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Structural analysis and engineering


Programme (detailed contents):


Static Structure Analysis :

-       Static Determintation

-       Strain Energy based methods :

  • Castigliano and Menabrea’s Theorems,
  • Clapeyron’s Theorem,
  • Virtual Work Principle (Virtual Force).

-       Displacements methods:

  • Kinematics analysis of the structure
  • Constraint and Blocking  moments
  • Virtual Work Principle (Virtual Displacement).


Dynamic Structure Analysis:

-       Oscillations of a discrete system (one or more degree of freedom).

-       Oscillation of a continuous system (beam under traction/compression or bending moment).

-       Rayleigh-Ritz method.




Classes, tutorials and seminars, guided projects.



Main difficulties for students:

·         Bases of mechanical engineering and solid mechanics (elasticity) as well as Beams Theory must be totally understood. Student must master the resolution methods for statically determined structures.


At the end of this module, the student will have understood and be able to explain (main concepts):

-       Internal efforts distribution in a Civil Engineering structure, with associated strain and stress fields, under static loading.

-       Dynamic behaviour of discrete and continuous structures.

-       Basic constitutive elements of a calculus note.



The student will be able to:

-       Formulate appropriate hypotheses for a static resolution of a structure (beam theory).

-       Determine the hyperstaticity degree of a structure (static determination).

-       Solve a hyperstatic (statically indeterminate) structure using a Force Method and a Displacement Method, and justify the choice of  the resolution method.

-       Represent the internal efforts in the whole structure, quantify the support forces and the displacements.

-       Formulate the equations describing the movement of a structure under dynamic solicitation, and solve the system.

-       Propose an approximate solution using Rayleigh-Ritz method, under appropriate hypotheses.

-       Redact a calclulus note.

Needed prerequisite

- Stress, strain, displacement notions.

- Support conditions.

- Beams Theory, Solid Mechanics, Elasticity.

- Internal Efforts:  bending moment, normal force, shear force.

- Static determination.

- Equilibrium Equations.

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

Additional information

Beams Thoeory, Statically Undeterminate Structures, Strain Energy based methods, Displacements methods.