Architecture

ANTONINO FAVATA

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.

Basic knowledge of structural mechanics.

Linear Algebra
Ambient space. Vector spaces of finite dimension. Operations among vector. Scalar product. Vector product. representation in an orthonormal basis. Mixed product.

Systems of forces and couples
Notion of force. Moment of a force about a point. Transport formula. Systems of forces, resultant, moment resultant. Elementary operations on forces and couples. Central axis.

Kinematics and statics of rigid bodies
Definition of rigid body. Kinematics of rigid bodies. Absolute and relative position. Absolute and relative velocity. Representation formula of rigid velocities. Infinitesimal displacement fields. External constraints. Kinematic and static characterization of rigid bodies.
Statics of rigid bodies: cardinal equations. Power associated to systems of forces and couples. Principle of powers.
Kinematic problem and kinematic classification: systems kinematically determined, indetermined, impossible, degenerate.
Static problem and static classification: systems statically determined, indetermined, impossible, degenerate.
Duality static-kinematic.

Systems of rigid bodies
Internal constraints. Methods of auxiliary equations for conditions of partial equilibrium: computing reactions of isostatic systems. Kinematic chains. Instantaneous center of rotation. Relative center of rotation. First and second theorem about centers of rotation. Diagrams of velocities/infinitesimal displacements. Method of powers for computing reactions in isostatic systems.

Plane straight beams
Beams: geometry, kinematics, applied loads, internal actions. Internal stress. Differential equilibrium equations. Systems of beams. Trusses.

Elastic beams
Axial deformations, of mechanical and thermal origin. Bending. Differential equation of elastica. Principle of virtual workings. Solution of hyperstatic structures.

Principles of structural design.

1) P. Podio-Guidugli, Lezioni di Statica, Aracne, 2014.
2) P. Podio-Guidugli, Lezioni di Scienza delle Costruzioni, Aracne, 2012.
3) A. Luongo, A. Paolone, Meccanica delle strutture. Sistemi rigidi ad elasticità concentrata, Masson, 1997.

Lessons at the blackboard

In presence

Written and oral exams

Old exams will be released.