Mechanics of structures
Course objectives
The course covers the principles of mechanics and structural modeling. It gives some elements of strength of materials and structural stability in order to allow preliminary structural assessment or design. Main topics addressed: fundamental laws of mechanics; kinematics and statics of a rigid body and of a system of connected rigid bodies; principle of virtual powers; one-dimensional beam theory; centroids, first and second moments of areas.
Channel 1
VINCENZO GATTULLI
Lecturers' profile
Program - Frequency - Exams
Course program
Structures in the Built Environment
Primary structural elements and their assemblies; classification of structures; structural response; introduction to modeling. Modeling of loads, connections (constraints), structures, and materials.
Truss Structures
Introduction; stability; forces in elements; three-dimensional trusses.
Beams as Flexural Elements
Beams in buildings; bending stresses; lateral-torsional buckling; shear and torsion; principal stresses. Continuous beams: general principles, stiffness, and stress characteristic diagrams.
Rigid-Frame Structures
General principles; analysis methods for rigid frames; beam-column relative stiffness; multi-story frames; Vierendeel beams.
Funicular Structures
General principles; suspended cable structures with concentrated or uniformly distributed loads.
Arch Structures
Masonry arches; rigid parabolic arches with distributed loads; funicular arches with point loads; three-hinged arches; fixed arches with two or three hinges.
Mathematical Models
Linear Algebra Refresher
Vector spaces of finite dimension; vector operations; dot, cross, and mixed products; orthonormal basis representation; linear combinations; matrices: definitions, operations, trace, product, rank, determinant, inverses.
Kinematics of Rigid Bodies
Definition of a rigid body; general form of infinitesimal rigid-body displacement; rigid-body systems; kinematic characterization of external and internal constraints; kinematic problem and classification: isokinematic, labile, hypokinematic, degenerate; analytical and graphical solution methods; infinitesimal displacement fields.
Statics of Rigid Bodies
Force concepts; moment about a point; transport formula; force systems, resultant and resultant moment; distributed loads; static characterization of constraints; static problem: equilibrium equations and calculation of support reactions; classification of systems: isostatic, hyperstatic, hypostatic, degenerate.
Statics-Kinematics Duality
Duality; principle of virtual work; applications of virtual work theorem.
Planar Beams with Straight Axis
Beam geometry, kinematics, applied loads, internal actions; stress characteristics; differential equilibrium equations; truss systems.
Rigid Planar Trusses
Plane rigid trusses; nodal equilibrium method; Ritter section method; static classification.
Prerequisites
Basic knowledge of mathematical analysis and linear algebra.
Frequency
Class attendance is not mandatory.
Exam mode
The assessment consists of a written exam and an oral exam.
The written exam, lasting 3 hours, involves solving exercises related to the topics covered in the course and aims to verify the student’s ability to correctly apply the principles of structural mechanics to problem solving.
Passing the written exam with a satisfactory result is a prerequisite for taking the oral exam, which includes further exercises and theoretical questions designed to assess understanding of the fundamental concepts and mastery of technical language.
Lesson mode
Lectures are conducted at the blackboard, with occasional use of slides, to allow students to follow in real time the development of reasoning, demonstrations, and the solving of exercises.
Channel 2
CECILIA RINALDI
Lecturers' profile
Program - Frequency - Exams
Course program
Structures in the Built Environment
Primary structural elements and their assemblies; classification of structures; structural response; introduction to modeling. Modeling of loads, connections (constraints), structures, and materials.
Truss Structures
Introduction; stability; forces in elements; three-dimensional trusses.
Beams as Flexural Elements
Beams in buildings; bending stresses; lateral-torsional buckling; shear and torsion; principal stresses. Continuous beams: general principles, stiffness, and stress characteristic diagrams.
Rigid-Frame Structures
General principles; analysis methods for rigid frames; beam-column relative stiffness; multi-story frames; Vierendeel beams.
Funicular Structures
General principles; suspended cable structures with concentrated or uniformly distributed loads.
Arch Structures
Masonry arches; rigid parabolic arches with distributed loads; funicular arches with point loads; three-hinged arches; fixed arches with two or three hinges.
Mathematical Models
Linear Algebra Refresher
Vector spaces of finite dimension; vector operations; dot, cross, and mixed products; orthonormal basis representation; linear combinations; matrices: definitions, operations, trace, product, rank, determinant, inverses.
Kinematics of Rigid Bodies
Definition of a rigid body; general form of infinitesimal rigid-body displacement; rigid-body systems; kinematic characterization of external and internal constraints; kinematic problem and classification: isokinematic, labile, hypokinematic, degenerate; analytical and graphical solution methods; infinitesimal displacement fields.
Statics of Rigid Bodies
Force concepts; moment about a point; transport formula; force systems, resultant and resultant moment; distributed loads; static characterization of constraints; static problem: equilibrium equations and calculation of support reactions; classification of systems: isostatic, hyperstatic, hypostatic, degenerate.
Statics-Kinematics Duality
Duality; principle of virtual work; applications of virtual work theorem.
Planar Beams with Straight Axis
Beam geometry, kinematics, applied loads, internal actions; stress characteristics; differential equilibrium equations; truss systems.
Rigid Planar Trusses
Plane rigid trusses; nodal equilibrium method; Ritter section method; static classification.
Prerequisites
Basic knowledge of mathematical analysis and linear algebra.
Books
D. L. Schodek, Strutture (translated by D. Coronelli and L. Martinelli)
P. Casini, M. Vasta, Scienza delle costruzioni, CittàStudi, 2019
A. Luongo, A. Paolone, Meccanica delle strutture. Sistemi rigidi ad elasticità concentrata, Masson, 1997
E. Viola, Esercitazioni di Scienza delle Costruzioni/1 - Strutture isostatiche e geometria delle masse, Pitagora Editrice
Frequency
Class attendance is not mandatory.
Exam mode
The assessment consists of a written exam and an oral exam.
The written exam, lasting 3 hours, involves solving exercises related to the topics covered in the course and aims to verify the student’s ability to correctly apply the principles of structural mechanics to problem solving.
Passing the written exam with a satisfactory result is a prerequisite for taking the oral exam, which includes further exercises and theoretical questions designed to assess understanding of the fundamental concepts and mastery of technical language.
Lesson mode
Lectures are conducted at the blackboard, with occasional use of slides, to allow students to follow in real time the development of reasoning, demonstrations, and the solving of exercises.
- Lesson code1025927
- Academic year2025/2026
- CourseProject Management in Building Construction
- CurriculumSingle curriculum
- Year2nd year
- Semester1st semester
- SSDICAR/08
- CFU6