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How to use the Legrange method to solve optimisation cantilever beam?

  1. Sep 3, 2013 #1
    esign a cantilever beam of minimum weight (volume) consisting of
    three steps that meets condition of strength. Given parameters are: total length of the beam
    L, force F at the end of the beam, and allowable stresses [sigma].

    Parametres to be determined:
    Beam Diameters d1 d2 d3
    Length x1 of the end shoulder
    Coordinate x2 that determines the length of the middle shoulder

    How to solve using Legrange!

    Conditions of strength
    σ A = Ma/Za = (32 x F x L) / (pi x d1 ^3)
    σ B= MB/ZB = (32 x F x L) / (pi x d2 ^3)
    σ C = Mc/Zc = (32 x F x L) / (pi x d3 ^3)

    where za = (pi x d1^3)/32 zB = (pi x d2^3)/32 zC = (pi x d3^3)/32 section modulus

    How would I use the legrange method to derive expressions for d1,d2,d3 and x2 minimum eight (volume) of the beam for the given L,F, σ
  2. jcsd
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