# Biomedical Engineering (MEng)

## Mechanics 2 Solids

### Module aims

To develop basic concepts of structural mechanics, show the relevance in design and risk analysis, and develop analytical skills in stress analysis.

### Learning outcomes

Learning Outcomes - Knowledge and Understanding

Recall, list, and define terms used in engineering properties of materials.

Recall, list, and define terms in:

• Generalised Hooke's Law
• Principal Stresses
• Principal Strains
• Tresca and von Mises failure criteria
• elastic constant relationships
• circumferential and longitudinal stresses in thin-walled vessels
• simple bending
• simple torsion
• buckling
• second moment of area and polar second moment of area for standard shapes
• parallel axis theorem

Apply the above list appropriately to solve well-posed, constrained stress analysis problems

Apply the above list appropriately to constrain a complex stress-analysis problem, carefully clarifying assumptions made and justifying these.

Determine the deformations of beams, rods and shafts with arbitrary X-section under general loadings which are statically determinate or indeterminate

Learning Outcomes - Intellectual Skills
• Analyse statically determinate and indeterminate force systems
• Analyse deformable bodies by the use of geometry of deformation concepts and theory: strain, connectivity, boundary conditions
• Analyse generalised two-dimensional stress and strain states in a solid
Learning Outcomes - Practical Skills

Be able to obtain the Young's modulus of a beam by experimental measurement.

Be able to quantify stress concentration factors experimentally

Learning Outcomes - Transferable Skills

Problem solving:
Identify problems that are amenable to Stress Analysis. Analyse the Stress Analysis approaches that are required in combination with other engineering tools to analyse the problem.

Report Writing:

Be able to write an appropriate report to quantify various physical mechanical properties of materials as well as the errors associated with these.

### Module syllabus

• Revision of Newtonian mechanics – rigid body analysis, free body diagrams
• Very brief revision of engineering properties of materials, introduction of time-dependent properties.
• Pin jointed structures,
• Applied forces and deformations
• Internal forces and moments
• Stress and strain
• General procedures for solving problems that include deformations
• Selection and use of engineering materials
• Statically determinate and indeterminate systems
• Equilibrium equations for 2D stress systems – 2D strain compatibility equations
• Multi axial deformations and stress analysis – Poisson’s ratio, biaxial stress, hydrostatic stress, triaxial stress, thermal strain, stress transformations. Derivation and use of principal stresses. Knowledge and use of principal strains.
• Failure theories, safety, fatigue, stress concentration
• Uniformly loaded thin shells – pressurised thin walled cylinder; pressurised thin walled sphere, rotating rings; resisted thermal expansion
• Beam analysis – shear force and bending moments. Derivation and use of direct stresses in beams. Knowledge and use of shear stresses in beams. Derivation and use of second moment of area. Derivation and use of beam deflection.
• Unsymmetrical bending. Knowledge and use of combined bending and axial load.
• Torsion. Derivation and use of the torsion equation.
• Combined bending, torsion and axial loading. Use of principle of superposition.

### Pre-requisites

Biomolecular Engineering I (or basic Engineering Properties of Materials course) Mechanics I (or basic statics course)

### Teaching methods

Lectures: 18 hours
Study groups: 9 hours
Labs: 18 hours

### Assessments

Examinations:
Mastery exam (60 minutes): takes place at start of second term
Written exam  (60 minutes): can only be sat subject to passing mastery

Coursework:
●  Item 1:Lab report Title:Lab report Description:Report on one of the experiments - assigned on completion of the labs Weighting: Pass/ Fail %
●  Item 2:Lab book Title: Description: Weighting: 0 %

Outline answers to past papers will be available

Exam rubric: Lab Report: Needs to be passed at 40%. Two exams: First exam mastery: 1 hour mastery. 80% pass required for progression. Answer all questions. Questions are of different lengths. Mastery exam takes place at start of second term. A retake can be taken before/at the start of the examination period. . A third retake is possible during the examination period. Final exam: 1 hour. no pass required. Answer all questions. Questions of different lengths. Passing mastery plus the Lab Report gives a 40% grade for the course, the final exam then counts for the remaining 60% of the overall final grade.

Feedback : There are 9 problem sheets (approx 1 PS per two lectures). One PS will form the basis of each tutorial. After tutorials, the tutors and the academic member of staff will review 'common' problems and these will be addressed at the start of the following lecture as formal feedback. All problem sheet worked solutions will be made available after this feedback has been given. The marked coursework is the lab report; this is summative.