# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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# 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 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 thin-walled structural members; the second covers the stability of structural elements and their analysis. Course description LECTURES Segment 1 Thin-walled structures L1 Introduction 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. 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; 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. L9 Revision TUTORIALS Bending of Beams Evaluation of thin-walled 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 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.
 Pre-requisites Co-requisites Prohibited Combinations Other requirements None
 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 Not entered Keywords Not entered
 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
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