Analysis of Static and Dynamic Structures

Objectifs

The student will be expected to understand and be able to explain (main concepts):
- the distribution of internal forces in structures under static mechanical loads (continuous beams, trusses, frames, etc.) and that of the associated stress, strain and displacement fields,
- the dynamic behaviour of discrete and continuous structures,
- The student must be able to: - understand the basic principles of the design process.

The student must be able to
- formulate and justify relevant assumptions for the static resolution of a structure,
- determine the degree of hyperstaticity of a structure,
- The student must be able to: formulate and justify relevant hypotheses for the static resolution of a structure, determine the degree of hyperstaticity of a structure, solve a hyperstatic structure by implementing the method of forces,
- solve a hyperstatic structure using the displacement method,
- argue on the choice of the method of resolution,
- calculate the support reactions of the structure,
- draw diagrams of internal forces (bending moment, shear force, normal force),
- calculate the deformation of the structure (displacements, rotations),
- formulate and justify relevant hypotheses for the dynamic resolution of a structure,
- Put into equations a simple dynamic problem (discrete or continuous system),
- determine the solution of a simple dynamic problem, including dissipative and excited,
- determine the eigenmodes of a dynamic system by solving the associated equations,
- determine the eigenmodes of a dynamical system by implementing the Rayleigh-Ritz method,
- write a clear, fair and synthetic calculation note.

Competences INSA (GC) mobilized :
1.1: Master the mathematical concepts and the calculatory tools of the engineer
1.2 : Master the concepts of physics, mechanics, chemistry, thermodynamics for the engineer
1.3 : Implement rigorous scientific reasoning and develop the capacity for abstraction
4.3 : Manage a group: lead a team, argue and negotiate, communicate in crisis situations
4.6 : Be able to integrate socially in a group to progress together

INSA competences (GC) evaluated :
2.1 : Know, understand and apply the methods of calculation of structures and evaluate or predict their behaviour
2.2 : Know and master the formulation, characteristics and performances of the main materials used
2.4: Know and implement the main procedures, regulations and methods applicable to construction operations
3.1: Formulate and model problems, especially in complex systems
3.2: Solve, in an analytical or systemic way, a problem (decompose, prioritise, mobilise resources)

Pré-requis

- Notions of stresses, strains, displacements, rigid body movements.
- Support conditions.
- Fundamental principle of Statics.
- Integration and derivation of polynomial functions.
- Geometry (calculation of surfaces, centres of gravity, lengths, angles, etc.).
- Characterisation of sections.
- Internal forces: bending moment, normal force, shear force.
- Degree of hyperstaticity.
- Resolution of isostatic structures (calculation of support reactions, internal force diagrams, calculation of the deformation by integration of the moment-curvature relation).
- Fundamental Principle of Dynamics.
- Solving second member differential equations, with constant coefficients and variable second member.

Évaluation

L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…