Mechanics of Deformable Solids | Column Buckling by Pavan | Learn Smarter
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Column Buckling

Column buckling is a critical property influencing the stability of structures subjected to axial loads, distinct from material yield failure. Euler's theory of buckling provides a mathematical framework for analyzing slender columns, identifying critical loads under various boundary conditions. The limitations of Euler's theory highlight its applicability to long, slender configurations while considering real-world factors like eccentric loading, which introduces complexities in design that require careful consideration of both axial forces and moments.

Sections

  • 1

    Introduction To Column Buckling

    This section introduces the concept of column buckling, a stability failure in structural members subjected to axial compressive loads.

  • 2

    Euler’s Theory Of Buckling

    Euler’s Theory of Buckling explains how slender columns become unstable under axial loads, defining a critical load at which buckling occurs.

  • 2.1

    Critical Load Equation

    The critical load equation helps determine the axial load at which a slender column becomes unstable and buckles.

  • 2.2

    Where

    This section discusses the critical aspect of column buckling, including Euler’s theory of buckling, boundary conditions, and effective column lengths.

  • 3

    Boundary Conditions And Effective Lengths

    This section explains how various boundary conditions affect the effective lengths of columns, influencing their stability under axial loads.

  • 3.1

    Effective Length Table

    This section outlines the concept of effective length in relation to column buckling and provides a table of effective lengths based on various boundary conditions.

  • 4

    Limitations Of Euler’s Formula

    Euler's formula for column buckling is applicable under specific conditions and has several limitations that need to be considered.

  • 5

    Eccentric Loading Of Columns

    Eccentric loading occurs when axial loads on columns are not applied exactly along the centroid, introducing bending stresses and increasing the risk of failure.

  • 5.1

    Total Stress Equation

    The section covers the total stress equation for columns under axial loads and discusses the implications of eccentric loading.

  • 5.2

    Eccentricity And Moment

    This section discusses the impact of eccentric loading on columns, detailing how bending stresses arise and affect buckling behavior.

Class Notes

Memorization

What we have learnt

  • Column buckling is a stabil...
  • Euler's formula allows the ...
  • Eccentric loading can lead ...

Final Test

Revision Tests