Mechanics, Structures and Materials

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Dynamics: - 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 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.
• 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).
• 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.
• 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 shear force and bending moment in 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.

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

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

Transferable and Generic Skills

Having successfully completed this module you will be able to:

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

Knowledge and Understanding

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

• Materials: - The physical origins of properties of materials and their control. - The ways in which properties of materials govern their selection in engineering applications.
• 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.
• Dynamics: - The kinematics and kinetics of particles. - The plane kinematics and kinetics of rigid bodies. - Impulse and momentum for particles - Work and energy principle, conservation of energy for particles and rigid bodies in 2D - The fundamental assumptions of lumped parameter mechanical systems - Free vibration analysis of a single degree of freedom mechanical system - 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.
• Statics 2: - Stress and strain in 2D/3D and their relationships. - The way that stress and strain transform in 2D. - The concept of principle stresses and strains. - Yield criteria

Learning Outcomes

Having successfully completed this module you will be able to:

• B1 As part of the final assessment, students will apply their knowledge of mathematics and engineering principles to a range of broadly defined problems in statics, dynamics and materials. B2 As part of the final assessment, students will analyse broadly defined problems using first principles of statics, dynamics and materials to reach substantiated conclusions. B3 As part of the final assessment, students will select and apply appropriate analytical techniques to model broadly defined problems in statics, dynamics and materials, while recognising the limitations of the underlying assumptions. B12 Students will use their laboratory skills to investigate the behaviour of structures and materials, which will be assessed in the Part 1 lab report. B13 Student will learn to select materials considering their mechanical and physical properties for specific applications, which will be assessed in the final assessment. B17 FEEG1002 contributes to the Part 1 lab report where students have to demonstrate their ability to communicate technical information effectively.

The syllabus of each part of the module is given below.

Statics-1

• Fundamental concepts 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

• 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 and strain transformation using Mohr circles.
• Principle stresses and strains
• Yield criteria and safety factors

Dynamics

• 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
• 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
• 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.

Materials

• 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 activities include Lectures and Tutorials as well as self-study with the solution of example problems both in a supervised environment and in their own time.

The laboratory sessions include:

• Statics beam bending lab
• Mechanical testing of materials.

Summative

This is how we’ll formally assess what you have learned in this module.