Basic Mechanics of Materials: Computing Stresses in Columns
Knowing how to compute the stress in a column (compression member) is a basic point of knowledge in mechanics of materials. Determine if the column is ‘ short, slender, or intermediate by computing its maximum slenderness ratio (KL/r). For short columns, the stress of a member in compression is the basic axial stress formulation. For intermediate and slender columns, you can use the generalized Euler’s buckling equation. Approximate slenderness ratios for steel columns are shown in parentheses.

Short columns: Slenderness ratio (KL/r < 50).

Slender columns: Slenderness ratio (KL/r ≥200). The calculation for slender columns uses the modulus of elasticity (E).

Intermediate columns: Slenderness ratio (50 ≤ KL/r < 200). The formula for intermediate columns uses the tangential modulus of elasticity (E_{t}).