Aims

The aims of the course are to:

• To extend understanding of the behaviour and analysis of structures.
• To introduce concepts of stress-state, strain-state and yield using simple thin-walled structures.
• To explain elastic analysis of statically indeterminate structures and implications of redundancy.
• To introduce plastic theory of structures.

Objectives

As specific objectives, by the end of the course students should be able to:

• To find, for thin-walled cylinders, the stresses and stress-resultants, strains and displacements resulting from applied loading.
• To understand the concept of stress-state and strain-state using 2-D and 3-D Mohr's Circles.
• To understand the Tresca and von Mises yield criteria.
• To analyse statically indeterminate truss and frame structures.
• To use the method of Virtual Work for beam bending calculations.
• To evaluate the fully plastic moment of a beam cross-section.
• To find upper bound estimates of the failure load of beams, plane portal frames, slabs and continua.
• To find lower bound estimates of the failure load of beams.

Content

The following material will be taught in the context of design:

Thin-walled Structures (3L)

• Stresses in cylinders due to axial loading, bending and shear, internal pressure and torsion.
• Strain in three dimensions, stress-strain-temperature relationships.
• Torsional rigidity.

Analysis of Stress and Strain (4L)

• 2-D stress and strain state, equilibrium equations, 2-D Mohr's circle.
• 3-D stress and strain state, 3-D Mohr's circle.
• Principal stresses, strains and directions.
• Yield criteria: Tresca; von Mises.

Elastic Structural Analysis (5L)

• Indeterminate truss structures, analysis by the Force Method.
• Deflections in beams, including curved beams, by Virtual Work.
• Indeterminate frame structures, analysis by the Force Method.
• Symmetry and anti-symmetry.

Plastic Structural Analysis (8L)

• Calculation of plastic section modulus Zp and fully plastic moment Mp.
• Collapse mechanisms for a statically determinate beam.
• Concept of an upper bound estimate of collapse load.
• Collapse mechanisms for statically indeterminate beams and plane portal frames.
• Yield lines for predicting collapse loads of slabs.
• Slip lines for predicting plane strain failure of continua.
• Equilibrium states for a statically indeterminate beam.
• Concept of a lower bound estimate of collapse load.
• Lower bound principle as a justification for elastic analysis.

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 26/08/2020 09:22