Buckling coefficient formula
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| \( K \;=\; \sqrt{ \dfrac{ \lambda \cdot I }{ k \cdot A_c \cdot l^2 } } \) | ||
| Symbol | English | Metric |
| \( K \) = Buckling Coefficient (Fixed-fixed and Pinned-pinned) | \(dimensionless\) | \(dimensionless\) |
| \( \lambda \) (Greek symbol lambda) = Material Elastic Modulus | \(lbf \;/\; in^2\) | \(Pa\) |
| \( I \) = Second Moment of Inertia | \(in^4\) | \(mm^4\) |
| \( k \) = Effective Length Factor (which Depends on the End Conditions) | \(in\) | \(mm\) |
| \( A_c \) = Material Area Cross-section | \(in^2\) | \(mm^2\) |
| \( l \) = Length of the Member | \(in\) | \(mm\) |
Buckling coefficient, abbreviated as K, also called slenderness ratio, a dimensionless number, is used in structural engineering to assess the stability of a slender structural element under axial compression that can lead to failure. When a structure is subjected to compressive stress, buckling may occure. Buckling is characterized by a sudden sideways deflection of a structural member. When a slender structural member is subjected to compressive forces, it may buckle, which refers to a sudden, uncontrollable lateral deflection or deformation. Buckling can lead to structural failure if not properly addressed in the design. The formula for the buckling coefficient depends on the type of end support conditions and the geometry of the column.
Buckling coefficient formula
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| \( K \;=\; \sqrt{ \dfrac{ 2 \cdot \lambda \cdot I }{ k \cdot A_c \cdot l^2 } }\) | ||
| Symbol | English | Metric |
| \( K \) = Buckling Coefficient (Fixed-free and Pinned-free) | \(dimensionless\) | \(dimensionless\) |
| \( \lambda \) (Greek symbol lambda) = Material Elastic Modulus | \(lbf \;/\; in^2\) | \(Pa\) |
| \( I \) = Second Moment of Inertia | \(in^4\) | \(mm^4\) |
| \( k \) = Effective Length Factor (which Depends on the End Conditions) | \(in\) | \(mm\) |
| \( A_c \) = Area Cross-section of Material | \(in^2\) | \(mm^2\) |
| \( l \) = Length of the Member | \(in\) | \(mm\) |