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Beams and bending

by chihin098
Tags: beams, bending
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Nov26-12, 07:49 AM
P: 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??
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