Environmental Engineering

PAOLO CASINI

The course provides the theoretical basis of structural engineering by illustrating
theoretical models and practical tools for the analysis of structural systems (mainly those
composed by beams), and examining their equilibrium, compatibility, strength and stability.
The topics dealt with contribute to form the necessary knowledge to identify, formulate and
solve the structural problems of the building design, and to understand the technical
language of structural engineering.


The students shall be able to analyze and solve simple structural patterns, such as
statically determinate and indeterminate systems of beams and trusses, by evaluating their
states of stress and deformation and carrying out the safety check of the cross sections.
Moreover they shall know the basics of continuum mechanics. In making judgements, the
students will acquire: 1.1 ability to choose the most appropriate theoretical models (rigid
body, elastic beam, deformable body) to address the analysis of real structures; 1.2 ability
to design and perform numerical analyses on basic structural problems, to interpret data
and draw conclusions; 1.3 Understanding the main structural analysis techniques and their
limits. In learning skills, the students will acquire: 2.1 ability to properly identify, formalize
and solve the structural problems; 2.2 ability to understand the technical terms used in
structural engineering; 2.3 skills needed to undertake further advanced courses on
structural engineering.

The students shall be able to analyze and solve simple structural patterns, such as statically determinate and indeterminate systems of beams and trusses, by evaluating their states of stress and deformation and carrying out the safety check of the cross sections. Moreover they shall know the basics of continuum mechanics.

In making judgements, the students will acquire: a) ability to choose the most appropriate theoretical models (rigid body, elastic beam, deformable body) to address the analysis of real structures; b) ability to design and perform numerical analyses on basic structural problems, to interpret data and draw conclusions; c) Understanding the main structural analysis techniques and their limits.

In learning skills, the students will acquire: a) ability to properly identify, formalize and solve the structural problems; b) ability to understand the technical terms used in structural engineering; c) skills needed to undertake further advanced courses on structural engineering.

Prerequisites: thorough knowledge of the topics covered in basic courses in Mathematics, Physics and Geometry.

Kinematics of rigid systems: generalized displacement; kinematic definition of constraints (internal and external); algebraic study of Kinematics of rigid systems. Statics of rigid systems: static definition of constraints (internal and external); cardinal equations of statics; static-kinematic duality; determination of constraint reactions; classification of systems of beams; line pressure; indefinite equations of equilibrium for plane beams; internal beam reactions and diagrams of characteristics of internal reactions; statically determinate systems of beams and trusses. Displacement method: formulation; application to statically determinate and indeterminate systems of beams. Force method: method of consistent deformations; applications to systems of beams. Behavior of materials used in construction: the case reinforced concrete, steel and masonry.

Analysis of the tension in a continuous three-dimensional medium: the concept of stress according to Cauchy; Cauchy’s theorem and stress tensor; principal stresses and stress invariant; Mohr's cir-cles;
equilibrium equations. Analysis of the strain in a continuous three dimensional medium; tensor of strains; principal strains; compatibility equations; distortions. Theorem of virtual work and the general formula of displacement. Linear elastic homogeneous isotropic material: Hooke’s law.
Analysis of stresses and strains of a beam: Saint Venant problem: normal and eccentric force; torsion; bending and shear.
Criteria of resistance. Stability of elastic equilibrium: the limits of validity of Euler's formula, the omega method.

More details can be found in: www.pcasini.it/disg/sdc

Paolo Casini, Marcello Vasta. Scienza delle Costruzioni (quarta edizione), DeAgostini Scuola-CittàStudi ed., ISBN 9788825174274 (2020)

Additional information and teaching materials can be found at: www.pcasini.it/disg/sdc

Paolo Casini, Marcello Vasta. Scienza delle Costruzioni (quarta edizione), DeAgostini Scuola-CittàStudi ed., ISBN 9788825174274 (2020)

Additional information and bibliography can be found at: www.pcasini.it/disg/sdc

Frontal lessons and in-class exercises. Learning assessments with exercises on classroom, corrected in person. Videos regarding lessons and exercises available on the website www.pcasini.it/disg/sdc under the 'video' section.

Class attendance is not mandatory but strongly recommended.

The learning process is verified during the course through exercises and written tests.

On the webpage www.pcasini.it/sdc, under the sections 'teaching materials' and 'exam samples', you will find numerous examples of oral questions and exercises for exam preparation.

• Introduction
  to the course.
  
  
  Rigid body: Introduction. Rigid body Kinematics: theory and exercises. Rigid body Statics: theory and exercises.


• Beam and beam systems: Introduction. Kinematics, displacements and rotations, strain measures, compatibility equations. Exercises. Statics, internal force characteristics, indeterminate equilibrium equations and exercises. Hooke’s Law. Elastic problem. Principle of Virtual Work. Force Method. Displacement Method. Exercises on the Force Method.


• Introduction. Kinematics, strain analysis. Exercises on beam systems. Statics, stress analysis. Cauchy’s theorem, principal stresses and directions. Constitutive law. Elastic problem. Exercises.


• Saint-Venant problem: Introduction. Centered normal force. Straight bending. Oblique bending. Eccentric bending. Exercises. Bending and shear. Exercises. Uniform torsion. Exercises. Shear center. Exercises. Review exercises.


• Structural instability. General review of the course, preparation for the oral exam.