Column Stiffness and Buckling Lengths

Lateral Stiffness of Columns

Critical Buckling Load

$$P_e=\frac{\pi^2EI}{\ell^2}$$

Effective Buckling Lengths

Idealized Cases of Individual Columns
Non-Sway Sway
Fixed Pinned Pinned Fixed Fixed Free
Fixed Fixed Pinned Fixed Pinned Fixed
$$0.5\ell$$ $$0.7\ell$$ $$\ell$$ $$\ell$$ $$2\ell$$ $$2\ell$$

Effective Buckling Cases for Frames

Idealized Frame Buckling Length Cases
Non-Sway Sway

Beam Influence on Column Effective Buckling Length

$$\frac{EI}{\ell}$$