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DRPS : Course Catalogue : School of Engineering : Mechanical

Undergraduate Course: Structural Mechanics and Dynamics 3 (MECE09036)

Course Outline
SchoolSchool of Engineering CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 9 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryStructural mechanics: students will gain a basic understanding of structural modelling and stress analysis of statically determinate and indeterminate structural members to check for their strength, stability and failure problems.Structural dynamics: students will achieve competence in the methods of dynamic analysis for lumped linear systems, covering their dynamic response and vibration analysis and, uses in engineering applications.

Accreditation of Higher Education Programmes Learning Outcomes:
SM2m, EA1b, EA2, EA3b, EA1m, P3,
Course description The structural mechanics part of the course will consist of:
-17 1-hour lectures + 5 1-hour example classes;
-1 laboratory session (2 hours each group of students) with 1 group assignment.

The structural dynamics part of the course will consist of:
-17 1-hour lectures + 5 1-hour example classes;
-1 laboratory session (2 hours each group of students) with 1 group assignment.

Structural mechanics:
We will focus on the behaviour of solid materials and structures under load and stress. This part includes the following elements: revision of second year core material (calculation of sectional properties), shear force and bending moment diagrams and bending stress;introduction of the ideas of structural modelling and loading actions; illustration of complex stresses on inclined sections and introduce graphical method of stress calculation; work on beams to cover practical cases of unsymmetric bending;introduction of the concept of shear centre and its calculation;introduction of the idea of strain energy;introduction of energy methods as an alternative approach to the use of differential equations in stress analysis;use of Unit Load and Castigliano's Method in solving simple structural problems.

Structural dynamics:
We will focus on mechanical vibrations of structures,which can be modelled as systems of discrete elements,thus providing the students with the tools for evaluating oscillations of real-world mechanical systems. We will investigate rigid body (lumped parameter) linear systems where the dynamic behaviour can be described using one or more spatial coordinates (single and multiple degrees of freedom systems). Students will be able to write the equation of motions of freely vibrating systems or under external exciting force in order to evaluate displacements, frequencies of oscillation, force transmitted and modes of vibration. We will be looking at issues arising from mechanical oscillations in real-world systems (i.e., IC engines, shafts, bridges and high-rise buildings) and devise solutions to minimise (or maximise!) mechanical vibrations. MATLAB will be used as additional and powerful tool to facilitate the procedure to investigate the mechanical oscillations of the studied systems.

Lectures and example classes list:

1. Structural mechanics [17 lectures+ 5 example classes] Deflection of beams

L1.1: Revision - shear force and bending moment diagrams, bending stresses, differential equation of flexure, problem arising from discontinuities in the bending moment.
L1.2: Singularity functions, application to beam deflections.
L1.3: Application of singularity functions to statically indeterminate beams, the problem of discontinuous distributed loading; Analysis of complex stresses.
L1.4: Plane stress, transformation equations for plane stress: stress components on inclined planes, two perpendicular normal stresses, two perpendicular normal stresses accompanied by simple shear.
L1.5: Principal stresses, principal planes, maximum shear stress.
L1.6: Mohr's circle for plane stress; Unsymmetrical bending.
L1.7: Skew loading on symmetric cross-sections.
L1.8: Skew loading on unsymmetrical cross-sections.
L1.9: Transformation of axes to find the position of principal planes, position of points of maximum stress, position of the neutral axis; Shear stresses in beams.
L1.10: Shear stress equation, application to structural cross-sections, shear flow.
L1.11: Shear centre for thin sections.
L1.12: Concept of strain energy, mechanical work, conservation of energy, strain energy in tension and shear, 3-D case.
L1.13: Strain energy in bending and torsion, Application to beams and shafts. Combined loading; Energy methods.
L1.14: Unit Load Methods, Castigliano's Theorems I and II; Application of energy methods.
L1.15: Application to beams, curved beams and frames.
Ex1.1: Singularity functions applied to beams.
Ex1.2: Complex stress analysis with Mohr's circle.
Ex1.3: Unsymmetrical bending analysis.
Ex1.4: Shear stress and shear centre examples.
Ex1.5: Energy methods calculations.

2. Structural dynamics [17 lectures+ 5 example classes]

L2.01: Module Overview: damped/undamped free/forced vibrations.
L2.02: Dynamics Review: d¿Alembert principle; translational/rotational dynamics, canonical form, natural frequency.
L2.03: Harmonic Oscillator: Euler¿s identity, complementary solutions, initial conditions.
L2.04: Damped Harmonic Oscillator - part 1: forms of damping, damping ratio, overdamped vibrations.
L2.05: Damped Harmonic Oscillator - part 2: underdamped vibrations, logarithmic decrement, critically damped vibrations.
L2.06: Driven Harmonic Oscillator - part 1: constant forcing, harmonic forcing (complexification - algebraic approach).
L2.07: Driven Harmonic Oscillator - part 2: harmonic forcing (complexification - phasor approach), magnification factor, phase delay.
L2.08: Numerical Methods for Vibration Analysis: free vibrations, underdamped/overdamped/critically damped vibrations.
L2.09: Force Transmission and Moving Base: transmissibility ratio; vibrometers; accelerometers.
L2.10: Out of Balance Systems - part 1: rotors.
L2.11: Out of Balance Systems - part 2: internal Combustion Engines.
L2.12: Non-Periodic Forcing: impulse excitation, convolution integral, Shock Response Spectrum.
L2.13: Multiple Degree of Freedom Oscillator - part 1: free undamped oscillations (normal frequencies and mode shapes).
L2.14: Multiple Degree of Freedom Oscillator - part 2: driven undamped/damped oscillations (normal modal analysis).
L2.15: Passive Vibrations Control Devices: tunable absorbers.

Ex2.01: Harmonic Oscillator: solution of linear ordinary differential equations, free-body diagrams.
Ex2.02: Damped Driven Harmonic Oscillator: overdamped/underdamped/critically damped systems.
Ex2.03: Damped Driven Harmonic Oscillator: non-periodic forcing, force transmission.
Ex2.04: Multiple Degree of Freedom Oscillator: normal frequencies and mode shapes.
Ex2.05: Multiple Degree of Freedom Oscillator: normal modal analysis.

Accreditation of Higher Education Programmes Learning Outcomes:
SM2m, EA1b, EA2, EA3b, EA1m, P3
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Dynamics 2 (MECE08009) AND Structural Mechanics 2 (CIVE08026)
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesTopics covered in Mechanical Engineering Structural Mechanics 2 (CIVE08026), and Dynamics 2 (MECE08009).
High Demand Course? Yes
Course Delivery Information
Academic year 2024/25, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 34, Seminar/Tutorial Hours 10, Supervised Practical/Workshop/Studio Hours 2, Formative Assessment Hours 2, Summative Assessment Hours 12, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 136 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Written Exam %: 80«br /»
Practical Exam %: 0«br /»
Coursework %: 20 (2laboratory group assignmentsat 10% each)
Feedback Feedback on lab reports, on coursework and formative feedback.
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)3:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Explain the terminology relevant to structural mechanics and mechanical oscillations;
  2. Analyse and calculate: complex in-plane stresses on normal and inclined planes, stresses and deflections for skew loading bending problems, strain energy due to combined loading;
  3. Derive the mathematical models and analyse the response of single and multi-degree of freedom lumped parameter linear systems under different excitation conditions;
  4. Describe, examine and evaluate different real-life and practical applications related to structural mechanics and mechanical oscillations;
Reading List
Structural Mechanics;

1. T. A. Philpot, Mechanics of Materials, 2014, John Wiley & Sons, SI version, Third edition, ISBN 978-1-118-32270-3.
2. J.M. Gere and B.J. Goodno, Mechanics of Materials, SI version, Seventhedition, 2009, Cengage Learning, ISBN-13:978-0-495-43807-6.
3. A. PytelandJ. Kiusalaas,Mechanics of Materials, Second edition, 2012, CENGAGE Learning, ISBN 13-978 14390 6220 3.
4. F.P. Beer, E.R. Johnstonand J.Y. Dewolf,Mechanics of Materials, Fourth edition, 2006, McGraw Hill, ISBN 007-124999-0.

Structural dynamics part:

Singiresu S. Rao, Mechanical Vibrations, SI version, Fifthor Sixth edition, Pearson, ISBN 978-981-06-8712-0(highly recommended, also for Dynamics 4).
Additional Information
Graduate Attributes and Skills Not entered
KeywordsDeflection of beams,complex stresses,Mohrs¿s circle,unsymmetricalbending,shear stresses
Course organiserDr Livio Gibelli
Tel: (0131 6)50 5715
Course secretaryMiss Maryna Vlasova
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