STATICS (Partizione B)
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- Versione italiana
- Academic year
- 2020/2021
- Teacher
- ENRICO MILANI
- Credits
- 9
- Didactic period
- Primo Semestre
- SSD
- ICAR/08
Training objectives
- The Course is the first one dealing with the Structural Analysis and Design that is carried out by the student. Main goals are:
- To educate the student to conceive of the architectural project in its structural components, that is as final synthesis of a process in which the structural approach contribute to define the quality of the product together with both the formal intuition and the functional organisation and the technological choices.
- To provide the basic notions of Structural Analysis that are both useful to solve simple structural problems and as starting point to cope with more complex structural problems in the successive years.
Knowledge:
• Features and modelling of the dead and live actions on the buildings.
• Types of connections among structural elements and between the structure and the soil.
• Basic knowledge of the structural model beam.
• The concept of equilibrium aimed at the computation of the reactions of the soil on the structure and of the internal reactions among structural elements.
• Basis of the concept of stress aimed at the design of simple beams.
Skills:
The main skill, that will be developed by the student, concerns the analysis and the structural check of simple continuous beams, trusses and frames, showing the ability to deal with operative numerical procedures. In particular, the student will be able to:
• To build a structural model as assembly of restrained, constrained, loaded beams.
• To compute the resultant force and moment of the applied loads.
• To measure the entity of the restraints on the beams and of the constraints among beams.
• To compute the normal stress occurring in the beams as a result of the external loads.
• To design the transversal section of simple beam elements. Prerequisites
- Students may attempt the exam of Statics after they have taken the exam of Mathematics
Furthermore it is necessary to have acquired:
• Knowledge of the most common measure units and of their transformation.
• Elementary concepts of Arithmetics and Geometry.
• Knowledge of the linear equations, of the linear system of equations and of the vector theory.
• Elementary concepts of Calculus and of Matrix theory.
• Knowledge of the main concepts in Physics, with special attention to Mechanics. Course programme
- Part I – Vector analysis and basic cinematics
Vectors. Moment of a force about a point. Equivalent systems of vectors.
The funicular polygon. Applications to the equilibrium of masonry panels and revetments.
Small displacement kinematics. Kinematics of the material point and of the rigid body. Fundamental relation of the kinematics. Definition of beam. Systems of beams in two dimensions. Kinematics of supports and connections. Kinematic analysis of systems of beams: statically determined and statically undetermined systems.
Structural typologies. Supports and connections in the reality. Correspondence between real structure and its structural model.
Modelling of the External actions. Equilibrium in two dimensions. Statics of supports and connections. Equilibrium of a particle, of a system of particles. Equilibrium of a both free and rigid body in two dimensions. Equilibrium of constrained two-dimensional structures.
Part II – Reactions, Axial force, Shear and Bending moment.
Computation of the Reactions at supports and connections for a two-dimensional loaded structure. Superposition principle. Axial force, shear and moment in statically determinate structures. General beam theory (differential relations). Mentions of line of thrust in arches. Planar pin-jointed frames (trusses): method of joints and method of sections. Symmetrical structures.
Part III – Stress and strain.
Introduction of the stress and strain concepts. Mechanical behaviour of some materials of engineering interest: steel, concrete, wood. Stress distributions due to axial force. Stress distributions due to bending moment. Member subjected to the coupling of bending moment and centered axial force. Structural check with the Admissible Stress approach. Short notes on the Ultimate Limite State approach for steel sections. Short notes on the analysis of no-tension materials (masonry wall, foundation-soil interface).
Part IV – Center of gravity, inertia parameters
Moments and Products of inertia of areas. Radius of gyration. Parallel-axis theorem. Principal axes and principal moments of inertia. Central core of inertia. Applications to the most common beam transversal sections. Didactic methods
- Organization: The Course is organised in theoretical lectures and exercises in hall and it is supported by the mentoring of older students (tutorato). Each Part of the syllabus is completed by one or two numerical exercise.
- Theoretical lessons: The main aspects of the theoretical lectures are exposed and discussed thoroughly with the aid of the blackboard, with continuous recalls to the real physical phenomena and to the observation of actual structural behaviors, and with the aid of power point presentations, photos and examples on the web. Students may stop the lecture to obtain clarifications or integrations and to ask any question.
- Esercises: The practical activity consists both in exercises developed by the Teacher on the blackboard to better understand the theory explained during the theoretical lesson, and in simple structural applications that the students resolve on their own sheets as much as independently possible but in groups, with the aid of the Teacher.
- Mentoring activity (tutorato): some older students (fourth, fifth year course or PhD students), chosen by “concorso”, provide some extra lessons, outside the scheduled lessons, in order to exercise further the students on the numerical applications.
Finally, the Teacher is available to receive the students in his own studio outside the lesson time, fate the laste week lesson , by appointament. Learning assessment procedures
- At the end of the Course the student may take the exam in one of the scheduled (at least two for each session) academic sessions.
The exam is taken by passing:
1. One written test concerning the resolution of four exercises mainly dealing with:
a. Computation of the restraint and constraint forces and drawing of the axial force, shear, bending moments diagramms with reference to simple beam systems;
b. Determination of the equilibrium of rigid bodies;
c. Identification of statically undetermined structures;
d. Computation of the stress in simple trasversal sections of beams.
2. One oral test concerning the contents of the Course, that is Principles, Theorems and Methods providing the numerical procedures used in the applications. Such a test is possible if the written test is first passed. The mark of the written test is emailed to the students. They can discuss the errors with the teacher before the oral test.
Each exercise of the written test has some questions. A score is given to the answer of each question. The final mark is obtained summing the scores of the answers. The written test is passed under two conditions: the score is at least higher than 50%, the mark of some mandatory questions (previously communicated to the students) are higher than 50%. The oral test is based on two questions. It is passed if at least one of the two is answered correctly. Reference texts
- 1) Notes on the web (see http://docente.unife.it/vincenzo.mallardo/dispensestatica)
2) B. D'Acunto, P. Massarotti, Elementi di Statica, De Frede
3) L. Gambarotta, L. Nunziante, A. Trallli, Scienza delle Costruzioni, Mc Graw Hill Italia
