Derivation of the Euler-Bernoulli Beam Equation EI·y″ = M(x)
From plane sections to the moment–curvature relation EI·y″ = M(x), step by step.
Euler-Bernoulli
Derivation of the Curvature Formula κ = y″/(1+y′²)^(3/2)
From the geometric definition of curvature to κ = y″/(1+y′²)^(3/2), and when it reduces to y″.