 # Structural analysis and engineering

## Presentation

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.

Organisation:

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.

## Objectives

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...