Buckling Coefficient

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 Fixed-Fixed (both ends are fixed) Pinned-Pinned (both ends are hinged or pinned)
\( K \;=\;  \sqrt{ \dfrac{ \lambda \cdot I }{ k \cdot A_c \cdot l^2 }   }  \)
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 formula Fixed-Free (one end is fixed, and the other end is free) Pinned-Free (one end is pinned, and the other end is free)
\( K \;=\; \sqrt{  \dfrac{ 2 \cdot \lambda \cdot I }{ k \cdot A_c \cdot l^2 }  }\)
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	\(in\)	\(mm\)