WPS 234 Buckling of columns

Buckling pressure

P = π²EI / (KL)²

P is in newtons

Crushing pressure

• σ = π²E / (KL/r)², where r is radius of gyration

• r = sqrt(I / A), where I is minimum area moment of inertia & A is cross-sectional area

Euler formula proof (buckling)

Connection types (K)

• 2 pins: K = 1

• Pin & fixed: K = 0.7

• Fixed ends: K = 0.5

• Fixed & free: K = 2

Combating buckling

Increase height to increase buckling capacity.

Buckling formula limitations

• Buckling formula only valid if column doesn’t get crushed first.

• Slenderness ratio (KL/r) has to be above certian value, where r is radius of gyration & KL is effective length of column. Increase in KL/r means increase in length of column, meaning higher tendency to buckle and not crush.

• Practical limit of slenderness ratio of wood is 52.

Column buckling & design

• Critical load independent of bending strength – only MOE involved.

• Columns designed so that I_y nearly equals I_z to prevent buckling.

• Load carrying ability increase with increase in I (material away from centroidal axis).