optimization purposes. Specifically, they are developed toward characterizing the structural collapse state, which can be considered in selecting the optimum geometrical configuration within appropriate form-finding procedures. The first algorithm, starting from [1], is able to trace a fully exact evolutive piece-wise linear elastoplastic response of the structure [2], up to plastic collapse, by reconstructing the true sequence of activation of made-available plastic joints (as a generalization of plastic hinges). The second algorithm is based on a kinematic iterative approach [3] and is able to determine collapse load multiplier and plastic mechanism in subdued computational time [4]. A rather impressive performance is achieved, in truly precipitating from above on the collapse load multiplier, by rapidly adjusting to the sought collapse mode, in very few iterations. The two algorithms could be conceived separately or all together, based on their own peculiarities, to set down a very efficient procedure toward ruling structural optimization problems based on form-finding quests relying on LA interpretations and concepts
Constitutive structural response of Concrete Damaged Plasticity model under Willam’s test
No full textThe present work aims at analysing and calibrating the mechanical description of plastic strain-induced anisotropy and damage coupling by the so-called Concrete Damaged Plasticity (CDP) constitutive model, which is rather well known also since it comes to be available within popular FEM platforms, such as ABAQUS, and shall be able to reproduce typical features of failure processes in quasi-brittle materials, like concrete. This is achieved by combining an effective stress-based non-associative hardening/softening plasticity model with an isotropic damage model based on plastic strains, at a smeared continuum scale. In the paper, focusing on the mere elastoplastic coupling for tensile-dominated responses, and introducing an enhanced tuning by setting tensile exponential softening and damage evolutions through a convenient plastic to inelastic strain ratio parameter, by means of an external user implementation, an exhaustive numerical parametrization analysis is performed, starting at a constitutive-driver level, to experiment the outcomes of the constitutive description and to quantify the amount of material anisotropy induced by plastic deformation, under biaxial elongation/shearing Willam’s test, which prescribes/involves the rotation of the principal axes of strains/stresses. It is shown that the constitutive response is effectively regularized, allowing to fulfill the requirements of Willam’s test, independently from the amount of inherent plastic dilatancy, showing a rather mild presence of plastic-induced anisotropy, at the pure constitutive-driver scale. Furthermore, first extrapolating implications and outcomes at the small (specimen) structural scale are also investigated, with clear appearance of strain localization and related much pronounced plastic-induced anisotropy, in the (imperfection-triggered) macroscopic response, with features that are similar to those coming e.g. from more sophisticated anisotropic damage models, while significant practical applications may subsequently follow, within different structural engineering contexts, as that of large-scale concrete structures under static and dynamic loading scenarios, toward informed safety assessment and evaluation
Computational Limit Analysis algorithms for large-scale truss-frame structures with interaction domain
No full textThe contribution revisits two recently developed computational algorithms for Limit Analysis (LA) aimed at predicting the elastoplastic response of large-scale 3D truss-frame structures [1]. The first LA algorithm accurately traces the piece-wise linear elastoplastic evolutive response of a structure up to plastic collapse [2], while the second deploys an iterative kinematic approach to directly determine the collapse characteristics based on the upper-bound theorem of LA [3], both being based on a boxed-form Rankine-type interaction domain, in the space of internal variables.
Herein, the kinematic algorithm is presented in an enhanced version, capable of handling an ellipsoidal yield domain, specifically with axial force and bending moments interaction, and potentially coupling other static internal actions. The potentiality of such improvements also relies on the possibility to offer comparative insights related to structural LA, particularly with respect to results for uncoupled Rankine-type yield domains inscribed within or circumscribed around an ellipsoidal interaction domain.
The manuscript first evaluates the load-bearing capacities of a large-scale structure with over 4000 degrees of freedom, using the enhanced versions of the LA algorithms to model the remarkable arch of historical San Michele Bridge (Italy, 1889). A particular focus is then placed on demonstrating the advantages of considering both coupled (hyper-ellipsoidal) and uncoupled (Rankine-type) yield domains represented in the space of static variables governing the problem.
To this end, a simplified space truss-frame cantilever beam is further analyzed, under varying loading conditions leading to bending and torsion, and allowing also for analytical treatment. Insights gained from this simplified case study are subsequently applied to refine and deepen the interpretation of the bridge arch analysis results.
The inherent peculiarities herein highlighted in relation to the devised computational LA algorithms shall significantly expand their applicability, making them highly effective for practical truss-frame analysis and realworld professional applications, truly accounting for structural bearing capacity, toward complying with current demands for resilience-focused design and assessment, in different structural contexts
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