MECH07006 2015 Mechanics and Mathematics 301
This module addresses the analytical aspects of both Mechanics and Thermodynamics.
Mechanics explore the analysis of the stresses induced in material under a variety of load types including direct loading, bending and torsion thought the study of complex stresses.
This mathematics part 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;
Use freebody diagram analysis forces in real world object
Analyse stresses induced by bending moments in beams
Analyse stresses due to combined bending and torsion.
Describe the zeroth, first, second and third laws of thermodynamics.
Describe internal combustion engine cycles and analyse combustion of hydrocarbons using the air standard cycles and chemical equations.
Solve problems involving conduction, convection and radiation
. Solve first order differential equations using separable variables techniques and the integrating factor method
Solve first and second order differential equations using Laplace transforms
Solve second order differential equations using the complementary function and particular integral
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 CA
Indicative Syllabus
Mechanics
Free body diagrams: Analysis of forces in everyday items: vice grips, front loader, crane, 2d framework, hoists, 3D space frame.
Bending stresses, Determination of I for rectangular, round sections and complex sections (parallel axis theorem), combined bending and direct stresses (eccentric loading), oblique loading (in plane stresses).
Torsion, Torque/shear stress/angle of twist relationship, torsion of not circular section, indeterminate torsion (shafts in series and parallel), combined bending and torsion. Equivalent bending moment / torque.
Complex stresses: Mathematical and graphical solution of complex stress problems. Principal stresses, pure shear, 3d stresses: problems involving direct, bending and shear stress.
Mathematics
First order differential equations: separation of the variables, exact and inexact forms.
Solution of homogeneous differential equations (use of the substitution y= vx )
Solution of linear differential equations using the Integrating Factor Method.
Definition of Laplace transform and calculation of the Laplace transform and inverse Laplace transform of functions.
First Shifting Theorem and Laplace transform of derivatives.
Solution of first and second order differential equations using Laplace transforms.
The homogeneous equation . Solution of the nonhomogeneous equation using the complementary function and particular integral.
Coursework & Assessment Breakdown
Coursework Assessment
Title  Type  Form  Percent  Week  Learning Outcomes Assessed  

1  Continuous Assessment  Continuous Assessment  UNKNOWN  30 %  OnGoing  1,2,3,4,5,6 
End of Semester / Year Assessment
Title  Type  Form  Percent  Week  Learning Outcomes Assessed  

1  Final Exam Final Exam  Final Exam  UNKNOWN  70 %  End of Term  1,2,3,4,5,6 
Full Time Mode Workload
Type  Location  Description  Hours  Frequency  Avg Workload 

Independent Learning  UNKNOWN  Study  2  Weekly  2.00 
Lecture  Lecture Theatre  Mechanics Lecture  2  Weekly  2.00 
Tutorial  Lecture Theatre  Mechanics Tutorial  1  Weekly  1.00 
Lecture  Lecture Theatre  Mathemathics Lecture  2  Weekly  2.00 
Tutorial  Lecture Theatre  Mathematics Tutorial  1  Weekly  1.00 
Module Resources
Essential Reading:
Authors 
Title 
Publishers 
Year 
K A Stround 
Engineering Mathematics 
Palgrave and Macmillan 
2015 
D.H. Bacon and R.C. Stephens 
Mechanical Technology 
ButterworthHeinemann 

Hearne E. J. 
Mechanics of Materials 
Butterworks Heinemann 
2012 
Hibbeler R. C. 
Mechanics of Materials 
Prentice Hall 
2010 
Recomended Reading
Authors 
Title 
Publishers 
Year 
























None
None