Structure theory

Learning outcomes

The course deals with the resolution methods of structural systems, with particular reference to the evaluation of stresses, deformations and displacements of isostatic and hyperstatic structures. The course includes the study of structures typically used in civil construction, such as multi-hyperstatic frame systems and flat and spatial reticular structures. During the course, some structures will be assigned that the student will have to solve both manually, applying the notions learned during the course attendance, and using a numerical calculation code. The execution of the assigned themes is a necessary condition to be able to take the oral exam.

Course contents

• The kinematic chains. The kinematic chain method. The theorems of kinematic chains. Kinematic analysis of structures with the use of kinematic chains. Examples.
  
• The reticular structures. The use of truss structures in civil engineering: recurring typologies. Kinematic analysis of lattice structures. Review of the solution methods of lattice structures: equilibrium method of nodes and Ritter's sections. Application of GSP to truss structures. Spatial lattice structures.
• Elastic line. The integration of the differential equation of the elastic line for beams in bending. The influence of shear strains and thermal actions. Resolution of hyperstatic systems using the elastic line. Mohr's theorem and corollaries. Applications.
• Frame structures. Symmetrical frames loaded symmetrically and antisymmetrically. The stitches closed. Applications of the GSP in the form of virtual forces (force method) and virtual displacements (displacement method). Stiffness coefficients of a member and a beam. Frames with fixed and movable nodes. Iterative resolution methods: Cross's method.
• The matrix method. Matrix of member and beam stiffnesses. Local and global reference system. Assembling the stiffness matrix of the structure. Nodal force vector. Calculation of nodal displacements.
  
• Applications. Applications of solution methods, in particular of the matrix method, to assigned structures. Resolution of the assigned structures with finite element calculation code and analysis of the results. Comparison of the obtained solutions.

Teaching methods:
Frontal lessons

Prerequisites

Construction Science, Rational and Static Mechanics

Reading/Bibliography

• AM Tarantino, Theory of Structures with applications, Pitagora publishing Bologna
• A. Luongo, A. Paolone, Structural Mechanics. Rigid systems with concentrated elasticity. Ambrosian publishing house.
• O. Belluzzi, Science of Construction, vol. 1,2. Zanichelli;
• P. Pozzati, Theory and Technique of Structures, vol. 2(1), UTET;
• L. Corradi dell'Acqua, Structural Mechanics, vol. 2, McGraw-Hill;
• A. Muttoni, The Art of Structures, Mendrisio Academic Press

Assessment methods

Oral exam with discussion of the exercises carried out