Aims

The aims of the course are to:

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

Objectives

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

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

Content

Introduction and Aims of the Course (1 Lecture)

1. External forces (3L)

Equilibrium of point forces, moments and couples

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

Distributed loads and friction forces

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

Supports and free-body diagrams

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

2. Internal forces (3L)

Pin-jointed trusses

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

Shear forces and bending moments

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

Sress

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

3. Deflection (5L)

Cables and compatibility

• Cables subjected to concentrated loads
• Cables subjected to distributed loads

Deflection of members in pin-jointed frames

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

Displacement Diagrams

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

Virtual work

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

Structural design

• Iterative design
• Structural optimisation

4. Equilibrium of Beams (2L)

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

5. Deflection of Straight Elastic Beams (2L)

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

6. Stresses in Elastic Beams (5L)

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

7. Buckling of Columns (3L)

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

REFERENCES

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

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

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Last modified: 30/07/2024 08:43

Aims

The aims of the course are to:

• Describe the importance of physics in medicine
• Understand the general principles of medical image reconstruction and registration
• Compare and contrast the medical imaging techniques that are available in a hospital setting and explain their relative merits
• Explain the difference between imaging with ionising and non-ionising radiation in the context of radiation dosimetry and risk
• Describe sensing and therapeutic applications of physics in medicine

Content

The material should be accessible to all Part IIA Bioengineering and Part III Physics students. The course was revised for the 2017-2018 academic year, including more extensive handouts and more in depth coverage of the core underlying material. The lectures include some guest lecturers who are medical physicists invited from Addenbrooke's to give a flavour of the clinical career options in the discipline.

Introduction

Historical background; radiation interactions; general imaging concepts; and contrast mechanisms.

Medical Imaging Methodology

For all clinically applicable imaging techniques, a detailed description of contrast mechanisms, data acquisition hardware and image reconstruction will be provided. This will cover: imaging with ionising radiation, including X-ray, CT, nuclear medicine, SPECT and PET; imaging with non-ionising radiation, including MRI and ultrasound; and general principles of image reconstruction and registration of images over time and between modalities.

Clinical Applications of Physics

Clinical examples of the utility of medical imaging in diagnosis and treatment of disease. Sensing applications of physics in hospitals, including patient monitoring. Therapeutic applications of physics, particularly radiotherapy in cancer patients.

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

Toggle display of UK-SPEC areas.

 
Last modified: 20/05/2021 07:50

Aims

The aims of the course are to:

• Describe the importance of physics in medicine
• Understand the general principles of medical image reconstruction and registration
• Compare and contrast the medical imaging techniques that are available in a hospital setting and explain their relative merits
• Explain the difference between imaging with ionising and non-ionising radiation in the context of radiation dosimetry and risk
• Describe sensing and therapeutic applications of physics in medicine

Content

The material should be accessible to all Part IIA Bioengineering and Part III Physics students. The course was revised for the 2017-2018 academic year, including more extensive handouts and more in depth coverage of the core underlying material. The lectures include some guest lecturers who are medical physicists invited from Addenbrooke's to give a flavour of the clinical career options in the discipline.

Introduction

Historical background; radiation interactions; general imaging concepts; and contrast mechanisms.

Medical Imaging Methodology

For all clinically applicable imaging techniques, a detailed description of contrast mechanisms, data acquisition hardware and image reconstruction will be provided. This will cover: imaging with ionising radiation, including X-ray, CT, nuclear medicine, SPECT and PET; imaging with non-ionising radiation, including MRI and ultrasound; and general principles of image reconstruction and registration of images over time and between modalities.

Clinical Applications of Physics

Clinical examples of the utility of medical imaging in diagnosis and treatment of disease. Sensing applications of physics in hospitals, including patient monitoring. Therapeutic applications of physics, particularly radiotherapy in cancer patients.

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

Toggle display of UK-SPEC areas.

 
Last modified: 01/08/2022 09:30

Aims

The aims of the course are to:

• Describe the importance of physics in medicine
• Understand the general principles of medical image reconstruction and registration
• Compare and contrast the medical imaging techniques that are available in a hospital setting and explain their relative merits
• Explain the difference between imaging with ionising and non-ionising radiation in the context of radiation dosimetry and risk
• Describe sensing and therapeutic applications of physics in medicine

Content

The material should be accessible to all Part IIA Bioengineering and Part III Physics students. The course is divided into two parts: the first 6 lectures concentrate on the basic physics of biomedical imaging, while the second 6 lectures (given by Addenbrookes hospital staff) provide a broad insight into the applications of physics in medicine. The latter half of the course should be accessible to all those with an interest in medical physics

Introduction

Historical background; radiation interactions; general imaging concepts; and contrast mechanisms.

Medical Imaging Methodology

For all clinically applicable imaging techniques, a detailed description of contrast mechanisms, data acquisition hardware and image reconstruction will be provided. This will cover: imaging with ionising radiation, including X-ray, CT, nuclear medicine, SPECT and PET; imaging with non-ionising radiation, including MRI and ultrasound; and general principles of image reconstruction and registration of images over time and between modalities.

Clinical Applications of Physics

Clinical examples of the utility of medical imaging in diagnosis and treatment of disease. Sensing applications of physics in hospitals, including patient monitoring. Therapeutic applications of physics, particularly radiotherapy in cancer patients.

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

Toggle display of UK-SPEC areas.

 
Last modified: 31/05/2017 10:02