Advanced Mechanics and Strength of Materials

Module summary

Module code: MECH1084
Level: 6
Credits: 15
School: Engineering and Science
Department: Engineering
Module Coordinator(s): Mark Bingley / Michael Okereke



To provide the student with the tools for the analysis of complex loading situations and the assessment of components for the prevention of ductile, brittle and fatigue fracture. The student will develop the ability to recognise the circumstances in which the various failure modes may operate. It will also enhance their understanding of the mechanical properties of the various classes of material.

Learning outcomes

On successful completion of this module a student will be able to:
1 Analyse complex loading situations and relate these to material failure criteria
2 Appraise real components and structures subject to mechanical loading and select the best material for these components.
3 Demonstrate the application of advanced engineering mechanics principles in the analysis of the load-bearing capacity of engineering structures.
4 Investigate experimentally engineering components, structures and materials and relate the experimental procedures and analysis to the wider engineering context

Indicative content


Torsional loading
Torsional deformation; Torsional shear stress;
stress concentrations in torsionally-loaded members;
Statically indeterminate torsion members; Angle of twist;
Torsion of non-circular sections; Torsion of thin-walled tubes (shear flow)
Gears in torsion assembly; Power transmission.
Advanced mechanics of beams
Flexural stresses in beams of two materials (i.e. composite beams)
Bending due to eccentric axial loads; Unsymmetric Bending
Horizontal shear forces and stresses in beams due to non-uniform bending
Shear Flow in built-up (fabricated) beams; Statically Indeterminate Beams
Analysis of Combined and/or complex Loaded structures
Revision of Principal Stresses and Strains; Revision of Mohr’s Circles construction;
Analysis of combined axial and flexural loads;
Analysis of combined axial and Torsional loads;
Buckling collapse of structures
Buckling of pin-ended columns; Slenderness Ratio; Euler’s buckling load;
Elastic collapse of columns; Effective lengths; Buckling modes
Effect of end conditions on buckling collapse; Eccentrically loaded columns.
Energy Methods
Principles of strain energy; Principles of Virtual work;
Impact loading; Castigliano’s theorem.
Introduction to Contact Mechanics
Motions and forces at a point of contact;
Normal contact of elastic (Hertz theory) and inelastic solids
Rolling contact of elastic and inelastic solids
Theories of Failure
Ductile Materials: Max Shear Stress (Tresca), Max Distortional Energy (von Mises); Von Mises equivalent stress formulation;
Brittle Materials: Max Normal Stress theory;
Brief introduction of computational solid mechanics
Introduction to finite element methods; Computational description of a solid mechanics problems
Numerical solution of structures under complex loading
Validation of numerical results using analytical/experimental methods.


Fracture Mechanics
Stress Intensity approach
Stress Intensity Factor Solutions (Simple and Complex crack configurations)
Cracks near stress raisers
Crack tip plasticity
Fracture Toughness Testing
Impact Toughness tests
Fatigue fracture surfaces
S-N Curves and fatigue strength
Effect of Mean Stress and Variable amplitude loading (independently and in combination)
Rainflow analysis
Strain controlled fatigue
Effect of notches
Short Fibre Composites
Strength of composites
Non-axial loading
Toughness of composites
Effect of pressure on Mechanical properties
Viscoelastic behaviour

Teaching and learning activity

The material will be delivered through a mixture of lectures, tutorials, self-learning activities - self-study guides and research essays, mini research projects. Case studies, discussion forums, laboratories and tutorials will additionally support the lectures.


Exam - 70%
LO - 2-4.
Pass mark - 40%
2 hours. Unseen closed book exam.

Logbook - 30%
LO - 1-4.
Pass mark - 40%
1500 words.
Portfolio of Lab reports.

Nature of FORMATIVE assessment supporting student learning:
Observations, Questioning, Discussion, Constructive Quizzes, Practice Lab Report, Practice Exam Paper.