Architecture

PAOLO CASINI

MECHANICS OF STRUCTURES
The course introduces the concepts and the fundamental procedures of Mechanics that are at the basis of the structural behaviour of both historical buildings and new structural typologies. In this framework, reference is mostly made to systems that can be modelled as rigid bodies, dealing with the main elementary structures that form parts of more complex architectural works. Yet, the main concepts relevant to systems of deformable beams are also addressed, paying special attention to the issues of structural strength and design.

The course aims to provide the theoretical models and the basic operational tools for the structural analysis and design. Continuous bodies, and in particular beams, are studied taking into account their equilibrium, strength and stability as well as the mechanical behavior of materials.
1. Making judgements. The students will acquire: ability to choose the most appropriate theoretical models (rigid body, elastic beam, deformable body) to address the analysis of real structures; ability to design and perform numerical analyses on basic structural problems, to interpret data and draw conclusions; understanding the main structural analysis techniques and their limits.
2. Learning skills. The students will acquire: ability to properly identify, formalize and solve the structural problems; ability to understand the technical terms used in structural engineering; skills needed to undertake further advanced courses on structural engineering.

Thorough knowledge of the topics covered in basic courses in Mathematics.

Prerequisites: thorough knowledge of the topics covered in basic courses in Mathematics. Theory of Vectors. Elements of classical mechanics. 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.

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

Paolo Casini, Marcello Vasta. Scienza delle Costruzioni (quarta edizione), DeAgostini Scuola-CittàStudi ed., ISBN 9788825174274 (2019)

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

Paolo Casini, Marcello Vasta. Scienza delle Costruzioni (quarta edizione), DeAgostini Scuola-CittàStudi ed., ISBN 9788825174274 (2019)

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

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/statica 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/statica, 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. Review of Mechanics. Review of Linear Algebra. Vector theory. Exercises.


• Rigid body: Kinematics, introduction. Rigid displacement and rotation. General formula of rigid displacement. Exercises.


• Rigid body: Statics, introduction. External active and reactive forces. Indeterminate equilibrium equations. Exercises.


• Beam and beam systems: Introduction, geometric model. Notation and conventions. Classification. Exercises.


• Geometry of areas. Exercises. In-class exercise.


• Beam and beam systems: Statics, internal force characteristics, indeterminate equilibrium equations. Typical static schemes. Exercises. Internal force diagrams. Exercises.


• Beam and beam systems: Deformation analysis. Hooke’s law. Elastic problem.


• Beam and beam systems: Principle of Virtual Work. Force Method.


• Truss structures: Introduction, joint method, Ritter section method. Exercises. General review of the course, preparation for the final examination.