Postgraduate Course: ThinWalled Members and Stability (PGEE10005)
Course Outline
School  School of Engineering 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Postgraduate) 
Availability  Not available to visiting students 
SCQF Credits  10 
ECTS Credits  5 
Summary  The two segments of this course introduce advanced elements of the theory of structures. The first provides an introduction to the behaviour and algebraic analysis of thinwalled structural members; the second covers the stability of structural elements and their analysis. 
Course description 
LECTURES
Segment 1 Thinwalled structures
L1 Introduction
Structure and aims of the course; uses and advantages of thinwalled members; section properties of thinwalled members; principal axes and rotation of axes; examples on the evaluation of section properties.
L2 Flexure of Beams and Biaxial Bending
Flexural stresses in elastic beams due to bending in the principal plane and due to biaxial bending; examples.
L3 Shear Stresses in Beams with Solid or Open CrossSections
Shear stresses in elastic beams with solid crosssections; Shear stresses in elastic beams with thin walled open crosssections; shear flow; example on the evaluation of shear flow distribution in an Isection.
L4 The Shear Centre
Shear centre; example on the evaluation of shear centre for a channel section; comparison of centroid and shear centre positions for some sections.
L5 Shear Stresses in Beams with Closed CrossSections
Shear stresses in elastic beams with thinwalled closed crosssections; box section example.
L6 Torsion in Structural Members
Introduction to uniform; warping and nonuniform torsion; Prandtl's membrane analogy for uniform torsion; evaluation of stresses under uniform torsion for general solid and rectangular crosssections.
L7 Uniform Torsion in Open and Closed Sections
Uniform torsion in thinwalled open crosssections; uniform torsion in thinwalled closed crosssections; elastic analysis of statically determinate and statically indeterminate members under uniform torsion; examples.
L8 Warping Torsion in Open Sections
Warping deflections and stresses; warping constant; example to demonstrate the evaluation of warping displacements, shear and longitudinal stresses due to warping torsion; warping torsion analysis of statically determinate and statically indeterminate members with examples; introduction to nonuniform torsion.
L9 Revision
SEGMENT 2 STABILITY OF STRUCTURES
L1 Introduction & elastic bifurcation buckling
Structure and aims of the course, linear buckling as an eigenvalue problem, bifurcation of equilibrium paths, stability of equilibrium.
L2 Imperfections and geometric nonlinearities in elastic structures
Effect of imperfections and nonlinearities; imperfection sensitivity; snapthrough buckling.
L3 Buckling in more complex systems
Bilinear elastic columns, testing machines.
L4 Inelastic buckling
Tangent and reduced modulus formulae; Shanley's explanation; Perry treatment.
L5 Local buckling: 1
Introduction to local buckling; derivation of plate buckling loads for various support conditions and directions of load; examination of buckling modes; critical width to thickness ratios.
L6 Local buckling: 2
Postbuckling strength of thin plates in compression and in shear; effect of initial imperfections and residual stresses; design rules.
L7 Torsional and flexuraltorsional buckling
Simple torsional buckling; example of a cruciform section; effect of nonuniform twisting; combined mode of twisting and flexure.
L8 Lateral torsional buckling of beams
Lateral torsional buckling of a deep rectangular section (various load cases) and an Isection; effect of level of application of load; overview of buckling phenomena.
L9 Revision
TUTORIALS
Bending of Beams
Evaluation of thinwalled section properties; evaluation of the shear centre position; evaluation of bending stress distribution.
Torsion
Evaluation of twist under uniform torsion and warping torsion; evaluation of torsion and warping constants; uniform and warping torsion analysis of structures.
Theory of elastic stability
Derivation of nonlinear law; derivation of equilibrium expressions for a single degree of freedom system, accounting for the effects of nonlinearities and imperfections; determination of the stability of equilibrium for this system and plotting of all equilibrium paths; explaining imperfection sensitivity.
Applied stability problems
Calculation of the critical stress using tangent and reduced modulus theories and the PerryRobertson equation; derivation of the critical load for a thin plate from energy equations; calculation of elastic critical stresses due to flexural, torsional, lateral torsional, and local buckling.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 demonstrate the ability to evaluate and explain the behaviour of thinwalled members under bending and torsional loads;
 demonstrate the ability to evaluate and explain the behaviour of structural elements undergoing buckling.

Reading List
 Trahair, N.S. and Bradford, M.A., The Behaviour and Design of Steel Structures, London: Chapman & Hall, 1995
 Calladine, C.R., Theory of Shell Structures, Cambridge: Cambridge University Press, 1983
 Timoshenko, S.P. & Gere, J.M., Theory of Elastic Stability, New York: McGrawHill, 1961 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  Not entered 
Contacts
Course organiser  Dr Yuner Huang
Tel: (0131 6)50 5736
Email: Yuner.Huang@ed.ac.uk 
Course secretary  Miss Margaret Robertson
Tel: (0131 6)50 5565
Email: margaret.robertson@ed.ac.uk 

