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. The formula for the buckling coefficient depends on the type of end support conditions and the geometry of the column.
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.
Buckling coefficient formulaFixed-Fixed (both ends are fixed) Pinned-Pinned (both ends are hinged or pinned) |
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\( K \;=\; \sqrt{ \lambda \; I \;/\; k \; A_c \; l^2 } \) (Buckling Coefficient) \( \lambda \;=\; K^2 \; k \; A_c \; l^2 \;/\; I \) \( I \;=\; K^2 \; k \; A_c \; l^2 \;/\; \lambda \) \( k \;=\; \lambda \; I \;/\; K^2 \; A_c \; l^2 \) \( A_c \;=\; \lambda \; I \; k \;/\; K^2 \; l^2 \) \( l \;=\; \sqrt{ \lambda \; I \;/\; k \; A_c \; K^2 } \) |
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| 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 formulaFixed-Free (one end is fixed, and the other end is free) Pinned-Free (one end is pinned, and the other end is free) |
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\( K \;=\; \sqrt{ 2 \; \lambda \; I \;/\; k \; A_c \; l^2 } \) (Buckling Coefficient) \( \lambda \;=\; K^2 \; k \; A_c \; l^2 \;/\; 2 \; I \) \( I \;=\; K^2 \; k \; A_c \; l^2 \;/\; 2 \; \lambda \) \( k \;=\; K^2 \;/\; 2 \; \lambda \; A_c \; l^2 \) \( A_c \;=\; K^2 \; k \; l^2 \;/\; 2 \; \lambda \; I \) \( l \;=\; \sqrt { k \; A_c \;/\; 2 \; \lambda \; I \; K^2 } \) |
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| 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 | \(in\) | \(mm\) |
Tags: Coefficient Strain and Stress Structural Steel Structural