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Chapter 13 – Buckling of Columns

Chapter 13 – Buckling of Columns. Failure mode of column = buckling (i.e. not stress) At P cr , stress less than yield strength!. At Pcr, column is on verge of being unstable so small lateral force, F will cause column to buckle.

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Chapter 13 – Buckling of Columns

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  1. Chapter 13 – Buckling of Columns

  2. Failure mode of column = buckling (i.e. not stress) At Pcr, stress less than yield strength!

  3. 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

  4. Derivation of Euler’s Equation: Homogeneous, second order, linear DE with constant coefficients.

  5. Solution to DE is: C1 and C2 = constants of integration. u=0 at x=0 so C2=0. Which leaves: Which is satisfied if: Smallest value of P??

  6. Euler’s 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 column’s cross-section L = unsupported length of the column, whose ends are pinned

  7. Examples:

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