The 'tangent modulus theory' for inelastic (non-Euler) column buckling uses:
Choose the correct answer
Linear elastic Euler formula directly
Tangent modulus Et at the current stress level replaces E in Euler formula — accounts for inelastic buckling
Shear modulus G only
Reduced modulus = zero beyond yield
Correct Answer
B. Tangent modulus Et at the current stress level replaces E in Euler formula — accounts for inelastic buckling
Why is this the answer?
Tangent modulus theory (Engesser/Shanley): when column stress exceeds proportional limit, modulus reduces from E to Et (tangent modulus = slope of stress-strain curve at that stress). Critical load: Pcr = π²EtI/(KL)². Since Et < E: inelastic Pcr < Euler Pcr. Real behaviour: between tangent modulus (lower bound) and double modulus (upper bound). AISC/IS 800 column curves account for inelastic buckling empirically.
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