*FEEG1002 *Mechanics, Structures and Materials

## Module Overview

This module covers the fundamentals of mechanics, statics, dynamics and materials. Providing a firm basis for all subsequent modules in these areas in later Parts and a further career in engineering. This module consists of six (6) inter-dependent, to some extent, parts, covering topics of Statics, Dynamics and Materials. These parts are named Statics-1 (S1), Statics-2 (S2), Statics-3 (S3), Dynamics-1 (D1), Dynamics-2 (D2), and Materials (M). The module may be studied in one of three Streams, each one corresponding to the needs of a different programme: - Stream-1, consisting of Statics-1, Dynamics-1 and -2 and Materials: Acoustical Engineering. - Stream-2, consisting of Statics-1 and -2, Dynamics-1 and Materials: Aerospace Engineering, Mechanical Engineering and Ship Science. - Stream-3, consisting of Statics-1, -2 and -3: Civil Engineering and Environmental Engineering. All Streams have Statics-1 in common.

### Aims and Objectives

#### Module Aims

All Streams aim to: - Introduce students to the essentials of engineering solid mechanics and provide an understanding of the basic concepts and techniques, with emphasis on the application of these to the solution of engineering problems. - Acquaint students with statics and the analysis of stress and deformation of simple structures under simple loads. - Provide a firm foundation for more advanced study. Stream-1 further aims to: - Review the principles of dynamics and introduce and apply fundamental dynamic modelling. - Discuss the nature of stiffness, mass and damping elements and determine their role in controlling the steady-state response of a mechanical system to harmonic loads and motion inputs - Develop a basic understanding of the properties of materials, and hence provide a sound rationale for selection and use of materials in engineering. Stream-2 further aims to: - Review the principles of dynamics and introduce and apply fundamental dynamic modelling. - Provide an understanding of the effects of forces, torques and motion on a variety of structures and vehicles. - Develop a basic understanding of the properties of materials, and hence provide a sound rationale for selection and use of materials in engineering. Stream-3 further aims to: - Provide students with a broader and deeper understanding of statics, including topics on the concept of safety factor and its application, three-pin arches, the solution of statically-indeterminate structures, the use of deformation compatibility and energy methods, biaxial bending with axial force and torsion of thin, non-circular shafts - Provide an understanding of plastic collapse of simple structures. - Introduce in detail elements of elastic solid mechanics, i.e. stress, strain, equations of stress equilibrium, links between elastic constants, and elastic anisotropy. - Introduce practical civil engineering applications where the theory developed is readily applicable, such as composite beams and pre-stressed concrete.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

- The distinction between internal and external forces and the difference between statically determinate structures, statically indeterminate ones, and mechanisms
- Stream 1 - The fundamental concepts of kinetics of systems of particles
- Stream 1 - Plane kinematics and kinetics of rigid bodies
- Stream 1 - Three-dimensional dynamics of rigid bodies
- Stream 1 - Conservation of energy and momentum
- Stream 1 - Rockets and jet propulsion
- Stream 1 - the fundamental assumptions of lumped parameter mass, stiffness and damper models
- Stream 1 - Free vibrations of a single degree of freedom mechanical system
- Stream 1 - Steady-state vibration analysis of a single degree of freedom mechanical system subjected to harmonic forces and base motion.
- Stream 1 - Vibration based transfer functions, how they are inter-related and portrayed graphically
- Stream 1 - The trade-off between high and low stiffness/damping for vibration isolation
- The conditions of equilibrium of particles and rigid bodies, and how to use them to calculate the reactions at the supports of statically-determinate structures.
- Stream 1 and 2 - The physical origins of properties of materials and their control.
- Stream 1 and 2 - The ways in which properties of materials govern their selection in engineering applications.
- Stream 2 and 3 - Stress and strain in 2D/3D. Free edge conditions
- Stream 2 and 3 - The way that stress and strain transform in 2D.
- Stream 2 and 3 - The concept of principle stresses and strains
- Stream 3 - The distributions of strain and stress in a beam due to bending and/or shear.
- Stream 3 - The distributions of stress in thin-walled, non-circular shafts under torsion.
- Stream 3 - Understand the concept of superposition, and how it is used to combine stresses in a member under more than one load effect, e.g. beam with axial load
- Stream 3 - How to solve three-pin arches.
- Stream 3 - The application of energy methods to the solution of simple structures
- How to calculate, and plot diagrams of, the internal forces and moments of staticallydeterminate beams
- Stream 3 - The concept of deformation compatibility, and how it is used to solve simple statically indeterminate structural problems
- Stream 3 - Appreciate the concept of plastic behaviour and plastic collapse of simple structures.
- Stream 3 - The concept of safety factor.
- Engineer’s Bending Theory and how to use it to determine beam deflection due to bending.
- How to calculate bending-induced shear stresses and their distribution in a beam.
- The behaviour of a structural member in torsion and how to calculate the stress in a circular section in torsion
- How to solve statically-determinate plane trusses.
- How elastic struts buckle and how to calculate the critical buckling load.
- Stream 1 - The fundamental concepts of kinematics and kinetics of particles

##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

- Information handling
- Self management (e.g. time management)
- Written communication
- Numeracy
- Being an independent learner

##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

- Carry out calculations relating to structural behaviour and strength of structural members
- Experiment on idealised forms of structure in the laboratory
- Collate experimental data
- Manipulate experimental data in order to draw specific conclusions

##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

- Stream 1 - Develop particle and rigid body trajectory equations
- Stream 1 and 2 - Calculate the motion of rigid bodies
- Stream 1 and 2 - Discuss the motion of rockets and jet-propelled vehicles
- Stream 1 - Determine both free and forced vibrations of single degree of freedom systems
- Stream 1 - Interpret, process and appropriately plot vibration based transfer functions
- Stream 1 - Predict the effectiveness of a vibration isolator given single degree of freedom assumptions
- Stream 1 and 2 - Demonstrate how defects in atomic structure affect mechanical properties
- Stream 1 and 2 - Relate the kinetics of a number of apparently different materials processes to the same underlying process (diffusion)
- Stream 1 and 2 - Explain how strengthening mechanisms occur on the microstructural scale and how this is related to the bulk mechanical properties we require in engineering structures
- Stream 1 and 2 - Apply the use of phase diagrams to explain the development of microstructure and hence how alloys are designed
- Stream 1 and 2 - Analyse failure problems and apply the correct fracture mechanics approach
- Stream 1 and 2 - Show how non-metallic bonding leads to very different properties (e.g. ceramics and polymers)
- Stream 2 and 3 - Carry out stress and strain transformations in 2D
- Stream 2 and 3 - Apply Mohr’s circle to solve stress and strain transformation problems and derive principle strains/stresses
- Stream 2 and 3 - Interpret measurements using strain gauge rosettes
- Stream 3 - Solve three-pin arches.
- Stream 3 - Discuss the concept of deformation compatibility and apply it to simple structures.
- Stream 3 - Solve simple structures using energy methods.
- Stream 3 - Determine the plastic collapse load and mechanism of simple structures.
- Stream 3 - Calculate a safety factor for different types of “failure”
- Stream 3 - Recognise common types of structural member and structural engineering problems
- Determine whether a structure is statically determinate, indeterminate or a mechanism.
- Assess whether theoretical assumptions are supported by laboratory observations.
- Construct free body diagrams and use them to solve mechanics problems.
- Calculate the reactions at the supports of statically determinate structures.
- Calculate stresses and strains due to bending and torsion.
- Solve statically-determinate plane trusses
- Calculate, and plot diagrams of, the internal actions of statically-determinate beams.
- Calculate the deflection due to bending at different points of a beam.
- Calculate the critical buckling load of elastic struts
- Interpret experimental data to deduce structural or material behaviour

### Syllabus

The syllabus of each one of the six parts is given below. Statics-1 (S1) - Fundamental Concepts: Concepts, Units, Scalar & Vector - Revision of statics (adding/resolving forces, moments), types of load/support. - Equilibrium of rigid bodies. Free body diagrams. Static determinacy. - Trusses: static determinacy, method of joints and method of sections. - Stress, strain, elastic constants, Hooke's law. - Beams: shear force and bending moment diagrams, differential relationships. - Engineer's Bending Theory. First and second moments of area. - Beam deflection due to bending, moment-curvature relationship. - Differential equation of the deflection curve. Solution by integration. - Shear stress in beams. Shear formula. Shear stress distribution in practical sections. - Torsion of circular section shafts, polar second moment of area. - Buckling of elastic struts. Concept of instability. Euler formula, effective length. Statics-2 (S2) - Stress, strain, elastic constants, thermal strain, Hooke's law (2D/3D) - Stresses in thin-walled cylinders subject to internal pressure. - Two-dimensional analysis of stress. - Stress transformation using Mohr circles. - Principle stresses and strains Statics-3 (S3) - Friction - Factors of safety: concept and application to the stability of rigid bodies. - Three-pin arches: reactions, axial and shear force and bending moment diagrams. - The parabolic three-pin arch. - Concept of virtual work & application to statically determinate structures. - Stress-strain relationships of common structural materials. - FLEA. Deformation compatibility for simple statically indeterminate structures. - Deflection coefficients, for non-standard cases and simple statically indet. beams. - Elastic section modulus and design of beams in bending: Principal axis. - Longitudinal shear stresses in beams. - Composite beams. - Biaxial bending. - Stresses in beams with axial load. Superposition. Examples incl. pre-stressed concrete. - Torsion of thin-walled non-circular shaft. - Plastic stresses in beams. Simple plastic collapse mechanisms. Dynamics-1 (D1) - Particle Dynamics: Newton’s Laws, particle motion for constant and variable force. - Work, Energy and Momentum: Work done by Force, Kinetic and Potential Energy. - Energy Conservation, Friction, Linear Momentum & Impulse, Simple Rotating Bodies. - Relative motion equation, Relative motion Diagrams. - System of Particles: Centre of Mass, Centre of Mass of a vehicle, Equivalent Particle. - Rocket and Jet Propulsion. - Dynamics of Rigid Bodies: Rotation of rigid body about a fixed axis. - Angular Momentum & its conservation, Moments of inertia, Inertia Matrix. Dynamics-2 (D2) - The fundamental assumptions of lumped parameter mechanical systems, and concepts of equivalent mass, stiffness and damping - Free vibration analysis of a single degree of freedom mechanical system. - Steady state forced vibration analysis of a single degree of freedom mechanical system. - Definition of the Frequency Response Function (FRF). - Converting between different types of FRF and ways of plotting and interpreting them (including dB). - Mass, stiffness and damping controlled behaviour. - Dynamics of a loudspeaker. - Vibration isolation: force and motion transmissibility. Materials (M) - Materials in Engineering: Metals, ceramics, polymers and composites. - Fundamentals: Atomic structure and interatomic bonding; electrons, atoms and molecules; the Periodic table; bonding and interatomic forces; the structure of crystalline solids; basic structures, unit cells; holes and lattices; imperfections in solids; point, linear, planar and volume defects; diffusion. - Mechanical properties: Stress and strain; elasticity; tensile properties; hardness; strengthening mechanisms; recovery, recrystallisation and grain growth. - Microstructures and their control: Phase diagrams; thermal processing; precipitation hardening. - Failure of metals: Failure; fracture, brittle and ductile failure; impact and fracture toughness; fatigue; creep. - Non metallic materials and their properties: Ceramics and glasses; main classes, properties. and uses; polymers; basic structures and bonding; polymerisation; cross linking; thermoplastics and thermosets; composites; main classes, properties and uses. - Materials in engineering applications: Case studies.

#### Special Features

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### Learning and Teaching

#### Teaching and learning methods

For all Streams, teaching methods include lectures, group tutorials and laboratory sessions. The laboratory sessions for Stream-1 are: 1. Stresses and strains in a beam due to bending. 2. Transfer functions of a loudspeaker, and effects of structural modification. 3. Mechanical testing of materials. The laboratory sessions for Stream-2 are: 1. Stresses and strains in a beam due to bending. Torsion of a circular shaft. Qualitative stress analysis using rubber sheets. 2. Three simple stress analysis experiments using a photoelastic bench-top kit. 3. Mechanical testing of materials. The laboratory sessions for Stream-3 are: 1. Stresses and strains in a beam due to bending. 2. Buckling of elastic struts. 3. Plastic collapse of portal frames. For all Streams, learning activities include self-study and the solution of example problems both in a supervised environment and in own time.

Type | Hours |
---|---|

Lecture | 69 |

Preparation for scheduled sessions | 15 |

Completion of assessment task | 40 |

Follow-up work | 104 |

Revision | 32 |

Practical classes and workshops | 15 |

Tutorial | 15 |

Wider reading or practice | 10 |

Total study time | 300 |

#### Resources & Reading list

W.D. Callister. Materials Science and Engineering, an Introduction.

R. C. Hibbler. Engineering Mechanics – Dynamics.

PP Benham, RJ Crawford and CG Armstrong. Mechanics of Engineering Materials.

### Assessment

#### Assessment Strategy

The learning outcomes of this module will be assessed under the Part I Assessment Schedule for FEE Engineering Programmes which forms an Appendix to your Programme Specification.

#### Summative

Method | Percentage contribution |
---|---|

Assessment | 100% |

### Linked modules

Pre-requisite - A level mathematics and physics or equivalent.

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Textbooks

Callister - Note - large number available in library.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.