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Question

A rectangular beam of dimensions b x d is to be cut from a circular log of wood of diameter D for the beam to be strongest in bending, the dimensions will be

A
D2 and D23
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B
D3 and D23
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C
D2 and 2D3
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D
D3 and 2D3
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Solution

The correct option is B D3 and D23

d2=D2sinθ

d=Dsinθ

b2=D2cosθ

b=Dcosθ

Z=bd26=D3cosθsin2θ6

=D36(cosθcos3θ)

For strongest flexural beam,

dzdθ=0

sinθ+3cos2θsinθ=0

sinθ(3cos2θ1)=0

cosθ=13

sinθ=23

b=D3

and d=D23

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