ES3C3 Planar Structures and Mechanisms

Module Leader: Dr D.A. Lockerby

Co-Lecturer: Professor D.G. Chetwynd

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 I.Mech.E. are expected to have a knowledge of the basis of stress analysis and an understanding of how stress, strain and strength affect the design of structures used to support mechanisms. They should also be aware of the dynamical behaviour of some classical cases of mechanisms. This module addresses those requirements.

The module concentrates on instilling an appreciation of the physical behaviour of solids that has led to classical linear models rather than on first principle proofs of linear theory. This approach reflects that all but the very simplest analyses will now use computer modelling that can deal with more complex geometrical forms and materials properties. Designers and analysts must nevertheless be able to visualize the behaviour of structures and to apply linear formulae in order to verify whether a particular computer model is appropriate to a particular situation.

Learning Outcomes

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

Understand the terminology and reasons for using linear elastic theory and apply commonly-used formulations to analyse simple structures.
Appreciate some common (idealized) states of stress and strain and the typical failure criteria that arise from them.
Predict the torsional behaviour of circular shafts and hence design simple cases.
Predict the deflection under load of basic forms of structures such as statically determinate and indeterminate pin-jointed frames and beams.
Appreciate the stability requirements for idealized struts and columns.
Appreciate the approximations inherent in linear elastic methods and converse with specialists on the use of finite element models.
Understand the behaviour of some simple planar mechanisms and calculate the velocities, accelerations and forces associated with their motion..
Appreciate how mechanism inertia can lead to shaking forces and calculate how to balance such forces in some important special cases.

Syllabus

1. Reprise of basic rigid body statics and dynamics – free-body-diagrams, centre of mass, moment of inertia; planar pin-jointed systems; static determinacy and mobility.

2. Basic linear elasticity (introduced mainly via axially-loaded members) – tension, compression and shear force; Hooke’s law; stress, strain and Poisson’s ratio; ideal elastic-plastic behaviour; equilibrium, compatibility and constitutive equations; notion of strain energy; shear effects in axially-loaded members and patterns of materials failure.

3. Deflection of planar pin-jointed structures – matrix methods.

4. Torsion of circular shafts – shear behaviour; multiple loads (e.g. gearbox shaft); tensile stress in ‘pure shear’ loading and patterns of failure; power transmission by shafts; comments on thin-wall and open sections.

5. Classical beam theory – shear force and bending moment; neutral axis, second moment of area and maximum stresses; effect of cross-sectional shape; deflection of prismatic beams; comments on composite beams; superposition of linear solutions (multiple loads, combined bending and torsion); statically indeterminate beams.

6. Idealized stress distributions – plane stress (uniaxial, biaxial); principal axes; triaxial stress; hydrostatic stress; relationship between plane stress and plane strain; comments on materials failure criteria; case study on pressure vessels.

7. Models and real systems – nature of approximations and limits of usefulness of linear theory; benefits and drawbacks of computer modelling by finite element methods.

8. Struts and columns – Euler buckling; critical load for various end conditions; slenderness ratio; simple case of eccentric loading.

9. Planar mechanisms – basic concepts; mobility revisited; Grashof condition; some classical mechanisms.

10. Kinematics of 4-link pinned and simple slider-crank mechanisms – vector solutions; velocity and acceleration diagrams as an illustration; complex number notation and matrix formulation.

11. Kinetics of 4-link pinned and simple slider-crank mechanisms – systematic schemes; ‘light’ mechanisms; power balance; forces at pins.

12. Dynamic balance – shaking forces; rotary dynamic balance; moments and products of inertia; principal axes; ideas in engine (crank-slider) balance.