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Unformatted text preview: , = ′ ′ = y y #2 #6 Consider a long slender vertical column of uniform crosssection and length L. Let y(x) denote the deflection of the column when a constant vertical compressive force, or load, P is applied to its top. Then 2 2 = + Py dx y d EI . If we let EI P / = λ we have ) ( , ) ( , = = = + ′ ′ L y y y y . As we saw earlier, = L x n c x y n π sin ) ( 2 , corresponding to the eigenvalues ,... 3 , 2 , 1 , / / 2 2 2 = = = n L n EI P n n . Physically this means that the column will buckle or deflect only when the compressive force is one of the values 2 2 2 / L EI n P n = . These different forces are called critical loads . The deflection curve corresponding to the smallest critical load 2 2 1 / L EI P = , called the Euler load , is ( 29 L x c x y / sin ) ( 2 1 = and is known as the first buckling mode. #23...
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 Fall '10
 PamelaSatterfield
 Differential Equations, Equations

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