## Structural Mechanics

### Module aims

• To build on the work in structural mechanics in years 1 and 2 to cover more advanced material essential to understanding of structural behaviour particularly near the ultimate limit state where structural failure is to be considered and necessarily avoided; issues regarding geometric and material nonlinearities become key.

### Learning outcomes

On successfully completing this course unit, students will be able to:

•  Appreciate various different structural scenarios particularly of structural failure: material and geometric.
• Analyse single degree of freedom systems for structural stability.
• Analyse and design fundamental structural components susceptible to instability.
• Appreciate the difference between elastic and plastic responses of structures.
• Evaluate plastic collapse loads for statically indeterminate frames.
• Design framed structures using plastic analysis methods.

### Module syllabus

Structural Stability (MAW: 18 hours)

• Revision of potential energy principles, methods of analysis, geometric nonlinearity, concepts of instability and bifurcations. Classification of nonlinear buckling responses of perfect elastic systems.
• Analysis of imperfect elastic systems. Concept of imperfection sensitivity.
• Instabilities in struts and columns: Euler buckling; effective length concept. Ultimate strength of real columns: Perry-Robertson formulation and implementation in structural design codes.
• Instabilities in beams: Lateral-torsional buckling; restraint and loading conditions; structural design procedure.
• Instabilities in plates: critical buckling of rectangular plates under axial loading and shear. Outline of post-buckling behaviour and the “effective width” concept for ultimate strength.

Plasticity (LM: 12 hours)

• Revision of cross-section properties for plasticity and analysis of statically determinate structures.
• Moment capacity of composite sections.
• Upper and lower bound theorems of plastic analysis.
• Method of combining mechanisms.
• Plastic analysis of statically indeterminate frames.
 No. Topic Staff 01 Introduction to Stability Concepts. Revision of potential energy methods. MAW 02 Perfect elastic systems: continuous and discrete models. Concept of strain energy from direct and bending strains. Classification of post-buckling behaviour. MAW 03 Analysis of systems with imperfections. Imperfection sensitivities for different post-buckling responses. MAW 04 Struts and Columns: Perfect column and effective lengths. Approximate analytical methods. Real columns: behaviour and design. MAW 05 Lateral-torsional buckling of beams under bending: Behaviour and design. MAW 06 Introduction to plate buckling. Critical buckling and ultimate behaviour; design concepts. MAW 07 Revision of plastic cross-section properties and simple analysis. LM 08 Effects of combined axial and shear loading. LM 09 Upper and lower bound theorems of plasticity. LM 10 Plastic analysis of statically indeterminate structures. LM

### Pre-requisites

CI1-130, CI1-131, CI2-231

### Teaching methods

Each session is three hours long. The course has lectures and supporting tutorials. Staff and GTAs will be available to answer specific questions

### Assessments

Assessment information will be provided separately.