[TowerTalk] Mast Wall Thickness

[Grant Saviers]

I have the same question for a tower in design.  My structural 
engineering skill is dubious, but nothing I've designed and built has 
failed, so caveat emptor!

There are some handy on-line calculators for stress in beams.  One I 
have used is at
http://www.engineersedge.com/beam_calc_menu.shtml
another at http://www.saecanet.com/list_of_beamcalculation.php

I think a mast in a tower can be modeled as a cantilever with an 
intermediate support.  The rotator is a rigid connection and the tower 
exit is a free support and the tower is very rigid vs the mast (i.e. 
moment of inertia of the tower >> mast).  Unfortunately, the particular 
case of such a overhanging cantilever is not among the calculators 
given, but others are useful for hams.

Many wood structures have cantilevered decks, second story overhangs, 
etc and one of the formulas for them seems to apply to the "mast inside 
a tower".  Not a calculator, but the formulas are there at  
http://www.awc.org/pdf/DA6-BeamFormulas.pdf  (figure 20) with pretty 
confusing notation.

I draw a conclusion from noodling this formula - the bending stress on 
the tower is reduced the longer the mast inside the tower (makes sense 
as they share the load) .  What may be more important is the amount of 
load on the tower.  Consider welding the mast to the tower top plate and 
none inside the tower.  This limiting case would impart a very high 
torque load on that top plate, so having a few feet of mast inside makes 
sense.

One needs to know the moment of inertia (and some other numbers) for a 
mast or any other beam to do stress or deflection calculations.  A 
calculator is at
http://civilengineer.webinfolist.com/str/micalc.htm

Using that calculator, you can verify the "bigger diameter is better" 
for a mast, for example
2 x .125 wall; moment = .325 in^4; metal in^2 = 0.73
2 x .25 wall; moment = .537 in^4; metal in^2 = 1.37
2.5 x .125 wall; moment = .660 in^4; metal in^2 = 0.93

so going up a half inch in diameter for the same wall thickness yields a 
doubling of moment for a 27% increase in metal.  Bending stress is 
proportional to 1/moment.  That stress  (from the calculators) needs to 
be below the yield stress of the mast material.

This can't go too far (thinner wall/larger diameter) because other 
failure modes than bending stress will cause a failure of the mast. 
(irrigation pipe with very thin walls and large diameters won't work as 
a mast).

At one QTH I had 17' of 2" x .375" wall 6061 mast outside and 3' inside 
a house braced Rohn 25 tilt over with a TH7DX at the top.  It was a 
pretty flexible mast but all survived 2 hurricanes with 60-80+ mph winds.

May the experts correct me.  Any other useful calculator links would be 
appreciated, especially an inch moment calculator.

Grant KZ1W



On 2/25/2014 6:54 AM, john at kk9a.com wrote:
> Yes a thicker wall will make the mast stronger. Keeping the same wall
> thickness and going to a larger diameter will also make it stronger and
> use less material. I do not see how the amount inside the tower has
> anything to do with mast strength, but it does put less lateral force on
> the rotator and top tower section.
>
> John KK9A
>
>
> To:	towertalk at contesting.com
> Subject:	 [TowerTalk] Mast Wall Thickness
> From:	 Chris Pinholster <k4win at mac.com>
> Date:	 Mon, 24 Feb 2014 12:39:33 -0500
> List-post:	 <towertalk at contesting.com">mailto:towertalk at contesting.com>
> I have been researching tower mast material. Both aluminum and steel.
>
> If aluminum 60601 tubing with 2"OD and .125 wall fails at 35000 ps, what
> happens when you increase wall thickness?
>
> If you increase the thickness of the mast wall, wouldn't that increase make a
> difference in the bend or failure rating?
> The charts at the metal company I visited seemed to indicate that would be
> true. (I was looking at aluminum 2"OD and 1.5"ID)
>
> Also I ran across a chart that showed that using a 14 ft mast, with 4 ft
> inside
> the tower and 10 ft above was stronger than an 11 ft mast with only 1ft
> inside
> the tower and 10 ft above.
>
> Any opinion or science from this learned group?
>
>
>
> CHRIS PINHOLSTER
> k4win at mac.com
>
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