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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: revision -Shear stress equation, application to structural cross-sections, shear flow;
L1.11: Shear centre for thin sections;Strain energy
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:energy methods in engineering, conservation of energy, complimentary strain energy,virtual force and virtual displacement;
L1.15: Unit Load Methods, Castigliano's Theorems I and II;Application of energy methods
L1.16: application to beams energy methods to curved beams;
L1.17: application to combined structures and frameworks.

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]

Free vibration of Single Degree of Freedom (SDF) systems

L2.01: introduction (oscillations, discrete systems, degrees of freedom, differential equations);
L2.02: basic concepts (moment of inertia, Hooke's law, Newton's second law, free body diagrams), translational simple harmonic motion (SHM), effect of gravity;
L.2.03: rotational SHM, damping in translational SDF systems, free vibration of SDF (underdamped and overdamped);
L2.04: canonical form of SDF, and rotational SDF;Forced vibration of SDF systems
L2.05: periodically forced vibration of SDF (steady-state response, amplitude and phase);
L2.06: periodically forced vibration of SDF (resonance, focus
on amplitude of vibration, plots, Q factor and bandwidth), force transmission to the support;
L2.07: motion of the base in SDF systems (moving boundary conditions and amplitude transmission);
L2.08: out of balance rotor and solutions;
L2.09: out of balance in reciprocating internal combustion engines;Multiple degree of freedom (MDF) systems
L2.10: two degree of freedom systems (2DoF) without damping free vibration;
L2.11: periodically forced vibration in 2DoF without damping, eigenvalue problems;
L2.12: 2DoF with damping, anti-resonance and vibration absorbers;
L2.13: MDF systems, uncoupling (diagonalization and orthogonal modes);Non-periodic forcing on SDF systems
L2.14: Non-periodic forcing(impulse excitation, general non-periodic forcing, convolution integral);
L2.15: Shock Response Spectrum (SRS), SRS of rectangular pulse, shock damping; Applications
L2.16: 2DoF applications (shaft whirling, coupled pendulums and beating);
L2.17: Self-excited vibration, positive feedback, stick-slip motion.

Ex2.01: SDF systems;
Ex2.02: solving dynamics problems using MATLAB;
Ex2.03: periodically forced vibration and force transmission;
Ex2.04: out of balance systems (formative feedback);
Ex2.05: MDF systems and non-periodic forcing.

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 2A (SCEE08002)
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesTopics covered in Mechanical Engineering 1(MECE08007), or Civil Engineering 1(CIVE08001), and Structural Mechanics 2A(SCEE08002), and Dynamics 2 (MECE08009).
High Demand Course? Yes
Course Delivery Information
Academic year 2018/19, 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;
  5. Use numerical software (MATLAB) to determine the dynamic response of multi-degree of freedom systems.
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 Enrico Mastropaolo
Tel: (0131 6)50 5651
Course secretaryMiss Jennifer Yuille
Tel: (0131 6)51 7073
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