Vector calculus. Bound vectors; thrust line. Kinematics of infinitesimal rigid motion. Equilibrium of rigid bodies. Constraints: kinematic and static properties. Kinematic and static analysis of beam systems. Internal forces in beams: bending moment, shear force and axial force. Differential equations of equilibrium for a beam element. Plane trusses. Theorem of virtual work. Centroid, second moment of area, principal axes of inertia, beam core.
- L. Boscotrecase, A. Di Tommaso, "La statica applicata alle costruzioni", Patron, Bologna.
- A. Bigoni, A. Di Tommaso, M, Gei, F. Laudiero, D. Zaccaria, "Geometria delle masse", Progetto Leonardo, Bologna.
As a guide for the exercitations the fallowing books can be used:
- E. Viola, "Esercitazioni di Scienza delle costruzioni / 1 Strutture isostatiche e geometria delle masse", Pitagora Ed., Bologna.
- M. Paradiso, G. Tempesta, "Problemi di statica delle costruzioni", Cedam, Padova.
An alternative book or a useful reading may be:
- E. Guagenti, F. Buccino, E. Garavaglia, G. Novati, "Statica - Fondamenti di meccanica strutturale", McGraw-Hill, Milano.
Learning Objectives - Last names E-M
The course is an introduction to structural design methods and problems.
The course, although designed to be useful to successive teachings, aims at forming the cultural background that provides a basis or opportunity for originality in developing and/or applying ideas, rather than at providing notions directly usable for the resolution of standardized problems; this is expected by second cycle higher education degree for the training of a professional Architect for A section of Ordine degli Architetti, Pianificatori, Paesaggisti e Conservatori (DPR 328-2001).
By the end of the course the student will be able to:
• define a model of a structure
• analyze non statically indeterminate structures
• justify their choice, discuss the method and interpret the results of the analysis
• conceive simple structures and systems
The course prepares students for Scienza delle Costruzioni courses and Progettazione strutturale labs. For this reason, some of the topics are not directly applicable, but are necessary for the further development of the structural design ability.
Prerequisites - Last names E-M
The course is designed for students who have a good knowledge of algebra, linear algebra, geometry, elementary physics and trigonometry; this knowledge is essential.
Registration for the examination is only open to students that have passed the exam of Matematica I
Teaching Methods - Last names E-M
Frontal in-door lessons according the time-table, alternating theoretical lessons and exercises. The attendance to lessons is not compulsory. The achievements of the objectives is evaluated via final exam.
In order to achieve the expected objectives, students are strongly recommended to: attend regularly and participate actively in the lessons; study individually during the semester; meet the teacher for further clarifications when necessary, both during office hours and during/after the lessons; attend the in-class tests.
Further information - Last names E-M
Every topic listed under “Content” is important; for this reason the grading in different areas cannot be summed. The evaluation is based on the acquiring of the following abilities that are reported in increasing order, from the minimum to the maximum grade:
- correctly use the acquired methods for the analysis;
- use the acquired methods in a critical way, opportunely interpret structural problems, making the best choice both for the analysis and for the design of a structure;
- justify properly and effectively the choices made and the methods employed.
Type of Assessment - Last names E-M
The exam consists of a written test and, after passing that, a following oral examination.
Details will be given during the lessons.
Course program - Last names E-M
First part (approximately 4 weeks)
Vector calculus. Bound vectors: moment of force, resultant, equivalent force systems, Varignon theorem. Funicular polygon and the equilibrium of suspended systems; thrust line.
Kinematics of infinitesimal rigid motion. Degrees of freedom and constrains; rigid body. Kinematic properties of constraints. Kinematic analysis of beam systems.
Second part (about five weeks):
Newton laws. Equilibrium of rigid bodies. Static properties of constraints. Static-kinematic duality. Static analysis of beam systems. Internal forces in beams: bending moment, shear force and axial force. Differential equations of equilibrium for a beam element. Plane trusses.
Third part (about three weeks)
Theorem of virtual work.
Centroid, area and mass moments of inertia, principal axes of inertia, beam core.