The bending stress on an antenna mast
is dependant on the following
items:
- The wind load area of the antennas mounted on the mast;
- The position of the antennas mounted on the mast;
- The cross sectional area of the mast;
- The velocity of the wind.
The strength of the mast is determined by the following mast properties:
- The yield strength of the mast material;
- The wind force on the mast which is determined by the
cross-sectional dimensions of the mast.
Common antenna tower and mast configurations consist of a round
tubular mast protruding from the top section of a fixed tower.
This analysis deals with the portion of the mast that protrudes above
the top of the tower.
The analysis is done in an
Excel spreadsheet that can be downloaded
here.
The spreadsheet also can be opened by Open Office which can be
downloaded
free. The calculations are based on equations stated
in the 2004 ARRL Antenna Book, Chapter 22 as follows.
The basic formula for wind pressure is:
P = .00256 V^{2}
where
P = the wind pressure (pounds per square foot)
V = wind speed (miles per hour)
The force (in pounds) created by the wind on a structure is:
F = P × A × Cd
where
P = the wind pressure
A = the flat projected area of the structure (square feet)
Cd = drag coefficient for the shape of the structure’s members.
The commonly accepted drag coefficient for long cylindrical members
like the tubing used for the mast and antenna is 1.20. The coefficient
for a flat plate is 2.0.
The bending stress in a simple beam like a mast is:
σ = (M x C) / I
where
σ = the stress in pounds per square inch (psi)
M = bending moment at the base of the mast (inch-pounds)
C = ½ of the mast outside diameter (inches)
I = moment of inertia of the mast section (inches^{4})
The moment of inertia for the round tubing mast section is:
I = (π/4) x (R^{4}- r^{4})
where
I = Moment of Inertia of the section (inches^{4}.)
R = Radius of tube outside diameter (inches.)
r = Radius of tube inside diameter (inches.) Zero for solid round
bar.
The equation used to compute the bending moment at the base of the mast
(where it is supported by the tower) is:
M = (F_{M} × L_{M}) + (F_{A}
× L_{A})
where
F_{M} = wind force on the mast (pounds.)
F_{M} = (Mast OD in feet) × (Length
of mast above the tower in feet) × P × Cd
L_{M} = Half of the length of the mast extending out the top of
the tower (inches.)
F_{A} = Wind force from the antenna (pounds.)
F_{A} = (Surface area of antenna in feet^{2})
× P × Cd
L_{A} = Distance from tower top to antenna attachment (inches.)
More antennas can be added to this formula by
adding their F × L terms.
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