The formula is sigma (stress in lb/sq.in) = m ( moment) times c (distance
from centroid) divided by I (area moment of intertia). The moment is 10500
in-lbs. The distance from the centroid is 1 inch and the area moment if
inertia is ) 0.670 in**4. Thus the bending stress at the outer surface of
the mast in the horizontal position (ignoring the weight of the mast and the
shear stress of the antennas) is approximately 15,500 psi. The shear stress
is less than 100 psi so no real need to determine the principal stresses.
Someone else may want to check this since it is a long time since aI did
----- Original Message -----
Sent: Wednesday, May 31, 2006 1:24 PM
Subject: [TowerTalk] Calculating dead weight stress on mast when tower
> To all the antenna & mast engineers out there,
> I have a 55' crankup / tiltover tower that uses a 24' aluminum mast
> 6061-T6511 2" OD .25" wall.
> My question is this: does anyone have a formula for calculating the dead
> weight load on the mast when the tower is horizontal? The mast extends 18'
> above the top of the tower (6' in the tower with two thrust bearings and
> rotor). At 3' above the top of the tower is mounted a HyGain TH7DX (75 lbs
> dead weight, 9.5 square feet wind load). Ten feet above that is a homebrew
> beam for 30, 17 and 12 meters that weighs 50 lbs and has a windload of
> approx 5 square feet. With the tower approaching horizontal, and the
> antennas just off the ground, the mast bends at an angle that really makes
> me think it is about to permanently deform, but so far it hasn't. I want a
> way to figure what margin of safety I have, if any, in lowering the
> antennas to make adjustments/changes. I probably need to change to a
> stiffer mast, but when I started this tower project, I didn't plan on
> adding the top antenna. The mast should be rated at 40,000 psi yield
> strength, but how does that relate to resistance to d
> eformation with a 50 lb load at 13' away from the tower along with a 75 lb
> load (TH7DX) at 3' from the tower?
> I am also concerned about wind loading with the tower vertical and the
> mast's ability to handle that. For the time being, I keep the tower nested
> when I'm not chasing DX, so it isn't exposed to high wind gusts.
> Any and all replies are appreciated. I searched the archives, but didn't
> see anything that fits this situation.
> Thanks & 73,
> Charles, K4ZRJ
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