Engineering Tripos Part IA, 1P1: Mechanics, 2024-25
Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8, Michaelmas term, 2 lectures/week
Aims
The aims of the course are to:
- Convey the fundamental role of mechanics in engineering.
- Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
- Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
- Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
- Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.
Objectives
As specific objectives, by the end of the course students should be able to:
- Apply concepts of kinematics to particles and rigid bodies in two dimensions.
- Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
- Differentiate a rotating vector.
- Understand and apply Newton's laws and the equations of energy and momentum of particles.
- Apply Newton's laws to variable mass problems.
- Apply the concept of angular momentum of a particle, and recognise when it is conserved.
- Apply the principles of particle dynamics to satellite motion.
- Determine the centre of mass and moment of inertia of a plane lamina
- Understand and apply the perpendicular and parallel axes theorems
- Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
- Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
- Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
- Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
- Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.
Content
The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.
Introduction
- Newton's laws of motion [I1]
- Units [I2]
- Forces [I3]
- Free Body Diagrams [I4]
- Frames of reference [I5]
Kinematics of Particles
- Cartesian coordinates [KP1]
- Polar coordinates [KP2]
- Intrinsic coordinates [KP3]
- Differentiation of a unit vector [KP4]
- Velocity and acceleration in different coordinate systems [KP5]
- Numerical differentiation [KP6]
- Relative position, velocity and acceleration [KP7]
Dynamics of Particles
- Newton's Laws applied to particles [DP1]
- D'Alembert force for a particle [DP2]
- Equations of motion [DP3]
- Numerical solution methods [DP4]
- Conservation of Energy [DP5]
- Potential energy, equilibrium and stability [DP6]
- Linear momentum [DP7]
- Variable mass systems [DP8]
- Angular momentum [DP9]
- Satellite motion in steady circular and elliptical orbits [DP10]
Kinematics of Rigid Bodies
- Relative motion [KRB1]
- Angular velocity as a vector [KRB2]
- Rotating reference frames [KRB3]
- Instantaneous centres for planar motion [KRB4]
Dynamics of Rigid Bodies
- Centre of mass of a rigid body [DRB1]
- Moment of inertia of a planar rigid body [DRB2]
- Dynamics of a rigid body with a fixed axis of rotation [DRB3]
- D'Alembert forces and moments for planar motion of a rigid body [DRB4]
- Linear and angular momentum of rigid bodies in planar motion [DRB5]
- Kinetic energy of a translating and rotating planar body [DRB6]
- Impact problems in plane motion [DRB7]
REFERENCES
[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
Comments:
Gregory [1] is a rigorous textbook with a physics perspective.
Malthe-Sorrensson [2] has many numerical examples.
Hibbeler [3] contains many illustrative diagrams and examples.
Meriam and Kraige [4] contains many illustrative diagrams and examples.
Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.
Topic cross references
| Gregory | Malthe-Sorrenssen | Hibbeler | Meriam Kraige | Prentis | |
|---|---|---|---|---|---|
| I1 | 3.1 | 5.3, 5.8, 5.9 | 1.2, 13.1 | 1.3 | |
| I2 | 3.1 | 3.1, 3.2 | 1.3, 13.1 | 1.4 | |
| I3 | 3.3 | 5.4 - 5.7 | 1.2 | ||
| I4 | 5.2, 7.1 | 3.2 | 3.3 | ||
| I5 | 3.2 | 5.8, 6.4 | 13.2 | 1.2 | |
| KP1 | (1.1 - 1.2) | 6.2 | 2.5 - 2.7 | 2.4 | |
| KP2 | 2.3 | 12.8 | 2.6 | ||
| KP3 | 12.7 | 2.5 | |||
| KP4 | 2.3 | 2.6, 5.7 | |||
| KP5 | (2.3) | 12.4, 12.5, 12.7 | 2.4 - 2.6 | ||
| KP6 | 4.1 - 4.2 | ||||
| KP7 | (2.6) | 12.10 | 2.8 | ||
| DP1 | 4.1 - 4.5 | 5.3, 7.2 - 7.6 | 13.1 - 13.2 | 3.1 - 3.5, 4.2 | |
| DP2 | 12.4 | 13.2 | (3.14) | ||
| DP3 | 4.1-4.5 | (7.2 - 7.6) | 13.2 - 13.6 | 3.4 - 3.5 | |
| DP4 | 4.2, 7.4, 7.5, 7.6, 10.3 | (C.12) | |||
| DP5 | 6.1,6.2, 6.4 | (11.1, 11.2) | 14.1 - 14.2, 14.5 - 14.6 | 3.6 - 3.7 | |
| DP6 | 6.3 | 11.3 | (3.7) | ||
| DP7 | 10.1 - 10.4 | 12.2 - 12.6 | 15.1 - 15.4 | 3.8 - 3.9 | |
| DP8 | (10.5) | 12.7 | 15.9 | 4.7 | |
| DP9 | 11.1 - 11.2 | 16.4 | 15.5 - 15.7 | 3.10 | 5.6 |
| DP10 | 7.1, 7.2, 7.3, 7.5, 7.6 | (5.5, 7.6) | 13.7 | 3.13 | |
| KRB1 | 2.6 | 16.7 - 16.8 | (3.14), 5.4, 5.6 | 4.3, 4.8 | |
| KRB2 | 16.1 | 14.6 | 16.3, 20.1 | 5.2, 7.3 | 4.4 |
| KRB3 | 17.1 | 20.4 | 5.7 | 4.3 | |
| KRB4 | 16.6 | 5.5 | 4.4, 4.7 | ||
| DRB1 | 3.5, A.1 | 13.2 | 9.2, 13.3 | ||
| DRB2 | 9.4, A.2, A.3 | 15.2 | 17.1 | 7.7, B.1 | |
| DRB3 | 11.6, 16.1 | 15.1 | 17.4 | 6.4 | |
| DRB4 | (11.6) | (17.2 - 17.5) | 6.1 - 6.5 | 5.3 | |
| DRB5 | 11.4, 11.5, 11.6 | 15.1 | 19.1 - 19.4 | 6.8 | 5.6, 5.8 |
| DRB6 | 9.4 | 15.2, 15.4, 15.5 | 18.1 - 18.5 | 6.6 | |
| DRB7 | 10.6 | 19.2 - 19.4 | 6.8 |
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
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.
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.
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.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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 08:42
Engineering Tripos Part IA, 1P1: Mechanics, 2020-21
Course Leader
Lecturer
Timing and Structure
Weeks 1-8, Michaelmas term, 2 lectures/week
Aims
The aims of the course are to:
- Convey the fundamental role of mechanics in engineering.
- Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
- Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
- Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
- Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.
Objectives
As specific objectives, by the end of the course students should be able to:
- Apply concepts of kinematics to particles and rigid bodies in two dimensions.
- Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
- Differentiate a rotating vector.
- Understand and apply Newton's laws and the equations of energy and momentum of particles.
- Apply Newton's laws to variable mass problems.
- Apply the concept of angular momentum of a particle, and recognise when it is conserved.
- Apply the principles of particle dynamics to satellite motion.
- Determine the centre of mass and moment of inertia of a plane lamina
- Understand and apply the perpendicular and parallel axes theorems
- Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
- Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
- Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
- Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
- Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.
Content
The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.
Introduction
- Newton's laws of motion [I1]
- Units [I2]
- Forces [I3]
- Free Body Diagrams [I4]
- Frames of reference [I5]
Kinematics of Particles
- Cartesian coordinates [KP1]
- Polar coordinates [KP2]
- Intrinsic coordinates [KP3]
- Differentiation of a unit vector [KP4]
- Velocity and acceleration in different coordinate systems [KP5]
- Numerical differentiation [KP6]
- Relative position, velocity and acceleration [KP7]
Dynamics of Particles
- Newton's Laws applied to particles [DP1]
- D'Alembert force for a particle [DP2]
- Equations of motion [DP3]
- Numerical solution methods [DP4]
- Conservation of Energy [DP5]
- Potential energy, equilibrium and stability [DP6]
- Linear momentum [DP7]
- Variable mass systems [DP8]
- Angular momentum [DP9]
- Satellite motion in steady circular and elliptical orbits [DP10]
Kinematics of Rigid Bodies
- Relative motion [KRB1]
- Angular velocity as a vector [KRB2]
- Rotating reference frames [KRB3]
- Instantaneous centres for planar motion [KRB4]
Dynamics of Rigid Bodies
- Centre of mass of a rigid body [DRB1]
- Moment of inertia of a planar rigid body [DRB2]
- Dynamics of a rigid body with a fixed axis of rotation [DRB3]
- D'Alembert forces and moments for planar motion of a rigid body [DRB4]
- Linear and angular momentum of rigid bodies in planar motion [DRB5]
- Kinetic energy of a translating and rotating planar body [DRB6]
- Impact problems in plane motion [DRB7]
REFERENCES
[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
Comments:
Gregory [1] is a rigorous textbook with a physics perspective.
Malthe-Sorrensson [2] has many numerical examples.
Hibbeler [3] contains many illustrative diagrams and examples.
Meriam and Kraige [4] contains many illustrative diagrams and examples.
Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.
Topic cross references
| Gregory | Malthe-Sorrenssen | Hibbeler | Meriam Kraige | Prentis | |
|---|---|---|---|---|---|
| I1 | 3.1 | 5.3, 5.8, 5.9 | 1.2, 13.1 | 1.3 | |
| I2 | 3.1 | 3.1, 3.2 | 1.3, 13.1 | 1.4 | |
| I3 | 3.3 | 5.4 - 5.7 | 1.2 | ||
| I4 | 5.2, 7.1 | 3.2 | 3.3 | ||
| I5 | 3.2 | 5.8, 6.4 | 13.2 | 1.2 | |
| KP1 | (1.1 - 1.2) | 6.2 | 2.5 - 2.7 | 2.4 | |
| KP2 | 2.3 | 12.8 | 2.6 | ||
| KP3 | 12.7 | 2.5 | |||
| KP4 | 2.3 | 2.6, 5.7 | |||
| KP5 | (2.3) | 12.4, 12.5, 12.7 | 2.4 - 2.6 | ||
| KP6 | 4.1 - 4.2 | ||||
| KP7 | (2.6) | 12.10 | 2.8 | ||
| DP1 | 4.1 - 4.5 | 5.3, 7.2 - 7.6 | 13.1 - 13.2 | 3.1 - 3.5, 4.2 | |
| DP2 | 12.4 | 13.2 | (3.14) | ||
| DP3 | 4.1-4.5 | (7.2 - 7.6) | 13.2 - 13.6 | 3.4 - 3.5 | |
| DP4 | 4.2, 7.4, 7.5, 7.6, 10.3 | (C.12) | |||
| DP5 | 6.1,6.2, 6.4 | (11.1, 11.2) | 14.1 - 14.2, 14.5 - 14.6 | 3.6 - 3.7 | |
| DP6 | 6.3 | 11.3 | (3.7) | ||
| DP7 | 10.1 - 10.4 | 12.2 - 12.6 | 15.1 - 15.4 | 3.8 - 3.9 | |
| DP8 | (10.5) | 12.7 | 15.9 | 4.7 | |
| DP9 | 11.1 - 11.2 | 16.4 | 15.5 - 15.7 | 3.10 | 5.6 |
| DP10 | 7.1, 7.2, 7.3, 7.5, 7.6 | (5.5, 7.6) | 13.7 | 3.13 | |
| KRB1 | 2.6 | 16.7 - 16.8 | (3.14), 5.4, 5.6 | 4.3, 4.8 | |
| KRB2 | 16.1 | 14.6 | 16.3, 20.1 | 5.2, 7.3 | 4.4 |
| KRB3 | 17.1 | 20.4 | 5.7 | 4.3 | |
| KRB4 | 16.6 | 5.5 | 4.4, 4.7 | ||
| DRB1 | 3.5, A.1 | 13.2 | 9.2, 13.3 | ||
| DRB2 | 9.4, A.2, A.3 | 15.2 | 17.1 | 7.7, B.1 | |
| DRB3 | 11.6, 16.1 | 15.1 | 17.4 | 6.4 | |
| DRB4 | (11.6) | (17.2 - 17.5) | 6.1 - 6.5 | 5.3 | |
| DRB5 | 11.4, 11.5, 11.6 | 15.1 | 19.1 - 19.4 | 6.8 | 5.6, 5.8 |
| DRB6 | 9.4 | 15.2, 15.4, 15.5 | 18.1 - 18.5 | 6.6 | |
| DRB7 | 10.6 | 19.2 - 19.4 | 6.8 |
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
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.
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.
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.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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 09:15
Engineering Tripos Part IA, 1P1: Mechanics, 2022-23
Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8, Michaelmas term, 2 lectures/week
Aims
The aims of the course are to:
- Convey the fundamental role of mechanics in engineering.
- Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
- Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
- Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
- Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.
Objectives
As specific objectives, by the end of the course students should be able to:
- Apply concepts of kinematics to particles and rigid bodies in two dimensions.
- Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
- Differentiate a rotating vector.
- Understand and apply Newton's laws and the equations of energy and momentum of particles.
- Apply Newton's laws to variable mass problems.
- Apply the concept of angular momentum of a particle, and recognise when it is conserved.
- Apply the principles of particle dynamics to satellite motion.
- Determine the centre of mass and moment of inertia of a plane lamina
- Understand and apply the perpendicular and parallel axes theorems
- Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
- Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
- Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
- Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
- Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.
Content
The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.
Introduction
- Newton's laws of motion [I1]
- Units [I2]
- Forces [I3]
- Free Body Diagrams [I4]
- Frames of reference [I5]
Kinematics of Particles
- Cartesian coordinates [KP1]
- Polar coordinates [KP2]
- Intrinsic coordinates [KP3]
- Differentiation of a unit vector [KP4]
- Velocity and acceleration in different coordinate systems [KP5]
- Numerical differentiation [KP6]
- Relative position, velocity and acceleration [KP7]
Dynamics of Particles
- Newton's Laws applied to particles [DP1]
- D'Alembert force for a particle [DP2]
- Equations of motion [DP3]
- Numerical solution methods [DP4]
- Conservation of Energy [DP5]
- Potential energy, equilibrium and stability [DP6]
- Linear momentum [DP7]
- Variable mass systems [DP8]
- Angular momentum [DP9]
- Satellite motion in steady circular and elliptical orbits [DP10]
Kinematics of Rigid Bodies
- Relative motion [KRB1]
- Angular velocity as a vector [KRB2]
- Rotating reference frames [KRB3]
- Instantaneous centres for planar motion [KRB4]
Dynamics of Rigid Bodies
- Centre of mass of a rigid body [DRB1]
- Moment of inertia of a planar rigid body [DRB2]
- Dynamics of a rigid body with a fixed axis of rotation [DRB3]
- D'Alembert forces and moments for planar motion of a rigid body [DRB4]
- Linear and angular momentum of rigid bodies in planar motion [DRB5]
- Kinetic energy of a translating and rotating planar body [DRB6]
- Impact problems in plane motion [DRB7]
REFERENCES
[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
Comments:
Gregory [1] is a rigorous textbook with a physics perspective.
Malthe-Sorrensson [2] has many numerical examples.
Hibbeler [3] contains many illustrative diagrams and examples.
Meriam and Kraige [4] contains many illustrative diagrams and examples.
Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.
Topic cross references
| Gregory | Malthe-Sorrenssen | Hibbeler | Meriam Kraige | Prentis | |
|---|---|---|---|---|---|
| I1 | 3.1 | 5.3, 5.8, 5.9 | 1.2, 13.1 | 1.3 | |
| I2 | 3.1 | 3.1, 3.2 | 1.3, 13.1 | 1.4 | |
| I3 | 3.3 | 5.4 - 5.7 | 1.2 | ||
| I4 | 5.2, 7.1 | 3.2 | 3.3 | ||
| I5 | 3.2 | 5.8, 6.4 | 13.2 | 1.2 | |
| KP1 | (1.1 - 1.2) | 6.2 | 2.5 - 2.7 | 2.4 | |
| KP2 | 2.3 | 12.8 | 2.6 | ||
| KP3 | 12.7 | 2.5 | |||
| KP4 | 2.3 | 2.6, 5.7 | |||
| KP5 | (2.3) | 12.4, 12.5, 12.7 | 2.4 - 2.6 | ||
| KP6 | 4.1 - 4.2 | ||||
| KP7 | (2.6) | 12.10 | 2.8 | ||
| DP1 | 4.1 - 4.5 | 5.3, 7.2 - 7.6 | 13.1 - 13.2 | 3.1 - 3.5, 4.2 | |
| DP2 | 12.4 | 13.2 | (3.14) | ||
| DP3 | 4.1-4.5 | (7.2 - 7.6) | 13.2 - 13.6 | 3.4 - 3.5 | |
| DP4 | 4.2, 7.4, 7.5, 7.6, 10.3 | (C.12) | |||
| DP5 | 6.1,6.2, 6.4 | (11.1, 11.2) | 14.1 - 14.2, 14.5 - 14.6 | 3.6 - 3.7 | |
| DP6 | 6.3 | 11.3 | (3.7) | ||
| DP7 | 10.1 - 10.4 | 12.2 - 12.6 | 15.1 - 15.4 | 3.8 - 3.9 | |
| DP8 | (10.5) | 12.7 | 15.9 | 4.7 | |
| DP9 | 11.1 - 11.2 | 16.4 | 15.5 - 15.7 | 3.10 | 5.6 |
| DP10 | 7.1, 7.2, 7.3, 7.5, 7.6 | (5.5, 7.6) | 13.7 | 3.13 | |
| KRB1 | 2.6 | 16.7 - 16.8 | (3.14), 5.4, 5.6 | 4.3, 4.8 | |
| KRB2 | 16.1 | 14.6 | 16.3, 20.1 | 5.2, 7.3 | 4.4 |
| KRB3 | 17.1 | 20.4 | 5.7 | 4.3 | |
| KRB4 | 16.6 | 5.5 | 4.4, 4.7 | ||
| DRB1 | 3.5, A.1 | 13.2 | 9.2, 13.3 | ||
| DRB2 | 9.4, A.2, A.3 | 15.2 | 17.1 | 7.7, B.1 | |
| DRB3 | 11.6, 16.1 | 15.1 | 17.4 | 6.4 | |
| DRB4 | (11.6) | (17.2 - 17.5) | 6.1 - 6.5 | 5.3 | |
| DRB5 | 11.4, 11.5, 11.6 | 15.1 | 19.1 - 19.4 | 6.8 | 5.6, 5.8 |
| DRB6 | 9.4 | 15.2, 15.4, 15.5 | 18.1 - 18.5 | 6.6 | |
| DRB7 | 10.6 | 19.2 - 19.4 | 6.8 |
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
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.
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.
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.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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: 27/09/2022 11:52
Engineering Tripos Part IA, 1P1: Mechanics, 2023-24
Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8, Michaelmas term, 2 lectures/week
Aims
The aims of the course are to:
- Convey the fundamental role of mechanics in engineering.
- Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
- Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
- Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
- Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.
Objectives
As specific objectives, by the end of the course students should be able to:
- Apply concepts of kinematics to particles and rigid bodies in two dimensions.
- Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
- Differentiate a rotating vector.
- Understand and apply Newton's laws and the equations of energy and momentum of particles.
- Apply Newton's laws to variable mass problems.
- Apply the concept of angular momentum of a particle, and recognise when it is conserved.
- Apply the principles of particle dynamics to satellite motion.
- Determine the centre of mass and moment of inertia of a plane lamina
- Understand and apply the perpendicular and parallel axes theorems
- Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
- Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
- Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
- Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
- Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.
Content
The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.
Introduction
- Newton's laws of motion [I1]
- Units [I2]
- Forces [I3]
- Free Body Diagrams [I4]
- Frames of reference [I5]
Kinematics of Particles
- Cartesian coordinates [KP1]
- Polar coordinates [KP2]
- Intrinsic coordinates [KP3]
- Differentiation of a unit vector [KP4]
- Velocity and acceleration in different coordinate systems [KP5]
- Numerical differentiation [KP6]
- Relative position, velocity and acceleration [KP7]
Dynamics of Particles
- Newton's Laws applied to particles [DP1]
- D'Alembert force for a particle [DP2]
- Equations of motion [DP3]
- Numerical solution methods [DP4]
- Conservation of Energy [DP5]
- Potential energy, equilibrium and stability [DP6]
- Linear momentum [DP7]
- Variable mass systems [DP8]
- Angular momentum [DP9]
- Satellite motion in steady circular and elliptical orbits [DP10]
Kinematics of Rigid Bodies
- Relative motion [KRB1]
- Angular velocity as a vector [KRB2]
- Rotating reference frames [KRB3]
- Instantaneous centres for planar motion [KRB4]
Dynamics of Rigid Bodies
- Centre of mass of a rigid body [DRB1]
- Moment of inertia of a planar rigid body [DRB2]
- Dynamics of a rigid body with a fixed axis of rotation [DRB3]
- D'Alembert forces and moments for planar motion of a rigid body [DRB4]
- Linear and angular momentum of rigid bodies in planar motion [DRB5]
- Kinetic energy of a translating and rotating planar body [DRB6]
- Impact problems in plane motion [DRB7]
REFERENCES
[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
Comments:
Gregory [1] is a rigorous textbook with a physics perspective.
Malthe-Sorrensson [2] has many numerical examples.
Hibbeler [3] contains many illustrative diagrams and examples.
Meriam and Kraige [4] contains many illustrative diagrams and examples.
Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.
Topic cross references
| Gregory | Malthe-Sorrenssen | Hibbeler | Meriam Kraige | Prentis | |
|---|---|---|---|---|---|
| I1 | 3.1 | 5.3, 5.8, 5.9 | 1.2, 13.1 | 1.3 | |
| I2 | 3.1 | 3.1, 3.2 | 1.3, 13.1 | 1.4 | |
| I3 | 3.3 | 5.4 - 5.7 | 1.2 | ||
| I4 | 5.2, 7.1 | 3.2 | 3.3 | ||
| I5 | 3.2 | 5.8, 6.4 | 13.2 | 1.2 | |
| KP1 | (1.1 - 1.2) | 6.2 | 2.5 - 2.7 | 2.4 | |
| KP2 | 2.3 | 12.8 | 2.6 | ||
| KP3 | 12.7 | 2.5 | |||
| KP4 | 2.3 | 2.6, 5.7 | |||
| KP5 | (2.3) | 12.4, 12.5, 12.7 | 2.4 - 2.6 | ||
| KP6 | 4.1 - 4.2 | ||||
| KP7 | (2.6) | 12.10 | 2.8 | ||
| DP1 | 4.1 - 4.5 | 5.3, 7.2 - 7.6 | 13.1 - 13.2 | 3.1 - 3.5, 4.2 | |
| DP2 | 12.4 | 13.2 | (3.14) | ||
| DP3 | 4.1-4.5 | (7.2 - 7.6) | 13.2 - 13.6 | 3.4 - 3.5 | |
| DP4 | 4.2, 7.4, 7.5, 7.6, 10.3 | (C.12) | |||
| DP5 | 6.1,6.2, 6.4 | (11.1, 11.2) | 14.1 - 14.2, 14.5 - 14.6 | 3.6 - 3.7 | |
| DP6 | 6.3 | 11.3 | (3.7) | ||
| DP7 | 10.1 - 10.4 | 12.2 - 12.6 | 15.1 - 15.4 | 3.8 - 3.9 | |
| DP8 | (10.5) | 12.7 | 15.9 | 4.7 | |
| DP9 | 11.1 - 11.2 | 16.4 | 15.5 - 15.7 | 3.10 | 5.6 |
| DP10 | 7.1, 7.2, 7.3, 7.5, 7.6 | (5.5, 7.6) | 13.7 | 3.13 | |
| KRB1 | 2.6 | 16.7 - 16.8 | (3.14), 5.4, 5.6 | 4.3, 4.8 | |
| KRB2 | 16.1 | 14.6 | 16.3, 20.1 | 5.2, 7.3 | 4.4 |
| KRB3 | 17.1 | 20.4 | 5.7 | 4.3 | |
| KRB4 | 16.6 | 5.5 | 4.4, 4.7 | ||
| DRB1 | 3.5, A.1 | 13.2 | 9.2, 13.3 | ||
| DRB2 | 9.4, A.2, A.3 | 15.2 | 17.1 | 7.7, B.1 | |
| DRB3 | 11.6, 16.1 | 15.1 | 17.4 | 6.4 | |
| DRB4 | (11.6) | (17.2 - 17.5) | 6.1 - 6.5 | 5.3 | |
| DRB5 | 11.4, 11.5, 11.6 | 15.1 | 19.1 - 19.4 | 6.8 | 5.6, 5.8 |
| DRB6 | 9.4 | 15.2, 15.4, 15.5 | 18.1 - 18.5 | 6.6 | |
| DRB7 | 10.6 | 19.2 - 19.4 | 6.8 |
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
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.
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.
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.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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, 1P1: Mechanics, 2021-22
Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8, Michaelmas term, 2 lectures/week
Aims
The aims of the course are to:
- Convey the fundamental role of mechanics in engineering.
- Introduce the concepts of kinematics to describe the motion of particles and rigid bodies.
- Introduce the concepts of dynamics and apply these to particles and to planar motion of rigid bodies.
- Develop an understanding of different methods for solving mechanics problems: Newton's Laws, Momentum and Energy.
- Develop skills in modelling and analysing mechanical systems using graphical, analytical and numerical approaches.
Objectives
As specific objectives, by the end of the course students should be able to:
- Apply concepts of kinematics to particles and rigid bodies in two dimensions.
- Specify the position, velocity and acceleration of a particle in 2-D motion in cartesian, polar and intrinsic coordinates using graphical, algebraic and vector methods.
- Differentiate a rotating vector.
- Understand and apply Newton's laws and the equations of energy and momentum of particles.
- Apply Newton's laws to variable mass problems.
- Apply the concept of angular momentum of a particle, and recognise when it is conserved.
- Apply the principles of particle dynamics to satellite motion.
- Determine the centre of mass and moment of inertia of a plane lamina
- Understand and apply the perpendicular and parallel axes theorems
- Understand and apply Newton's laws to rotational motion of planar motion of rigid bodies.
- Understand the concepts of energy, linear momentum and angular momentum of a rigid body, and recognise when they are conserved.
- Apply concepts of relative velocity, angular velocity and instantaneous centre of rigid bodies.
- Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples
- Be able to apply the concepts of linear momentum, angular momentum, impulses and energy to planar motion of rigid bodies, including impact problems.
Content
The course structure is summarised below: the square brackets are topic codes that correspond to the textbook reference table.
Introduction
- Newton's laws of motion [I1]
- Units [I2]
- Forces [I3]
- Free Body Diagrams [I4]
- Frames of reference [I5]
Kinematics of Particles
- Cartesian coordinates [KP1]
- Polar coordinates [KP2]
- Intrinsic coordinates [KP3]
- Differentiation of a unit vector [KP4]
- Velocity and acceleration in different coordinate systems [KP5]
- Numerical differentiation [KP6]
- Relative position, velocity and acceleration [KP7]
Dynamics of Particles
- Newton's Laws applied to particles [DP1]
- D'Alembert force for a particle [DP2]
- Equations of motion [DP3]
- Numerical solution methods [DP4]
- Conservation of Energy [DP5]
- Potential energy, equilibrium and stability [DP6]
- Linear momentum [DP7]
- Variable mass systems [DP8]
- Angular momentum [DP9]
- Satellite motion in steady circular and elliptical orbits [DP10]
Kinematics of Rigid Bodies
- Relative motion [KRB1]
- Angular velocity as a vector [KRB2]
- Rotating reference frames [KRB3]
- Instantaneous centres for planar motion [KRB4]
Dynamics of Rigid Bodies
- Centre of mass of a rigid body [DRB1]
- Moment of inertia of a planar rigid body [DRB2]
- Dynamics of a rigid body with a fixed axis of rotation [DRB3]
- D'Alembert forces and moments for planar motion of a rigid body [DRB4]
- Linear and angular momentum of rigid bodies in planar motion [DRB5]
- Kinetic energy of a translating and rotating planar body [DRB6]
- Impact problems in plane motion [DRB7]
REFERENCES
[1] Gregory, R. D. Classical Mechanics
[2] Malthe-Sorenssen, A. Elementary Mechanics Using Python
[3] Hibbeler, R.C. Engineering Mechanics: Statics / Dynamics (two books with continuing chapters)
[4] Meriam, J.L. & Kraige, L.G., Engineering Mechanics. Vol.2: Dynamics
[5] Prentis, J.M. Dynamics of Mechanical Systems
Comments:
Gregory [1] is a rigorous textbook with a physics perspective.
Malthe-Sorrensson [2] has many numerical examples.
Hibbeler [3] contains many illustrative diagrams and examples.
Meriam and Kraige [4] contains many illustrative diagrams and examples.
Prentis [5] has a different perspective with a strong emphasis on mechanism analysis and graphical methods.
Topic cross references
| Gregory | Malthe-Sorrenssen | Hibbeler | Meriam Kraige | Prentis | |
|---|---|---|---|---|---|
| I1 | 3.1 | 5.3, 5.8, 5.9 | 1.2, 13.1 | 1.3 | |
| I2 | 3.1 | 3.1, 3.2 | 1.3, 13.1 | 1.4 | |
| I3 | 3.3 | 5.4 - 5.7 | 1.2 | ||
| I4 | 5.2, 7.1 | 3.2 | 3.3 | ||
| I5 | 3.2 | 5.8, 6.4 | 13.2 | 1.2 | |
| KP1 | (1.1 - 1.2) | 6.2 | 2.5 - 2.7 | 2.4 | |
| KP2 | 2.3 | 12.8 | 2.6 | ||
| KP3 | 12.7 | 2.5 | |||
| KP4 | 2.3 | 2.6, 5.7 | |||
| KP5 | (2.3) | 12.4, 12.5, 12.7 | 2.4 - 2.6 | ||
| KP6 | 4.1 - 4.2 | ||||
| KP7 | (2.6) | 12.10 | 2.8 | ||
| DP1 | 4.1 - 4.5 | 5.3, 7.2 - 7.6 | 13.1 - 13.2 | 3.1 - 3.5, 4.2 | |
| DP2 | 12.4 | 13.2 | (3.14) | ||
| DP3 | 4.1-4.5 | (7.2 - 7.6) | 13.2 - 13.6 | 3.4 - 3.5 | |
| DP4 | 4.2, 7.4, 7.5, 7.6, 10.3 | (C.12) | |||
| DP5 | 6.1,6.2, 6.4 | (11.1, 11.2) | 14.1 - 14.2, 14.5 - 14.6 | 3.6 - 3.7 | |
| DP6 | 6.3 | 11.3 | (3.7) | ||
| DP7 | 10.1 - 10.4 | 12.2 - 12.6 | 15.1 - 15.4 | 3.8 - 3.9 | |
| DP8 | (10.5) | 12.7 | 15.9 | 4.7 | |
| DP9 | 11.1 - 11.2 | 16.4 | 15.5 - 15.7 | 3.10 | 5.6 |
| DP10 | 7.1, 7.2, 7.3, 7.5, 7.6 | (5.5, 7.6) | 13.7 | 3.13 | |
| KRB1 | 2.6 | 16.7 - 16.8 | (3.14), 5.4, 5.6 | 4.3, 4.8 | |
| KRB2 | 16.1 | 14.6 | 16.3, 20.1 | 5.2, 7.3 | 4.4 |
| KRB3 | 17.1 | 20.4 | 5.7 | 4.3 | |
| KRB4 | 16.6 | 5.5 | 4.4, 4.7 | ||
| DRB1 | 3.5, A.1 | 13.2 | 9.2, 13.3 | ||
| DRB2 | 9.4, A.2, A.3 | 15.2 | 17.1 | 7.7, B.1 | |
| DRB3 | 11.6, 16.1 | 15.1 | 17.4 | 6.4 | |
| DRB4 | (11.6) | (17.2 - 17.5) | 6.1 - 6.5 | 5.3 | |
| DRB5 | 11.4, 11.5, 11.6 | 15.1 | 19.1 - 19.4 | 6.8 | 5.6, 5.8 |
| DRB6 | 9.4 | 15.2, 15.4, 15.5 | 18.1 - 18.5 | 6.6 | |
| DRB7 | 10.6 | 19.2 - 19.4 | 6.8 |
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
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.
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.
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.
E4
Understanding of and ability to apply a systems approach to engineering problems.
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: 11/10/2021 07:55
Engineering Tripos Part IB, 2P2: Structures, 2024-25
Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8 Michaelmas term (12 lectures) and weeks 1-4 Lent term, 2 lectures/week
Aims
The aims of the course are to:
- To extend understanding of the behaviour and analysis of structures.
- To introduce concepts of stress-state, strain-state and yield using simple thin-walled structures.
- To explain elastic analysis of statically indeterminate structures and implications of redundancy.
- To introduce plastic theory of structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- To find, for thin-walled cylinders, the stresses and stress-resultants, strains and displacements resulting from applied loading.
- To understand the concept of stress-state and strain-state using 2-D and 3-D Mohr's Circles.
- To understand the Tresca and von Mises yield criteria.
- To analyse statically indeterminate truss and frame structures.
- To use the method of Virtual Work for beam bending calculations.
- To evaluate the fully plastic moment of a beam cross-section.
- To find upper bound estimates of the failure load of beams, plane portal frames, slabs and continua.
- To find lower bound estimates of the failure load of beams.
Content
The following material will be taught in the context of design:
Thin-walled Structures (3L)
- Stresses in cylinders due to axial loading, bending and shear, internal pressure and torsion.
- Strain in three dimensions, stress-strain-temperature relationships.
- Torsional rigidity.
Analysis of Stress and Strain (4L)
- 2-D stress and strain state, equilibrium equations, 2-D Mohr's circle.
- 3-D stress and strain state, 3-D Mohr's circle.
- Principal stresses, strains and directions.
- Yield criteria: Tresca; von Mises.
Elastic Structural Analysis (5L)
- Indeterminate truss structures, analysis by the Force Method.
- Deflections in beams, including curved beams, by Virtual Work.
- Indeterminate frame structures, analysis by the Force Method.
- Symmetry and anti-symmetry.
Plastic Structural Analysis (8L)
- Calculation of plastic section modulus Zp and fully plastic moment Mp.
- Collapse mechanisms for a statically determinate beam.
- Concept of an upper bound estimate of collapse load.
- Collapse mechanisms for statically indeterminate beams and plane portal frames.
- Yield lines for predicting collapse loads of slabs.
- Slip lines for predicting plane strain failure of continua.
- Equilibrium states for a statically indeterminate beam.
- Concept of a lower bound estimate of collapse load.
- Lower bound principle as a justification for elastic analysis.
Examples papers
There are five examples papers.
Booklists
Please refer to the Booklist for Part IB 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
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.
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.
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).
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: 30/07/2024 08:49
Engineering Tripos Part IB, 2P2: Structures, 2017-18
Lecturers
Dr J P Talbot and Prof Tim Ibell
Timing and Structure
Weeks 1-8 Michaelmas term (12 lectures) and weeks 1-4 Lent term, 2 lectures/week
Aims
The aims of the course are to:
- To extend understanding of the behaviour and analysis of structures.
- To introduce concepts of stress-state, strain-state and yield using simple thin-walled structures.
- To explain elastic analysis of statically indeterminate structures and implications of redundancy.
- To introduce plastic theory of structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- To find, for thin-walled cylinders, the stresses and stress-resultants, strains and displacements resulting from applied loading.
- To understand the concept of stress-state and strain-state using 2-D and 3-D Mohr's Circles.
- To understand the Tresca and von Mises yield criteria.
- To analyse statically indeterminate truss and frame structures.
- To use virtual work for beam bending calculations.
- To evaluate the fully plastic moment of a beam cross-section.
- To find upper bound estimates of the failure load of beams, plane portal frames, slabs and continua.
- To find lower bound estimates of the failure load of beams.
Content
The following material will be taught in the context of design:
Thin-walled Structures (3L)
- Stresses in cylinders due to axial loading, bending and shear, internal pressure and torsion.
- Strain in three dimensions, stress-strain-temperature relationships.
- Torsional rigidity.
Analysis of Stress and Strain (4L)
- 2-D stress and strain state, equilibrium equations, 2-D Mohr's circle.
- 3-D stress and strain state, 3-D Mohr's circle.
- Principal stresses, strains and directions.
- Yield criteria: Tresca; von Mises.
Elastic Structural Analysis (5L)
- Indeterminate truss structures, analysis by the force method.
- Deflections in beams, including curved beams, by virtual work.
- Indeterminate frame structures, analysis by the force method.
- Symmetry and anti-symmetry.
Plastic Structural Analysis (8L)
- Calculation of plastic section modulus Zp and fully plastic moment Mp.
- Collapse mechanisms for a statically determinate beam.
- Concept of an upper bound estimate of collapse load.
- Collapse mechanisms for statically indeterminate beams and plane portal frames.
- Yield lines for predicting collapse loads of slabs.
- Slip lines for predicting plane strain failure of continua.
- Equilibrium states for a statically indeterminate beam.
- Concept of a lower bound estimate of collapse load.
- Lower bound principle as a justification for elastic analysis.
Examples papers
There are five examples papers.
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
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.
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.
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).
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: 27/06/2017 07:06
Engineering Tripos Part IB, 2P2: Structures, 2025-26
Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8 Michaelmas term (12 lectures) and weeks 1-4 Lent term, 2 lectures/week
Aims
The aims of the course are to:
- To extend understanding of the behaviour and analysis of structures.
- To introduce concepts of stress-state, strain-state and yield using simple thin-walled structures.
- To explain elastic analysis of statically indeterminate structures and implications of redundancy.
- To introduce plastic theory of structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- To find, for thin-walled cylinders, the stresses and stress-resultants, strains and displacements resulting from applied loading.
- To understand the concept of stress-state and strain-state using 2-D and 3-D Mohr's Circles.
- To understand the Tresca and von Mises yield criteria.
- To analyse statically indeterminate truss and frame structures.
- To use the method of Virtual Work for beam bending calculations.
- To evaluate the fully plastic moment of a beam cross-section.
- To find upper bound estimates of the failure load of beams, plane portal frames, slabs and continua.
- To find lower bound estimates of the failure load of beams.
Content
The following material will be taught in the context of design:
Thin-walled Structures (3L)
- Stresses in cylinders due to axial loading, bending and shear, internal pressure and torsion.
- Strain in three dimensions, stress-strain-temperature relationships.
- Torsional rigidity.
Analysis of Stress and Strain (4L)
- 2-D stress and strain state, equilibrium equations, 2-D Mohr's circle.
- 3-D stress and strain state, 3-D Mohr's circle.
- Principal stresses, strains and directions.
- Yield criteria: Tresca; von Mises.
Elastic Structural Analysis (5L)
- Indeterminate truss structures, analysis by the Force Method.
- Deflections in beams, including curved beams, by Virtual Work.
- Indeterminate frame structures, analysis by the Force Method.
- Symmetry and anti-symmetry.
Plastic Structural Analysis (8L)
- Calculation of plastic section modulus Zp and fully plastic moment Mp.
- Collapse mechanisms for a statically determinate beam.
- Concept of an upper bound estimate of collapse load.
- Collapse mechanisms for statically indeterminate beams and plane portal frames.
- Yield lines for predicting collapse loads of slabs.
- Slip lines for predicting plane strain failure of continua.
- Equilibrium states for a statically indeterminate beam.
- Concept of a lower bound estimate of collapse load.
- Lower bound principle as a justification for elastic analysis.
Examples papers
There are five examples papers.
Booklists
Please refer to the Booklist for Part IB 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
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.
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.
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).
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: 05/06/2025 11:16
Engineering Tripos Part IB, 2P2: Structures, 2022-23
Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8 Michaelmas term (12 lectures) and weeks 1-4 Lent term, 2 lectures/week
Aims
The aims of the course are to:
- To extend understanding of the behaviour and analysis of structures.
- To introduce concepts of stress-state, strain-state and yield using simple thin-walled structures.
- To explain elastic analysis of statically indeterminate structures and implications of redundancy.
- To introduce plastic theory of structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- To find, for thin-walled cylinders, the stresses and stress-resultants, strains and displacements resulting from applied loading.
- To understand the concept of stress-state and strain-state using 2-D and 3-D Mohr's Circles.
- To understand the Tresca and von Mises yield criteria.
- To analyse statically indeterminate truss and frame structures.
- To use the method of Virtual Work for beam bending calculations.
- To evaluate the fully plastic moment of a beam cross-section.
- To find upper bound estimates of the failure load of beams, plane portal frames, slabs and continua.
- To find lower bound estimates of the failure load of beams.
Content
The following material will be taught in the context of design:
Thin-walled Structures (3L)
- Stresses in cylinders due to axial loading, bending and shear, internal pressure and torsion.
- Strain in three dimensions, stress-strain-temperature relationships.
- Torsional rigidity.
Analysis of Stress and Strain (4L)
- 2-D stress and strain state, equilibrium equations, 2-D Mohr's circle.
- 3-D stress and strain state, 3-D Mohr's circle.
- Principal stresses, strains and directions.
- Yield criteria: Tresca; von Mises.
Elastic Structural Analysis (5L)
- Indeterminate truss structures, analysis by the Force Method.
- Deflections in beams, including curved beams, by Virtual Work.
- Indeterminate frame structures, analysis by the Force Method.
- Symmetry and anti-symmetry.
Plastic Structural Analysis (8L)
- Calculation of plastic section modulus Zp and fully plastic moment Mp.
- Collapse mechanisms for a statically determinate beam.
- Concept of an upper bound estimate of collapse load.
- Collapse mechanisms for statically indeterminate beams and plane portal frames.
- Yield lines for predicting collapse loads of slabs.
- Slip lines for predicting plane strain failure of continua.
- Equilibrium states for a statically indeterminate beam.
- Concept of a lower bound estimate of collapse load.
- Lower bound principle as a justification for elastic analysis.
Examples papers
There are five examples papers.
Booklists
Please refer to the Booklist for Part IB 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
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.
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.
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).
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: 15/09/2022 16:13
Engineering Tripos Part IB, 2P2: Structures, 2021-22
Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8 Michaelmas term (12 lectures) and weeks 1-4 Lent term, 2 lectures/week
Aims
The aims of the course are to:
- To extend understanding of the behaviour and analysis of structures.
- To introduce concepts of stress-state, strain-state and yield using simple thin-walled structures.
- To explain elastic analysis of statically indeterminate structures and implications of redundancy.
- To introduce plastic theory of structures.
Objectives
As specific objectives, by the end of the course students should be able to:
- To find, for thin-walled cylinders, the stresses and stress-resultants, strains and displacements resulting from applied loading.
- To understand the concept of stress-state and strain-state using 2-D and 3-D Mohr's Circles.
- To understand the Tresca and von Mises yield criteria.
- To analyse statically indeterminate truss and frame structures.
- To use the method of Virtual Work for beam bending calculations.
- To evaluate the fully plastic moment of a beam cross-section.
- To find upper bound estimates of the failure load of beams, plane portal frames, slabs and continua.
- To find lower bound estimates of the failure load of beams.
Content
The following material will be taught in the context of design:
Thin-walled Structures (3L)
- Stresses in cylinders due to axial loading, bending and shear, internal pressure and torsion.
- Strain in three dimensions, stress-strain-temperature relationships.
- Torsional rigidity.
Analysis of Stress and Strain (4L)
- 2-D stress and strain state, equilibrium equations, 2-D Mohr's circle.
- 3-D stress and strain state, 3-D Mohr's circle.
- Principal stresses, strains and directions.
- Yield criteria: Tresca; von Mises.
Elastic Structural Analysis (5L)
- Indeterminate truss structures, analysis by the Force Method.
- Deflections in beams, including curved beams, by Virtual Work.
- Indeterminate frame structures, analysis by the Force Method.
- Symmetry and anti-symmetry.
Plastic Structural Analysis (8L)
- Calculation of plastic section modulus Zp and fully plastic moment Mp.
- Collapse mechanisms for a statically determinate beam.
- Concept of an upper bound estimate of collapse load.
- Collapse mechanisms for statically indeterminate beams and plane portal frames.
- Yield lines for predicting collapse loads of slabs.
- Slip lines for predicting plane strain failure of continua.
- Equilibrium states for a statically indeterminate beam.
- Concept of a lower bound estimate of collapse load.
- Lower bound principle as a justification for elastic analysis.
Examples papers
There are five examples papers.
Booklists
Please refer to the Booklist for Part IB 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
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.
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.
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).
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: 20/05/2021 07:27
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