Postgraduate Course: Thin-Walled Members and Stability (PGEE10005)
|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
|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 thin-walled structural members; the second covers the stability of structural elements and their analysis.
Segment 1 Thin-walled structures
Structure and aims of the course; uses and advantages of thin-walled members; section properties of thin-walled 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 Cross-Sections
Shear stresses in elastic beams with solid cross-sections; Shear stresses in elastic beams with thin walled open cross-sections; shear flow; example on the evaluation of shear flow distribution in an I-section.
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 Cross-Sections
Shear stresses in elastic beams with thin-walled closed cross-sections; box section example.
L6 Torsion in Structural Members
Introduction to uniform; warping and non-uniform torsion; Prandtl's membrane analogy for uniform torsion; evaluation of stresses under uniform torsion for general solid and rectangular cross-sections.
L7 Uniform Torsion in Open and Closed Sections
Uniform torsion in thin-walled open cross-sections; uniform torsion in thin-walled closed cross-sections; 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 non-uniform torsion.
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; snap-through 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 flexural-torsional buckling
Simple torsional buckling; example of a cruciform section; effect of non-uniform 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 I-section; effect of level of application of load; overview of buckling phenomena.
Bending of Beams
Evaluation of thin-walled section properties; evaluation of the shear centre position; evaluation of bending stress distribution.
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 Perry-Robertson 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)
||Other requirements|| None
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- demonstrate the ability to evaluate and explain the behaviour of thin-walled members under bending and torsional loads;
- demonstrate the ability to evaluate and explain the behaviour of structural elements undergoing buckling.
|- 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: McGraw-Hill, 1961
|Graduate Attributes and Skills
|Course organiser||Dr Yuner Huang
Tel: (0131 6)50 5736
|Course secretary||Miss Margaret Robertson
Tel: (0131 6)50 5565