|SCIENTIFIC DISCIPLINARY SECTOR||ICAR/08|
|MODULES||This unit is a module of:|
The main objective of the course is to provide methods of understanding the behavior of structures made up of rods, beams, frames, trusses through quantitative and qualitative descriptions according to a methodological process already introduced in previous courses, but that is extended here to hyperstatic structures including new concepts concerning the dynamic and seismic behavior of constructions from the contemporary Architecture. The analysis methodologies are extended to the elastic-plastic behavior and to the limit strength up to the structural collapse according to an approach useful to the introduction to the method of limit states. The aforementioned objectives will be pursued through the identification and adoption of quantitative structural models that are the basis of structural design. The concept of model is intended as a rigorous conceptual tool of a mathematical nature capable of correlating causes with effects, forces applied with displacements and stresses. The Student will reach the awareness that the representative structural model of the building and its structure must be obtained through simplifying hypotheses in the mechanical description of the empirical behavior of structural elements and structural systems.
At the end of the course Students should be able to:
The course is given through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
This course is delivered in Italian. The final oral exam may be given in English. The students who would like to be examined in English must inform the teacher.
Introduction and Aims of the Course
Statically determinate beams, frames and trusses
The structural model of straight beam; generalized applied forces; supports and reactions; equilibrium equation of the in-plane loaded beam; static discussion on the efficiency of the supports; evaluation of the reaction forces;
Internal forces in the beam: axial, shearing forces and bending moment; the diagrams of the internal forces; local equation of equilibrium; plane frames and internal releases; static equation of the release; multiple connected structures; plane trusses: the method of joints and the method of sections (Ritter);
The virtual work theorem and it application to evaluate displacements and rotations in structures ; thermal effects on the deformation of beams; qualitative description of the deformed configuration of beams and frames from the diagram of the curvature; evaluation of displacements in plane trusses;
How to simplify the structural analysis taking into account the structural symmetry and the principle of superposition for linear systems.
Statically indeterminate structures
Evaluation of the grade of redundancy of frames and trusses; the force method to solve in-plane loaded statically indeterminate structures; the equations of Muller-Breslau; the effects of thermal variation and support settlement on the statics of redundant beams, frames and trusses; symmetric structures. The displacement method to solve statically indeterminate frames, Application to single and two-story frames under vertical and horizontal forces. The shear-type structural model.
Introduction to the dynamic analysis and seismic response of simple structures
Formulation of the equation of motion of the shear-type one story frame; Equations of motion and initial conditions; free vibrations and period of vibration of the structure; forced vibrations induced by horizontal sinusoidal oscillations of the foundation; Seismic action; response spectrum; evaluation of the maximum stresses and displacements through the response spectrum technique.
Introduction to the limit analysis of elasto-plastic structures
Elasto-plastic response of simple structures as the applied forces increase; Moment-curvature response of a perfectly elastic-plastic rectangular section; Incremental elasto-plastic analysis; Concept of plastic hinge for beams; Limit state and ultimate collapse load; direct determination of the collapse load; limit analysis of simple framed structures; Limit Analysis Theorems of elasto-plastic structures with Examples. The static theorem and the limit state method. Evaluation of the N-M interaction limit states.
Introduction to aided structural design
Presentation of the SAP 2023 aided structural design environment for the structural analysis of framed structures. Classroom development of structural models in SAP environment and determination of the structural response to environmental and anthropogenic actions.
L. Gambarotta, L. Nunziante, A. Tralli. Scienza delle Costruzioni, 3a Edizione, McGraw-Hill, 2011.
Office hours: Monday 16.30-18.00 at the teacher's office in DAD Tuesday 9.00-11.00 at the teacher's office in DICCA
LUIGI GAMBAROTTA (President)
STEFANO PODESTA' (President Substitute)
All class schedules are posted on the EasyAcademy portal.
The exam consists of a written and an oral test.
The written test is based on the resolution of problems similar to those carried out during the course. In such a test is proven the ability to solve two or three problems. In the oral exam is assessed the understanding of the concepts and reasoning skills acquired by the students and the knowledge of the theoretical part of the program.
The exams are given in Italian. The final oral exam may be given in English. The students who would like to be examined in English must inform the teacher.