# MECH07007 2015 Mechanics and Mathematics 302

### General Details

Full Title
Mechanics and Mathematics 302
Transcript Title
Mechanics and Mathematics 302
Code
MECH07007
Attendance
N/A %
Subject Area
MECH - Mechanics
Department
MENG - Mech. and Electronic Eng.
Level
07 - NFQ Level 7
Credit
05 - 05 Credits
Duration
Stage
Fee
Start Term
2015 - Full Academic Year 2015-16
End Term
9999 - The End of Time
Author(s)
Kevin Collins, Sean Dalton
Programme Membership
SG_EPREC_B07 201500 Bachelor of Engineering in Precision Engineering and Design SG_EPREC_B07 201500 Bachelor of Engineering in Precision Engineering and Design SG_EPREC_J07 201700 Bachelor of Engineering in Precision Engineering and Design
Description

Mechanics studies the consequences of appying loads in terms for deflection, and material failure. It also explores how strain guage results can be use to calculate stresses.

This mathematics section of this module consists of topics from Intergal and Differential Calculus, Linear Algebra and Complex Numbers. These topics include differental equations and applications, Laplace Transforms, De Moivre's Theorem, Fourier Transforms, Gaussian Elemination and z Transforms.

### Learning Outcomes

On completion of this module the learner will/should be able to;

1.

Calculate beam deflection for standard load cases

2.

Determine stresses in components due to applicaiton of strain gauges

3.

Determine factor of safety against failure under complex load using failure theories

4.

Solve dynamic systems involving inertia, linear and angular displacement, velocity and acceleration.

5.

Calculate powers of complex numbers using theorems of DeMoivre and Euler

6.

Solve linear systems using Gaussian Elemination and apply this to engineering problems

7.

Evaluate eigenvalues and eigenvectors

### Teaching and Learning Strategies

Lectures, tutorials and assignments

### Module Assessment Strategies

Mechanics 50%, (Continuous assessment 30%, Final Exam 70%)

Mathematics 50% (Continuous assessment 30%, Final Exam 70%)

### Repeat Assessments

Repeat exam and/or continuous assessment

### Indicative Syllabus

Mechanics

Slope and deflection of beams. Slope and deflection of beams for standard load cases. Derivation of standard formulae by direct integration method.

Strain gauges: Use of strain gauges in Tension, Bending, Torsion and bi-axial loading. Practical aspects of strain gauge application and monitoring.

Built in beams, Determination of bending moment and deflection for built in beams, carrying concentrated, distributed and variable distributed loads.

Failure theories. Max. Shear stress (tresca), Max. shear strain energy (Von Misses), stress concentrations.

Dynamics: Revision of Equation, periodic motion (pendulum, scotch yoke mechanism), Dynamics of rotation and moments of inertia.

Mathematics

DeMoivre's Theorem and Euler's Theorem for the polar form of a complex number.

Argand diagrams and powers of complex numbers.

z transforms of functions.

Use of z-transform to solve first and second order difference equations.

Gaussian Elimination and applications.

Eigenvalues and eigenvectors

### Coursework & Assessment Breakdown

Coursework & Continuous Assessment
30 %
End of Semester / Year Formal Exam
70 %

### Coursework Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 Continuous Assessment Continuous Assessment UNKNOWN 30 % Week 8 1,2,3,5,6,7,8,9

### End of Semester / Year Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 Final Exam Final Exam UNKNOWN 70 % End of Term 1,2,3,4,5,6,7,8,9,10,11

Type Location Description Hours Frequency Avg Workload
Lecture Flat Classroom Mathematics Lecture 2 Weekly 2.00
Lecture Flat Classroom Mechanics Lecture 2 Weekly 2.00
Independent Learning UNKNOWN Reading assignments 1 Weekly 1.00
Independent Learning UNKNOWN Revision / solution of problems set in lecture 1 Weekly 1.00
Tutorial Flat Classroom Mathematics Tutorial/Practical 1 Weekly 1.00
Tutorial Flat Classroom Mechanics Tutorial/Practical 1 Weekly 1.00
Total Full Time Average Weekly Learner Contact Time 6.00 Hours

### Module Resources

Non ISBN Literary Resources
 Authors Title Publishers Year E. J. Hearne Mechanics of Materials Butterwork Heinemann R.C. Hibbeller Mechanics of Materials Prentice Hall D.H. Bacon and R.C. Stephens Mechanical Technology Butterworth-Heinemann 1998 K A Stroud Engineering Mathematics Palgrave and Macmillan
Other Resources

None