• 092841 - THEORY OF STRUCTURES

The module aims at the thorough description of the mechanical response of elastic structures, such as thin walled beams, curved beams, plates. The structural theories are completely developed, with special focus on the applications in the field of structural engineering. 

The student should achieve understanding of the general framework of structural theories and of the structural behavior of thin walled beams, curved beams and plates. The student should gain knowledge of the governing equations for the above mentioned problems and of their solution.

The student should be able to apply knowledge and understanding to the solution of structural problems by means of analytical tools.

1. Saint Venant’s problem

            - Field of application and basic hypotheses

            - General solution based on the “stress approach”

            - Remarks on the effect of actual force distribution on the bases

2. Saint Venant’s case of torsion

            - Displacement approach, definition of warping, center of torsion

            - Analytical solution of special cases

            - Rectangular cross-section solved by means of Fourier expansion

            - Approximate solution of thin-walled open sections

            - Theoretical framework for not simply connected cross-sections

            - Thin-walled closed section in the occurrence of torsion and shear

3. Non-uniform torsion and theory of thin-walled beams

            - Problem definition

            - Evaluation of the warping rigidity

            - Physical interpretation for the I-shaped beam

            - Analysis of thin-walled sections with null warping on the mean line

            - The equation of non-uniform torsion and its solution

            - The theory of thin-walled open section: Wagner-Vlasov hypotheses

            - Kinematic model and generalized variables

            - Equilibrium equation obtained by means of the virtual work principle

            - Introduction of the linear elastic model

            - Formulation of the governing equations

4. Theory of curved beams

            - Theoretical framework and kinematic model

            - Computational examples

            - Application to arches

5. Theory of plates

            - Problem definition and basic hypotheses for the Mindlin-Reissner theory

            - Kinematic model and generalized variables

            - Equilibrium equation obtained by means of the virtual work principle

            - Introduction of the linear elastic model

            - Formulation of the governing equations: membrane behaviour vs. bending behaviour

            - Kirchhoff theory as a special case of Mindlin-Reissner

            - Solution of axisymmetric plates     

6. Computational aspects

            - Computer-based solution of the rectangular beams subject to torsion

            - Finite Element Method for thin-walled beams

            - Numerical solution of plates

No pre-requisites.

The examination is represented by a take-home test and an oral interrogation. The take-home test will be published on the website and sent by e-mail to the candidates one week before the examination date. The exercises must be solved by the students individually and the solution must be delivered on the examination date. By means of the take home test, the teacher evaluates the capability of the students to apply knowledge and understanding of the structural theories to the solution of non-trivial problems. The oral aims at the assessment of the student’s knowledge and understanding of the mathematical formulation for thin walled beams, curved beams and plates. The interrogation might be preceded by the written answers to some theoretical questions.