Analysis of Structures IIA


This course complements the fundamental training of civil engineers in the field of plates, shells and thin-walled bars. Relevant aspects concerning safety, stability and computational modeling are treated. The "engineering judgment" of students is enhanced by encouraging the interpretation of the modeling results.

General characterization





Responsible teacher

Rodrigo de Moura Gonçalves


Weekly - 5

Total - 70

Teaching language



Not applicable.


Subject collection (presentations, tables, exercises)
A Ugural, “Stresses in plates and shells”, McGraw-Hill, 1999.
A Reis e D Camotim, “Estabilidade Estrutural”, McGraw-Hill, 2001.
W Nash, “Resistência de Materiais” (Colecção Shaum’s outlines), McGraw-Hill, 2001.

Teaching method

Theoretical-practical classes. Critical thinking, reflection and interpretation of the results are stimulated. Several group exercises are executed.

Evaluation method

There is no "frequency" evaluation.

Theoretical-practical component (CTP): exam or 2 tests, with CTP >= 8,0 points (minimum grade)

Laboratory/project component (CLP): seven assignments, totalling 6 points, CLP = T1 + T2 + T3 + T4 + T5 + T6 + T7

Final grade: NF = 0,7CTP + CLP

Students pass the course if NF>=9.5 and CTP>=8.0 points. If NF>16 the student is invited to an oral exam to defend the grade. If he/she does not undergo the oral exam then NF=16.

Subject matter

1. Reviews. Fundamental concepts. Review of Continuum Mechanics. The Principle of stationary potential energy. Review of Kirchhoff plate theory.

2. Introduction to the Theory of Stability. Applications. Linear Stability Analysis (LSA). Discrete and continuous systems.

3. The Finite Difference (FDM) and Rayleigh-Ritz (RRM) methods in structural analysis. Application to the linear analysis of bars and Kirchhoff plates. Application to the LSA of bars. 

4. Thin plates subjected to in-plane loads. Linear analysis and LSA. Application of the FDM and RRM. Post-buckling behaviour. Effective length concept. Analysis of the rules in EC3-1-5.

5. Thin-walled bars. Non-uniform torsion. Deformable cross-section: the Generalised Beam Theory (GBT). Linear analysis and LSA. Local, distortional and flexural-torsional buckling. Reference to the determination of the resistance to distortional buckling.

6. Thin shells. Membrane theory. Shells of revolution under axissymmetric deformation. Hyperbolic paraboloids. DMV linear theory for circular cylindrical shells under axissymetric loading. LSA  for circular cylindrical shells. Extensional and inextensional deformation. Form-finding. Case studies.


Programs where the course is taught: