Learning objectives
AIM of the COURSE
At the end of the Corse, the students should be able to compute the structural safety level of frames (beam systems) with elastic behaviour.
Prerequisites
Laboratorio di Matematica
Course unit content
CONTENTS of the COURSE
The Course “Laboratorio di Costruzione I” presents basic concepts and tools for structural design, with reference to the methods for computation of statically determinate and indeterminate elastic frames (beam systems) with elastic behaviour. The topics are treated by analysing problems related to real structures.
Full programme
Programme for Modulus of STATICS
(A1) Theory of the vectors
(A2) Systems of forces
(A3) Geometry of areas. Introduction. Static moment and centroid. Moments of inertia. Laws of transformation. Principal axes and moments of inertia. Mohr’s circle.
(A4) Simple (beams) and complex (frames) structural systems. Plane beams and frames. Problem of structural system equilibrium: kinematic definition of plane constraints; static definition of plane constraints (constraint reactions) and cardinal equations of statics. Framed structures: statically determinate (or isostatic); hypostatic; statically indeterminate (or hyperstatic). Principle of superposition.
(A5) Statically determinate framed structures. Cardinal equations of statics; kinematic procedure; auxiliary equations. Exercises.
(A6) Internal beam reactions. Direct method; differential method (indefinite equations of equilibrium for plane beams). Diagrams of characteristics of internal beam reactions. Exercises.
(A7) Particular problems. Closed-frame structures. Plane trusses. Exercises.
(A8) Structural problems. Real structures and theoretical models. Exercises.
-----------------------------
Programme for Modulus of STRUCTURAL MECHANICS
(B1) Analysis of stresses (for three-dimensional solids). Stress tensor, equations of Cauchy, law of reciprocity. Principal stress directions, Mohr’s circles. Plane stress condition and Mohr’s circle. Boundary conditions of equivalence and indefinite equations of equilibrium.
(B2) Analysis of strains (for three-dimensional solids). Rigid displacements, strain tensor. Strain components: dilatations and shearing strains. Principal strain directions.
(B3) The theorem of virtual work (for three-dimensional solids).
(B4) Theory of elasticity (for deformable three-dimensional solids). Real work of deformation, elastic material, linear elasticity, homogeneity and isotropy, linear elastic constitutive equations. Real work of deformation: Clapeyron’s theorem; Betti’s theorem. The problem of a linear elastic body: solution uniqueness theorem (or Kirckhoff’s theorem).
(B5) Strength criteria. Criteria by Rankine, Grashof, Tresca, von Mises.
(B6) The problem of De Saint-Venant. Fundamental hypotheses, indefinite equations of equilibrium, elasticity equations and boundary conditions. Centred axial force, flexure (bending moment), biaxial flexure, eccentric axial force, torsion, bending and shearing force. Exercises.
(B7) Computation of displacements for framed structures. Differential equation of the elastic line; theorem of virtual work for deformable beams; constraints (like thermal distortions and constraint settlements). Exercises.
(B8) Statically indeterminate framed structures. Theorem of virtual work: structures subjected to loads and constraints (like thermal distortions and constraint settlements). Exercises.
(B9) Instability of elastic equilibrium. Euler’s critical load and free length of deflection; omega method. Exercises.
Bibliography
DOCUMENTATION of the COURSE
- Documentation provided by the teacher (Centro Documentazione - Ingegneria – Sede Didattica)
- A. Carpinteri, “Scienza delle Costruzioni” Vol.1, Pitagora Ed., Bologna
- A. Carpinteri, “Scienza delle Costruzioni” Vol.2, Pitagora Ed., Bologna
- M. Capurso, "Lezioni di Scienza delle Costruzioni", Ed. Pitagora, Bologna
- E. Viola, “Esercitazioni di Scienza delle Costruzioni – Vol.1: Strutture isostatiche e geometria delle masse”, Pitagora Ed., Bologna
- E. Viola, “Esercitazioni di Scienza delle Costruzioni – Vol.2: Strutture iperstatiche e verifiche di resistenza”
- L. Boscotrecase, A. Di Tommaso, “La statica applicata alle costruzioni”, Patron, Bologna
All books are available by the library (Biblioteca Politecnica di Ingegneria e Architettura)
Teaching methods
METHODS of TEACHING
Theory supported by exercises
Assessment methods and criteria
ASSESSMENT METHOD
Written and oral examination
Other information
Students must compulsorily attend all lectures and tutorials.
