Slenderness Ratio

Slenderness ratio is the ratio of the effective length of a column (Le) and the least radius of gyration (r) about the axis under consideration. It is given by the symbol “λ” (lambda).

slenderness ratio formula

Effective slenderness ratio of the section about the minor axis of cross-section = Le/ry.
Effective slenderness ratio of the section about the major axis of cross section = Le/rx.

Significance:
As slenderness ratio increases, permissible stress or critical stress reduces. Consequently, load carrying capacity also reduces.

  • Radius of gyration will be least along major axis of cross section.
    Example: For a rectangular column along yy-axis.
  • For a given area, Tubular section will have maximum radius of gyration.
  • H-Section is more efficient than I-Section.
    section
    Iy = Imin  (Column buckles about y-axis)
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