# ES3C3 Planar Structures and Mechanisms

Co-Lecturer: Dr Y. Tian

## Module Information

### Scope

This 15 CATS module is one of the third year modules for:

 Core: Optional: Mechanical Engineering Engineering

### Aims

All engineers accredited by the IMechE are expected to have a knowledge of stress analysis and an understanding of how stress, strain and strength affect the design of structures. They should also be aware of the dynamical behaviour of some classical cases of mechanisms. This module addresses those requirements.

The module lectures are split between two main themes. The first theme is the analysis of planar pin-jointed structures and mechanisms in terms of position, velocity and acceleration and matrix solutions of the equations of motion (geometry, kinematics and dynamics). The approach progresses from simple analysis to complex cases requiring computer modelling.

The second set of lectures covers strength of materials topics in linear elasticity i.e. how stresses and strains in the material result from the imposed forces. These topics were introduced in year 2 (ES2B0); the effect of these stresses and strains is now investigated in a number of classical settings including beams, shafts, columns, disks and pressure vessels. Students are introduced to the physical properties of materials and failure criteria so that they can analyse simple systems by hand and choose suitable materials. In particular they are introduced to concepts such as strength, weight, and stiffness with a view to developing understanding to allow interpretation and assessment of computer models in more complicated cases.

### Learning Outcomes

By the end of the module the student should be able to...

• Model the behaviour of some common planar mechanisms and calculate the velocities, accelerations (kinematics) and forces (kinetics) associated with their motion.
• Understand how mechanism inertia can lead to shaking forces and calculate how to compensate for such forces (balance) in some important special cases (e.g., reciprocating engines).
• Understand the terminology and rationale for using linear elastic theory and how to apply common formulations to analyse simple systems. Recognise the approximations inherent in linear elastic methods and be able to converse with specialists, e.g., on the use of finite element models.
• Choose between and apply some common (idealized) states of stress and strain and the typical failure criteria that arise from them, including von Mises’ stresses Assess material suitability in terms of application criteria.
• Predict the deflections, stresses, etc. under load and hence design simple cases for planar structural systems including:
• Statically determinate and indeterminate pin-jointed frames; beams; simple assemblies of planar components; stability of struts; thermal expansion; stresses in pressure vessels and rotating discs
• Predict rotation angles and stresses in shafts under torsion, including torques applied via gearing or pulley systems.
• Understand the cause and effects of stress concentrations.

### Syllabus

The analysis of planar pin-jointed structures and mechanisms in terms of:
• Position
• Velocity
• Acceleration
• Matrix solutions of the equations of motion:
o Geometry
o Kinematics
o Dynamics
(The approach progresses from simple analysis to complex cases requiring computer modelling.)

Strength of materials topics :
• Linear elasticity i.e. how stresses and strains in the material result from the imposed forces.
(These topics were introduced in year 2 (ES2B0));

• the effect of these stresses and strains is investigated in a number of classical settings including :
o beams
o shafts
o columns
o discs
o pressure vessels.
• Students are introduced to the physical properties of materials and failure criteria so that they can analyse simple systems by hand and choose suitable materials. In particular they are introduced to concepts such as strength, weight, and stiffness, with a view to developing understanding to allow interpretation and assessment of computer models in more complicated cases.

### Teaching Methods

This module includes 30 hours of lectures and 2 hours of revision classes.

Required guided self-study: 118 hours

### Assessment

A 15 CATS module: 80% examined via a 3 hour paper

Exam rubric information:

• 4 Compulsory Questions

and 20% assessed consisting of an analysis assignment combining computer simulation, hand calculations and discussion.

Student Resources

Staff Pages

#### Recommended Textbook:

Hibbeler RC, 2005, Mechanics of Materials (SI 6th Ed.)

and

Shigley JE and Uicker JJ, 1995, Theory of Machines and Mechanisms, McGraw Hill, QC194.S4