Mechanics of bridges
Denominazione del corso: Mechanics of bridgesCorso di studi: I4C - Laurea magistrale in Ingegneria Civile
Quadrimestre/Semestre: 1°
Anno: 1°
Numero di moduli: 1
Crediti: 9
Ore: 90
Tipologia: B - Attivitą caratterizzanti
Struttura: monodisciplinare
Settore Scientifico Disciplinare: ICAR/09 (Tecnica Delle Costruzioni)
Docente: Francesco D'Annibale (60 ore). Titolo copertura: Mutuata
Orario di ricevimento: Wednesday, 6:00-8:00 pm, room A+1.23, Roio or online (Microsoft Teams)
Docente: Silvio Masciocchi (30 ore). Titolo copertura: a contratto
Programma sintetico del corso:
THEORETICAL LECTURES
- types of bridges;
- isotropic and orthotropic plates;
- discretization methods;
- profilati sottili;
- actions on bridges;
- analysis of local effects;
- girder bridges;
- box-girder bridges;
- mechanics of ropes;
- suspended bridges;
- cable-stayed bridges.
LECTURES ON NUMERICAL ASPECTS
Use of Finite-Element codes and semi-analytical methods to:
- build up the influence lines;
- to solve isotropic and orthotropic plates;
- analyze local effects;
- analyze the behavior of girder bridges;
- analyze the behavior of box-girder bridges.
LECTURES ON DESIGN ASPECTS (Silvio Masciocchi):
- presentation and discussion of the Bridge over the Po river in Piacenza, the Cable-stayed Bridge over the Garigliano, the Cable-stayed Bridge over the Tigris in Baghdad, the Morandi method for the design of cable-stayed bridges with prestressed cables;
- geometry of the bridge decks; loads, combinations and verify; secondary elements (joints, disposal of rainwater, flooring, waterproofing); support devices;
- road bridges: viaducts, single-span bridges, cable-stayed bridges;
- setting of the overall design of a viaduct and design choices for deck, piles and wing walls;
- pre-designing of a prestressed deck, a mixed steel-concrete section, in steel as an orthotropic plate.
- formation of designing groups and assignment of project work.
Programma esteso del corso:
Programma completo (PDF)
(Aggiornato il 2-08-2023)
THEORETICAL LECTURES
- Types of bridges: Overview of static schemes of longitudinal and transversal bridges;
- Isotropic and orthotropic plates: of Mindlin and Kircchoff; considerations on torsional stiffness; geometric orthotropy and homogenization; plane grid with infinitesimal meshes.
- Discretization methods: Ritz, finite elements, finite strips, Generalized Beam Theory.
- Actions on bridges: dynamic effects due to transit, critical velocity of resonance; mass impacts on parapets and guard rails; braking and centrifugal forces; nonlinear thermal variations; prestressing; viscosity in structures with a static scheme variable over time and / or subject to constraining failures; seismic action.
- Analysis of local effects: models of isotropic shell or frame for reinforced concrete slabs; homogenized models of steel orthotropic shell, with single-field or multiple fields on elastic supports.
- Girder bridges: collaborative width (shear lag effect); finite elements of plane grid; approximate beam models: infinitely rigid transverse; Courbon method; Engesser method; surface of influence of the moment in the transverse; Massonet shell models.
- Box-girder bridges: unicellular: approximate model type GBT; multicellular: equivalent orthotropic shell model, shear deformable: connected by cross beams: beam model, by force method; connected by slab: approximate model with 'striped' slab and refined by finite macro-element of plate-shell; juxtaposed: model of adjacent hinged beams.
- Mechanics of Ropes: governing equations; catenary of the own weight; horizontal or inclined parabolic cable; apparent stiffness of suspended cables with sliding support; suspended cables subject to additional forces, with fixed or elastic supports; free oscillations of the cables.
- Suspended bridges: continuous model, flexural and torsional analysis of the bridge; notes of dynamics.
- Cable-stayed bridges: continuous model, flexural and torsional analysis of the bridge; notes of dynamics.
LECTURES ON NUMERICAL ASPECTS
- Influence lines: direct and indirect method; theorems of Betti, Maxwell and Land-Colonnetti.
- Analytical and numerical methods to solve isotropic and orthotropic plates, i.e., Mindlin and Kirchhoff, under different load conditions; considerations on the evaluation of torsional stiffness and examples; numerical examples of structures having geometric orthotropy and homogenization; examples on plane grid with infinitesimal meshes.
- Analytical and numerical modelling of the analysis of local effects: examples on models of isotropic shell or frame for reinforced concrete slabs, homogenized models of steel orthotropic shell, with single-field or multiple fields on elastic supports.
- Girder bridges: evaluation of the effective width (shear lag effect); finite elements of plane grid; approximate beam models: infinitely rigid transverse; Courbon method; Engesser method; surface of influence of the moment in the transverse; Massonet shell models.
- Analytical/numerical models of box-girder bridges: Unicellular, approximate GBT-like model; multicellular, examples on equivalent orthotropic shell model, shear deformable; connected by cross beams, examples on beam model, by force method; connected by slab, examples on approximate model with 'striped' slab and refined by finite macro-element of plate-shell; juxtaposed, examples on model of adjacent hinged beams.
LECTURES ON DESIGN ASPECTS (Silvio Masciocchi):
- presentation and discussion of the Bridge over the Po river in Piacenza, the Cable-stayed Bridge over the Garigliano, the Cable-stayed Bridge over the Tigris in Baghdad, the Morandi method for the design of cable-stayed bridges with prestressed cables;
- geometry of the bridge decks; loads, combinations and verify; secondary elements (joints, disposal of rainwater, flooring, waterproofing); support devices;
- road bridges: viaducts, single-span bridges, cable-stayed bridges;
- setting of the overall design of a viaduct and design choices for deck, piles and wing walls;
- pre-designing of a prestressed deck, a mixed steel-concrete section, in steel as an orthotropic plate.
- formation of designing groups and assignment of project work.
Testi consigliati:
Mario P. Petrangeli, Progettazione e Costruzione di Ponti, CEA, IV edizione, 1996, Milano.
Lecture Notes
Circolare applicativa n. 617 02.02.2009, Circolare Applicativa NTC 2018.
Modalità d'esame:
A first oral test, aimed at evaluating the assimilation of the theoretical contents of the course. A second oral test, to be carried out after the first, aimed at evaluating the ability to manage the tools of numerical analysis, illustrated during the course. A third oral test, to be performed before to the previous two, also on a different day, which focuses on the discussion of the design work that the student will have produced with the assistance of an engineer, assigned to design exercises.
Risultati di apprendimento previsti:
It is expected that the student, at the end of the course: (1) has sufficient mastery of the theory of bridges and of the analytical tools able to model the relative structures; (2) knows how to use numerical methods and tools and to critically analyze the results, recognizing the degree of reliability of the models used; (3) is able to draw up a preliminary draft of a bridge of medium difficulty.
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