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Bending and torsion of beams

This teaching and learning package (TLP) provides an introduction to the mechanics of beam bending and torsion, looking particularly at the bending of cantilever and free-standing beams and the torsion of cylindrical bars.

There are no specific prerequisites for this TLP, but it would be useful to be familiar with stress and strain, elastic strain and Plastic deformation, Young modulus, E and yield stress, σY. While a basic knowledge of mechanical deformation is assumed, this teaching and learning package covers all the fundamentals of beam mechanics.

On completion of this tutorial package, you should:

• Understand the stress distribution within beams subject to bending or torsion.
• Be familiar with the concepts of the radius of curvature of a section of a beam (and its reciprocal, the curvature), second moment of area, polar moment of inertia, beam stiffness and torsional stiffness.
• Be able to calculate the moments acting in a beam subject to bending or torsion.
• Be able to calculate the deflections of a beam on bending and the angle of twist of a bar under torsion.
• Be able to predict the effect of plastic deformation, at least with simple beam geometry.

Questions and links to further reading and websites are also included.

[Description and screenshot taken from the DoITPoMS page for this TLP. (c) University of Cambridge used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://www.doitpoms.ac.uk/tlplib/beam_bending/index.php
Publication Date: 2007-11
Source: http://www.doitpoms.ac.uk/tlplib/index.php
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Rights: Copyright University of Cambridge. Except where otherwise noted (see http://www.doitpoms.ac.uk/tlplib/terms.php), content on this page is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.0 Licence

Topic: Machine elements.

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Manufacturing

This introductory level study unit introduces manufacturing as a system and will describe some of the many different ways of making products. It will illustrate how the required properties of the materials in a product influence the choice of manufacturing process used.

After studying this unit you will be able to:
• Explain the difference between industrial and engineering design with reference to familiar products; and for specific products explain whether it is the product’s form or its function that enhances its value in the marketplace.
• Understand the concept of a product design specification (PDS), and be able to indicate some to the factors which should be included in producing one.

• Describe the role of marketing in developing the PDS for a product.
• Classify products simply in terms of their basic shape.
• Describe the difference between the hot and cold working of metals and give the advantages of each.
• Indicate which types of manufacturing process are suited to producing different shapes of product.
• Indicate which processes are likely to be used for producing a particular product using a specific material or class of material.
• Describe the advantages and disadvantages of the different classes of manufacturing processes.
• Outline the concept of surface engineering for improving the properties of a component.

The unit looks at the manufacturing process, casting, forming, cutting, joining, making the gearwheel, and surface engineering.

The unit takes on average 20 hours to complete.

[Description and screenshot taken from the OU page for this course. (c) Open University used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://openlearn.open.ac.uk/mod/oucontent/view.php?id=399740
Source: http://openlearn.open.ac.uk/
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Rights: Copyright The Open University. Except for third party materials and otherwise stated (see http://www8.open.ac.uk/about/main/admin-and-governance/policies-and-statements/conditions-use-open-university-websites), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Topic: Manufacturing processes.

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Introduction to structural integrity

This advanced level study unit looks at the investigation that followed the collapse of the Silver Bridge over the Ohio River in 1967 which demonstrates how the study of safe design and the assessment of components and structures under load is of increasing importance in engineering design.

Structural integrity is the study of the safe design and assessment of components and structures under load, and has become increasingly important in engineering design. It integrates aspects of stress analysis, materials behaviour and the mechanics of failure into the engineering design process.
After you have completed this unit you should be able to:
• differentiate between and describe dissolution, degredation and corrosion as they affect the deterioration of structural materials;
• predict electrochemical behaviour between dissimilar metals;
• explain galvanic corrosion in terms of the electrochemical series;
• distinguish between the hoop and longitudinal stresses in a pressure-vessel wall, and specify them in terms of the pressure, wall thickness and diameter of the vessel;
• describe the loads in the various parts of a structure and the most likely load path;
• indicate the procedures needed in practical failure analysis;
• specify the failure mechanisms possible when a nominally ductile material fails in a brittle fashion;
• relate crack formation to the loads on a component, bearing in mind the importance of stress concentrations in the component concerned;
• provide a likely sequence of events involved in the failure of a part made from several different components;
• describe the problem of fretting wear at a bearing joint;
• describe the key circumstances of a particular accident or disaster, and relate the sequence of events to specific causes supported by the relevant evidence.

The unit is split into 3 parts:
[1] Engineering for purpose
[2] Environmental deterioration
[3] Case study: The Silver Bridge

The unit takes on average 20 hours to complete.

[Description and screenshot taken from the OU page for this course. (c) Open University used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://openlearn.open.ac.uk/mod/oucontent/view.php?id=397857
Source: http://openlearn.open.ac.uk/
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Rights: Copyright The Open University. Except for third party materials and otherwise stated (see http://www8.open.ac.uk/about/main/admin-and-governance/policies-and-statements/conditions-use-open-university-websites), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Topic: Machine elements, Principles of design.

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Systems engineering: challenging complexity

This masters level study unit examines system engineering and why it is important. You will learn to identify and evaluate the importance of relationships within the process and assess the relative importance of stakeholders. You will also be able to classify a systems engineering project in terms of the balance of demands, choice and constraints.

Complex systems have many components – hardware, software, people, machinery, buildings, all of which interact – and many stakeholders with requirements to be met. The essence of systems engineering is that it combines technical, interpersonal and managerial knowledge and skills. By studying this course, practitioners and anyone responsible for or working in the systems engineering environment will gain an understanding of the principles, tools and techniques of a multi-functional approach to increasingly complex systems planning.

The aim of this unit is to answer five questions:
Why is systems engineering important?
What is modern engineering?
What is systems?
What is systems engineering?
What approach to systems engineering does the course adopt?

The unit takes on average 25 hours to complete.

[Description and screenshot taken from the OU page for this course. (c) Open University used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://openlearn.open.ac.uk/mod/oucontent/view.php?id=397849
Source: http://openlearn.open.ac.uk/
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Rights: Copyright The Open University. Except for third party materials and otherwise stated (see http://www8.open.ac.uk/about/main/admin-and-governance/policies-and-statements/conditions-use-open-university-websites), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Topic: Principles of design.

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Engineering: the nature of problems

The optimistic approach to a problem is to view it as a challenge and an opportunity – a chance to make progress. In this intermediate level study unit, the nature of problems is explored by looking at the way they are used as a stimulus for finding solutions. It is presumed from the start that you want to be involved in the process of finding solutions and that you are not expecting simply to be given the answers.

One example that is investigated in this unit concerns how to devise lighter bicycle frames, and the way to assess the merits of alternative materials from which to make them. There is no single way to move from a problem like this to possible solutions. In fact there are often several ways to set about finding several solutions, but there are a few general factors that are important to the search. First it is important to appreciate the needs from which a problem arises. For the bicycle frame it’s not just a lighter material that is required, but rather it is one that can be deployed to bear specific loads imposed on a fully functional frame. Next it is valuable to understand the challenge well enough to be able to specify the nature of solutions, perhaps using the formal languages of engineering, mathematics, science and problem solving. For example, it is unwise to take part in a discussion on ‘the best materials for bike frames’ without a technical appreciation of both the job a frame has to do and the relevant attributes of the candidate materials. Establishing what you don’t yet know usually starts by recognising how effectively you can tell someone else where the challenges arise. You must be able to communicate with a wide range of people, sometimes ‘calling a spade a spade’, and at other times describing precisely what the word ‘spade’ actually means.

After studying this unit you should be able to:

View solutions as belonging to particular categories, broadly classified as:
innovation by context
innovation by practice
routine

See how external factors affect engineering projects, and appreciate the range of engineering involved in meeting the basic needs of our society.

Recognise and apply a range of problem-solving techniques from each stage of the engineering design cycle, to include the following:
physical modelling
mathematical modelling
iteration
use of reference data
refining an engineering specification.

Identify when models are likely to be useful and when they are no longer valid.

Recognise and distinguish between the following technical terms:
differential equation
simultaneous equation
boundary condition
constraint
finite element analysis (FEA)
mathematical model
physical model
prototype
demonstrator
anthropometric
ergonomic
product specification
functional specification

The unit takes on average 40 hours to complete.

[Description and screenshot taken from the OU page for this course. (c) Open University used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://openlearn.open.ac.uk/mod/oucontent/view.php?id=397841
Source: http://openlearn.open.ac.uk/
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Rights: Copyright The Open University. Except for third party materials and otherwise stated (see http://www8.open.ac.uk/about/main/admin-and-governance/policies-and-statements/conditions-use-open-university-websites), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Topic: Principles of design.

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Systems modelling

This introductory OpenLearn study unit will introduce you to the modelling process enabling you to recognise that systems models may be used in different ways as part of a process for: improving understanding of a situation; identifying problems or formulating opportunities and supporting decision making.

In order to get the most out of this unit, you need to be familiar with, or at least not worried by, simple mathematics, and recognise some related concepts such as chance and probability. Working through the first self-assessment question (SAQ) will give you an indication of the skills and attitudes involved. If you find you are having a lot of difficulty with SAQ 1, put this unit aside and select a more appropriate unit from the topic list. As well as providing an introduction to models, the unit looks at systems modelling in practice.

After working through these materials you should be able to:
• describe and use a general classification of models
• outline and discuss the process of systems modelling, where models are used as part of a systemic approach to a range of different situations
• recognise that systems models may be used in different ways as part of a process for: improving understanding of a situation; identifying problems or formulating opportunities; supporting decision making

The unit takes on average 4 hours to complete.

[Description and screenshot taken from the OU page for this course. (c) Open University used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://openlearn.open.ac.uk/mod/oucontent/view.php?id=397801&direct=1
Source: http://openlearn.open.ac.uk/
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Rights: Copyright The Open University. Except for third party materials and otherwise stated (see http://www8.open.ac.uk/about/main/admin-and-governance/policies-and-statements/conditions-use-open-university-websites), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Topic: Design processes.

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Engineering mechanics: solids

This course introduces the subject areas of kinematics, statics and dynamics, in the context of engineering mechanics. The course is mainly concerned with the application of these topics to the analysis and design of solid bodies, as distinct from the closely related areas of fluid mechanics and thermodynamics. The materials are presented in a series of pdf documents.

Kinematics is the study of motion. Statics is the study of forces on stationary objects. Dynamics is the study of forces on moving bodies. These are the analytical tools used by the design engineer. The aims of the course are therefore two fold. Firstly, it aims to teach the basic analytical methods, that is, the fundamental concepts and techniques of solid engineering mechanics. Secondly, it aims, in a limited way, to show the implementation of these methods in engineering design. The limited time available to study the course has meant that the course team have had to lay the emphasis on the analytical methods. The underlying assumption has been that, if students acquired a solid foundation in analysis from this course, then its implementation in design would become apparent both in future courses and in the mechanical engineering that surrounds them every day.

Course materials:
Block 1: Geometry of mechanisms
Unit 1: Mechanisms
Unit 2: Mechanisms 2
Block 2: Statics
Unit 3: Forced and moments
Unit 4: Modelling with free-body diagrams
Block 3: Kinematics
Unit 5: Motion
Unit 6: Velocity diagrams
Block 4: Dynamics
Unit 7/8: Dynamics
Block 5: Acceleration
Unit 9A: Compensation forces
Unit 9B: Acceleration diagrams
Block 6: Structures
Unit 10: Stress analysis
Unit 11: Structural components
Block 7: Energy and momentum
Unit 12/13: Energy and momentum
Block 8: Vibration
Unit 14: Vibration
Block 9: Design study
Unit 15: The mechanics of an electric lift

The unit takes on average 135 hours to complete.

[Description and screenshot taken from OpenLearn page for this material. (c) Open University used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://labspace.open.ac.uk/course/view.php?id=6520
Author: John Byrne
Source: http://openlearn.open.ac.uk/
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Rights: Copyright The Open University. Except for third party materials and otherwise stated (see http://www8.open.ac.uk/about/main/admin-and-governance/policies-and-statements/conditions-use-open-university-websites), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Topic: Mechanisms.

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Engineering the future: the process of design

This introductory level OpenLearn study unit looks at the process of design – from assessing the complexity of design as an activity, to exposing the difficulty in making general conclusions about how designers work. You will be able to identify innovation in a wide variety of designed objects and evaluate the impact of this innovation.

Having studied this unit you should be able to: recognise that functional artefacts have had input from a designer, with greater and lesser degrees of engineering input; identify that engineering designers work within constraints of finance, materials properties, desired functionality, human factors, etc.; understand that design exploits models of the product being designed, whether those models are physical mock-ups, computer-based models, or mathematical models which explore an element of the product’s performance; understand how models of the design process are formulated, and how they can be applied to understand the development of a particular product or product family; understand design-related terminology such as innovation, context, uncertainty and style.

The learning unit is divided into 7 parts and takes on average 28 hours to complete.

[1] Design and designing
[2] Design and innovation 1: the plastic kettle
[3] Models of the design process
[4] Conceptual design
[5] Concept to prototype
[6] Design and innovation 3: the Brompton folding bicycle
[7] Conclusions

Link: http://labspace.open.ac.uk/course/view.php?id=7154
Author: Janice Friend
Source: http://openlearn.open.ac.uk/
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/
Rights: Copyright The Open University. Except for third party materials and otherwise stated, content on this site is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence.

Topic: Design processes, Principles of design.

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TALAT lecture 3300: fundamentals of metal forming

This lecture gives a brief review of the fundamental terms and laws governing metal forming at room temperature as well as at high temperatures. It is provided as a pdf document.

It looks at the terms for classifying forming processes and the characteristic values and basic laws of metal forming including flow stress, plastic strain, plastic flow under combined stresses, flow curves, average flow stress and energy considerations. This lecture is a necessary prerequisite to understand the more specific treatment of metal forming subjects such as forging, impact extrusion and sheet metal forming in the subsequent TALAT lectures 3401 to 3805.

A general background in production engineering and machine tools is assumed.

[Description and screenshot taken from TALAT page for this material. (c) European Aluminium Association used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://core.materials.ac.uk/repository/eaa/talat/3300.pdf
Author: European Aluminium Association; Klaus Siegert; Eckart Dannenmann
Publication Date: 2009-09-25
Source: http://core.materials.ac.uk/search/detail.php?id=2100&view=list
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/legalcode
Rights: By European Aluminium Association, Brussels, Klaus Siegert, Eckart Dannenmann and released under a CC BY-NC-SA 2.0 license.

Topic: Forming.

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TALAT lecture 4601: introduction to brazing of aluminium alloys

This lecture describes the characteristics of brazing aluminium and the process involved and helps to understand the use potential and the limitations of brazing aluminium. It is provided as a pdf document.

The lecture introduces terms, definitions and brazeable alloys and looks at the brazing process and different brazing methods – torch brazing, flux-dip brazing, furnace brazing, and vacuum and controlled atmosphere brazing. The properties of brazed joints and quality control testing methods are also detailed.

Basic knowledge of aluminium alloys designation system, surface treatment and corrosion behaviour is assumed.

[Description and screenshot taken from TALAT page for this material. (c) European Aluminium Association used under the terms of their CC BY-NC-SA 2.0 license.]

Link: http://core.materials.ac.uk/repository/eaa/talat/4601.pdf
Author: R. Mundt; European Aluminium Association
Publication Date: 2009-09-25
Source: http://core.materials.ac.uk/search/detail.php?id=2100&view=list
License: http://creativecommons.org/licenses/by-nc-sa/2.0/uk/legalcode
Rights: By European Aluminium Association, Brussels, R. Mundt and released under a CC BY-NC-SA 2.0 license.

Topic: Joining.

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