ENGINEERING TRIPOS PART IB - 2012/2013

PAPER 2 - STRUCTURES

Structures

Leader: Dr K.A. Seffen, Dr. S. D. Guest

Timing: Weeks 5-8 Michaelmas term and weeks 1-4 Lent term, 2 lectures/week; weeks 5-8 Lent term, 1 lecture/week

Structure: 20 lectures

AIMS

The aims of the course are to:

• Extend understanding of how structures behave, and can be analysed.
• Introduce concepts of stress-state, strain-state and yield by considering the behaviour of simple thin-walled structures.
• Explain the elastic analysis of statically indeterminate structures, and to show some of the implications of redundancy.
• Introduce the plastic theory of structures. 

OBJECTIVES

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

• Find, for thin-walled cylinders, the stresses and stress-resultants, strains and displacements resulting from applied loading.
• Understand the concept of stress-state and strain-state; be able to represent them in 2-D and 3-D by Mohr's Circles.
• Understand the Tresca and von Mises yield criteria.
• Analyse statically indeterminate truss and frame structures.
• Use virtual work for beam bending calculations.
• Evaluate the fully plastic moment of a beam cross-section.
• Find upper bound estimates of the failure load of beams, plane portal frames, slabs and continua.
• Find lower bound estimates of the failure load of beams.

SYLLABUS

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

1. Thin-walled Structures (3L, Dr S.D. Guest)

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

2. Analysis of Stress and Strain (4L, Dr S.D. Guest)

• 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.

3. Elastic Structural Analysis (5L, Dr S.D. Guest)

• 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.

4. Plastic Structural Analysis (8L, Dr S.D. Guest)

• 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

REFERENCES

Please see the Booklist for Part IB Courses for references for this module.

Last updated: May 2102
teaching-office@eng.cam.ac.uk