*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 five inter-dependent, to some extent, parts, covering topics of Statics, Dynamics and Materials. These parts are named Statics-1 (S1), Statics-2 (S2), Dynamics-1 (D1), Dynamics-2 (D2), and Materials (M). The module is studied in one of two Streams, each one corresponding to the needs of a different programme: - Acoustical Engineering. - Stream-1, consisting of Statics-1 and -2, Dynamics-1 and Materials: Aerospace Engineering, Mechanical Engineering and Ship Science. - Stream-2, consisting of Statics-1 and -2, Dynamics-2 and Materials: Civil and Environmental Engineering, Acoustical Engineering. Note: this module is only available to student taking degree programmes in the School of Engineering.

### 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. - Develop a basic understanding of the properties of materials, and hence provide a sound rationale for selection and use of materials in engineering. - 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. - Provide an understanding of the effects of forces, torques and motion on a variety of structures and vehicles. Stream-2 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

#### Learning Outcomes

##### Knowledge and Understanding

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

- Statics 1: - The distinction between internal and external forces and the difference between statically determinate structures, statically indeterminate ones, and mechanisms. - 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. - How to calculate, and plot diagrams of, the internal forces and moments of statically-determinate beams. - 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.
- Statics 2: - Stress and strain in 2D/3D. Free edge conditions. - The way that stress and strain transform in 2D. - The concept of principle stresses and strains.
- Dynamics 1: Having successfully completed Stream 1, you will additionally be able to demonstrate knowledge and understanding of: - The kinematics and kinetics of particles. - The plane kinematics and kinetics of rigid bodies. - The work done by forces. - The Kinetic/Potential energy and impulse/momentum for particles and rigid bodies in 2D. - The conservation of energy and momentum for particles and rigid bodies in 2D. - The motion of systems with variable mass. - The fundamental concepts of rigid body dynamics in 3D.
- Dynamics 2: Having successfully completed Stream-2, you will additionally be able to demonstrate knowledge and understanding of:- - The fundamental concepts of kinematics and kinetics of particles. - The fundamental concepts of plane kinematics and kinetics of rigid bodies. - The Kinetic/Potential energy (for particles and rigid bodies in 2D) and impulse/momentum (for particles). - The conservation of energy (for particles and rigid bodies in 2D) and conservation of momentum (for particles). - The fundamental assumptions of lumped parameter mass, stiffness and damper models. - Free vibrations of 1 and 2 degree of freedom systems. - The use of frequency response functions to represent the steady-state vibration of a single degree-of-freedom system. - How the free vibration of multiple degree-of-freedom systems can be derived and solved using a matrix representation.
- Materials: - The physical origins of properties of materials and their control. - The ways in which properties of materials govern their selection in engineering applications.

##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

- Statics 1: - Determine whether a structure is statically determinate, indeterminate or a mechanism. - 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. - Assess whether theoretical assumptions are supported by laboratory observations.
- Statics 2: - Carry out stress and strain transformations in 2D. - Apply Mohr’s circle to solve stress and strain transformation problems and derive principle strains/stresses. - Interpret measurements using strain gauge rosettes.
- Dynamics 1: Having successfully completed Stream-1, you will additionally be able to: - Develop particle and rigid body trajectory equations. - Write the equations of motion for particles and rigid bodies. - Apply the principle of work and energy to particle and rigid bodies in 2D. - Apply the principle of impulse and momentum to particles and rigid bodies in 2D.
- Materials : - Demonstrate how defects in atomic structure affect mechanical properties. - Relate the kinetics of a number of apparently different materials processes to the same underlying process (diffusion). - Explain how strengthening mechanisms occur on the microstructural scale and how this is related to the bulk mechanical properties we require in engineering structures. - Apply the use of phase diagrams to explain the development of microstructure and hence how alloys are designed. - Analyse failure problems and apply the correct fracture mechanics approach. - Show how non-metallic bonding leads to very different properties (e.g. ceramics and polymers).
- Dynamics 2: Having successfully completed Stream-2, you will additionally be able to: - Develop simple particle and rigid body trajectory equations. - Write the equations of motion for particles and rigid bodies. - Apply the principle of work and energy to particles and rigid bodies in 2D. - Apply the principle of linear impulse and momentum to particles. - Determine both free and (harmonically) forced vibrations of a single degree-of-freedom system. - Analyse the free vibration of a two degree-of-freedom system.

##### 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.

### Syllabus

The syllabus of each part of the module 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 Dynamics-1 (D1) • Particle Dynamics: rectilinear and curvilinear motion; motion of projectiles; dependent and relative motion; Newton’s Laws; free body diagrams; equations of motion. • Work and Energy for particles: principle of work and energy; Energy Conservation; Power and efficiency • Principle of linear/angular impulse and momentum for particles • Equations of motion for systems with variable mass • Rigid bodies Dynamics in 2D: kinematics relationships, centre of mass, mass moment of inertia and equations of motion, • Work and energy principle for rigid bodies • Principle of linear/angular impulse and momentum for rigid bodies • Introduction to rigid bodies motion in 3D Dynamics-2 (D2) • Particle Dynamics: rectilinear and curvilinear motion; Newton’s Laws; free body diagrams; equations of motion. • Work and Energy for particles: principle of work and energy; Energy Conservation. • Principle of linear impulse and momentum for particles • Rigid bodies Dynamics in 2D: kinematics relationships, centre of mass, mass moment of inertia and equations of motion, • Work and energy principle for rigid bodies • 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 with examples from civil and mechanical engineering • Steady state forced vibration analysis of a single degree of freedom system • Definition of the Frequency Response Function (FRF) • Mass, stiffness and damping controlled behaviour • Introduction to multiple degree of freedom systems, the derivation of the equations of motion and a matrix representation of them. Subsequent free vibration solution in terms of modes and the corresponding natural frequencies. 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.

### Learning and Teaching

#### Teaching and learning methods

For both Streams, teaching methods include lectures, group tutorials and laboratory sessions. The laboratory sessions for both Streams include: • Stress analysis in various structures including beams subject to bending and rubber sheets. • Mechanical testing of materials. Additionally, Stream-2 includes the following laboratory session: • Vibration of a loudspeaker or a two-storey building. For both Streams, learning activities include self-study and the solution of example problems both in a supervised environment and in their own time.

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

Tutorial | 15 |

Wider reading or practice | 10 |

Follow-up work | 115 |

Practical classes and workshops | 12 |

Revision | 32 |

Preparation for scheduled sessions | 45 |

Lecture | 69 |

Completion of assessment task | 2 |

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. Feedback will be available on the formative work undertaken during the module.

#### Summative

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

Part I Assessment Schedule | 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.