Title:  Mechanical Materials (3D) 
Long Title:  Mechanical Materials (3D) 
Field of Study: 
Mechanical Engineering

Valid From: 
Semester 1  2016/17 ( September 2016 ) 
Module Coordinator: 
MATTHEW COTTERELL 
Module Author: 
Sean F OLeary 
Module Description: 
This module will cover three dimensional mechanical linear elastic and nonlinear elastic/plastic analysis and design, from first principles, of rotating and statically loaded structures including curved bars, thick pressure vessels, solid and hollow discs, beams, shafts and portal frameworks. Finite element modelling of 3D stess analysis application is introduced by hands on computer aided design laboratory. 
Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Determine the fundamental governing/transformation relations of three dimensional strength of materials analysis. 
LO2 
Analyse 3D mechanical linear elastic structures for critical elastic design parameters. 
LO3 
Analyse nonlinear elastic/plastic mechanical structures for critical plastic design parameters. 
LO4 
Apply and interpret computer based finite element modelling of stress/ strain displacement application. 
LO5 
Review, undertake analysis of and report on strength of materials applications. 
Prerequisite learning 
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s). 
Mechanical Materials (2D) 
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. 
No incompatible modules listed 
Corequisite Modules

No Corequisite modules listed 
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.

No requirements listed 
Module Content & Assessment
Indicative Content 
Introduction to NonLinear/Plastic Material Behaviour
Rigid/plastic, rigid/elastic, elastic/plastic material behaviour. Tensile testing. Relationships between nominal/true stress/strain. Power law plasticity behaviour. Experimental determination of work hardening and strength coefficients. Considere’s method. Elastic/plastic work done. Strain energy stored.

Three Dimensional Stress/Strain Analysis
Introduction to the theory of Elasticity: equations of equilibrium in 3D. The stress tensor. Variation of stress within a body. Two and three dimensional Stress at a point. Principal stresses in three dimensions. Matrix rotation method. Matrices solution techniques for magnitudes and direction cosines of principal stresses. Cofactors of determinant method. Stresses on an oblique plane in terms of principal Stresses. Octahedral shearing stress. Mohr’s Circle of 3D stress. Stressstrain relations. Equation of compatibility in 3D. State of strain at a point.

Theories of Failure and Fracture
Function of theories. Maximum principal stress/maximum shear stress/maximum principal strain/total and shear strain energy theories of elastic failure. Comparison of the yielding theories. Graphical representations. 3D envelopes of failure. Loadline solutions. Theories of fracture.

Fatigue Strength Evaluation
Failure criteria for fatigue. Soderberg, Gerber, modified Goodman, SAE criteria. Combined states of stress. Maximum and minimum stress tensor fatigue life evaluation. Composite strength. Impact performance and fatigue strengths of metals and composites.

Curved Bar Analysis
Simple bending theory for bars of small initial curvature. Nonlinear stress evaluation in bars of large initial curvature of rectangular, trapezoidal and circular crosssections. Comparison with photoelastic determination of curved bar stresses. Application of Castigliano’s Theorem to the solution of elastic deflections and statically indeterminate members and structures. Concepts of strain energy due to thrust, shear force and bending moment. Evaluation of shear force correction factors. Use of dummy loads. Calculation of deflections/redundant forced in curved bars / comparison with experimentally determined deflections.

ThickWalled Vessel Analysis
Development of Lamé theory. Variation of circumferential, radial and longitudinal stresses in thickwalled cylinders. Principal/maximum shear stress in 3D. Change of dimensions and volume. Comparison of thin/thick vessel theory. Limitations of applicability. Lamé line graphical treatment. Application of boundary condition approach to solution of Lamé constants. Compound cylinders. Shrinkage/interference allowances. Force fit. Hub on solid shaft. Uniform heating of compound cylinders of different materials. Application of failure/fatigue theories to pressurised vessels.

Rotating Structures
Development of theory for variation of stresses in rotating solid and hollow discs. Determination of location and magnitude of maximum design stresses for thinwalled plane stress rotating structures. Application of plane stress/plane strain transformations to develop theory for variation of stresses in rotating thick cylinders and solid shafts. Rotating disc of uniform strength. Combined rotational and thermal stresses in uniform discs and thick cylinders including linear thermal variation and steady heat flow applications.

Plastic Design Theory
Assumptions in plastic theory, plastic bending of beams, elastic design moment, partially plastic moment, fully plastic moment, plastic hinge, shape factor. Symmetrical and unsymmetrical sections. Deflection of partially plastic beams. Residual stresses. Collapse mechanisms, collapse load and load factors. Plastic torsion, elastic design torque, partially plastic torque, fully plastic torque in solid and hollow shafts. Angle of twist of shapes in plastic torsion. Casehardened shafts. Residual stresses in plastic torsion. Autofrettage of thick cylinders. Tresca criterion. Plastic penetration of pressurised cylinders. Development of theory analysing variation of circumferential, radial and longitudinal stresses in plastic and elastic regions under autofrettage pressure. Residual and working stress distributions. Plastic theory for frames. Theorem of independent mechanisms. Determination of load factor through combination of mechanisms.

Finite Element Analysis Laboratory
Introduction to Finite Element Analysis. Hands On Computer Laboratory Finite Element Stress/Strain/Displacement Analysis Application. Interpretation of Results.

Assessment Breakdown  % 
Course Work  30.00% 
End of Module Formal Examination  70.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Short Answer Questions 
3D Stress Analysis Fundamentals 
1,2,5 
15.0 
Week 5 
Written Report 
Finite Element Stress/Strain/Displacement Analysis Application Laboratory 
2,3,4,5 
15.0 
Week 10 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 
1,2,3,5 
70.0 
EndofSemester 
Reassessment Requirement 
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The institute reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
Theoretical Development and Analysis 
3.0 
Every Week 
3.00 
Tutorial 
Worked Numerical Examples and Problems 
1.0 
Every Week 
1.00 
Independent & Directed Learning (Noncontact) 
Self Directed Study 
2.5 
Every Week 
2.50 
Lab 
Finite Element Analysis Application Laboratory 
2.0 
Every Month 
0.50 
Total Hours 
8.50 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
4.50 
This module has no Part Time workload. 
Module Resources
Recommended Book Resources 

 Hearn E.J. 1997, Mechanics of Materials Volume 2, 3rd Edition Ed., Butterworth Heinemann [ISBN: 0 7506 3266 6]
 Ugural A.C., Fenster S.K. 2011, Advanced Mechanics of Materials and Applied Elasticity, 5th Ed., Prentice Hall [ISBN: 0 1370 79206]
 Craig R.R. 2011, Mechanics of Materials, 3rd Edition Ed., Wiley [ISBN: 0 4704 81811]
 Cook R.D., Malkus D.S., Plesha M.E. 2007, Concepts and Applications of Finite Element Analysis, 4th Edition Ed., Wiley [ISBN: 8126513365]
 Supplementary Book Resources 

 Mark E. Tuttle 2013, Structural Analysis of Polymeric Composite Materials, Second Edition, 2nd Edition Ed., CRC Press [ISBN: 143987512X]
 Boresi A.P., Chong K., Lee J.D. 2010, Elasticity in Engineering Mechanics, 3rd Edition Ed., Wiley [ISBN: 0 470 402 555]
 Goodno B.J., Gere J.M. 2014, Mechanics of Materials, 8th Ed., Engage Learning [ISBN: 1111136031]
 Hinton M., Soden, P.D., Kaddour A.S. 2004, Failure Criteria in FibreReinforced Polymer Composites, Elsevier Science [ISBN: 0 08 044475 X]
 Solecki R., Conant R.J. 2003, Advanced Mechanics of Materials, 1st Edition Ed., Oxford University Press [ISBN: 0 1951 4372 0]
 Benham P.P., Crawford R.J., Armstrong C.G. 1996, Mechanics of Engineering Materials, 2nd Edition Ed., Longman [ISBN: 0 5822 5164 8]
 Coates R.C., Coutie M.G., Kong F.K. 1990, Structural Analysis, 3rd Edition Ed., E. & F.N. Spon [ISBN: 0 2780 0035 3]
 Ward I.M., Sweeney J. 2004, An Introduction to the Mechanical Properties of Solid Polymers, 2nd Edition Ed., Wiley [ISBN: 0 4714 9626 7]
 This module does not have any article/paper resources 

Other Resources 

 Website: Engineering Fundamentals  Mechanics of
Materials Website
 Website: Engineers Edge  Mechanics of Materials
Website
 Website: ANSYS Finite Element Website
 Website: Finite Element Demonstration Room
Website

Module Delivered in
