Undergraduate Teaching 2025-26

Lecturers

Dr R Foster, Prof A Lawrence, Prof F A McRobie

Lab Leader

Dr C Morley

Timing and Structure

Michaelmas Term. 16 Lectures.

Aims

The aims of the course are to:

cover the basic principles of practical design of typical engineering structures, with applications across a range of commonly-used structural materials.
establish links between the theory of structures, taught in the Part I courses IA Structural Mechanics and IB Structures, and the properties of materials as covered in courses on Materials and Engineering Applications.
study what differing approaches to design are appropriate for structures in different materials.
develop a design methodology that provides a firm basis for the structures courses taught in Part IIA and for the more advanced courses in the fourth year.

Objectives

As specific objectives, by the end of the course students should be able to:

have developed a good understanding of the structural forms appropriate in the various materials.
be aware of the likely critical factors (requirements, properties, behaviour) for design in the different materials.
be able to make sensible initial layout and sizing choices for simple structures in the various materials.
be able to carry out design calculations for basic structural elements in the various materials.
be aware of what design approaches will be appropriate, and what calculations necessary, for more complex structures in the various materials.
appreciate the influence of risk, and variability of loading and material properties, on structural design and calculations.

Content

The implications of the general principles of structural mechanics – equilibrium, compatibility, constitutive laws, and stability – are investigated for different materials. This leads to discussion of typical structural forms in the various materials, the reasons for adopting them, and appropriate methods of construction. The significant types of structural behaviour, and therefore the most useful methods of analysis and calculation, are investigated for the different material types. A basic aim is to establish means of making reasonable preliminary decisions about structural form and layout, and initial sizing of members, before detailed calculation need begin.

Design methodologies will be developed, and design of typical elements will be discussed, for the following materials:

high-strength, ductile materials such as steel and aluminium alloys
moderate- to high-strength, anisotropic, brittle materials such as advanced composites and timber
materials of low tensile but high compressive strength, such as concrete and masonry
reinforced concrete where concrete is combined with a ductile tensile material
brittle materials, such as glass

The critical modes of failure of structures made from these materials tend to differ – for example, global and local instability play a very significant role in thin-walled structures of high-strength materials, while shear-induced delamination is a major concern only in wood and composites. So design approaches will be correspondingly different.

Overview and principles (5L)

Introduction to the course and overview of structural materials and implications of material properties for structural design
Load paths and the application (and limitations) of the lowerbound theory in structural design
Limit state design and consideration of material variability in achieving appropriate levels of reliability
Resource efficiency and sustainability in structural design
Form, forces and masonry - "I like an arch"

Ductile Metals (primarily steel) (3L)

Timber (3L)

Fibre Composites (1L)

Concrete and reinforced concrete (3L)

Concrete and reinforced concrete
Ultimate design for flexure, shear and compression
Serviceability design and detailing

Glass (1L)

Coursework

Concrete Lab

Learning objectives:

To be familiar with the common ingedients of concrete and their properties;
To be able to design a concrete mix to satisfy certain technical requirements and cast a trial cube;
To have first-hand experience of casting reinforced concrete beams and various plain concrete specimens for subsequent testing
To be able to observe and record results of destructive testing and identify different failure modes in concrete
To be able to compare empirical results with theoretical predictions based on as built-data, and to evaluate the effectiveness and limitations of the theory

Practical information:

Sessions will take place in the Concrete Lab, Trumpington Street site, during weeks [1-8].
This activity does not involve preliminary work.
A sign-up sheet will be posted on the Inglis Mezzanine noticeboard.

Full Technical Report:

Students will have the option to submit a Full Technical Report.

Booklists

Please see the Booklist for Part IIA Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

S1

The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.

S3

Understanding of the requirement for engineering activities to promote sustainable development.

S4

Awareness of the framework of relevant legal requirements governing engineering activities, including personnel, health, safety, and risk (including environmental risk) issues.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P4

Understanding use of technical literature and other information sources.

P6

Understanding of appropriate codes of practice and industry standards.

P7

Awareness of quality issues.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

An awareness of developing technologies related to own specialisation.

Last modified: 02/10/2019 15:02

Engineering Tripos Part IIA, 3D3: Structural Materials & Design, 2022-23

Module Leader

Lecturers

Dr R Foster, Dr J Becque

Lab Leader

Timing and Structure

Michaelmas Term. 16 Lectures.

Aims

The aims of the course are to:

Provide a general understanding of the relationship between the properties of common structural materials, and the principles and approaches underpinning their use in structural design
Provide a bridge between the fundamental general engineering understanding of structures and materials developed in Part I and the applied specialist modules of Part II
Provide knowledge and knowhow enabling structural designers to improve our use of energy and material in the design of the built environment while providing safe, useful structures for people to use

Objectives

As specific objectives, by the end of the course students should be able to:

[1] Use the lower-bound theory of plasticity to perform load-path design of structural arrangements and to appreciate the benefits and limitations of the approach
[2] Consider the influence of risk, and variability of loading and material properties, in structural design and calculation
[3] Explain the environmental impacts of structural material and design choices
[4] Understand and carry out early-stage structural design with various structural materials
[4.1] Identify the theoretical and practical considerations governing structural design in various materials and explain how these may be accommodated in design
[4.2] Make reasonable conceptual design decisions regarding appropriate structural form, initial layout and initial member sizing for simple structures in various materials;
[4.3] Perform preliminary technical design calculations for simple structures in various materials
[4.4] Determine what design approaches may be appropriate, and what calculations necessary, for more complex structures in various materials

Content

The implications of the general principles of structural mechanics – equilibrium, compatibility, constitutive laws, and stability – are investigated for different materials. This leads to discussion of typical structural forms in the various materials, the reasons for adopting them, and appropriate methods of construction. The significant types of structural behaviour, and therefore the most useful methods of analysis and calculation, are investigated for the different material types. Our basic aim is to establish means of making reasonable preliminary decisions about structural form, layout and initial sizing of structural members made from a range of common construction materials.

Design methodologies will be developed, and design of typical elements will be discussed, for:

materials of low tensile but high compressive strength, such as masonry and glass;
composite materials of low tensile strength combined with a ductile tensile material, such as reinforced concrete;
high-strength, ductile materials such as steel and aluminium alloys;
moderate- to high-strength, anisotropic, brittle materials such as engineered timber.

The critical modes of failure of structures made from these materials tend to differ, as do other considerations such as environmental impacts, so design approaches will be correspondingly different.

Weeks 1-2 provide an introduction to a number of important considerations and approaches in structural design across materials, such as: loadpaths and the lowerbound theorem; limit state design and variability; resource efficiency and sustainability

Weeks 3-8 apply these considerations and approaches to design with various structural materials including: masonry; glass; reinforced concrete; steel and timber.

Coursework

Concrete Lab

Learning objectives:

To be able to:

1.Describe the common ingredients of concrete and their properties;

2.Design a concrete mix to satisfy certain technical requirements and cast a trial cube;

3.Supervise the casting of reinforced concrete beams and various plain concrete specimens for subsequent testing;

4.Observe and record results of destructive testing and identify different failure modes in concrete;

5.Compare empirical results with theoretical predictions based on as built-data, and evaluate the effectiveness and limitations of the theory.

Practical information:

Details will be available on the course Moodle page early in the term.

Full Technical Report:

Students will have the option to submit a Full Technical Report.

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

S1

The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.

S3

Understanding of the requirement for engineering activities to promote sustainable development.

S4

Awareness of the framework of relevant legal requirements governing engineering activities, including personnel, health, safety, and risk (including environmental risk) issues.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P4

Understanding use of technical literature and other information sources.

P6

Understanding of appropriate codes of practice and industry standards.

P7

Awareness of quality issues.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

Last modified: 24/05/2022 15:53

Engineering Tripos Part IIA, 3D3: Structural Materials & Design, 2017-18

Module Leader

Dr M Overend

Lecturers

Dr M Overend and Mr F A McRobie

Lab Leader

Dr C Morley

Timing and Structure

Michaelmas Term. 16 Lectures.

Aims

The aims of the course are to:

cover the basic principles of practical design of typical engineering structures, with applications across a range of commonly-used structural materials.
establish links between the theory of structures, taught in the Part I courses IA Structural Mechanics and IB Structures, and the properties of materials as covered in courses on Materials and Engineering Applications.
study what differing approaches to design are appropriate for structures in different materials.
develop a design methodology that provides a firm basis for the structures courses taught in Part IIA and for the more advanced courses in the fourth year.

Objectives

As specific objectives, by the end of the course students should be able to:

have developed a good understanding of the structural forms appropriate in the various materials.
be aware of the likely critical factors (requirements, properties, behaviour) for design in the different materials.
be able to make sensible initial layout and sizing choices for simple structures in the various materials.
be able to carry out design calculations for basic structural elements in the various materials.
be aware of what design approaches will be appropriate, and what calculations necessary, for more complex structures in the various materials.
appreciate the influence of risk, and variability of loading and material properties, on structural design and calculations.

Content

Design methodologies will be developed, and design of typical elements will be discussed, for the following materials:

high-strength, ductile materials such as steel and aluminium alloys
moderately-high-strength, anisotropic, brittle materials such as advanced composites and timber
materials of low tensile but high compressive strength, such as concrete and masonry
reinforced concrete where concrete is combined with a ductile tensile material
brittle materials, such as glass

Overview and General Principles (5L)

evolution of structural form, with case studies. Influence of available construction techniques. Bridge forms and materials economic in certain span ranges.
requirements of a successful structure (considering collapse, buckling, deflection, cracking, imposed deformation, fatigue, fire, accident, corrosion etc, as well as construction method, cost and sustainability)
relevant material properties (modulus, anisotropy, strength, toughness, cost, fabrication possibilities, energy content)
risk, variability, and limit state design (brief introduction)
Span-to-depth ratio and design.
‘load path’ approaches to simplified design, and the ‘lower bound’ theorem as a design tool, with limitations.

Design approaches for different materials

(in most cases, highlighting the important aspects of behaviour, covering the initial design of typical elements such as beams, columns and joints, and studying forms for complete structures).

Ductile Metals (primarily steel) (3L)

Masonry (mention) and Reinforced Concrete (3L)

Timber and Advanced Composites (3L)

Glass (2L)

Coursework

[Coursework Title]

Learning objectives:

Practical information:

Sessions will take place in [Location], during week(s) [xxx].
This activity [involves/doesn't involve] preliminary work ([estimated duration]).

Full Technical Report:

Students [will/won't] have the option to submit a Full Technical Report.

Booklists

Please see the Booklist for Part IIA Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

S1

The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.

S3

Understanding of the requirement for engineering activities to promote sustainable development.

S4

Awareness of the framework of relevant legal requirements governing engineering activities, including personnel, health, safety, and risk (including environmental risk) issues.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P4

Understanding use of technical literature and other information sources.

P6

Understanding of appropriate codes of practice and industry standards.

P7

Awareness of quality issues.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

Last modified: 03/08/2017 15:31

Engineering Tripos Part IIA, 3D3: Structural Materials & Design, 2025-26

Module Leader

Lecturers

Dr R Foster, Dr J Becque, Prof A Lawrence

Lab Leader

Timing and Structure

Michaelmas Term. 16 Lectures.

Aims

The aims of the course are to:

Provide a general understanding of the relationship between the properties of common structural materials, and the principles and approaches underpinning their use in structural design
Provide a bridge between the fundamental general engineering understanding of structures and materials developed in Part I and the applied specialist modules of Part II
Provide knowledge and knowhow enabling structural designers to improve our use of energy and material in the design of the built environment while providing safe, useful structures for people to use

Objectives

As specific objectives, by the end of the course students should be able to:

[1] Use the lower-bound theory of plasticity to perform load-path design of structural arrangements and to appreciate the benefits and limitations of the approach
[2] Consider the influence of risk, and variability of loading and material properties, in structural design and calculation
[3] Explain the environmental impacts of structural material and design choices
[4] Understand and carry out early-stage structural design with various structural materials
[4.1] Identify the theoretical and practical considerations governing structural design in various materials and explain how these may be accommodated in design
[4.2] Make reasonable conceptual design decisions regarding appropriate structural form, initial layout and initial member sizing for simple structures in various materials;
[4.3] Perform preliminary technical design calculations for simple structures in various materials
[4.4] Determine what design approaches may be appropriate, and what calculations necessary, for more complex structures in various materials

Content

The implications of the general principles of structural mechanics – equilibrium, compatibility, constitutive laws, and stability – are investigated for different materials. This leads to discussion of typical structural forms in the various materials, the reasons for adopting them, and appropriate methods of construction. The significant types of structural behaviour, and therefore the most useful methods of analysis and calculation, are investigated for the different material types. Our basic aim is to establish means of making reasonable preliminary decisions about structural form, layout and initial sizing of structural members made from a range of common construction materials.

Design methodologies will be developed, and design of typical elements will be discussed, for:

materials of low tensile but high compressive strength, such as masonry and glass;
composite materials of low tensile strength combined with a ductile tensile material, such as reinforced concrete;
high-strength, ductile materials such as steel and aluminium alloys;
moderate- to high-strength, anisotropic, brittle materials such as engineered timber.

The critical modes of failure of structures made from these materials tend to differ, as do other considerations such as environmental impacts, so design approaches will be correspondingly different.

Weeks 3-8 apply these considerations and approaches to design with various structural materials including: masonry; glass; reinforced concrete; steel and timber.

Coursework

Concrete Lab

Learning objectives:

To be able to:

1.Describe the common ingredients of concrete and their properties;

2.Design a concrete mix to satisfy certain technical requirements and cast a trial cube;

3.Supervise the casting of reinforced concrete beams and various plain concrete specimens for subsequent testing;

4.Observe and record results of destructive testing and identify different failure modes in concrete;

5.Compare empirical results with theoretical predictions based on as built-data, and evaluate the effectiveness and limitations of the theory.

Practical information:

Details will be available on the course Moodle page early in the term.

Full Technical Report:

Students will have the option to submit a Full Technical Report.

Booklists

Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Prof J M Allwood and Prof Simon Guest

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

S1

The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.

S3

Understanding of the requirement for engineering activities to promote sustainable development.

S4

Awareness of the framework of relevant legal requirements governing engineering activities, including personnel, health, safety, and risk (including environmental risk) issues.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P4

Understanding use of technical literature and other information sources.

P6

Understanding of appropriate codes of practice and industry standards.

P7

Awareness of quality issues.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

Last modified: 04/06/2025 13:18

Engineering Tripos Part IA, 1P2: Structures, 2018-19

Lecturers

Timing and Structure

Weeks 1-8 Michaelmas term and weeks 3-8 Lent term. 24 lectures

Aims

The aims of the course are to:

Inform students of the key role of structures in different branches of engineering
Illustrate the way in which structural engineers use the principles of structural mechanics to understand the behaviour of structures and so to design structures in order to meet specified requirements
Examine in detail certain simple structural forms, including triangulated frameworks, beams and cables; to understand how such structures carry applied loads, how they deform under load, and how slender members may buckle

Objectives

As specific objectives, by the end of the course students should be able to:

Describe, qualitatively, the way in which different kinds of structure (frameworks, beams, cables, pressure vessels, etc.) support the loads that are applied to them.
Analyse the limiting equilibrium conditions of bodies in frictional contact.
Determine the axial force in any member of a statically determinate pin-jointed framework, making use of structural symmetry and of the principle of superposition when appropriate
Explain and determine the shape of an inextensional cable subject to concentrated and distributed loads, as well as the tension distribution and support reactions.
Test the stability of a simple, statically determinate arch structure
Determine the displacement of any point of a pin-jointed framework subject to prescribed bar extensions by using a displacement diagram
Understand and apply the equation of virtual work for pin-jointed frameworks and know how to choose appropriate equilibrium and compatible sets
Construct bending-moment and shearing-force diagrams for simple beam structures, and to explain the relationship between them.
Explain curvature, and how it changes in an elastic beam when the bending moment changes.
Explain and compute the geometry of deflection of an initially straight beam on account of curvature within it.
Explain and compute the detailed distribution of bending stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a bending moment.
Explain and compute the distribution of shearing stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a shearing force.
Determine the buckling load of a column, and be able to approach the design of columns accounting for the effects of yielding of the material and geometric imperfections.

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

Equilibrium of point forces, moments and couples

Forces as vectors
Moments as vectors
Couples [3, Sect 1/1-1/5, 1/7-2/5]
Resultants [3, Sect 2/6]
Equilibrium [3, Sect 2/6, 3/3]
Accuracy in structural mechanics

Distributed loads and friction forces

Forms of distributed load [3, Sect 1/6, 5/1- 5/3, 5/9]
Contact forces (without friction)
Contact forces (with friction) [3, Sect 6/1-6/3, 6/8]
Distributed friction

Supports and free-body diagrams

Pin-joints
Roller supports
Built-in or ‘encastré’ supports
Catalogue of support options
Free-body diagrams [3, Sect 3/1- 3/2, 3/4]

2. Internal forces (3L)

Pin-jointed trusses

Method of joints [3, Sect 4/3]
Method of sections [3, Sect 4/4]
Some simplifications in analysing planar pin-jointed trusses
Superposition
Symmetry

Shear forces and bending moments

Beams with transverse loading
Free-body diagrams with shear forces and bending moments
Arches [4, Sect 5.1, 5.6], [7, Ch. 5]

Sress

Two-dimensional plane stress in thin-walled shells
Thin-walled shells with uniform stress

3. Deflection (5L)

Cables and compatibility

Cables subjected to concentrated loads
Cables subjected to distributed loads

Deflection of members in pin-jointed frames

Statically determinate frames
Strains, Hooke’s Law and bar extensions [5, Sect 5.2, 5.3, 5.4]
Internal states of stress [5, Sect 5.5]

Displacement Diagrams

Procedure for drawing displacement diagrams [5, Sect 2.3]
Displacement diagram used for analysing real structures
Interpreting displacement diagrams

Virtual work

Real work
Derivation of virtual work for pin-jointed frames
Using virtual work to find extensions or nodal displacements
Using virtual work to find forces or bar tensions

Structural design

Iterative design
Structural optimisation

4. Equilibrium of Beams (2L)

Introduction, hypotheses, sign conventions (5) Sect. 3.1, 3.2
Distortion produced by internal forces
Calculation of M, S, and T by analysis of free bodies (5) Sect. 3.2-3.4
Differential relationships between q, S, and M (5) Sect. 3.5
Construction of bending moment diagrams
Statical indeterminacy
Case study

5. Deflection of Straight Elastic Beams (2L)

Curvature and change of curvature, integration of curvature to find deflection
(5) Sect. 8.1,8.2
Deflection of elastic beams by integration (5) Sect. 8.3
Deflection of elastic beams by superposition of deflection coefficients (5) Sect. 8.4

6. Stresses in Elastic Beams (5L)

Introduction, basic geometric concepts (5) Sect. 7.2
Bending of beams with rectangular cross-section (5) Sect. 7.5
Bending of beams with non-rectangular cross-section, centroid and second-moment of area
Use of section tables
Combined bending moment and axial force
Bending stresses in composite beams, transformed section, bending of reinforced concrete beams
Shear stresses in beams (5) Sect. 7.6

7. Buckling of Columns (3L)

Introduction, examples, hypotheses
Euler column, fixed-end conditions, effective length (5) Sect. 9.4 (6) Sect 5.1
Critical stress
Imperfections (6) Sect 5.2
Design of columns

REFERENCES

(1) GORDON, J.E. STRUCTURES OR WHY THINGS DON'T FALL DOWN
(2) HEYMAN, J. THE SCIENCE OF STRUCTURAL ENGINEERING
(3) MERIAM,J.L. & KRAIGE,L.G. ENGINEERING MECHANICS.VOL.1:STATICS
(4) FRENCH, M. INVENTION AND EVOLUTION
(5) CRANDALL,S.H.DAHL,N.C. & LARDNER,T.J INTRODUCTION TO THE MECHANICS OF SOLIDS,with SI Units
(6) HEYMAN,J.BASIC STRUCTURAL THEORY
(7) HEYMAN, J. STRUCTURAL ANALYSIS: A HISTORICAL APPROACH

Booklists

Please see the Booklist for Part IA Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

D3

Identify and manage cost drivers.

D5

Ensure fitness for purpose for all aspects of the problem including production, operation, maintenance and disposal.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

Last modified: 30/09/2018 17:48

Engineering Tripos Part IA, 1P2: Structures, 2021-22

Timing and Structure

Weeks 1-8 Michaelmas term and weeks 3-8 Lent term. 24 lectures

Aims

The aims of the course are to:

Inform students of the key role of structures in different branches of engineering
Illustrate the way in which structural engineers use the principles of structural mechanics to understand the behaviour of structures and so to design structures in order to meet specified requirements
Examine in detail certain simple structural forms, including triangulated frameworks, beams and cables; to understand how such structures carry applied loads, how they deform under load, and how slender members may buckle

Objectives

As specific objectives, by the end of the course students should be able to:

Describe, qualitatively, the way in which different kinds of structure (frameworks, beams, cables, pressure vessels, etc.) support the loads that are applied to them.
Analyse the limiting equilibrium conditions of bodies in frictional contact.
Determine the axial force in any member of a statically determinate pin-jointed framework, making use of structural symmetry and of the principle of superposition when appropriate
Explain and determine the shape of an inextensional cable subject to concentrated and distributed loads, as well as the tension distribution and support reactions.
Test the stability of a simple, statically determinate arch structure
Determine the displacement of any point of a pin-jointed framework subject to prescribed bar extensions by using a displacement diagram
Understand and apply the equation of virtual work for pin-jointed frameworks and know how to choose appropriate equilibrium and compatible sets
Construct bending-moment and shearing-force diagrams for simple beam structures, and to explain the relationship between them.
Explain curvature, and how it changes in an elastic beam when the bending moment changes.
Explain and compute the geometry of deflection of an initially straight beam on account of curvature within it.
Explain and compute the detailed distribution of bending stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a bending moment.
Explain and compute the distribution of shearing stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a shearing force.
Determine the buckling load of a column, and be able to approach the design of columns accounting for the effects of yielding of the material and geometric imperfections.

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

Equilibrium of point forces, moments and couples

Forces as vectors
Moments as vectors
Couples [3, Sect 1/1-1/5, 1/7-2/5]
Resultants [3, Sect 2/6]
Equilibrium [3, Sect 2/6, 3/3]
Accuracy in structural mechanics

Distributed loads and friction forces

Forms of distributed load [3, Sect 1/6, 5/1- 5/3, 5/9]
Contact forces (without friction)
Contact forces (with friction) [3, Sect 6/1-6/3, 6/8]
Distributed friction

Supports and free-body diagrams

Pin-joints
Roller supports
Built-in or ‘encastré’ supports
Catalogue of support options
Free-body diagrams [3, Sect 3/1- 3/2, 3/4]

2. Internal forces (3L)

Pin-jointed trusses

Method of joints [3, Sect 4/3]
Method of sections [3, Sect 4/4]
Some simplifications in analysing planar pin-jointed trusses
Superposition
Symmetry

Shear forces and bending moments

Beams with transverse loading
Free-body diagrams with shear forces and bending moments
Arches [4, Sect 5.1, 5.6], [7, Ch. 5]

Sress

Two-dimensional plane stress in thin-walled shells
Thin-walled shells with uniform stress

3. Deflection (5L)

Cables and compatibility

Cables subjected to concentrated loads
Cables subjected to distributed loads

Deflection of members in pin-jointed frames

Statically determinate frames
Strains, Hooke’s Law and bar extensions [5, Sect 5.2, 5.3, 5.4]
Internal states of stress [5, Sect 5.5]

Displacement Diagrams

Procedure for drawing displacement diagrams [5, Sect 2.3]
Displacement diagram used for analysing real structures
Interpreting displacement diagrams

Virtual work

Real work
Derivation of virtual work for pin-jointed frames
Using virtual work to find extensions or nodal displacements
Using virtual work to find forces or bar tensions

Structural design

Iterative design
Structural optimisation

4. Equilibrium of Beams (2L)

Introduction, hypotheses, sign conventions (5) Sect. 3.1, 3.2
Distortion produced by internal forces
Calculation of M, S, and T by analysis of free bodies (5) Sect. 3.2-3.4
Differential relationships between q, S, and M (5) Sect. 3.5
Construction of bending moment diagrams
Statical indeterminacy
Case study

5. Deflection of Straight Elastic Beams (2L)

Curvature and change of curvature, integration of curvature to find deflection
(5) Sect. 8.1,8.2
Deflection of elastic beams by integration (5) Sect. 8.3
Deflection of elastic beams by superposition of deflection coefficients (5) Sect. 8.4

6. Stresses in Elastic Beams (5L)

Introduction, basic geometric concepts (5) Sect. 7.2
Bending of beams with rectangular cross-section (5) Sect. 7.5
Bending of beams with non-rectangular cross-section, centroid and second-moment of area
Use of section tables
Combined bending moment and axial force
Bending stresses in composite beams, transformed section, bending of reinforced concrete beams
Shear stresses in beams (5) Sect. 7.6

7. Buckling of Columns (3L)

Introduction, examples, hypotheses
Euler column, fixed-end conditions, effective length (5) Sect. 9.4 (6) Sect 5.1
Critical stress
Imperfections (6) Sect 5.2
Design of columns

REFERENCES

Booklists

Please refer to the Booklist for Part IA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

D3

Identify and manage cost drivers.

D5

Ensure fitness for purpose for all aspects of the problem including production, operation, maintenance and disposal.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

Last modified: 20/05/2021 07:33

Engineering Tripos Part IA, 1P2: Structures, 2019-20

Course Leader

Lecturer

Lecturer

Timing and Structure

Weeks 1-8 Michaelmas term and weeks 3-8 Lent term. 24 lectures

Aims

The aims of the course are to:

Inform students of the key role of structures in different branches of engineering
Illustrate the way in which structural engineers use the principles of structural mechanics to understand the behaviour of structures and so to design structures in order to meet specified requirements
Examine in detail certain simple structural forms, including triangulated frameworks, beams and cables; to understand how such structures carry applied loads, how they deform under load, and how slender members may buckle

Objectives

As specific objectives, by the end of the course students should be able to:

Describe, qualitatively, the way in which different kinds of structure (frameworks, beams, cables, pressure vessels, etc.) support the loads that are applied to them.
Analyse the limiting equilibrium conditions of bodies in frictional contact.
Determine the axial force in any member of a statically determinate pin-jointed framework, making use of structural symmetry and of the principle of superposition when appropriate
Explain and determine the shape of an inextensional cable subject to concentrated and distributed loads, as well as the tension distribution and support reactions.
Test the stability of a simple, statically determinate arch structure
Determine the displacement of any point of a pin-jointed framework subject to prescribed bar extensions by using a displacement diagram
Understand and apply the equation of virtual work for pin-jointed frameworks and know how to choose appropriate equilibrium and compatible sets
Construct bending-moment and shearing-force diagrams for simple beam structures, and to explain the relationship between them.
Explain curvature, and how it changes in an elastic beam when the bending moment changes.
Explain and compute the geometry of deflection of an initially straight beam on account of curvature within it.
Explain and compute the detailed distribution of bending stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a bending moment.
Explain and compute the distribution of shearing stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a shearing force.
Determine the buckling load of a column, and be able to approach the design of columns accounting for the effects of yielding of the material and geometric imperfections.

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

Equilibrium of point forces, moments and couples

Forces as vectors
Moments as vectors
Couples [3, Sect 1/1-1/5, 1/7-2/5]
Resultants [3, Sect 2/6]
Equilibrium [3, Sect 2/6, 3/3]
Accuracy in structural mechanics

Distributed loads and friction forces

Forms of distributed load [3, Sect 1/6, 5/1- 5/3, 5/9]
Contact forces (without friction)
Contact forces (with friction) [3, Sect 6/1-6/3, 6/8]
Distributed friction

Supports and free-body diagrams

Pin-joints
Roller supports
Built-in or ‘encastré’ supports
Catalogue of support options
Free-body diagrams [3, Sect 3/1- 3/2, 3/4]

2. Internal forces (3L)

Pin-jointed trusses

Method of joints [3, Sect 4/3]
Method of sections [3, Sect 4/4]
Some simplifications in analysing planar pin-jointed trusses
Superposition
Symmetry

Shear forces and bending moments

Beams with transverse loading
Free-body diagrams with shear forces and bending moments
Arches [4, Sect 5.1, 5.6], [7, Ch. 5]

Sress

Two-dimensional plane stress in thin-walled shells
Thin-walled shells with uniform stress

3. Deflection (5L)

Cables and compatibility

Cables subjected to concentrated loads
Cables subjected to distributed loads

Deflection of members in pin-jointed frames

Statically determinate frames
Strains, Hooke’s Law and bar extensions [5, Sect 5.2, 5.3, 5.4]
Internal states of stress [5, Sect 5.5]

Displacement Diagrams

Procedure for drawing displacement diagrams [5, Sect 2.3]
Displacement diagram used for analysing real structures
Interpreting displacement diagrams

Virtual work

Real work
Derivation of virtual work for pin-jointed frames
Using virtual work to find extensions or nodal displacements
Using virtual work to find forces or bar tensions

Structural design

Iterative design
Structural optimisation

4. Equilibrium of Beams (2L)

Introduction, hypotheses, sign conventions (5) Sect. 3.1, 3.2
Distortion produced by internal forces
Calculation of M, S, and T by analysis of free bodies (5) Sect. 3.2-3.4
Differential relationships between q, S, and M (5) Sect. 3.5
Construction of bending moment diagrams
Statical indeterminacy
Case study

5. Deflection of Straight Elastic Beams (2L)

Curvature and change of curvature, integration of curvature to find deflection
(5) Sect. 8.1,8.2
Deflection of elastic beams by integration (5) Sect. 8.3
Deflection of elastic beams by superposition of deflection coefficients (5) Sect. 8.4

6. Stresses in Elastic Beams (5L)

Introduction, basic geometric concepts (5) Sect. 7.2
Bending of beams with rectangular cross-section (5) Sect. 7.5
Bending of beams with non-rectangular cross-section, centroid and second-moment of area
Use of section tables
Combined bending moment and axial force
Bending stresses in composite beams, transformed section, bending of reinforced concrete beams
Shear stresses in beams (5) Sect. 7.6

7. Buckling of Columns (3L)

Introduction, examples, hypotheses
Euler column, fixed-end conditions, effective length (5) Sect. 9.4 (6) Sect 5.1
Critical stress
Imperfections (6) Sect 5.2
Design of columns

REFERENCES

Booklists

Please see the Booklist for Part IA Courses for references for this module.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

D3

Identify and manage cost drivers.

D5

Ensure fitness for purpose for all aspects of the problem including production, operation, maintenance and disposal.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

Last modified: 16/05/2019 07:43

Engineering Tripos Part IA, 1P2: Structures, 2024-25

Course Leader

Lecturer

Prof A McRobie

Lecturer

Timing and Structure

Weeks 1-8 Michaelmas term and weeks 1-8 Lent term. 24 lectures. Michaelmas Term lectures will not be recorded; rather, the Moodle page will contain pre-prepared recordings of the material. Lent Term lectures will be recorded.

Aims

The aims of the course are to:

Inform students of the key role of structures in different branches of engineering
Illustrate the way in which structural engineers use the principles of structural mechanics to understand the behaviour of structures and so to design structures in order to meet specified requirements
Examine in detail certain simple structural forms, including triangulated frameworks, beams and cables; to understand how such structures carry applied loads, how they deform under load, and how slender members may buckle

Objectives

As specific objectives, by the end of the course students should be able to:

Describe, qualitatively, the way in which different kinds of structure (frameworks, beams, cables, pressure vessels, etc.) support the loads that are applied to them.
Analyse the limiting equilibrium conditions of bodies in frictional contact.
Determine the axial force in any member of a statically determinate pin-jointed framework, making use of structural symmetry and of the principle of superposition when appropriate
Explain and determine the shape of an inextensional cable subject to concentrated and distributed loads, as well as the tension distribution and support reactions.
Test the stability of a simple, statically determinate arch structure
Determine the displacement of any point of a pin-jointed framework subject to prescribed bar extensions by using a displacement diagram
Understand and apply the equation of virtual work for pin-jointed frameworks and know how to choose appropriate equilibrium and compatible sets
Construct bending-moment and shearing-force diagrams for simple beam structures, and to explain the relationship between them.
Explain curvature, and how it changes in an elastic beam when the bending moment changes.
Explain and compute the geometry of deflection of an initially straight beam on account of curvature within it.
Explain and compute the detailed distribution of bending stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a bending moment.
Explain and compute the distribution of shearing stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a shearing force.
Determine the buckling load of a column, and be able to approach the design of columns accounting for the effects of yielding of the material and geometric imperfections.

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

Equilibrium of point forces, moments and couples

Forces as vectors
Moments as vectors
Couples [3, Sect 1/1-1/5, 1/7-2/5]
Resultants [3, Sect 2/6]
Equilibrium [3, Sect 2/6, 3/3]
Accuracy in structural mechanics

Distributed loads and friction forces

Forms of distributed load [3, Sect 1/6, 5/1- 5/3, 5/9]
Contact forces (without friction)
Contact forces (with friction) [3, Sect 6/1-6/3, 6/8]
Distributed friction

Supports and free-body diagrams

Pin-joints
Roller supports
Built-in or ‘encastré’ supports
Catalogue of support options
Free-body diagrams [3, Sect 3/1- 3/2, 3/4]

2. Internal forces (3L)

Pin-jointed trusses

Method of joints [3, Sect 4/3]
Method of sections [3, Sect 4/4]
Some simplifications in analysing planar pin-jointed trusses
Superposition
Symmetry

Shear forces and bending moments

Beams with transverse loading
Free-body diagrams with shear forces and bending moments
Arches [4, Sect 5.1, 5.6], [7, Ch. 5]

Sress

Two-dimensional plane stress in thin-walled shells
Thin-walled shells with uniform stress

3. Deflection (5L)

Cables and compatibility

Cables subjected to concentrated loads
Cables subjected to distributed loads

Deflection of members in pin-jointed frames

Statically determinate frames
Strains, Hooke’s Law and bar extensions [5, Sect 5.2, 5.3, 5.4]
Internal states of stress [5, Sect 5.5]

Displacement Diagrams

Procedure for drawing displacement diagrams [5, Sect 2.3]
Displacement diagram used for analysing real structures
Interpreting displacement diagrams

Virtual work

Real work
Derivation of virtual work for pin-jointed frames
Using virtual work to find extensions or nodal displacements
Using virtual work to find forces or bar tensions

Structural design

Iterative design
Structural optimisation

4. Equilibrium of Beams (2L)

Introduction, hypotheses, sign conventions (5) Sect. 3.1, 3.2
Distortion produced by internal forces
Calculation of M, S, and T by analysis of free bodies (5) Sect. 3.2-3.4
Differential relationships between q, S, and M (5) Sect. 3.5
Construction of bending moment diagrams
Statical indeterminacy
Case study

5. Deflection of Straight Elastic Beams (2L)

Curvature and change of curvature, integration of curvature to find deflection
(5) Sect. 8.1,8.2
Deflection of elastic beams by integration (5) Sect. 8.3
Deflection of elastic beams by superposition of deflection coefficients (5) Sect. 8.4

6. Stresses in Elastic Beams (5L)

Introduction, basic geometric concepts (5) Sect. 7.2
Bending of beams with rectangular cross-section (5) Sect. 7.5
Bending of beams with non-rectangular cross-section, centroid and second-moment of area
Use of section tables
Combined bending moment and axial force
Bending stresses in composite beams, transformed section, bending of reinforced concrete beams
Shear stresses in beams (5) Sect. 7.6

7. Buckling of Columns (3L)

Introduction, examples, hypotheses
Euler column, fixed-end conditions, effective length (5) Sect. 9.4 (6) Sect 5.1
Critical stress
Imperfections (6) Sect 5.2
Design of columns

REFERENCES

Booklists

Please refer to the Booklist for Part IA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

D3

Identify and manage cost drivers.

D5

Ensure fitness for purpose for all aspects of the problem including production, operation, maintenance and disposal.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

Last modified: 30/07/2024 08:43

Engineering Tripos Part IA, 1P2: Structures, 2023-24

Course Leader

Lecturer

Lecturer

Timing and Structure

Aims

The aims of the course are to:

Inform students of the key role of structures in different branches of engineering
Illustrate the way in which structural engineers use the principles of structural mechanics to understand the behaviour of structures and so to design structures in order to meet specified requirements
Examine in detail certain simple structural forms, including triangulated frameworks, beams and cables; to understand how such structures carry applied loads, how they deform under load, and how slender members may buckle

Objectives

As specific objectives, by the end of the course students should be able to:

Describe, qualitatively, the way in which different kinds of structure (frameworks, beams, cables, pressure vessels, etc.) support the loads that are applied to them.
Analyse the limiting equilibrium conditions of bodies in frictional contact.
Determine the axial force in any member of a statically determinate pin-jointed framework, making use of structural symmetry and of the principle of superposition when appropriate
Explain and determine the shape of an inextensional cable subject to concentrated and distributed loads, as well as the tension distribution and support reactions.
Test the stability of a simple, statically determinate arch structure
Determine the displacement of any point of a pin-jointed framework subject to prescribed bar extensions by using a displacement diagram
Understand and apply the equation of virtual work for pin-jointed frameworks and know how to choose appropriate equilibrium and compatible sets
Construct bending-moment and shearing-force diagrams for simple beam structures, and to explain the relationship between them.
Explain curvature, and how it changes in an elastic beam when the bending moment changes.
Explain and compute the geometry of deflection of an initially straight beam on account of curvature within it.
Explain and compute the detailed distribution of bending stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a bending moment.
Explain and compute the distribution of shearing stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a shearing force.
Determine the buckling load of a column, and be able to approach the design of columns accounting for the effects of yielding of the material and geometric imperfections.

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

Equilibrium of point forces, moments and couples

Forces as vectors
Moments as vectors
Couples [3, Sect 1/1-1/5, 1/7-2/5]
Resultants [3, Sect 2/6]
Equilibrium [3, Sect 2/6, 3/3]
Accuracy in structural mechanics

Distributed loads and friction forces

Forms of distributed load [3, Sect 1/6, 5/1- 5/3, 5/9]
Contact forces (without friction)
Contact forces (with friction) [3, Sect 6/1-6/3, 6/8]
Distributed friction

Supports and free-body diagrams

Pin-joints
Roller supports
Built-in or ‘encastré’ supports
Catalogue of support options
Free-body diagrams [3, Sect 3/1- 3/2, 3/4]

2. Internal forces (3L)

Pin-jointed trusses

Method of joints [3, Sect 4/3]
Method of sections [3, Sect 4/4]
Some simplifications in analysing planar pin-jointed trusses
Superposition
Symmetry

Shear forces and bending moments

Beams with transverse loading
Free-body diagrams with shear forces and bending moments
Arches [4, Sect 5.1, 5.6], [7, Ch. 5]

Sress

Two-dimensional plane stress in thin-walled shells
Thin-walled shells with uniform stress

3. Deflection (5L)

Cables and compatibility

Cables subjected to concentrated loads
Cables subjected to distributed loads

Deflection of members in pin-jointed frames

Statically determinate frames
Strains, Hooke’s Law and bar extensions [5, Sect 5.2, 5.3, 5.4]
Internal states of stress [5, Sect 5.5]

Displacement Diagrams

Procedure for drawing displacement diagrams [5, Sect 2.3]
Displacement diagram used for analysing real structures
Interpreting displacement diagrams

Virtual work

Real work
Derivation of virtual work for pin-jointed frames
Using virtual work to find extensions or nodal displacements
Using virtual work to find forces or bar tensions

Structural design

Iterative design
Structural optimisation

4. Equilibrium of Beams (2L)

Introduction, hypotheses, sign conventions (5) Sect. 3.1, 3.2
Distortion produced by internal forces
Calculation of M, S, and T by analysis of free bodies (5) Sect. 3.2-3.4
Differential relationships between q, S, and M (5) Sect. 3.5
Construction of bending moment diagrams
Statical indeterminacy
Case study

5. Deflection of Straight Elastic Beams (2L)

Curvature and change of curvature, integration of curvature to find deflection
(5) Sect. 8.1,8.2
Deflection of elastic beams by integration (5) Sect. 8.3
Deflection of elastic beams by superposition of deflection coefficients (5) Sect. 8.4

6. Stresses in Elastic Beams (5L)

Introduction, basic geometric concepts (5) Sect. 7.2
Bending of beams with rectangular cross-section (5) Sect. 7.5
Bending of beams with non-rectangular cross-section, centroid and second-moment of area
Use of section tables
Combined bending moment and axial force
Bending stresses in composite beams, transformed section, bending of reinforced concrete beams
Shear stresses in beams (5) Sect. 7.6

7. Buckling of Columns (3L)

Introduction, examples, hypotheses
Euler column, fixed-end conditions, effective length (5) Sect. 9.4 (6) Sect 5.1
Critical stress
Imperfections (6) Sect 5.2
Design of columns

REFERENCES

Booklists

Please refer to the Booklist for Part IA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

GT1

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA3

Comprehend the broad picture and thus work with an appropriate level of detail.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

D1

Wide knowledge and comprehensive understanding of design processes and methodologies and the ability to apply and adapt them in unfamiliar situations.

D3

Identify and manage cost drivers.

D5

Ensure fitness for purpose for all aspects of the problem including production, operation, maintenance and disposal.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

US3

An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.

US4

An awareness of developing technologies related to own specialisation.

Last modified: 30/05/2023 15:08

Engineering Tripos Part IA, 1P2: Structures, 2022-23

Course Leader

Lecturer

Lecturer

Timing and Structure

Aims

The aims of the course are to:

Inform students of the key role of structures in different branches of engineering
Illustrate the way in which structural engineers use the principles of structural mechanics to understand the behaviour of structures and so to design structures in order to meet specified requirements
Examine in detail certain simple structural forms, including triangulated frameworks, beams and cables; to understand how such structures carry applied loads, how they deform under load, and how slender members may buckle

Objectives

As specific objectives, by the end of the course students should be able to:

Describe, qualitatively, the way in which different kinds of structure (frameworks, beams, cables, pressure vessels, etc.) support the loads that are applied to them.
Analyse the limiting equilibrium conditions of bodies in frictional contact.
Determine the axial force in any member of a statically determinate pin-jointed framework, making use of structural symmetry and of the principle of superposition when appropriate
Explain and determine the shape of an inextensional cable subject to concentrated and distributed loads, as well as the tension distribution and support reactions.
Test the stability of a simple, statically determinate arch structure
Determine the displacement of any point of a pin-jointed framework subject to prescribed bar extensions by using a displacement diagram
Understand and apply the equation of virtual work for pin-jointed frameworks and know how to choose appropriate equilibrium and compatible sets
Construct bending-moment and shearing-force diagrams for simple beam structures, and to explain the relationship between them.
Explain curvature, and how it changes in an elastic beam when the bending moment changes.
Explain and compute the geometry of deflection of an initially straight beam on account of curvature within it.
Explain and compute the detailed distribution of bending stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a bending moment.
Explain and compute the distribution of shearing stress in the cross-section of an elastic beam having a symmetrical cross-section, and sustaining a shearing force.
Determine the buckling load of a column, and be able to approach the design of columns accounting for the effects of yielding of the material and geometric imperfections.

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

Equilibrium of point forces, moments and couples

Forces as vectors
Moments as vectors
Couples [3, Sect 1/1-1/5, 1/7-2/5]
Resultants [3, Sect 2/6]
Equilibrium [3, Sect 2/6, 3/3]
Accuracy in structural mechanics

Distributed loads and friction forces

Forms of distributed load [3, Sect 1/6, 5/1- 5/3, 5/9]
Contact forces (without friction)
Contact forces (with friction) [3, Sect 6/1-6/3, 6/8]
Distributed friction

Supports and free-body diagrams

Pin-joints
Roller supports
Built-in or ‘encastré’ supports
Catalogue of support options
Free-body diagrams [3, Sect 3/1- 3/2, 3/4]

2. Internal forces (3L)

Pin-jointed trusses

Method of joints [3, Sect 4/3]
Method of sections [3, Sect 4/4]
Some simplifications in analysing planar pin-jointed trusses
Superposition
Symmetry

Shear forces and bending moments

Beams with transverse loading
Free-body diagrams with shear forces and bending moments
Arches [4, Sect 5.1, 5.6], [7, Ch. 5]

Sress

Two-dimensional plane stress in thin-walled shells
Thin-walled shells with uniform stress

3. Deflection (5L)

Cables and compatibility

Cables subjected to concentrated loads
Cables subjected to distributed loads

Deflection of members in pin-jointed frames

Statically determinate frames
Strains, Hooke’s Law and bar extensions [5, Sect 5.2, 5.3, 5.4]
Internal states of stress [5, Sect 5.5]

Displacement Diagrams

Procedure for drawing displacement diagrams [5, Sect 2.3]
Displacement diagram used for analysing real structures
Interpreting displacement diagrams

Virtual work

Real work
Derivation of virtual work for pin-jointed frames
Using virtual work to find extensions or nodal displacements
Using virtual work to find forces or bar tensions

Structural design

Iterative design
Structural optimisation

4. Equilibrium of Beams (2L)

Introduction, hypotheses, sign conventions (5) Sect. 3.1, 3.2
Distortion produced by internal forces
Calculation of M, S, and T by analysis of free bodies (5) Sect. 3.2-3.4
Differential relationships between q, S, and M (5) Sect. 3.5
Construction of bending moment diagrams
Statical indeterminacy
Case study

5. Deflection of Straight Elastic Beams (2L)

Curvature and change of curvature, integration of curvature to find deflection
(5) Sect. 8.1,8.2
Deflection of elastic beams by integration (5) Sect. 8.3
Deflection of elastic beams by superposition of deflection coefficients (5) Sect. 8.4

6. Stresses in Elastic Beams (5L)

Introduction, basic geometric concepts (5) Sect. 7.2
Bending of beams with rectangular cross-section (5) Sect. 7.5
Bending of beams with non-rectangular cross-section, centroid and second-moment of area
Use of section tables
Combined bending moment and axial force
Bending stresses in composite beams, transformed section, bending of reinforced concrete beams
Shear stresses in beams (5) Sect. 7.6

7. Buckling of Columns (3L)

Introduction, examples, hypotheses
Euler column, fixed-end conditions, effective length (5) Sect. 9.4 (6) Sect 5.1
Critical stress
Imperfections (6) Sect 5.2
Design of columns

REFERENCES

Booklists

Please refer to the Booklist for Part IA Courses for references to this module, this can be found on the associated Moodle course.

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard: