MECH07007 2015 Mechanics and Mathematics 302
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
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 biaxial 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.
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 ztransform to solve first and second order difference equations.
Gaussian Elimination and applications.
Eigenvalues and eigenvectors
Coursework & Assessment Breakdown
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 
Module 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 
ButterworthHeinemann 
1998 




K A Stroud 
Engineering Mathematics 
Palgrave and Macmillan 

















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