page_title: Johnson's parabolic formula
hierarchical_section_title: Johnson's parabolic formula
caption_attribution_description: English: Unit-less depiction of the Euler curve for critical stress and slenderness ratio
context_page_description: The Johnson formula is an empirically based formula relating the slenderness ratio to the stress illustrating the critical load required to buckle a column. The formula is based on empirical results by J. B. Johnson from around 1900 as an alternative to Euler's critical load formula under low slenderness ratio conditions.
  Buckling refers to a mode of failure in which the structure loses stability. It is caused by a lack of structural stiffness. Placing a load on a long slender bar will cause a buckling failure before the specimen can fail by compression.
  One way to calculate buckling is to utilize Euler's formula, which produces a critical stress vs. slenderness curve such as the one illustrated to the right.
  However, depending on the geometry of the structure under stress, this equation is not always applicable, and the Johnson parabola should be used.
context_section_description: The Johnson formula is an empirically based formula relating the slenderness ratio to the stress illustrating the critical load required to buckle a column. The formula is based on empirical results by J. B. Johnson from around 1900 as an alternative to Euler's critical load formula under low slenderness ratio conditions.
  Buckling refers to a mode of failure in which the structure loses stability. It is caused by a lack of structural stiffness. Placing a load on a long slender bar will cause a buckling failure before the specimen can fail by compression.
  One way to calculate buckling is to utilize Euler's formula, which produces a critical stress vs. slenderness curve such as the one illustrated to the right.
  However, depending on the geometry of the structure under stress, this equation is not always applicable, and the Johnson parabola should be used.
caption: Curve of Euler's formula for buckling. The area above the curve indicates failure while the area under the curve represents scenarios that would not cause failure.
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