## MECHANICS OF SOLIDS (CCE)

 SHE Level 2 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M2H324720 Module Leader Babakalli Alkali School School of Computing, Engineering and Built Environment Subject SCEBE - School Office Trimesters A (September start) B (January start)

### Pre-Requisite Knowledge

Mechanical Principles

### Summary of Content

The aim of this module is to develop an understanding of: -360b7 Simple stresses, strains and deformation in components due to external loads. b7 Stress and strain analysis in two dimensions b7 Application of different methods for evaluating displacements of a member under given loading b7 Development of stresses in cylinders under pressure Free and forced vibrations for one-degree of freedom systems with without damping.

### Syllabus

SIMPLE STRESSES & STRAINS Types of stresses & strains, Hooke's law, stress-strain diagram, Working stress, Factor of safety, Lateral strain, Poisson's ratio, volumetric strain, elastic moduli, Deformation of simple and compound bars under axial load, analysis of composite bar with varying cross section. SHEAR FORCE AND BENDING MOMENT: Definition of beam, Types of beams and loading. Shear force and bending moment diagram for cantilever, simply supported and overhanging beams subjected to point loads, UDL and combination of these loads. THEORY OF SIMPLE BENDING: Theory of simple bending, assumptions, neutral axis, section modulus of rectangular, circular, I, T, angle and channel sections, bending stress in beams. DEFLECTION OF BEAMS: Deflection, slope and radius of curvature for cantilever and simply supported beams subjected to different loading conditions. TORSION OF SHAFTS: Simple torsion theory, shear stress and strain in shafts, torsion of hollow shaft. Stresses in shafts subjected to bending, torsion, axial and combined loading. ANALYSIS OF STRESSES AND STRAINS IN TWO DIMENSIONS Biaxial state of stresses, Biaxial stresses at a point, Stresses on inclined plane, Principal planes and stresses, Mohr's circle for biaxial stresses and strains, Maximum shear stress, Strain energy in bending and torsion. THIN CYLINDERS AND SPHERES Thin seamless cylindrical shells, Derivation of formula for longitudinal and circumferential stresses, hoop, longitudinal and Volumetric strains, changes in diameter, and volume of thin cylinders, Thin spherical shells. DYNAMICS OF STRUCTURES Concept of free vibration and forced vibration of one degree of freedom systems; determination of natural frequencies in rectilinear, torsional and transverse modes; Vibration with viscous damping. Application to mechanical, electrical and electro-mechanical systems.

### Learning Outcomes

On completion of this module the student should be able to:1. Analyse stress and strain of simple components subject to direct and shear loading. (AM1)2. Identify the types of beams and draw the shear force and bending moment diagrams under different loading conditions. (AM1)3. Analyse the underlying theory/principles in simple bending and determine the deflection, slope and radius of curvature of beams. (AM1, AM4)4. Discuss the torsion of the shaft and evaluate stresses in circular shafts due to bending, torsion, axial and combined loading. (AM1)5. Perform analyses of 2D stress and strain systems and determine the stresses and strains in thin cylinders and spheres. (AM1)6. Demonstrate the vibration concepts on one-degree of freedom systems with and without damping and with and without an external forcing function. (AM1, AM4)

### Teaching / Learning Strategy

The material covered during lectures will be reinforced and consolidated through tutorials. Practical work in the laboratory will be used to encourage team work, enhance understanding and application of the engineering principles. Additional practical problem solving will, through coursework, form part of the learning process.

E J Hearn 1997, Mechanics of Materials , Vol. 1 & 2; Butterworth Heinmann, 3rd Edition. Timoshenko S.P1997, Elements of Strength of Materials , Tata McGraw-Hill, New Delhi. Popov E.P, 1997, Engineering Mechanics of Solids , Prentice-Hall of India, New Delhi. Beer F. P. and Johnston R, 2002, Mechanics of Materials, McGraw-Hill Book Co, Third Edition. Ryder G.H, 2002, Strength of Materials , Third Edition, Macmillan India Ltd.. W T Thomson,1997, Theory of Vibrations with Applications , Chapman & Hall, 4th Edition

### Transferrable Skills

Tutorials provide: Development of skills in problem solving, numerical analysis Laboratories provide: Practical, Interpersonal / team skills Reports provide: Writing skill /Communication/Literacy/Linguistic/Critical Evaluation

### Module Structure

Activity Total Hours
Independent Learning (FT) 100.00
Assessment (FT) 16.00
Practicals (FT) 28.00
Lectures (FT) 56.00

### Assessment Methods

Component Duration Weighting Threshold Description
Coursework 1 n/a 30.00 35% Lab report of 1500 words + lab Test
Exam (Exams Office) 2.00 50.00 45% Final Examination- Unseen written examination - 2 Hours
Exam (School) 1.50 20.00 35% Mid-Term Test -Unseen written examination-1½ Hours