Buckling Coefficient

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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.  The formula for the buckling coefficient depends on the type of end support conditions and the geometry of the column.

Buckling coefficient Index

 

Buckling coefficient formula

Fixed-Fixed (both ends are fixed)

Pinned-Pinned (both ends are hinged or pinned)

\( K =  \sqrt{ \lambda \; I \;/\; k \; A_c \; l^2 }  \)

\( \lambda =  K^2 \; k \; A_c \; l^2 \;/\; I  \)

\( I =  K^2 \; k \; A_c \; l^2 \;/\; \lambda \)

\( k =  \lambda \; I \;/\; K^2 \; A_c \; l^2 \)

\( A_c =  \lambda \; I \; k \;/\; K^2 \; l^2 \)

\( l =  \sqrt{ \lambda \; I  \;/\;  k \; A_c \; K^2 }  \)

Symbol English Metric
\( K \) = buckling coefficient (fixed-fixed and pinned-pinned) \(dimensionless\)
\( \lambda \)  (Greek symbol lambda) = elastic modulus of material \(lbf \;/\; in^2\) \(Pa\)
\( I \) = 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 \(in\) \(mm\)

 

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)

\( K =  \sqrt{ 2 \; \lambda \; I \;/\; k \; A_c \; l^2 }  \)

\( \lambda =  K^2 \; k \; A_c \; l^2 \;/\; 2 \; I \)

\( I = K^2 \; k \; A_c \; l^2 \;/\; 2 \; \lambda \)

\( k =  K^2 \;/\; 2 \; \lambda \; A_c \; l^2 \)

\( A_c =  K^2 \; k \; l^2 \;/\; 2 \; \lambda \; I \)

\( l =  \sqrt { k \; A_c \;/\; 2 \; \lambda \; I \; K^2 }  \)

Symbol English Metric
\( K \) = buckling coefficient (fixed-free and pinned-free) \(dimensionless\)
\( \lambda \)  (Greek symbol lambda) = elastic modulus of material \(lbf \;/\; in^2\) \(Pa\)
\( I \) = 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 \(in\) \(mm\)

 

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Tags: Coefficient Strain and Stress Structural Steel Structural