Chapter 13 Buckling of Columns

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Chapter 13 Buckling of Columns
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Failure mode of column buckling (i.e. not
stress) At Pcr, stress less than yield strength!
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At Pcr, column is on verge of being unstable so
small lateral force, F will cause column to
buckle.
When F is removed, stays buckled. If P reduced
to below Pcr will straighten out, if P increased
beyond Pcr will increase lateral deflection
Load P can be increased until failure occurs by
yield or fracture
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Derivation of Eulers Equation
Homogeneous, second order, linear DE with
constant coefficients.
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Solution to DE is
C1 and C2 constants of integration. u0 at x0
so C20.
Which leaves
Which is satisfied if
Smallest value of P??
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Eulers Equation
PCR critical or maximum axial load on the
column just before it begins to buckle. E
modulus of elasticity for the material I least
moment of inertia of the columns cross-section L
unsupported length of the column, whose ends
are pinned
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Examples
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