﻿ Theory of Structures - Construção e ReabilitaçãoInstituto Politécnico de Tomar

# Bachelor's Degree in Construção e Reabilitação

## Theory of Structures

Publication in the Diário da República: Despacho nº 9398/2015 - 18/08/2015

5 ECTS; 2º Ano, 2º Semestre, 30,0 T + 30,0 PL

Lecturer
- Carlos Jorge Trindade da Silva Rente

Prerequisites
Not applicable

Objectives
With this course students should be able to understand, model and calculate hyperstatic reticulated structures, namely:
A. Understand the fundamental principles of the static behaviour of elastic linear reticulated structures.
B. Develop calculation models adapted to common situations found in structural systems.
C. Analyse and solve hyperstatic structures based on stress, displacement and Cross methods.
D. Use Energy Theorems as an expeditious form of structural calculation.
E. Understand and use the influence line theory to calculate the components of support reactions, stresses and displacements for structures
F. Use 2D computational programs to calculate planar reticulated structures as a support tool for analytical verification of results and awareness raising to the factors influencing their structural behaviour.

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
A written exam in the end-of-term assessment period.

Bibliography
- Ziemian, R. e Gallager, R. e McGuire, W. (2000). Matrix Structural Analysis. New York: John Wiley and Sons
- Hibbeler, R. (2006). Structural Analysis. Singapore: Prentice Hall
- Ghali, A. e Neville, A. (1997). Structural Analisys. A unified classical and matrix approach. London: E&FN Spon
- Martha, L. (2010). Análise de Estruturas - Conceitos e Métodos Básicos. Rio de Janeiro: Campus

Teaching Method
Theoretical presentation of the key aspects of the contents of the course. Resolution of practical exercises that develop reasoning skills.

Software used in class
FTOOL - 2D Frame Analysis Tool