Structures 1

Module aims

This module introduces the fundamental concepts for all structural analysis, viz equilibrium, compatibility and the stress/strain law. It illustrates the use of these concepts to solve simple problems, mainly concerning frameworks and beams, and to apply them in tutorials and laboratory practicals. 

Learning outcomes

On successfully completing this module, you should be able to:

1. define stress and strain and the symbols and conventions in 3-D, introduce the material properties and show their relationship to stress and strain via constitutive laws.
2. demonstrate understanding of the small displacement hypothesis for pin-jointed frameworks, find all the forces in a pin-jointed framework using joint equilibrium and apply the principles of superposition and symmetry. Use this to identify a pin-jointed framework as being: statically determinate, redundant or a mechanism.
3. express the strain in any bar in terms of its end displacement components and construct the deflected shape of a framework if the bar forces are known.
4. solve for the deflection in a statically-determinate framework using the virtual work method and in terms of the joint.
5. derive the governing equations for slender beams using the same principles of compatibility, equilibrium and the stress/strain law, construct the shear force and bending moment diagrams for a variety of beam problems and solve for beam deformations by direct integration and by the virtual work method.
6. identify statically-indeterminate beams and solve for single redundancies using the principles and methods learned earlier.
7. derive the equations for a circular section beam loaded in torsion and to show that these are similar to the equations for beam bending and solve some examples for displacement and shear stresses.
8. derive the equations for the analysis of thin-walled beams with non-symmetric sections and solve for bending stresses and deflections.

Module syllabus

Introduction: structural analysis as part of the design process.
Stress/Strain: definition and convention for all stress components in 3-D. Definitions of: strain, including thermal strain; constitutive (stress/strain) law; Young’s modulus; shear modulus; Poisson’s ratio.
Pin-jointed frameworks: statically determinate: forces and displacements. The virtual work method.
Redundant frameworks: solution in terms of joint displacements.
Engineer’s Theory of Beams: assumptions, strain/curvature and stress/moment relationships.
Shear force and bending moment diagrams.
Direct solution of deflections from curvature.
Displacement by the virtual work method.
Statically-indeterminate beams.
Torsion of circular section beams.
Thin-walled beams with non-symmetric sections and the concept of principal axes.

Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological. The content is presented via a combination of slides, whiteboard and visualiser.

Learning will be reinforced through tutorial question sheets and laboratory exercises, featuring analytical, computational and experimental tasks representative of those carried out by practising engineers.

Assessments

This module presents opportunities for both formative and summative assessment. 
You will be formatively assessed through progress tests and tutorial sessions.
You will have additional opportunities to self-assess your learning via tutorial problem sheets.
You will be summatively assessed by a written examination at the end of the module as well as through practical laboratory assessments and a written laboratory report. 

Reading list