# 72768 - Structural Engineering M (L-Z)

## Learning outcomes

The course aims at providing the design techniques for the main structural typologies (frames, plates, shells) and the expertise for the critic examination of the actual technical codes.

Real examples and applications teach the right way to face the structural design.

## Course contents

A) REQUIREMENTS/PRIOR KNOWLEDGE

A prior knowledge and understanding of key concept as stiffness/flexibility and strength, section forces, stress, strain, constitutive model of a material. Futher, he is able to solve by hand statically determinated and redundant simple structural and knows the concepts for the axial-flexural and shear verification with regards to the Ultimate Limit States method (approach, loading combinations and properly checks). In addition, students should be able to manipulate structural resolution based on the principle of virtual works and linear effects superimposition in order to attend with profit this course. All these knowledge are, tipically, achieved in the course of Scienza delle Cotruzioni T e Fondamenti di Tecnica delle Costruzioni T. Fluent spoken and written Italian is a necessary pre-requisite: all lectures, presentations and all study material will be in Italian.

B) COURSE CONTENTS

STRUCTURAL SYSTEMS

Difference between construction and structure, main structural typologies, structural arrangement of RC and steel frames,role and positioning of bracing systems and shear walls (introduction).

FRAMED SYSTEMS

Rigid connection, semi-rigid connection, hinge connection. Equilibrium method. Classical stiffness matrix (direct method calculation). Simplified method. Analytical description of a beam on elastic soil: exact solution and applicative cases (unlimited and semi-unlimited beams).

DUCTILITY OF RC STRUCTURES

Ductilityof construction materials. Bending moment-curvature diagrams and their bi- and tri-linear simplifications for RC cross sections under flexure. Ductility of cross-section under flexure. Plastic hinges and allowable plastic rotation for RC structural elements under flexure. Effect of axial force on ductility. Examples. Structural ductility.

PLATES UNDER FLEXURE

Kirchhoff's theory for plate under flexure: Lagrange's equation and boundary conditions, Kirchhoff's shear. Simply supported and clamped plates. RC plates: design criteria, construction details. Flat plates and slabs: simplified methods of evaluation of bending moments,design criteria and construction details; punching shear, examples.

SHELL STRUCTURES

Plane structures with in-plane load. Slabs of revolution. Membrane of revolution. Examples for slabs and membranes. Cylindrical R.C. tank. Prestressed tanks. Spherical membrane. Semi-spherical membrane. Conical membrane. Displacements and deformations of membranes. Foundation hoop. Spheric dome: Geckeler solution.

PRESTRESSED R.C. ELEMENTS

Basic theory. Prestress techniques. Stress and strain calculation for statically determined structures. Tension for sliding and adherent cables. Bending for sliding and adherent cables. Post-tension techniques. Technical codes verifications. Structural details and local verifications. Tension loss. Examples.

INTRODUCTION TO FOUNDATION SYSTEMS

Introduction to different typologies of foundation systems. Code prescriptions for Ultimate Limit States design of foundation elements. Design of phlint elements for the possible external loading conditions. Evaluation of the bearing capacity for pole foundations. Definition of the forces on a pole in case of phlint supported by multi poles system.

Refer to teacher's note for most of the considered arguments.

Ang - Tang, "Probability concepts in engineering palnning and design. Vol. 1: Basic principles", John Wiley, New York, 1975 (per l'affidabilità strutturale).

Ang - Tang, "Probability concepts in engineering palnning and design. Vol. 2: Decision, risk and reliability", John Wiley, New York, 1984 (per l'affidabilità strutturale).

Pozzati, P., Ceccoli, C., "Teoria e Tecnica delle Strutture", UTET, Torino, 1972 (beams).

Belluzzi, O., "Scienza delle Costruzioni" (shells).

Walther, R., Miehlbradt, M., "Progettare in calcestruzzo armato", Hoepli editore, Milano, 1990 (reinforced concrete).

Cestelli-Guidi, C., "Cemento armato precompresso", settima edizione,  Hoepli editore, Milano, 1987 (prestressed reinforced concrete).

## Teaching methods

In regular classes, problems concerning the modelling and the design of reinforced concrete structures are discussed. Finally, details of nodes, steel positioning, etc. will be shown and discussed. Guidelines for different structural problems reported in national and international codes will be considered. Some classes will be devoted to show designs of actual realizations concerning the subjects of regular classes.

## Assessment methods

A final verification is prescribed for this exam. During the oral will be verified the personal preparation of the student and his knowledge on the main theoretical aspects of the course. The oral tests are composed of two questions, and the assessment procedure will clarify if the student acquired a sufficient number of the predicted learning outcomes. They aim to establish the knowledge and skills achieved by the student as well as to evaluate its technical language with reference to the topics discussed. Passing of the exam will be granted to students who demonstrate mastery and operational capacity in relation to the key-concepts discussed in the course showing, in particular, that the student learned the basic theoretical concepts and is able to argue in a comprehensive manner and in autonomous way the various steps leading to the definition of the main results. The higher scores will be awarded to students who demonstrate to understand with breadth of content and appropriate language, the subjects taught and, further, will show to be able to apply all the teaching content in operating autonomy even for the most complex cases. Failure to pass the exam will be due instead to insufficient knowledge of the key-concepts (such as the static equilibrium rules), failure to properly master technical language, or it can be due to low operational autonomy shown in the performance of the tests.

## Teaching tools

Blackboard, slide presentations showed by videoprojector, further notes of the teacher, documentation of shell elements in flexure and a presentation on the ductility as integration of the class notes uploaded on the AMS Campus web-site.

## Office hours

See the website of Claudio Mazzotti