Buckling-lecture-2010

Buckling-lecture-2010 - 1 Buckling Analysis When a...

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Unformatted text preview: 1 Buckling Analysis When a structure ( subjected to compression or shear ) undergoes visibly large displacements transverse to the load then it is said to buckle. Buckling may be demonstrated by pressing the opposite edges of a flat sheet of cardboard towards one another. Local buckling of plates is indicated by the growth of bulges or ripples, and is commonly seen in the component plates of thin structural members. 2 Stable, Neutral and Unstable Equilibrium Buckling proceeds in manner which may be either: S table : in which case displacements increase in a controlled manner as loads are gradually increased, ie. the structure's ability to sustain loads is maintained Neutral equilibrium: is also a theoretical possibility during buckling - this is characterised by deformation increase without change in load. Unstable: in which case deformations increase instantaneously, the load carrying capacity drops suddenly and the structure collapses catastrophically. 3 2 2 dz v d EI M = In bending these moments are largely independent of the resulting deflections , whereas in buckling the moments and deflections are inter-dependent . If buckling deflections become too large then the structure fails - this is a geometric consideration and separate from any material strength consideration. Therefore If a component or part is prone to buckling then its design must satisfy both strength and buckling safety constraints. v denotes the deflection along Z z z Buckling and bending are similar in that they both involve bending moments Beam bending theory 4 Compression Members The failure of a short compression member can be illustrate as shown in the figure However, when a compression member is relatively long, the role of the geometry and stiffness (Youngs modulus) is more important. For a long (slender) column , buckling occurs before the normal stress reaches the strength of the column material. 5 F o r a n intermediate length compression member , kneeling occurs when some areas yield before buckling The failure of a compression member is related to the strength and stiffness of the material and the geometry (slenderness ratio) of the member. A compression member is categorized as short, intermediate, or long depends on these factors 6 Simple Buckling Example P L k (a) P Lsin (b) sin PL k = sin L k P = Restoring force Disturbing force To illustrate the buckling phenomena a highly simplified model is used as an example. A vertical rigid rod of length L is pinned at its lower end. It is held vertical by a rotational spring of stiffness k. It is loaded by a compressive force P....
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Buckling-lecture-2010 - 1 Buckling Analysis When a...

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