Entering the Euler Domain In Column Design (Part 3) , we established the "Decision Rule." If your actual Slenderness Ratio (KL/r) is greater than the Column Constant (C c ), your column is classified as Long . For these slender members, failure occurs via Elastic Instability . We calculate the Critical Load (P cr ) using the famous formula derived by Swiss mathematician Leonhard Euler in the 18th century. Search for Mechanical Engineering Handbooks The Euler Formula The critical buckling load is defined as: We can also express this in terms of the Moment of Inertia (I) by substituting r 2 = I/A: Engineering Insight: Stiffness vs. Strength Look closely at the variables in the formula above. The buckling load depends on: Length (L) : Longer columns buckle easier. Cross-section (I or A) : Thicker columns resist buckling. Material Stiffness (E) : The Modulus of Elasticity. Notice what...
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