Valentino Paolo BERARDI | RATIONAL MECHANICS AND STRUCTURAL MECHANICS

cod. 0612300049

RATIONAL MECHANICS AND STRUCTURAL MECHANICS

	0612300049
	DEPARTMENT OF INDUSTRIAL ENGINEERING
	EQF6
	MECHANICAL ENGINEERING
	2023/2024

PERCORSO IN COMMON

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2018
	FULL ACADEMIC YEAR

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
1	MECCANICA RAZIONALE
	MAT/07	8	80	LESSONS	BASIC COMPULSORY SUBJECTS
2	SCIENZA DELLE COSTRUZIONI
	ICAR/08	6	60	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

PROFESSORS

	ANTONIO SELLITTO1 T Curriculum
	VALENTINO PAOLO BERARDI2 Curriculum

	Objectives
	THE COURSE IS MADE OF THE FOLLOWING TWO MODULES: RATIONAL MECHANICS (I SEMESTER) AND STRUCTURAL MECHANICS (II SEMESTER). REGARDING TO THE MODULE OF RATIONAL MECHANICS, THE COURSE AIMS AT THE FOLLOWING EDUCATIONAL OBJECTIVES: -) KNOWLEDGE AND UNDERSTANDING. THE STUDENT SHOULD KNOW THE BASIC ELEMENTS OF THE VECTOR CALCULATION IN ORDER TO STUDY BOTH THE KINEMATICS AND THE DYNAMICS OF A MATERIAL POINT, OF SYSTEMS OF MATERIAL POINTS AND RIGID BODIES. THE STUDENT HAS ALSO TO BE ABLE TO UNDERSTAND SIMPLE PROBLEMS OF MASS GEOMETRY. -) APPLYING KNOWLEDGE AND UNDERSTANDING. THE STUDENT SHOULD BE ABLE TO SOLVE SIMPLE PROBLEMS OF MASS GEOMETRY (IN THE CASE OF FLAT SYSTEMS), OF DYNAMICS (IN THE CASE OF PLAN SYSTEMS WITH ONE OR MORE DEGREES OF FREEDOM) AND STATIC OF MECHANICAL SYSTEMS (FOR PLAN SYSTEMS, BY MEANS OF CARDINALS EQUATIONS OF THE STATIC, AND BY MEANS OF THE PRINCIPLE OF VIRTUAL WORKS). -) JUDGMENT AUTONOMY. THE STUDENT HAS TO BE ABLE TO DEEPEN INTO OWN KNOWLEDGE, IN ORDER TO USE IT AS A STARTING POINT TO REACH FURTHER NEW RESULTS WHICH MAY BE MORE COMPLEX. -) COMMUNICATION SKILLS. THE STUDENT HAS TO BE ABLE OF EXPLAINING IN A SIMPLE WAY, WITH DETAILS AND PRECISIONS, ALL THE METHODS AND TECHNIQUES ADOPTED TO SOLVE A PROBLEM OF MECHANICS, AS WELL AS THE PROCEDURE WHICH HAS BEEN USED TO GET THE AIMED RESULTS. HE MUST BE ALSO ABLE TO APPLY THE OBTAINED KNOWLEDGE TO PRACTICAL APPLICATIONS. -) LEARNING SKILLS. THE STUDENT HAS TO DEVELOP THE LEARNING SKILLS THAT WILL BE NECESSARY FOR INSERTING HIM IN THE FOLLOWING STUDIES WITH A HIGH AUTONOMY OF STUDY, AND CRITICALLY FACE MORE GENERAL PROBLEMS. REGARDING TO THE MODULE OF STRUCTURAL MECHANICS, THE COURSE AIMS AT THE FOLLOWING EDUCATIONAL OBJECTIVES: -) KNOWLEDGE AND UNDERSTANDING. THE COURSE PROVIDES THE FUNDAMENTALS OF CONTINUUM MECHANICS (CONCEPTS OF STRESS AND STRAIN, CONSTITUTIVE EQUATIONS, FAILURE CRITERIA) AND STRUCTURAL MECHANICS (STATIC, KINEMATIC AND ELASTIC PROBLEMS, DESIGN AND VERIFICATION OF BEAMS FOR AXIAL FORCE, SHEAR, BENDING AND TORSION, BASIC ELEMENTS OF ELASTIC STABILITY). -) APPLYING KNOWLEDGE AND UNDERSTANDING: THE COURSE ENABLE STUDENTS TO ACQUIRE AN APPROACH TO STRUCTURAL DESIGN AND VERIFICATION OF BEAMS AND BEAM SYSTEMS, AND TO EVALUATE THE STRESS AND STRAIN FIELDS OF CONTINUOUS BODIES. -) MAKING JUDGEMENTS: BY THE END OF THE COURSE, THE STUDENT WILL BE ABLE TO MODEL THE MECHANICAL BEHAVIOR OF BEAMS AND FRAMED SYSTEMS SUBJECT TO EXTERNAL ACTIONS, AND TO PERFORM THE DESIGN AND VERIFICATION OF STRUCTURAL MEMBERS. -) COMMUNICATION SKILLS: EXPLAINING THE KEY ASPECTS OF STRUCTURAL MODELLING IS THE MOST IMPORTANT EXPECTED COMMUNICATION SKILL. -)LEARNING SKILLS: THE ABILITY OF APPLYING THE ACQUIRED KNOWLEDGE TO STRUCTURAL PROBLEMS IN CONTEXTS DIFFERENT FROM THOSE PRESENTED DURING THE COURSE.

THE COURSE IS MADE OF THE FOLLOWING TWO MODULES: RATIONAL MECHANICS (I SEMESTER) AND STRUCTURAL MECHANICS (II SEMESTER).
REGARDING TO THE MODULE OF RATIONAL MECHANICS, THE COURSE AIMS AT THE FOLLOWING EDUCATIONAL OBJECTIVES:
-) KNOWLEDGE AND UNDERSTANDING.
THE STUDENT SHOULD KNOW THE BASIC ELEMENTS OF THE VECTOR CALCULATION IN ORDER TO STUDY BOTH THE KINEMATICS AND THE DYNAMICS OF A MATERIAL POINT, OF SYSTEMS OF MATERIAL POINTS AND RIGID BODIES. THE STUDENT HAS ALSO TO BE ABLE TO UNDERSTAND SIMPLE PROBLEMS OF MASS GEOMETRY.
-) APPLYING KNOWLEDGE AND UNDERSTANDING.
THE STUDENT SHOULD BE ABLE TO SOLVE SIMPLE PROBLEMS OF MASS GEOMETRY (IN THE CASE OF FLAT SYSTEMS), OF DYNAMICS (IN THE CASE OF PLAN SYSTEMS WITH ONE OR MORE DEGREES OF FREEDOM) AND STATIC OF MECHANICAL SYSTEMS (FOR PLAN SYSTEMS, BY MEANS OF CARDINALS EQUATIONS OF THE STATIC, AND BY MEANS OF THE PRINCIPLE OF VIRTUAL WORKS).
-) JUDGMENT AUTONOMY.
THE STUDENT HAS TO BE ABLE TO DEEPEN INTO OWN KNOWLEDGE, IN ORDER TO USE IT AS A STARTING POINT TO REACH FURTHER NEW RESULTS WHICH MAY BE MORE COMPLEX.
-) COMMUNICATION SKILLS.
THE STUDENT HAS TO BE ABLE OF EXPLAINING IN A SIMPLE WAY, WITH DETAILS AND PRECISIONS, ALL THE METHODS AND TECHNIQUES ADOPTED TO SOLVE A PROBLEM OF MECHANICS, AS WELL AS THE PROCEDURE WHICH HAS BEEN USED TO GET THE AIMED RESULTS. HE MUST BE ALSO ABLE TO APPLY THE OBTAINED KNOWLEDGE TO PRACTICAL APPLICATIONS.
-) LEARNING SKILLS.
THE STUDENT HAS TO DEVELOP THE LEARNING SKILLS THAT WILL BE NECESSARY FOR INSERTING HIM IN THE FOLLOWING STUDIES WITH A HIGH AUTONOMY OF STUDY, AND CRITICALLY FACE MORE GENERAL PROBLEMS.

REGARDING TO THE MODULE OF STRUCTURAL MECHANICS, THE COURSE AIMS AT THE FOLLOWING EDUCATIONAL OBJECTIVES:
-) KNOWLEDGE AND UNDERSTANDING.
THE COURSE PROVIDES THE FUNDAMENTALS OF CONTINUUM MECHANICS (CONCEPTS OF STRESS AND STRAIN, CONSTITUTIVE EQUATIONS, FAILURE CRITERIA) AND STRUCTURAL MECHANICS (STATIC, KINEMATIC AND ELASTIC PROBLEMS, DESIGN AND VERIFICATION OF BEAMS FOR AXIAL FORCE, SHEAR, BENDING AND TORSION, BASIC ELEMENTS OF ELASTIC STABILITY).
-) APPLYING KNOWLEDGE AND UNDERSTANDING:
THE COURSE ENABLE STUDENTS TO ACQUIRE AN APPROACH TO STRUCTURAL DESIGN AND VERIFICATION OF BEAMS AND BEAM SYSTEMS, AND TO EVALUATE THE STRESS AND STRAIN FIELDS OF CONTINUOUS BODIES.
-) MAKING JUDGEMENTS:
BY THE END OF THE COURSE, THE STUDENT WILL BE ABLE TO MODEL THE MECHANICAL BEHAVIOR OF BEAMS AND FRAMED SYSTEMS SUBJECT TO EXTERNAL ACTIONS, AND TO PERFORM THE DESIGN AND VERIFICATION OF STRUCTURAL MEMBERS.
-) COMMUNICATION SKILLS:
EXPLAINING THE KEY ASPECTS OF STRUCTURAL MODELLING IS THE MOST IMPORTANT EXPECTED COMMUNICATION SKILL.
-)LEARNING SKILLS:
THE ABILITY OF APPLYING THE ACQUIRED KNOWLEDGE TO STRUCTURAL PROBLEMS IN CONTEXTS DIFFERENT FROM THOSE PRESENTED DURING THE COURSE.

	Prerequisites
	FOR THE SUCCESSFUL ACHIEVEMENT OF THE GOALS OF THE COURSE, STUDENTS ARE REQUIRED TO HAVE THE FOLLOWING PREREQUISITES: -) BASIC KNOWLEDGE OF MATHEMATICAL ANALYSIS (I.E., FUNDAMENTAL THEORY BOTH OF DIFFERENTIAL CALCULATION, AND OF INTEGRALS); -) BASIC KNOWLEDGE OF ORDINARY DIFFERENTIAL EQUATIONS; -) BASIC KNOWLEDGE OF TENSORIAL CALCULATION; -) BASIC KNOWLEDGE OF PHYSICS. THE AFOREMENTIONED BASIC KNOWLEDGES ARE COMPULSORY: EACH PART OF THE EXAM WILL BE FORBIDDEN IF THE FOLLOWING EXAMS DON'T HAVE BEEN PREVIOUSLY PASSED: MATHEMATICS I, MATHEMATICS II AND PHYSICS I.

Prerequisites

FOR THE SUCCESSFUL ACHIEVEMENT OF THE GOALS OF THE COURSE, STUDENTS ARE REQUIRED TO HAVE THE FOLLOWING PREREQUISITES:
-) BASIC KNOWLEDGE OF MATHEMATICAL ANALYSIS (I.E., FUNDAMENTAL THEORY BOTH OF DIFFERENTIAL CALCULATION, AND OF INTEGRALS);
-) BASIC KNOWLEDGE OF ORDINARY DIFFERENTIAL EQUATIONS;
-) BASIC KNOWLEDGE OF TENSORIAL CALCULATION;
-) BASIC KNOWLEDGE OF PHYSICS.

THE AFOREMENTIONED BASIC KNOWLEDGES ARE COMPULSORY: EACH PART OF THE EXAM WILL BE FORBIDDEN IF THE FOLLOWING EXAMS DON'T HAVE BEEN PREVIOUSLY PASSED: MATHEMATICS I, MATHEMATICS II AND PHYSICS I.

	Contents
	THE COURSE IS MADE OF THE FOLLOWING TWO MODULES: RATIONAL MECHANICS (I SEMESTER) AND STRUCTURAL MECHANICS (II SEMESTER). MODULE OF RATIONAL MECHANICS, 80 HOURS (THEORETICAL LECTURES: 50 HOURS; CLASSROOM PRACTICES: 30 HOURS) VECTORIAL CALCULUS (5 HOURS OF THEORY): VECTORS AND BASIC OPERATIONS. APPLICATIONS TO DIFFERENTIAL GEOMETRY. APPLIED VECTORS (2 HOURS OF THEORY): SYSTEM OF APPLIED VECTORS. RESULTANT VECTOR AND RESULTANT TORQUE FOR A SYSTEM OF APPLIED VECTORS. CENTRAL AXIS. SYSTEMS OF APPLIED VECTORS. TENSOR CALCULUS (3 HOURS OF THEORY): TENSORS AND MATRIX. KINEMATICS OF A MATERIAL POINT (2 HOURS OF THEORY): SPEED. ACCELARATION. IN-PLANE MOTION. CENTRAL MOTION. HARMONIC MOTION. KINEMATICS OF A SYSTEM OF MATERIAL POINTS (8 HOURS OF THEORY): DEGREES OF FREEDOM AND LAGRANGIAN COORDINATES. HOLONOMIC SYSTEMS. KINEMATICS OF RIGID-BODY SYSTEMS. EULER DEGREE. PARTICULAR RIGID MOTIONS. POISSON FORMULAS. MOZZI THEOREM. KINEMATICS OF RELATIVE MOTIONS. IN-PLANE RIGID MOTION. STATICS AND DYNAMICS OF A FREE PARTICLE (10 HOURS OF THEORY). WORK OF A FORCE. CONSERVATIVE FORCES. MECHANICAL ENERGY AND RELATIVE THEOREMS. DIFFERENTIAL EQUATIONS OF THE MOTION OF A FREE PARTICLE BOTH IN AN INERTIAL REFERENCE FRAME, AND IN A NON-INERTIAL REFERENCE FRAME. STATICS OF A FREE PARTICLE. HARMONIC OSCILLATOR, DAMPED HARMONIC OSCILLATOR, RESONANCE. STATICS AND DYNAMICS OF A RESTRICTED PARTICLE (4 HOURS OF THEORY): EQUATIONS OF MOTION. STATICS. EQUILIBRIUM. DYNAMICS. SIMPLE GRAVITY PENDULUM. THE MASS GEOMETRY (4 HOURS OF THEORY AND 12 HOURS OF EXERCISE): BARYCENTER AND ITS PROPERTIES. LINEAR AND ANGULAR MOMENTUM. KOENING THEOREM. KINETIC ENERGY AND MOMENT OF INERTIA. HUYGENS THEOREM AND INERTIA ELLIPSOID. GENERAL THEOREMS OF MATERIAL-SYSTEM MECHANICS (2 HOURS OF THEORY AND 2 HOURS OF EXERCISE): CARDINAL EQUATIONS OF DYNAMICS. THEOREM OF THE MOTION OF BARYCENTER. THEOREMS ABOUT THE WORK OF INTERNAL AND EXTERNAL FORCES. THEOREM OF ENERGY CONSERVATION. STATICS OF RIGID BODIES (2 HOURS OF THEORY AND 2 HOURS OF EXERCISE): CARDINAL EQUATIONS OF STATICS. GENERAL CONDITIONS FOR THE EQUILIBRIUM OF A RIGID BODY AND SOME APPLICATIONS. VINCULAR REACTIONS FOR A RIGID BODY IN EQUILIBRIUM. DYNAMICS OF A RIGID BODY (2 HOURS OF THEORY): THE MOTION OF A RIGID BODY. ANALYTICAL MECHANICS (6 HOURS OF THEORY AND 14 HOURS OF EXERCISE): VIRTUAL DISPLACEMENTS OF A HOLONOMIC SYSTEM. VIRTUAL WORK. THE SYMBOLIC EQUATION OF DYNAMICS AND THE D'ALAMBERT PRINCIPLE. THE SYMBOLIC EQUATION OF STATICS AND THE PRINCIPLE OF VIRTUAL WORK. EQUILIBRIUM OF A HOLONOMIC SYSTEM. THE LAGRANGE EQUATIONS. THE KINETIC ENERGY OF HOLONOMIC SYSTEMS AND RELATIVE THEOREMS. MODULE OF STRUCTURAL MECHANICS, 60 HOURS (THEORETICAL LECTURES: 40 HOURS; CLASSROOM PRACTICES: 20 HOURS) GENERAL PRINCIPLES OF SOLID MECHANICS (THEORETICAL LECTURES: 15 HOURS): DISPLACEMENTS AND STRAINS, COMPATIBILITY DIFFERENTIAL EQUATION AND KINEMATICAL BOUNDARY CONDITIONS, FORCES AND STRESSES, EQUILIBRIUM DIFFERENTIAL EQUATIONS AND STATIC BOUNDARY CONDITIONS, CONSTITUTIVE LAWS, BASIC PROPERTIES OF THE LINEAR ELASTIC STATIC PROBLEM. AREA PROPERTIES (THEORETICAL LECTURES: 3 HOURS; CLASSROOM PRACTICES: 2 HOURS): INTRODUCTION, NOTATION, FIRST MOMENT OF AREA, CENTROID, SECOND MOMENT OF AREA. ELASTIC BEAMS (THEORETICAL LECTURES: 10 HOURS; CLASSROOM PRACTICES: 5 HOURS): THE THEORIES OF TIMOSHENKO AND EULERO-BERNOULLI, GENERALIZED STRAIN AND STRESS RESULTANTS, COMPATIBILITY AND EQUILIBRIUM EQUATIONS, EXTERNAL AND INTERNAL CONSTRAINS, THE KINEMATICAL PROBLEM, THE STATICAL PROBLEM. PLANE FRAMED SYSTEMS (THEORETICAL LECTURES: 5 HOURS; CLASSROOM PRACTICES: 10 HOURS): STATICALLY DETERMINATE AND INDETERMINATE BEAM SYSTEMS, KINEMATICALLY INDETERMINATE BEAM SYSTEMS, REACTION FORCES, DIAGRAMS OF STRESS RESULTANTS, DEFLECTION CURVE. SAFETY VERIFICATIONS (THEORETICAL LECTURES: 7 HOURS; CLASSROOM PRACTICES: 3 HOURS): THE BEAM STRESS STATE, FAILURE CRITERIA, BUCKLING OF COMPRESSED BARS.

Contents

THE COURSE IS MADE OF THE FOLLOWING TWO MODULES: RATIONAL MECHANICS (I SEMESTER) AND STRUCTURAL MECHANICS (II SEMESTER).

MODULE OF RATIONAL MECHANICS, 80 HOURS (THEORETICAL LECTURES: 50 HOURS; CLASSROOM PRACTICES: 30 HOURS)
VECTORIAL CALCULUS (5 HOURS OF THEORY):
VECTORS AND BASIC OPERATIONS. APPLICATIONS TO DIFFERENTIAL GEOMETRY.
APPLIED VECTORS (2 HOURS OF THEORY):
SYSTEM OF APPLIED VECTORS. RESULTANT VECTOR AND RESULTANT TORQUE FOR A SYSTEM OF APPLIED VECTORS. CENTRAL AXIS. SYSTEMS OF APPLIED VECTORS.
TENSOR CALCULUS (3 HOURS OF THEORY):
TENSORS AND MATRIX.
KINEMATICS OF A MATERIAL POINT (2 HOURS OF THEORY):
SPEED. ACCELARATION. IN-PLANE MOTION. CENTRAL MOTION. HARMONIC MOTION.
KINEMATICS OF A SYSTEM OF MATERIAL POINTS (8 HOURS OF THEORY):
DEGREES OF FREEDOM AND LAGRANGIAN COORDINATES. HOLONOMIC SYSTEMS. KINEMATICS OF RIGID-BODY SYSTEMS. EULER DEGREE. PARTICULAR RIGID MOTIONS. POISSON FORMULAS. MOZZI THEOREM. KINEMATICS OF RELATIVE MOTIONS. IN-PLANE RIGID MOTION.
STATICS AND DYNAMICS OF A FREE PARTICLE (10 HOURS OF THEORY).
WORK OF A FORCE. CONSERVATIVE FORCES. MECHANICAL ENERGY AND RELATIVE THEOREMS. DIFFERENTIAL EQUATIONS OF THE MOTION OF A FREE PARTICLE BOTH IN AN INERTIAL REFERENCE FRAME, AND IN A NON-INERTIAL REFERENCE FRAME. STATICS OF A FREE PARTICLE. HARMONIC OSCILLATOR, DAMPED HARMONIC OSCILLATOR, RESONANCE.
STATICS AND DYNAMICS OF A RESTRICTED PARTICLE (4 HOURS OF THEORY):
EQUATIONS OF MOTION. STATICS. EQUILIBRIUM. DYNAMICS. SIMPLE GRAVITY PENDULUM.
THE MASS GEOMETRY (4 HOURS OF THEORY AND 12 HOURS OF EXERCISE):
BARYCENTER AND ITS PROPERTIES. LINEAR AND ANGULAR MOMENTUM. KOENING THEOREM. KINETIC ENERGY AND MOMENT OF INERTIA. HUYGENS THEOREM AND INERTIA ELLIPSOID.
GENERAL THEOREMS OF MATERIAL-SYSTEM MECHANICS (2 HOURS OF THEORY AND 2 HOURS OF EXERCISE):
CARDINAL EQUATIONS OF DYNAMICS. THEOREM OF THE MOTION OF BARYCENTER. THEOREMS ABOUT THE WORK OF INTERNAL AND EXTERNAL FORCES. THEOREM OF ENERGY CONSERVATION.
STATICS OF RIGID BODIES (2 HOURS OF THEORY AND 2 HOURS OF EXERCISE):
CARDINAL EQUATIONS OF STATICS. GENERAL CONDITIONS FOR THE EQUILIBRIUM OF A RIGID BODY AND SOME APPLICATIONS. VINCULAR REACTIONS FOR A RIGID BODY IN EQUILIBRIUM.
DYNAMICS OF A RIGID BODY (2 HOURS OF THEORY):
THE MOTION OF A RIGID BODY.
ANALYTICAL MECHANICS (6 HOURS OF THEORY AND 14 HOURS OF EXERCISE):
VIRTUAL DISPLACEMENTS OF A HOLONOMIC SYSTEM. VIRTUAL WORK. THE SYMBOLIC EQUATION OF DYNAMICS AND THE D'ALAMBERT PRINCIPLE. THE SYMBOLIC EQUATION OF STATICS AND THE PRINCIPLE OF VIRTUAL WORK. EQUILIBRIUM OF A HOLONOMIC SYSTEM. THE LAGRANGE EQUATIONS. THE KINETIC ENERGY OF HOLONOMIC SYSTEMS AND RELATIVE THEOREMS.

MODULE OF STRUCTURAL MECHANICS, 60 HOURS (THEORETICAL LECTURES: 40 HOURS; CLASSROOM PRACTICES: 20 HOURS)
GENERAL PRINCIPLES OF SOLID MECHANICS (THEORETICAL LECTURES: 15 HOURS):
DISPLACEMENTS AND STRAINS, COMPATIBILITY DIFFERENTIAL EQUATION AND KINEMATICAL BOUNDARY CONDITIONS, FORCES AND STRESSES, EQUILIBRIUM DIFFERENTIAL EQUATIONS AND STATIC BOUNDARY CONDITIONS, CONSTITUTIVE LAWS, BASIC PROPERTIES OF THE LINEAR ELASTIC STATIC PROBLEM.
AREA PROPERTIES (THEORETICAL LECTURES: 3 HOURS; CLASSROOM PRACTICES: 2 HOURS):
INTRODUCTION, NOTATION, FIRST MOMENT OF AREA, CENTROID, SECOND MOMENT OF AREA.
ELASTIC BEAMS (THEORETICAL LECTURES: 10 HOURS; CLASSROOM PRACTICES: 5 HOURS):
THE THEORIES OF TIMOSHENKO AND EULERO-BERNOULLI, GENERALIZED STRAIN AND STRESS RESULTANTS, COMPATIBILITY AND EQUILIBRIUM EQUATIONS, EXTERNAL AND INTERNAL CONSTRAINS, THE KINEMATICAL PROBLEM, THE STATICAL PROBLEM.
PLANE FRAMED SYSTEMS (THEORETICAL LECTURES: 5 HOURS; CLASSROOM PRACTICES: 10 HOURS):
STATICALLY DETERMINATE AND INDETERMINATE BEAM SYSTEMS, KINEMATICALLY INDETERMINATE BEAM SYSTEMS, REACTION FORCES, DIAGRAMS OF STRESS RESULTANTS, DEFLECTION CURVE.
SAFETY VERIFICATIONS (THEORETICAL LECTURES: 7 HOURS; CLASSROOM PRACTICES: 3 HOURS):
THE BEAM STRESS STATE, FAILURE CRITERIA, BUCKLING OF COMPRESSED BARS.

	Teaching Methods
	BOTH COURSES CONSIST OF THEORETICAL LECTURES, DEVOTED TO THE EXPLANATION OF ALL THE COURSE CONTENTS AND CLASSROOM PRACTICES, PROVIDING THE STUDENTS WITH THE MAIN TOOLS NEEDED TO PROBLEM-SOLVING ACTIVITIES. LECTURES ARE IN ITALIAN.

	Verification of learning
	FOR EACH MODULE BOTH WRITTEN TESTS, AND ORAL INTERVIEWS WILL BE PLANNED. THE WRITTEN TESTS OF THE TWO MODULES WILL BE GENERALLY DONE IN THE SAME DAY. THE WRITTEN TESTS WILL CONSIST IN SOLVING TYPICAL PROBLEMS. THE SCORES WILL BE EXPRESSED ON A SCALE FROM 1 TO 30. TO PASS TO THE ORAL INTERVIEWS A MINIMUM SCORE OF 18 WILL BE ALWAYS NEEDED. THE WRITTEN TESTS WILL BE NOT PRESERVATIVE. THE WRITTEN TEST REFERRED TO THE MODULE OF RATIONAL MECHANICS IS MADE OF 2 EXERCISES: ONE REGARDING THE GEOMETRY OF MASSES (MAXIMUM THRESHOLD: 15 SCORES), AND THE OTHER ONE REGARDING THE ANALYTICAL MECHANICS (MAXIMUM THRESHOLD: 15 SCORES). THE STUDENT HAS 2 HOURS AND 30 MINUTES TO CARRY OUT THE WRITTEN TEST. THE SCORE IS EXPRESSED ON A SCALE FROM 0 TO 30 AND IT IS THE SUM OF THE SCORES OBTAINED IN EACH EXERCISES ABOVE. THOSE SCORES DEPEND ON THE STUDENT'S ABILITY IN APPLYING OWN KNOWLEDGE. TO PASS THE WRITTEN TEST A MINIMUM SCORE (BASED ON THE SINGLE SCORES ABOVE) OF 18 IS REQUIRED. THE WRITTEN TEST REFERRED TO THE MODULE OF STRUCTURAL MECHANICS IS MADE OF 2 EXERCISES (ONE ON THE SOLVING OF A PLANE SYSTEM OF BEAMS, ANOTHER ON THE SOLVING OF A CONTINUOUS BEAM). THE STUDENT HAS 3 HOURS TO WORK ON THE WRITTEN TEST. THE ORAL INTERVIEW OF EACH MODULE IS SUBJECTED TO BEING SELECTED IN THE CORRESPONDING WRITTEN TEST, AND AIMS AT EVALUATING THE KNOWLEDGE OF ALL TOPICS, AND COVERS DEFINITIONS, ARGUMENTS AND PROOFS. IN THE CASE OF THE MODULE OF RATIONAL MECHANICS, THE ORAL TEST CONSISTS IN 3 QUESTIONS RELATED TO THE ARGUMENTS WHICH HAVE BEEN TREATED DURING THE COURSE. A SCORE IN THE RANGE [0; 10] WILL BE ASSIGNED TO EACH ANSWER. THE ORAL TEST WILL BE PASSED ONLY IF THE TOTAL SCORE (I.E., THE ARITHMETIC SUM OF THOSE SCORES) IS LARGER THAN (OR EQUAL TO) 18. IN THE CASE OF THE MODULE OF STRUCTURAL MECHANICS, THE ORAL TEST, DEVELOPED THROUGH A WRITTEN TEST, AND COMPLETED WITH AN ORAL DISCUSSION AFTERWARDS, CONSISTS IN 6 QUESTIONS/EXCERCICE : I) 2 QUESTIONS ON THE CONTINUUM MECHANICS; II) 2 ON THE BEAM THEORY; III) 1 QUESTION STRESS STATE IN A BEAM; IV) 1 EXERCISE ON SAFETY VERIFICATION OF A BEAM. FOR EACH CORRECT ANSWER, THE STUDENT GETS 30 POINTS AS A MAXIMUM. A MINIMUM OF 18 POINTS IS REQUIRED FOR EACH ANSWER. THE FINAL MARK OF EACH MODULE IS, USUALLY, THE MEAN VALUE OF THE MARKS OF THE WRITTEN AND THE ORAL TESTS AND IT IS EXPRESSED ON A SCALE FROM 18 TO 30 (POSSIBLY WITH LAUDEM). ONCE MARKS HAVE BEEN OBTAINED IN THE TWO MODULES, THE OVERALL (I.E., FINAL) MARK WILL BE THE WEIGHTED ARITHMETIC MEAN OF THE AFOREMENTIONED TWO SINGLE MARKS. THE WEIGHTS ARE THE UNIVERSITY EDUCATIONAL CREDITS. LAUDEM WILL BE CONFERRED ONLY IN THE CASE OF AN EXCELLENT METHODOLOGIC ACCURACY.

Verification of learning

FOR EACH MODULE BOTH WRITTEN TESTS, AND ORAL INTERVIEWS WILL BE PLANNED.

THE WRITTEN TESTS OF THE TWO MODULES WILL BE GENERALLY DONE IN THE SAME DAY. THE WRITTEN TESTS WILL CONSIST IN SOLVING TYPICAL PROBLEMS. THE SCORES WILL BE EXPRESSED ON A SCALE FROM 1 TO 30. TO PASS TO THE ORAL INTERVIEWS A MINIMUM SCORE OF 18 WILL BE ALWAYS NEEDED. THE WRITTEN TESTS WILL BE NOT PRESERVATIVE.

THE WRITTEN TEST REFERRED TO THE MODULE OF RATIONAL MECHANICS IS MADE OF 2 EXERCISES: ONE REGARDING THE GEOMETRY OF MASSES (MAXIMUM THRESHOLD: 15 SCORES), AND THE OTHER ONE REGARDING THE ANALYTICAL MECHANICS (MAXIMUM THRESHOLD: 15 SCORES). THE STUDENT HAS 2 HOURS AND 30 MINUTES TO CARRY OUT THE WRITTEN TEST. THE SCORE IS EXPRESSED ON A SCALE FROM 0 TO 30 AND IT IS THE SUM OF THE SCORES OBTAINED IN EACH EXERCISES ABOVE. THOSE SCORES DEPEND ON THE STUDENT'S ABILITY IN APPLYING OWN KNOWLEDGE. TO PASS THE WRITTEN TEST A MINIMUM SCORE (BASED ON THE SINGLE SCORES ABOVE) OF 18 IS REQUIRED.

THE WRITTEN TEST REFERRED TO THE MODULE OF STRUCTURAL MECHANICS IS MADE OF 2 EXERCISES (ONE ON THE SOLVING OF A PLANE SYSTEM OF BEAMS, ANOTHER ON THE SOLVING OF A CONTINUOUS BEAM). THE STUDENT HAS 3 HOURS TO WORK ON THE WRITTEN TEST.

THE ORAL INTERVIEW OF EACH MODULE IS SUBJECTED TO BEING SELECTED IN THE CORRESPONDING WRITTEN TEST, AND AIMS AT EVALUATING THE KNOWLEDGE OF ALL TOPICS, AND COVERS DEFINITIONS, ARGUMENTS AND PROOFS.

IN THE CASE OF THE MODULE OF RATIONAL MECHANICS, THE ORAL TEST CONSISTS IN 3 QUESTIONS RELATED TO THE ARGUMENTS WHICH HAVE BEEN TREATED DURING THE COURSE. A SCORE IN THE RANGE [0; 10] WILL BE ASSIGNED TO EACH ANSWER. THE ORAL TEST WILL BE PASSED ONLY IF THE TOTAL SCORE (I.E., THE ARITHMETIC SUM OF THOSE SCORES) IS LARGER THAN (OR EQUAL TO) 18.

IN THE CASE OF THE MODULE OF STRUCTURAL MECHANICS, THE ORAL TEST, DEVELOPED THROUGH A WRITTEN TEST, AND COMPLETED WITH AN ORAL DISCUSSION AFTERWARDS, CONSISTS IN 6 QUESTIONS/EXCERCICE : I) 2 QUESTIONS ON THE CONTINUUM MECHANICS; II) 2 ON THE BEAM THEORY; III) 1 QUESTION STRESS STATE IN A BEAM; IV) 1 EXERCISE ON SAFETY VERIFICATION OF A BEAM. FOR EACH CORRECT ANSWER, THE STUDENT GETS 30 POINTS AS A MAXIMUM. A MINIMUM OF 18 POINTS IS REQUIRED FOR EACH ANSWER.

THE FINAL MARK OF EACH MODULE IS, USUALLY, THE MEAN VALUE OF THE MARKS OF THE WRITTEN AND THE ORAL TESTS AND IT IS EXPRESSED ON A SCALE FROM 18 TO 30 (POSSIBLY WITH LAUDEM).

ONCE MARKS HAVE BEEN OBTAINED IN THE TWO MODULES, THE OVERALL (I.E., FINAL) MARK WILL BE THE WEIGHTED ARITHMETIC MEAN OF THE AFOREMENTIONED TWO SINGLE MARKS. THE WEIGHTS ARE THE UNIVERSITY EDUCATIONAL CREDITS.

LAUDEM WILL BE CONFERRED ONLY IN THE CASE OF AN EXCELLENT METHODOLOGIC ACCURACY.

	Texts
	-) ONLINE NOTES. -) M. FABRIZIO, ELEMENTI DI MECCANICA CLASSICA, ED. ZANICHELLI. -) J. N. REDDY, "AN INTRODUCTION TO CONTINUUM MECHANICS WITH --APPLICATIONS", CAMBRIDGE UNIVERSITY PRESS, 2013. -) SADD, M.H., ELASTICITY: THEORY, APPLICATIONS, AND NUMERICS, ELSEVIER, 2014.

	More Information
	RATIONAL MECHANICS HTTPS://DOCENTI.UNISA.IT/021400/HOME STRUCTURAL MECHANICS HTTPS://DOCENTI.UNISA.IT/004668/HOME SUBJECT DELIVERED IN ITALIAN. SUBJECT DELIVERED IN ITALIAN.

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Valentino Paolo BERARDI | RATIONAL MECHANICS AND STRUCTURAL MECHANICS