Columns — Worked Examples

A solid rectangular column section is $100\text{ mm}\times200\text{ mm}$. Determine the radius of gyration about its weak centroidal axis.

The section from Example 1 is used in a $3.00\text{ m}$ pin-ended column. Determine weak-axis slenderness.

For the column in Examples 1–2, take $E=200\text{ GPa}$. Determine the weak-axis Euler critical load.

Use the same section, material, and physical length as Example 3, but make the column fixed at one end and free at the other. Compare its ideal Euler load with the pin-ended case.

Use the same column section and physical length but assume ideal fixed-fixed ends with $K=0.5$. Euler theory would predict four times the pin-ended load. If the material yield stress is $250\text{ MPa}$, compare the corresponding squash load with the Euler prediction.

A hollow square tube has outer dimension $100\text{ mm}$, wall thickness $5\text{ mm}$, $L=4.0\text{ m}$, $E=200\text{ GPa}$, and ideal fixed-pinned ends with $K=0.7$. Determine the Euler load.

A solid circular steel column has $d=50\text{ mm}$, $L=3.0\text{ m}$, $E=200\text{ GPa}$, and ideal fixed-free ends. Determine its Euler critical load.

For a $100\text{ mm}\times200\text{ mm}$ rectangle, compare the two centroidal second moments of area and identify the governing ideal Euler axis.

An ideal pin-ended slender column has Euler load $P_{cr}$. If its physical length doubles while $E$, $I$, and $K$ remain unchanged, determine the new critical load.

An ideal elastic column has $E=200\text{ GPa}$ and slenderness $KL/r=100$. Compute Euler critical stress.

A thin-walled box column develops a localized wrinkle in one wall while the member centerline remains nearly straight. Is the observed mode global Euler buckling?