Learning topic
Column Buckling Modes
First and higher Euler modes, flexural buckling, torsional buckling and flexural-torsional buckling of compression members.
A buckling mode describes the deformation pattern that becomes possible at a critical load. Several mathematical modes may exist, but the mode associated with the lowest critical load normally governs.
First Euler mode
For a pinned-pinned column, the first mode contains one half-wave:
\[y_1(x)=C\sin\frac{\pi x}{L}.\]
It has no intermediate nodes and corresponds to \(P_{cr,1}=\pi^2EI/L^2\).
Higher modes
The higher ideal modes are
\[y_n(x)=C\sin\frac{n\pi x}{L},\qquad P_{cr,n}=n^2P_{cr,1}.\]
They contain two or more half-waves and require higher loads. They are important in eigenvalue analysis even though they usually do not govern a simple uniform column.
Flexural buckling
The member axis bends in a principal plane. With identical end conditions in both planes, buckling about the axis with the smaller flexural rigidity \(EI\) is critical.
Torsional and flexural-torsional buckling
Thin-walled open sections may buckle by twisting about the longitudinal axis. When twisting is coupled with lateral bending, the mode is called flexural-torsional buckling. It cannot be assessed by the elementary Euler formula using only one second moment of area.
About this topic
Buckling modes describe the deformation pattern of a compression member. The governing mode is the one with the lowest critical load.