Beams and bending

  1. A couple M will be applied to a beam of rectangular cross section from a log of circular cross section. determine the ratio d/b so that maximum stress will be minimum

    σmax = M(d/2)/((1/12)bd3)
    σmax = 6M/(b*d2)

    and d2 + b2 = D2
    D =diameter of the circle

    but i can't find the ratio..
    i know the answer of d/b is sqrt 2
    how can i get the answer?
    do i need differentiate?
    if yes how should i do the differentiation??
  2. jcsd
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