Structures 3

Module aims

This module covers two main topics: idealized thin-walled structures and plate theory. The structural principles developed in the first year are applied to thin-walled structures representative of parts of airframes. These structures deform under transverse loads and are prone to instability under compressive or shear loading and students will learn how to analyse the effect of such loads.

Learning outcomes

On successfully completing this module, you should be able to:

1. Demonstrate understanding of methods for basic structural analysis for airframes through idealization of the structure.

2. Evaluate the shear stress and shear strain distribution in open and closed thin-walled sections.

3. Describe the modification of the stress distribution due to the presence of booms and to develop the beam/pure shear panel idealisation.

4. Extend the work done on a single cell tube to the case of a multi-cell tube loaded by transverse shear forces and calculate the influence of taper.

5. Describe the fundamentals of plate theory and evaluate deflections in thin plates under transverse loads using Navier’s method and Rayleigh-Ritz energy method.

6. Apply the Rayleigh-Ritz method to study the buckling of flat plates under a compressive load and to identify the shear buckling in plates and their interaction. 

7. Differentiate between local and global buckling in rectangular tubes.

Module syllabus

- Open thin-walled tube under torsion: stiffness, strains and the membrane analogy.
- Single cell tube loaded by shear Forces: stress distribution and twist. Shear centre.
- Boom/shear panel idealisations: simplified modelling of assemblies of skin, stiffeners and spars.
- Deflection of a thin-walled tube: due to bending shear and torsion.  Warping of the cross section.
- Multi-Cell tube:  stress distribution and twist due to transverse shear forces. Influence of taper.
- Frame in fuselage:  stress distribution in frame and fuselage under a concentrated load. 
- Plate bending: small deflection of thin plates. Moment/curvature relationship, stress distribution, stress resultants.
- Rayleigh-Ritz method: The use of energy methods to obtain an approximate solution.
- Plate Buckling:  Influence of compressive stresses and shear stresses.  Post-buckling behaviour.
- Stiffened panels: global and local buckling modes. Use of data sheets for interaction of plate assemblies.
- Post-buckling of plates, buckling of cylinders, Brazier effect.

Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological.  The content is presented via a combination of slides, whiteboard and visualizer.

Learning will be reinforced through tutorial question sheets and laboratory exercises, featuring analytical, computational and experimental tasks representative of those carried out by practising engineers. 


This module presents opportunities both for formative and summative assessment.  

You will be formatively assessed through a number of progress tests and tutorial sessions. 

Additional opportunities are provided for you to self-assess your learning via tutorial problem sheets. 

Summative Assessment takes the form of a written closed-book exam at the end of the module as well as practical laboratory assessments and one written laboratory report.

Assessment type Assessment description Weighting Pass mark
Examination Closed-book written examination  80% 40%
Practical Laboratory assessment 20% 40%

You will receive feedback both during the laboratory sessions and following the coursework submission.

You will receive feedback on examinations in the form of an examination feedback report on the performance of the entire cohort.

You will receive feedback on your performance whilst undertaking tutorial exercises, during which you will also receive instruction on the correct solution to tutorial problems.

Further individual feedback will be available to you on request via this module’s online feedback forum, through staff office hours and discussions with tutors.


Reading list

Module leaders

Professor Paul Robinson