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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

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

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

Class attendance is not mandatory but strongly recommended.

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

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.

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

Lessons at the blackboard