esign a cantilever beam of minimum weight (volume) consisting of(adsbygoogle = window.adsbygoogle || []).push({});

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

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

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