SCHOOL OF ENGINEERING AND ELECTRONICS - Solid Mechanics 3

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UNIVERSITY OF EDINBURGH
SCHOOL OF ENGINEERING AND ELECTRONICS

COURSE DESCRIPTOR (2008 - 2009)

TITLE Solid Mechanics 3
CODE U01100
LEVEL 3
CREDITS (EDINBURGH/SCOTCAT) 10
SEMESTER(S) Semester 1
PREREQUISITES Structural Mechanics 2A
DEGREE PROGRAMMES Electrical and Mechanical Engineering 3 (E&M3)
Mechanical Engineering 3 (ME3)
Mechanical Engineering with Management 3 (MEM3)
Mechanical Engineering with Renewable Energy 3 (MERE3)

COURSE STRUCTURE Learning Method Hours in Course
Lectures 20
Practicals 10
Seminars
Tutorials 10
Workshops
Project
Placement
Assignments
Independent Study 60
Other (please specify)
Notional Student Effort Hours (Total) 100

COURSE CO-ORDINATOR Dr.Vengatesan Venugopal, School of Engineering and Electronics

COURSE STAFF Dr. Vengatesan Venugopal, School of Engineering and Electronics
Institute for Energy Systems, Faraday, Room 4.123
Email:
V.Venugopal@ed.ac.uk

SUMMARY To give a basic understanding of structural modelling and stress
analysis to the student to check design work for strength and stability,
to check stress existing designs and to investigate failure problems.

COURSE OBJECTIVES

1. To revise second year core material – calculation of sectional
properties, shear force and bending moment diagrams and bending
stress;
2. To introduce the ideas of structural modelling and loading actions;
3. To illustrate complex stresses on inclined sections and introduce
graphical method of stress calculation;
4. To expand the work on beams to cover practical cases of unsymmetric
bending;
5. To introduce the concept of shear centre and its calculation;
6. To introduce fundamental concepts of buckling and structural stability
in columns;
7. To introduce the idea of strain energy;
8. To appreciate the effects of impact on structures;
9. To introduce energy methods as an alternative approach to the use of
differential equations in stress analysis;
10. The use of Castigliano’s Method in solving simple structural problems.
SPECIFIC LEARNING OUTCOMES On completion of the course, students should be able to:

1. Use singularity functions in bending moment equations
2. Analysis of complex in-plane stresses on normal and inclined planes
3. Calculate principal stresses, principal planes and shear stresses by
Mohr’s circle graphical method
4. Recognise unsymmetric bending problems
5. Calculate stresses and deflections for skew loading bending problems
6. Calculate the position of the principal axes for an un-symmetric cross
section
7. Find the position of the NA in an unsymmetric cross section
8. Calculate the shear stresses in thin sections with one axis of symmetry
9. Calculate the position of the shear centre of a cross section
10. Apply Euler's buckling equation
11. Appreciate the errors in the Euler’s buckling equation
12. Use the slenderness ratio in the design of struts
13. Apply eccentric loading as a design approach to real struts
14. Calculate the work done by external forces on structures
15. Calculate the strain energy stored in a structure due standard loading
actions
16. Calculate the strain energy due to combined loading
17. Use strain energy to calculate impact stresses
18. Conservation of energy in structures
19. Apply unit force method to simple structures
20. Apply Castigliano's Theorem 1&2 to beams, curved beams, combined
structures and frameworks.

LEARNING RESOURCES There is no recommended text for this course but the following will be
useful.
Gere, J.M. Mechanics of Materials, Sixth edition, 2006, Thomson
Publishing Services, International Student Edition, ISBN 0495073075.
Philpot, T. A. Mechanics of Materials: An Integrated Learning System,
2007, John Wiley & Sons, Inc, ISBN 978-0-470-04438-4.
Beer, F.P, Johnston, E.R and Dewolf, J.T. Mechanics of Materials,
Fourth edition, 2006, McGraw Hill, ISBN 007-124999-0.
Riley, W.F, Sturges, L,D. and Morris, D.H. Mechanics of Materials,
Sixth Edition, 2007, John Wiley & Sons, Inc. , ISBN 0-471-70511-X.
COMPONENTS OF ASSESSMENT Element Contribution (%)
Assignment(s)
Class Examination
Practicals 20
Oral
Project
Placement
Final Examination 80
Other (please specify)
Total (100%) 100
Degree examination is in December: 3 questions from 4 (duration = 1.5
hrs)
COURSE SYLLABUS

Sec Lec Content
1.0

Deflection of Beams
1 Revision - Shear Force and Bending Moment Diagrams, Bending Stresses, Differential
Equ. of Flexure, problem arising from discontinuities in the bending moment.
2 Singularity functions, application to beam deflections.
3 Application of singularity functions to statically indeterminate beams, the problem of
discontinuous distributed loading.
2.0 Analysis of Complex Stresses

4 Plane stress, Transformation equations for plane stress: Stress components on inclined
planes, Two perpendicular normal stresses, Two perpendicular normal stresses
accompanied by simple shear
5 Principal stresses, Principal planes, Maximum shear stress, Mohr’s circle for plane
stress.
3.0

Unsymmetric Bending
6 Skew loading on symmetric cross-sections, unsymmetric cross-sections.
7-8 Transformation of axes to find the position of principal planes, position of points of
maximum stress, position of the neutral axis.
4.0

Shear Stresses in Beams
9 Revision - Shear stress equation, application to structural cross-sections, shear flow.
10 Shear centre for thin sections
5.0

Euler Buckling of Struts
11 Euler approach to buckling, Euler failure load for a pin-pin strut, Slenderness ratio,
Euler failure load for vertical cantilever.
12 Approximate method for determination of other cases, Practical problems, eccentric
loading approach; other methods
6.0

Strain Energy
13 Concept of strain energy, mechanical work, conservation of energy; strain energy in
tension and shear; 3-D case.
14 Strain energy in bending and torsion; application to beams and shafts. Combined
loading.
7.0

Impact
15 Problem of impact in engineering structures, use of energy approach to find equivalent
static load in impact loading; impact loading on a beam.
8.0

Energy Methods
16 Energy Methods in Engineering. Conservation of Energy; complimentary strain energy.
Virtual Force and Virtual Displacement.
17-18 Unit Load Methods, Castigliano’s Theorem Parts 1 and 2.
9.0

Application of Energy Methods
19-20 Application to beams, to curved beams, combined structures, Application to
frameworks
LABORATORY

Lab1- Proving Ring
Aims
i) To assess the validity of simple theory
ii) To comment on the assumptions in simple theory
iii) To critically assess the experimental apparatus
iv) To assess the use of energy methods in structural analysis
v) To comment on the use of the Proving Ring as a simple load transducer

Lab2 - Unsymmetric Bending
Aims
i) To assess the validity of simple theory
ii) To comment on the assumptions in simple theory
iii) To critically assess the experimental apparatus