Unit STRUCTURAL PLASTICITY AND STABILITY
- Course
- Civil engineering
- Study-unit Code
- A004665
- Curriculum
- Structural engineering
- Teacher
- Federico Cluni
- Teachers
-
- Federico Cluni
- Vittorio Gusella (Codocenza)
- Hours
- 60 ore - Federico Cluni
- 12 ore (Codocenza) - Vittorio Gusella
- CFU
- 9
- Course Regulation
- Coorte 2024
- Offered
- 2024/25
- Learning activities
- Caratterizzante
- Area
- Ingegneria civile
- Academic discipline
- ICAR/08
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Plasticity. Yield criteria. Postulates of plasticity. Limit analysis with applications to frame structures. Plane problems. Structural stability
- Reference texts
- * English books
- R. Hill, " The mathematical Theory of Plasticity ", Oxford Classic Texts
- W.F. Chen, D.J. Han, “Plasticity for structural engineers”, Springer
* Italian books
- R. Baldacci, G. Ceradini, E. Giangreco, "Plasticità", Cisia
- R. Baldacci, G. Ceradini, E. Giangreco, "Dinamica e stabilità", Italsider - Educational objectives
- The course presents the base elements and the conceptual and analytical tools for the study of the civil engineering structures in the elasto-plastic range and the evaluation of the safety of structures with regards to instability.
Main knowledge acquired will be:
- modeling of the behavior of materials in elasto-plastic range;
- use and limits of the main yield criteria;
- limit analysis, both with upper- and lower-bound approaches;
- modeling of plane problems;
- stability of structural elements and structures.
The main competence (i.e. the ability to apply the acquired knowledge) will be:
- estimation of critical load of structural elements;
- estimation of the collapse load and the collapse mechanism of structures;
- assessment of the strains/stresses in plane problems;
- estimation of instability load. - Prerequisites
- The Course is in the first year.
The topics of the Course require the ability to solve ordinary and partial differential equations and simple integrals.
Moreover it is required the of structural mechanics and strength of materials (mechanics of solids materials, stress analysis, strain analysis, linear elasticity, mechanics of beam).
Knowledge of these techniques represents a mandatory prerequisite for students planning to follow the course with profit. - Teaching methods
- The course is organized as follows:
- Face-to-face lectures on all subjects of the course.
The lecture notes will be available at: https://www.unistudium.unipg.it/unistudium/ - Other information
- -
- Learning verification modality
- The exam consists of an oral test consisting on an interview about half an hour long, aiming to ascertain the knowledge level and the understanding capability acquired by the student on theoretical and methodological contents as indicated on the program (plastic analysis, limit analysis, plane problems, instability).
The oral exam will also test the student communication skills and his autonomy in the organization and exposure of the theoretical topics and case studies.
For information on support services for students with disability and/or specific learning disorders visit the page http://www.unipg.it/disabilita-e-dsa - Extended program
- Plasticity. Yelding Function. Description of the Yelding Function. Deviatoric stresses. Yeld criteria: Rankine, Grashof, Tresca, Huber-Von Mises-Hencky, Hill, Coulomb, Drucker-Prager. Constitutive relations. Elasto-plastic material. Levy-Mises equations. Prandtl-Reuss equations. Stable material (Drucker). Postulates of plasticity. Plastic potential, convexity, normality. Limit analysis. Lower bound theorem. Upper bound theorem. Elasto-plastic internal forces. Plastic hinge. Application of limit analysis to frame structures. Plane problems. Strain plane problem. Stress plane problem. Generalized plane problem. Mechanics of cable. Mechanics of membrane and plate. Structural stability. Influence of shear deformability. Influence of imperfections. Elasto-plastic analysis of stability.