IA3

Engineering Tripos Part IA, 1P2: Structures, 2017-18

Lecturers

Dr Matt DeJong and Prof Simon Guest

Timing and Structure

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

Aims

The aims of the course are to:

Make students aware 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.
Explain the importance of assumptions and hypotheses in the development of theory.
Convince students of the important role of observation and experiment in the development of a proper theory of structures, and to provide practical examples of structural experiment, structural design and structural failure.
Examine in detail certain simple structural forms, including triangulated frameworks, beams and cables; to understand how such structures carry applied loads, and 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.
Explain and determine the shape of an inextensional cable subject to concentrated and distributed loads, as well as the tension distribution and support reactions.
Determine the internal stress resultants at any section of a simple, statically determinate arch structure, and to find the maximum values of the stress resultants.
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.
Determine the displacement of any point of a pin-jointed framework subject to prescribed bar extensions.
Understand the equation of virtual work for pin-jointed frameworks and 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 (1L)

1. Equilibrium in Two Dimensions (3L)

Forces, moments and couples (3) Sect 1/1-1/5,1/7-2/5
Resultants (3) Sect 2/6
Free-body diagrams (3) Sect 3/1-3/2,3/4
Polygon of forces (3) Sect 2/6, 3/3
Two-force problems (3) Sect 3/3
Three-force problems (3) Sect 3/3
Distributed forces: gravity (centre of mass), pressure and hydrostatic loads (centroid) (3) Sect 1/6,5/1-5/3,5/9
Friction(3) Sect 6/1-6/3,6/8

2. Forces in Structures (4L)

2.1 Calculation of Bar Forces in Statically Determinate Frameworks

Triangulated frameworks, pin-jointed idealisation (3) Sect 4/1-4/2
Method of joints (3) Sect 4/3
Method of sections (3) Sect 4/4
Superposition
Symmetry
Mechanisms and statically indeterminate frameworks
Classification of two-dimensional structures

2.2 Cables, Pressure Vessels, and Arches (4) Sect 5.1, 5.6, (7) Ch. 5

3. Displacements in Pin-Jointed Frameworks (2L)

3.1 Calculation of Bar Elongations

Elastic stress-strain relationship (5) Sect 5.2, 5.3, 5.4
Thermal strains (5) Sect 5.5

3.3 Calculation of Displacements by Displacement Diagrams

Assembly of an imperfect framework
Displacements due to small bar elongations (5) Sect 2.3

4. Principle of Virtual Work (2L)

Particles and rigid bodies in two dimensions (3) Sect 7/3
Reactions, bar forces and displacements in pin-jointed frameworks

5. 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

6. 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

7. 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

8. 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:

Toggle display of UK-SPEC areas.

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.

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: 31/05/2017 10:00

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

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:

Toggle display of UK-SPEC areas.

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: 26/07/2022 10:44

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

Lecturers

Prof J M Allwood and Prof Simon Guest

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:

Toggle display of UK-SPEC areas.

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, 2025-26

Course Leader

Prof Julian Allwood

Lecturer

Prof S Haigh

Lecturer

Prof J Allwood

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:

Toggle display of UK-SPEC areas.

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: 05/06/2025 11:12

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

Course Leader

Prof Simon Guest

Lecturer

Prof Simon Guest

Lecturer

Prof Julian Allwood

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:

Toggle display of UK-SPEC areas.

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, 2020-21

Course Leader

Prof Simon Guest

Lecturer

Prof Simon Guest

Lecturer

Prof Julian Allwood

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:

Toggle display of UK-SPEC areas.

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: 26/08/2020 09:16

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

Course Leader

Prof Simon Guest

Lecturer

Prof Simon Guest

Lecturer

Prof Julian Allwood

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:

Toggle display of UK-SPEC areas.

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, 2021-22

Course Leader

Prof Simon Guest

Lecturer

Prof Simon Guest

Lecturer

Prof Julian Allwood

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:

Toggle display of UK-SPEC areas.

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, 2024-25

Course Leader

Prof Julian Allwood

Lecturer

Prof A McRobie

Lecturer

Prof Julian Allwood

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:

Toggle display of UK-SPEC areas.

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 IB, 2P8: Manufacturing and Management, 2018-19

Lecturers

Prof T Minshall, Dr J Moultrie, Dr F Tietze

Lecturer

Dr J Moultrie

Lecturer

Dr F Tietze

Lecturer

Dr L Mortara

Timing and Structure

Easter Term: 12 lectures + 2 Industrial cases, 2 examples classes, 4 lectures/week.

Prerequisites

None

Aims

The aims of the course are to:

Introduce the excitement of business development related to technology innovations.
Cover the key choices facing anybody seeking to exploit the commercial potential of a technology based innovation – whether as an entrepreneur or acting within an existing business; however we can’t promise to make you millionaires

Objectives

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

Understand the likely stages of development from innovation to profit
Design an appropriate exploitation route for the given innovation
Describe the main features of how a business works

Content

Specific objectives are given for each lecture, and both the examples sheet questions and exam questions will be designed to test students learning against these objectives.

The lectures follow a series of key questions which represent the decisions that must be taken in finding an exploitation route for a technical innovation.

Where do inventions come from?

Inventions may arise from a spontaneous inventive step, a market demand, or a development of an existing idea. The purpose of this course is to explore the path from invention to business, but we start by examining the source of inventions and the conditions in which they are likely to occur. By the end of the lecture, given a perceived market need, students should be able to:

list at least six strategies by which new inventions are found
give at least one example for each strategy, and in the examples paper, think about how each strategy might apply in developing a new writing instrument
describe the structure of this course

Is there a market?

Two major sources of invention are ‘push’ – the inventor thinks of something new and must establish a market; and ‘pull’ – there is a clearly defined market demand. In both cases, successful exploitation depends on understanding of the nature of the market and identifying precisely what the need of the users and customers are. By the end of the lecture, given a proposed new technology or concept, students should be able to:

Apply the concept of the 'design mix' determine the key product attributes
Map the whole market for this product, identifying viable market segments - to name clusters of like minded customers

What do the users want?

It is important that any design meets the requirements of potential users, customers, and any other stakeholder who might be influenced by the design, from maintenance to distribution. There are a number of different ways in which these requirements might be captured and considered. By the end of the lecture, students should be able to:

Identify the stakeholders who are influenced by the design
Understand two distinct appraoches to understanding customer neds
Apply the Kano model

From specification to concept

Usually the inventive step is not a whole product but some feature of a broader ‘package’ offered to customers. In the early stages of the design process, it is important to clarify the exact product proposal, and to create viable concepts that might satisfy user requirements. By the end of the lecture, given a target market and a clear understanding of user needs, students should be able to:

Clearly specify what is needed
Understand how to generate and trest concepts, including the role of prototyping
Understand the importance of a design process

How will the product be made?

Having considered the idea, the relationships between the invention and the market, the protection of the idea and the ‘business model’ the product must now be made. This involves decisions about whether components are made ‘in house’ or ‘out-sourced’, how jobs should be designed for manual workers, and how to manage relationships with partner companies. By the end of the lecture, given a description of a product and a delivery system, students should be able to:

Describe the reasons why it is both desirable and impossible to balance supply and demand and suggest some strategies for managing both
Discuss the use of automated technology in designing a production system
Describe the choices made by managers of a supply chain to ensure efficient collaboration

How can your ideas be protected? An introduction to intellectual property

Before any public disclosure of an innovation, an inventor must decide how to prevent competitors copying the new features. By the end of the lecture, students should be able to:

understand what is meant by Intellectual Property
understand the implications of different methods of protection by:

trade marks
copyright
design right
registered designs
patents

How can your ideas be protected? More on patents and other aspects of IP

One method for protecting intellectual property is through a patent - but these are not as simple or as protective as is generally thought. By the end of the lecture, given a patent for an artefact or process, students should be able to:

identify whether a patent may be an appropriate method for protecting an idea, and weigh up some of the advantages and disadvantages of this method
understand the tests of novelty, usefulness and the inventive step which an invention must satisfy in order to be patentable
appreciate the need for confidentiality before a patent application is filed
understand the structure of a typical patent, especially the claims
talk reasonably intelligently to a patent agent

How does the innovation make money?

This lecture focuses attention onto two related issues. Firstly, we examine and compare the different 'business models', i.e. the various ways in which your business can generate revenue. This is trying to address the question of 'What are you actually going to sell?' Secondly, we turn attention back to looking at who the customer really is for your idea (a theme highlighted in lecture 2) and link this to the business model. By the end of the lecture, you should be able to:

List and compare the different types of business model
Link the choice of business model to a clear understanding of who the customer really is

How to get investment?

Businesses need resources (people, equipment, consumables, etc.) to create value. Many new firms need external financial investment in order to acquire these resources. External financial investment comes in different forms from a variety of sources. The aim of this lecture is to provide an overview of these different types and sources of investment, and explain what entrepreneurs need to do to in order to acquire investment. By the end of the lecture, students should be able to:

Compare the differnet types and sources of money available to start a new business
Select the appropriate source of funding for different stages of the technology commercialisation process
describe the basic sections of a business plan written to raise investment

How to work with other companies

Very few companies are able to create value by operating alone. Working in partnership with other businesses is a very common feature of innovation-based businesses. Partnerships can encompass joint development agreements, licensing deals, co-branding, market channel access, and many more. However, there are many management challenges that need to be overcome if partnerships are to deliver value to all partners. By the end of the lecture students should be able to:

describe the motives for forming partnerships
understand the different ways in which companies can work together
appreciate some of the complexities of setting up and managing partnerships

Keeping ahead through innovation

Implementing one good idea is not sufficient to ensure the long-term survival of a company. Companies need to innovate if they are to continue to grow. In this lecture, we will review the different types of innovation – such as product, process, service and business model – and the challenges of managing a portfolio of innovation projects in a growing business. By the end of the lecture, students should be able to:

list the different types of innovation
describe some of the challenges of managing a portfolio of 'old' and 'new' products/services
compare the challenges of managing radical versus incremental innovations

Managing growth

As companies grow, new management challenges need to be addressed. For example, when a company has only a few employees who all know each other very well, decisions can be made quickly. As a company grows and has hundreds or thousands of employees, things get more complicated. In this lecture, we will examine the differences between the management of a start-up and a larger, long-established company. By the end of the lecture, students should be able to:

compare the characteristics of a start-up versus,long established company
describe some of the different managemnet challenges resulting from these different characteristics

Case studies

As a conclusion to the course, two external speakers – one high-tech start-up founder, one senior manager from a large multinational firm – will discuss their own experience of successful innovation, giving students the chance to test knowledge gained in the sessions against real experience.

REFERENCES

Cagan & Vogel, (2002), Creating breakthrough products: innovation from product planning to program approval, Prentice-Hall, USA

Goffin, K. and R. F. Mitchell (2010). Innovation Management: Strategy and Implementation Using the Pentathlon Framework, Palgrave.

Lang (2002) The High-tech Entrepreneur's Handbook: How to Start and Run a High-tech Company, FT.com

Moore, (1998, 2008), Crossing the chasm: marketing and selling technology products to mainstream customers, Chichester, Sussex.

Ulrich & Eppinger, (2000, 2004 and 2008), Product design and development, McGraw-Hill Higher Education

IfM Design Management Group website: http://www.ifm.eng.cam.ac.uk/research/dmg/design-and-npd-management-tools/

Booklists

Please see the Booklist for Part IB 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:

Toggle display of UK-SPEC areas.

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.

D2

Understand customer and user needs and the importance of considerations such as aesthetics.

D3

Identify and manage cost drivers.

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.

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.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

P5

Awareness of nature of intellectual property and contractual issues.

US1

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

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: 23/04/2019 09:28

Search form

IA3

Lecturers

Timing and Structure

Aims

Objectives

Content

Introduction and Aims of the Course (1L)

1. Equilibrium in Two Dimensions (3L)

2. Forces in Structures (4L)

3. Displacements in Pin-Jointed Frameworks (2L)

4. Principle of Virtual Work (2L)

5. Equilibrium of Beams (2L)

6. Deflection of Straight Elastic Beams (2L)

7. Stresses in Elastic Beams (5L)

8. Buckling of Columns (3L)

REFERENCES

Booklists

Examination Guidelines

UK-SPEC

GT1

IA1

IA3

KU1

KU2

D1

D3

D5

E1

E2

E3

US1

US2

US3

US4

Course Leader

Lecturer

Lecturer

Timing and Structure

Aims

Objectives

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

2. Internal forces (3L)

3. Deflection (5L)

4. Equilibrium of Beams (2L)

5. Deflection of Straight Elastic Beams (2L)

6. Stresses in Elastic Beams (5L)

7. Buckling of Columns (3L)

REFERENCES

Booklists

Examination Guidelines

UK-SPEC

GT1

IA1

IA3

KU1

KU2

D1

D3

D5

E1

E2

E3

US1

US2

US3

US4

Lecturers

Timing and Structure

Aims

Objectives

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

2. Internal forces (3L)

3. Deflection (5L)

4. Equilibrium of Beams (2L)

5. Deflection of Straight Elastic Beams (2L)