19088 - Structures and Statics for Architecture

Learning outcomes

At the end of the course, the student has the fundamental concepts of structural mechanics. In particular, he/she is able to solve isostatic structures, truss structures and calculate the inertial characteristics of cross-sections. Some applications about arches, vaulted roofs are presented.

Course contents

The Course of Structures and Statics in Architecture (8 CFU) consists of a single module of 80 hours of lectures.

1. Recall of the thoery of vectors:

Sum of vectors; Scalar and vectorial product; versors; projection of a vector in one direction; Cartesian representation of vectors; components of a vector; momentum of a vector; resultant moment of a system of vectors; law of transposition of moments; resultant of a system of vectors; vector equivalent systems; definition of couple; plane vector systems; polygon of resultants; plane systems of parallel vectors: graphic constructions.

2. Kinematics of the rigid body:

a) kinematics of the material point and hypothesis of small displacements; b) constraints and degrees of freedom of a material point and systems of material points; c) stiffness constraint between two material points (assuming small displacements); d) definition of rigid body and degrees of freedom of the rigid body; e) kinematics of the rigid body in the field of small displacements: center of instantaneous rotation; f) plane rigid body: kinematic performance of constraints.

3. Static analysis of the rigid body: a) cardinal equations of statics; b) principle of virtual work for rigid bodies; c) plane rigid body: static performance of plane constraints.

4. Static-kinematic analysis of the beam: a) geometric definition of a one-dimensional solid; b) structural model and the physical reality: definition of the structural scheme; c) isostatic, hyperstatic and labile structures; d) the external actions applied to the structures; e) the case of the constrained flat beam (curvilinear or rectilinear axis); f) determination of the support reactions for a flat beam (restrained) using the cardinal equations of statics and the Principle of virtual work; g) characteristics of the internal stress for the beam; h) indefinite equilibrium equations for the flat beam (curvilinear and rectilinear axis); i) internal constraints in plane structures made up of beam systems; l) kinematic chains for labile structures and their properties; m) use of auxiliary equations for the determination of the constraint reactions in structures made up of several rigid bodies; n) determination of internal stress characteristics in isostatic structures formed by beam systems; o) curve of the resultants; p) determination of the constraint reactions of a plane isostatic structure by means of graphical considerations.

5. Static-kinematic analysis of plane reticular structures: a) definition of plane reticular structure; b) kinematic analysis of reticular structures; c) static analysis: node method and Ritter section method.

6. Geometry of Areas: a) definition of centroid and its properties; b) definition of first (static moment) and second order moments (moment of inertia, centrifugal moment, polar moment); c) radius of inertia d) Huygens theorem; e) principal axes of inertia; f) Mohr's circle g) Culmann's ellipse; f) polarity of inertia, conjugation relation, polar-antipolar, graphic constructions, g) central core: definition and its properties.

Readings/Bibliography

• L. Boscotrecase, A. Di Tommaso, Statica Applicata alle Costruzioni,Patron Editore.
• Lecture note.
• P. Casini, M. Vasta, Scienza delle costruzioni, Terza Edizione, CittàStudiEdizioni, 2016 (euro 37,00).
• E. Guagenti, F. Buccino, E. Garavaglia, G. Novati, Statica: Fondamenti di Meccanica Strutturale, McGraw-Hill.
• D.L. Schodek, Strutture, Patron Editore.

Teaching methods

The course is divided into lectures and exercises with the teacher. Additional guided exercises are carried out with the tutor.

Assessment methods

The exam consists of a written test and an oral test.

The written test consists of solving 3 exercises: the first exercise concerns the resolution of an isostatic structure with an internal constraint (weight 15/30), the second concerns the resolution of an exercise on the geometry of the areas (weight 8/30) and the third concerns the resolution of a reticular structure (weight 7/30). Duration 3 hours.

It is necessary to carry out exercises 1 and 2 correctly for minimum mark. In particular, it is necessary to carry out the moment diagram correctly and to identify the center of gravity. Evaluation goes from the minimum grade of 18/30, to the maximum of 30/30. Those who pass the written test can take the oral test. If a student is not satisfied with the mark obtained in the written test, he can do again the written test. Only the vote of the last essay is considered. The oral test consists of a question that concerns all the topics of the course. The evaluation of the oral test, if positive, can lead to an increase of 3/4 points in respect to the evaluation of the written test. The oral exam is usually scheduled about a week after the written exam. The written tests will be scheduled for June, July, September, January and February. The writing is valid until February of the current academic year. If the student has not taken the oral exam by that date, has to do again the written exam. As stated by the regulations, it is not possible to do the exam of Structures and Statics in Architecture without Mathematics.

Teaching tools

Teaching material: the teaching material presented in class (slides, notes, video of the lessons) will be made available to the student on the virtual website.unibo.it using the University credentials

Office hours

See the website of Luisa Molari