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.
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.
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.
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.
- For the matrix version of the stiffness method, the programming language Python will be used.
- The educational software of structural analysis “issd” (www.issd.be) is an advised complement and its use during the exercise sessions will help to the understanding of the course contents.
- Lecture slides (available on Moodle) and other files.
« 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.