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[TowerTalk] Multiple-layer stress modulus???

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Subject: [TowerTalk] Multiple-layer stress modulus???
From: (Mike Valentine - W8MM)
Date: Wed, 07 May 1997 14:40:24 -0400
Hello all!

In a effort to reduce the weight of a mast for my antenna project,
it would be desirable to use a light-weight mast that is reinforced
with an interior cylinder or rod in the lower portion where the moment
is greater.  A constant outside diameter makes boom-to-mast clamps
easier and provides a bigger "grip diameter" for the top-most antenna,
although the mast self-load from wind pressure is a tad higher compared
to a conventionally tapered mast.

My question:  Does one merely add the section modulii for the mast and
the reinforcer to get the composite stress result???

I did some preliminary calculations for a 2"O.D./1.75"I.D. mast with the
addition of a 1.75"O.D./1.5"I.D. reinforcer that actually looked
stronger by a small amount than a continuous section of 2"O.D./1.5"I.D..

That got me thinking that my assumtions might be out in left field.

For 2"O.D./1.5"I.D. -> pi((2*4)-(1.5*4))/32(2) = 0.537 in*3

For 2"O.D./1.75"I.D. -> pi((2*4)-(1.75*4))/32(2) = 0.325 in*3
    1.75"O.D./1.5"I.D. -> pi((1.75*4)-(1.5*4))/32(1.75) = 0.242 in*3

    Sum of modulii = 0.325 + 0.242 = 0.567 

0.567/0.537 -> 5.6% improvement from taking it in two layers???

Weird, eh?  What am I doing wrong here??

Mike - W8MM - EM79sd

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