Structural Analysis

lgciv1023  2020-2021  Louvain-la-Neuve

Structural Analysis
Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h + 30.0 h
Saraiva Esteves Pacheco De Almeida João;

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
See "Content"

At the end of this learning unit, the student is able to :

1 Contribution of the course to the program objectives: AA 1.1, AA 1.2, et AA 1.3
At the end of this learning unit, the student is able to:
- Determine the degree of static indeterminacy of a structure and solve statically indeterminate structures with the flexibility method, considering additionally the particular cases of variations of temperature, elastic supports, and imposed displacements.
- Identify the number of degrees of freedom of statically indeterminate structures and solve them manually with the stiffness method.
- Draw the distribution of internal forces in frame structures with corresponding values, as well as the deformed configuration, of statically determinate and indeterminate structures.
- Program a structural analysis code for 2D truss and frame structures, and compare with results from educational / commercial structural analysis software.
- Understand the concepts and application of the finite element method.
- Determine influence lines for statically determinate and indeterminate structures.
  • Revision of strength of materials.
  • Statically determinate structures: computation of displacements with the unit dummy force method (Mohr’s integration tables) and by integration of differential equations.
  • Statically determinate and indeterminate structures: external / global / internal indeterminacy.
  • Calculation of degree of static indeterminacy: intuitive and systematic approaches.
  • Flexibility (or force) method: primary system, static unknown(s), general solution procedure, compatibility equation, calculation of internal forces, computation of displacements (Pasternak’s theorem).
  • Simplifications due to symmetry.
  • Statically indeterminate trusses.
  • Elastic supports: replacement method and adaptation method.
  • Thermal effects.
  • Imposed displacements and derivation of local stiffness matrix coefficients.
  • Stiffness (or displacement) method: degree of kinematic indeterminacy, free and restrained degrees of freedom, primary system, kinematic unknown(s), general solution procedure, equilibrium equation, calculation of internal forces.
  • Stiffness method versus Flexibility method.
  • Stiffness method (matrix form for computer implementation): global and local reference systems; beam and truss elements; disassembly and connectivity array; assembly, solution, and support reactions; properties of the stiffness matrix; condensation and beam with hinge element.
  • Finite element method: meshing, finite element, nodes, and types of finite elements; boundary conditions (kinematic and static); weak and strong formulations; Galerkin method, displacement and virtual displacement fields, interpolation functions; application to 2D beam element; general application examples.
  • Influence lines: statically determinate and indeterminate structures.
Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Lectures based on course slides and exercises solving with student participation. Group project.
Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Group project (15%) and written final exam (85%).
NOTE: These instructions take into account a “green” or "yellow" Covid scenario at UCLouvain. Modifications can be made in case of “orange” or “red” scenario, or restrictions in classroom capacities.
Other information
  • For the matrix version of the stiffness method, the programming language Python will be used.
  • The educational software of structural analysis “issd” ( is an advised complement and its use during the exercise sessions will help to the understanding of the course contents.
Online resources
  • Lecture slides (available on Moodle) and other files.
  • Slides (Moodle).
  • « Calculer une structure, de la théorie à l’exemple », P. Latteur, Editions L’Harmattan/Academia.
  • « Analyse des structures et milieux continus », Volume 4 : Structures en barres et poutres, Pierino Lestuzzi et Léopold Pflug, Presses polytechniques et universitaires romandes.
  • « Méthode des éléments finis », Volume 6 : Analyse des structures et milieux continus, François Frey et Jaroslav Jirousek, Presses polytechniques et universitaires romandes.
Faculty or entity
Force majeure
Evaluation methods
30-minute oral exam (on the entire course content), corresponding to 85% of the final course grade. The weight of the group project is kept (15%).

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Minor in Construction

Bachelor in Engineering : Architecture

Minor in Engineering Sciences: Construction (only available for reenrolment)

Specialization track in Construction