MECH07007 2015 Mechanics and Mathematics 302

General Details

Full Title
Mechanics and Mathematics 302
Transcript Title
Mechanics and Mathematics 302
N/A %
Subject Area
MECH - Mechanics
MENG - Mech. and Electronic Eng.
07 - NFQ Level 7
05 - 05 Credits
Start Term
2015 - Full Academic Year 2015-16
End Term
9999 - The End of Time
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

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;


Calculate beam deflection for standard load cases


Determine stresses in components due to applicaiton of strain gauges


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


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


Calculate powers of complex numbers using theorems of DeMoivre and Euler


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


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


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.

Buckling of struts (Euler theory), end conditions, eccentric loading. Laterally loaded struts, concentrated and distributed loads. Euler validity limit

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


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

Full Time Mode Workload

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





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







 K A Stroud

Engineering Mathematics 

Palgrave and Macmillan


















Other Resources


Additional Information