Column Buckling Stress

Column buckling stress, abbreviated as \(\tau\) (Greek symbol tau), is the allowable buckling stress of a column.  It describes the stress at which a slender structural element, such as a column or beam, becomes unstable and fails due to lateral (buckling) deformation rather than direct compression.  When a compressive load is applied to a slender column, it tends to buckle or deflect laterally rather than uniformly compressing. This lateral deflection can lead to the failure of the column if it exceeds a certain critical value.  The column buckling stress is the maximum stress that the column can withstand before buckling occurs.

It's important to note that this formula provides an idealized theoretical prediction of column buckling behavior.  Real world columns may have additional factors to consider, such as imperfections in the column, material nonlinearity, and geometric irregularities, which can affect the actual buckling behavior.  Engineers use safety factors and more complex analysis methods to account for these practical considerations when designing columns and other structural elements to ensure they are safe and stable under expected loads.

 

Column Buckling Stress formula
\( \sigma \;=\; \pi^2 \; E \;/\; \left( l \;/\; r \right)^2  \)     (Column Buckling Stress) \( E \;=\; \sigma \; ( l \;/\; r ) ^2  \;/\; \pi^2   \) \( l \;=\; r \; \sqrt{ \sigma \;/\; \pi^2 \; E } \) \( r \;=\; l \;/\;  \sqrt{ \pi^2 \; E \;/\; \sigma  }  \)
Symbol	English	Metric
\( \sigma \) (Greek symbol sigma) = critical buckling of allowable stress of a column	\(lbf\;/\;in^2\)	\( Pa \)
\( \pi \) = Pi	\(3.141 592 653 ...\)
\( E \) = Young's modulus	\(lbf\;/\;in^2\)	\( Pa \)
\( l \) = unsupported length of column	\( in \)	\( in \)
\( r \) = least radius of column	\( in \)	\( mm\)