The bottom line is that INNER Sleeving reduces the strength of
the mast by a LOT, assuming the same yield strength material
for the sleeve as the outer mast.
The maximum allowable bending moment for a circular tube
includes the factor (D^4 - d^4) where D is the outside diameter,
d is the inside diameter, and ^4 means raised to the 4th power.
Consider a 2 inch solid OD mast. D^4 = 16
Then a 1.5 inch solid tube D^4 = 5.0625
And a 1.0 inch solid tube D^4 = 1.0
>From this we see that a 2 inch solid tube is 16 times stronger
than a 1 inch solid tube in terms of bending moment.
A 1.5 inch solid tube is 5.0625 times as strong as a 1 inch solid tube.
A 2.0 inch solid tube is 3.16 times as strong as a 1.5 inch solid tube.
A 2 inch OD mast with 1/4 inch wall thickness can be thought
of as a 2 inch solid tube with a 1.5 inch solid tube removed.
D^4-d^4 = 10.9375
A 1.5 inch OD mast with 1/4 inch wall thickness can be thought
of as a 1.5 inch solid tube with a 1.0 inch solid tube removed.
D^4 - d^4 = 4.0625
>From this we see that a 2 inch OD, 1/4 inch wall tube is
10.9375 / 4.0625 = 2.6923 stronger than a 1.5 inch OD, 1/4 inch wall
in terms of bending moment. Going to a SOLID 1.5 inch inner
sleeve still results in 10.9375 / 5.0625 = 2.16. Not much benefit
for a whole lot more weight!
There is one factor in your favor if you *still* want to use an
inner sleeve and that is that the bending moment for the smaller
tube only acts over the length from the junction to the load, NOT
the full length of the mast above the tower. You will still need to
address how to hold the inner sleeve in position across the junction,
unless you intend to add an inner sleeve that runs all the way down
to the rotor.
de Tom N4KG
On Fri, 13 Jul 2001 14:29:33 -0400 "Bob Thacker" <firstname.lastname@example.org> writes:
> Hello all,
> Next project is to increase the antenna spacing on the crank up
> mast. Currently a TH11 is 6" above the tower top and a 402BA old
> HyGain 40
> meter monobander is about 10' above it. Currently, there is some
> degradation on the TH11's 15 and 17 meter bands resulting in a
> slightly high
> (3.0 on 17 and 2.2 on 15...not too bad) VSWR.
> The new antenna project calls for a Force 12 EF-30/40 to replace the
> 402BA. However, after discussions with Force 12 and this reflector,
> think that 12' spacing would lessen interaction between the
> antennas. So the
> question is, without purchasing a new mast, how does one elongate
> current one? I have considered both internal and external sleeving
> measuring about 3' for an 18" overlap. To accomplish the extra 2 to
> 3' in
> mast length, the extension would be the same size as the current
> one. The
> internal sleeving method appeals most since the antenna can be
> placed on the
> mast at a lower level then slid up the mast into the 12' position.
> current mast is 2" OD and .250" wall thickness. Any one tried this
> Bob, K3GT
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