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(adsbygoogle = window.adsbygoogle || []).push({});

σmax = M(d/2)/((1/12)bd^{3})

σmax = 6M/(b*d2)

and d^{2}+ b^{2}= D^{2}

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??

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# Beams and bending

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