# Structures I

Civil Engineering

6 ECTS; 2º Ano, 2º Semestre, 30,0 T + 30,0 PL + 15,0 OT

Lecturer
- Carlos Jorge Trindade da Silva Rente

Prerequisites
Not applicable.

Objectives
A - Formulation and application of methods of analysis of statically indeterminate structures in linear elasticity. B - Awareness of the factors that contribute to the structural behavior in the context of structural design.

Program
1. General principles of equilibrium of elastic solids.
Review of static. Structures in static equilibrium. One body structures and several bodies structures.
2. Introduction to structural analysis.
Types of structures. Structural loads and actions. Structural problem. Displacements and deformations. State of tension. Relationship between stress and strain. Equilibrium equations. The principle of superposition.
3. Theorem of virtual work.
Virtual deformation. Principle of virtual work. Work of external forces. Internal strain energy. Determination of internal strain energy stored by axial force, shear force, bending moment and torsion. Theorem of virtual work. Determination of displacements in frame structures.
4. Structural analysis by the Force Method.
Static indeterminacy of truss and frame structures. Concept of elastic displacement compatibility. Description of the Force Method. Flexibility matrix and vector of independent terms for multiple loading patterns. Systematization of the Force Method . Influence of temperature variations, pretension, settlement of supports or elastic supports. Truss structures, frame structures and mixed structures. Simplifications of symmetry. Calculation of displacements in statically indeterminate structures.
5. Energy Methods.
Clapeyron's theorem. Theorems of Betti and Maxwell. Castigliano's theorem. Menabrea theorem. Application of Energy Theorems to calculate displacements and efforts.
6. Structural analysis by the Displacement Method.
Basic principles of the Displacement Method. Kinematic indeterminacy. Description of the method. Stiffness matrix and load vector. Equations of equilibrium of forces. Direct formulation and matrix formulation. Systematization of the application of the Displacement Method.
7. Moment Distrubution Method.
Non-sway structures and sway structures. Stiffness factor and bending moment transmission coefficient. Bending moment distribution coefficient . Initial moments. Resolution procedure for non-sway structures (direct process) and sway structures (indirect process).
8. Influence lines.
Concept and scope of influence lines for the determination of forces and displacements of frame and truss structures.

Evaluation Methodology
One final written exam during the regular assessment season and practical exercises proposed on class.

Bibliography
- McGuire, W. e Gallagher, R. e Ziemian, R. (2000). Matrix Structural Analysis. New York: John Wiley and Sons
- Hibbeler, R. (2006). Structural Analysis. Singapore: Prentice Hall
- Neville, A. e Ghali, A. (1997). Structural Analysis. A unified classical and matrix approach.. London: E&FN Spon

Method of interaction
Lectures on the fundamental aspects related to the main topics of the course. Practical resolution of exercises
oriented to promote critical skills and participation of students in the class topics.

Software used in class
Ftool - 2D Frame Analysis Tool