# Detailed module information

Module information on this degree can be found below, separated by year of study.

The module information below applies for the current academic year. The academic year runs from August to July; the 'current year' switches over at the end of July.

Students select optional courses subject to rules specified in the Mechanical Engineering Student Handbook,  for example at most three Design and Business courses. Please note that numbers are limited on some optional courses and selection criteria will apply.

## Stress Analysis 3

### Module aims

The aim of the course is to reinforce the student's knowledge of stress analysis, to extend this knowledge to more advanced theories and techniques and to apply these to practical problems. Most of these will be developments of methods which have been previously acquired but applied to more sophisticated problems. New areas of thermal stresses, plastic deformation and residual stresses will be treated and a new technique of analysis using energy methods will also be introduced and developed.

ECTS units:    6
Contributing to Course Elements: 6 to ME3-LCTVS or ME4-LCTVS

### Learning outcomes

On successfully completing this module, students will be able to:

• Recall the basic laws which must be applied and conditions identified to solve elasticity problems
• Explain the principles and application of energy methods
• Solve problems concerning membrane, bending and thermally induced stresses in axi-symmetric, elastic monobloc and compound thick walled cylinders, laterally loaded plates and thin walled shells, arising from temperature difference, rotation and gravity
• Solve simple problems involving non-work hardening, plastic behaviour of monobloc cylinders and the generation of residual stresses
• Use energy methods to solve problems concerning, e.g. statically indeterminate pin jointed structures, and deflections of curved beams, under load

### Module syllabus

• Thick-walled cylinder theory (including the effects of radial temperature distribution and body forces): revision of Lame equations and boundary conditions for monobloc cylinders; extension of Lame equations to include thermal effects and body forces (thin rotating discs); stress distributions, examples; compound cylinders
• Compound Cylinders: Deficiencies of monobloc cylinders, interference stresses, modified stress distribution under internal pressure; applications and examples
• Yielding of thick-walled cylinders: first yield, full yield, partial yield for non work hardening materials; limit loads, residual stresses, autofrettage; examples
• Bending theory of axi-symmetric plates: review of bending of beams; extension to axi-symmetric plates; boundary conditions, applications and examples including built in and simply supported solid plates with uniform load, central point load and annular loads, plates with central holes. Thermal stresses
• Theory of shells: membrane theory of axi-symmetric shells; derivation of relationships between applied loads, stresses and geometry of shells; examples including internal pressure, hydrostatic loading and self weight. Axi-symmetric bending of this walled cylinders; examples
• Energy methods: elastic strain energy for multi-axial loading systems; Castigliano's theorem; applications to statically indeterminate and deflections in pin jointed structures; straight and curved beams and other examples.

### Pre-requisites

ME1-hSAN; ME2-hSAN or equivalent.

### Teaching methods

• Duration: Autumn and Spring terms (21 weeks)
• Lecture: 1 x 1hr per week
• Tutorials: 1 x 1hr per week

 Summary of student timetabled hours Autumn Spring Summer Lectures 10 11 Tutorials 10 11 Total 26 (assuming 5 tutorials attended) Expected private study time 3-4 hrs per week, plus exam revision

### Assessments

 Written examinations: Date (approx.) Max. mark Pass mark Stress Analysis (3h) A list of Supplementary Formulae are provided. This is a CLOSED BOOK Examination. April/ May 200 n/a