Module manager: Dr Qingen Meng
Email: Q.Meng@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2025/26
This module is not approved as a discovery module
This module will introduce students to estimating the safety of mechanical designs from the point of view of mechanics. Therefore, a wide range of mechanics topics (i.e., direct stress in asymmetric bending, shear stress, deflection, buckling, collapse, elasticity theory and reliability analyses) will be addressed. Moreover, the mathematical techniques (e.g., solving second order differential equations using analytical methods, solving differential equations numerically, and vector calculus, etc.) necessary for the mechanics topics will also be covered.
On completion of this module, students will be able to
1- model mechanical systems in terms of one or more differential equations and solve these equations using appropriate analytical or numerical techniques;
2- analyse the stresses, strains, deflection, displacement, and critical loading causing buckling or collapse for solid mechanical and structural systems under particular conditions and evaluate and improve the safety of the systems from the point of view of mechanics.
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
1- Model the behaviour of second order mechanical and electrical systems, and solve the associated ordinary differential equations analytically
2- Use finite differences to formulate numerical solutions of ordinary differential equations representing engineering systems
3- Apply the concepts and notation of vector calculus to analyse relevant scalar and vector fields and represent partial differential equations efficiently
4- Use Fourier Series to capture the behaviour of periodic systems
5- Analyse the direct stress of asymmetric beams under pure bending making use of the formulae derived
6- Examine the shear stress of symmetric beams under bending
7- Solve the deflection of beams under the combination of various loading conditions making use of the superposition method and the direct integration method
8- Construct and analyse the Euler’s critical load for slender beams with different fixation conditions
9- Solve the limiting bending moment and limit loads of beams in the context of collapse
10- Formulate the governing equations of the mathematical theory of elasticity under the cylindrical coordinate system and solve and analyse the stress and strain state of mechanical systems under the cylindrical coordinate system
11- Evaluate the reliability of a mechanical system using statistical theory
These module learning outcomes contribute to the following AHEP4 learning outcomes:
12- Apply knowledge of mathematics, statistics, natural science and engineering principles to broadly-defined problems. Some of the knowledge will be informed by current developments in the subject of study. [C1]
13- Analyse broadly-defined problems reaching substantiated conclusions using first principles of mathematics, statistics, natural science and engineering principles. [C2]
14- Select and apply appropriate computational and analytical techniques to model broadly-defined problems, recognising the limitations of the techniques employed. [C3]
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills:
a- Teamwork & collaboration
b- Problem solving & analytical skills
c- laboratory practice
- Revision of first-order ordinary differential equations (ODEs)
- Examples of first and second-order ODEs relevant to engineering
- Introduction to Laplace Transforms and their use in the solution of ODEs
- General solution of linear ODEs and associated physical interpretations
- Taylor series and Finite Difference methods for the numerical solution of differential equations
- Introduction to Vector Calculus.
- Fourier Series.
- Revision of moments of area, free body diagram, and the calucaltion of direct stresses of symmetric beams under pure bending.
- Calculation of (i) direct stress in asymmetric beam sections, (ii) shear stress distributions in symmetric beams.
- Derivation of relationships between bending moment and deflection of symmetric beams.
- Derivation and solution of equations for the limit loads causing the instability of axially loaded beams and for the limit loads and moments causing the collapse of beams.
- Mathematical theory of elasticity: derivation of the force equilibrium equation and strain-displacement equation in an axisymetric stress field; simplication of these equations under the plain stress and plain strain states; mathematical solution of these equations with application to problems of a pressurized thick walled cylinder and rotating discs.
- Reliability analysese of mechanical systems.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Example Class | 22 | 1 | 22 |
| Lecture | 44 | 1 | 44 |
| Practical | 2 | 1 | 2 |
| Independent online learning hours | 4 | ||
| Private study hours | 128 | ||
| Total Contact hours | 68 | ||
| Total hours (100hr per 10 credits) | 200 | ||
Online self-test questions are available for students after each Unit is delivered. Students automatically receive well-designed feedback after they submit their answers to the questions.
The reading list is available from the Library website
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team