Structures 1

Description

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. 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.