# MECH07006 2015 Mechanics and Mathematics 301

### General Details

Full Title
Mechanics and Mathematics 301
Transcript Title
mech maths
Code
MECH07006
Attendance
75 %
Subject Area
MECH - Mechanics
Department
MENG - Mech. and Electronic Eng.
Level
07 - NFQ Level 7
Credit
05 - 05 Credits
Duration
Semester
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

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;

1.

Use freebody diagram analysis forces in real world object

2.

Analyse stresses induced by bending moments in beams

3.

Analyse stresses due to combined bending and torsion.

4.

Describe the zeroth, first, second and third laws of thermodynamics.

5.

Describe internal combustion engine cycles and analyse combustion of hydrocarbons using the air standard cycles and chemical equations.

6.

Solve problems involving conduction, convection and radiation

7.

. Solve first order differential equations using separable variables techniques and the integrating factor method

8.

Solve first and second order differential equations using Laplace transforms

9.

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 non-homogeneous equation using the complementary function and particular integral.

### 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 % 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

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
Total Full Time Average Weekly Learner Contact Time 6.00 Hours

### Module Resources

Non ISBN Literary Resources