This lesson covers the concept of buckling of columns, focusing on the difference between slender and short columns. It explains how the stress in a slender column remains below the proportional limit, making linear elastic analysis valid. However, for short columns, the axial stress exceeds the proportional limit, necessitating inelastic buckling analysis. The lesson also introduces the double modulus theory, which considers both the tangent modulus and elastic modulus. It further explains the tangent modulus theory, which leads to a lower buckling load than the double modulus theory. The lesson concludes with a detailed explanation of the double modulus theory and how to find the effective modulus.

- Slender columns can be analyzed using linear elastic analysis, while short columns require inelastic buckling analysis.
- The double modulus theory considers both the tangent modulus and elastic modulus.
- The tangent modulus theory results in a lower buckling load than the double modulus theory.
- The double modulus theory assumes that the axial load remains constant as the column moves from a straight to a deformed position.
- The effective modulus in the double modulus theory can be calculated using specific mathematical expressions.

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