K7LXC@aol.com wrote:
>
> In a message dated 7/17/2010 7:47:04 P.M. Pacific Daylight Time,
> towertalk-request@contesting.com writes:
>
>> I doubt solid legs would change the load rating much, but they would be
> very nice for towers installed in corrosive locations.
>
> Umm, actually it would change the load rating significantly. Especially
> since tower capacity is a direct function of leg strength.
>
I'm not so sure about that. Most towers are limited by the buckling load
on the various short segments of tubing which are quite slender (that
is, you consider it a slender column from one joint where the diagonal
or horizontal brace attaches to to the next. The buckling load is
proportional to the Young's modulus (stiffness of the materials, the
radius to the 4th(!) power, and inversely proportional to the length
squared.
A tube and a solid bar don't have much difference here.. (that is, the
term on top is Router^4-Rinner^4... going from a medium thickness wall
to a solid doesn't change it a whole lot.
Here's an example, giving relative strength compared to a solid rod
Router Rinner Buckling
1 0 1
1 0.1 1.00
1 0.2 1.00
1 0.3 0.99
1 0.4 0.97
1 0.5 0.94
1 0.6 0.87
1 0.7 0.76
1 0.8 0.59
1 0.9 0.34
You can see that with a 0.2" wall on a 2" tube, you've got about 60% of
the strength for less than 40% of the material.
The amount of material (cost) for thin wall tubes goes roughly as a
function of the diameter, while the buckling load goes as the fourth
power. It's usually better to go to a larger diameter tube to get more
strength, unless there's some constraint on tube size.
here's a chart comparing buckling strength for constant wall thickness,
and assuming cost is proportional to cross sectional area.
Router Rinner Buckle Area strength/$
1 0.9 0.3439 0.19 1.81
1.1 1 0.46 0.21 2.21
1.2 1.1 0.61 0.23 2.65
1.3 1.2 0.78 0.25 3.13
1.4 1.3 0.99 0.27 3.65
1.5 1.4 1.22 0.29 4.21
1.6 1.5 1.49 0.31 4.81
1.7 1.6 1.80 0.33 5.45
1.8 1.7 2.15 0.35 6.13
1.9 1.8 2.53 0.37 6.85
Or here, where I held the cross sectional area constant
Router Rinner Wall Buckle Area strength/$
1 0.81 0.19 0.5775 0.35 1.65
1.1 0.93 0.17 0.72 0.35 2.07
1.2 1.04 0.16 0.89 0.35 2.53
1.3 1.16 0.14 1.06 0.35 3.03
1.4 1.27 0.13 1.25 0.35 3.57
1.5 1.38 0.12 1.45 0.35 4.15
1.6 1.49 0.11 1.67 0.35 4.77
1.7 1.59 0.11 1.90 0.35 5.43
1.8 1.70 0.10 2.15 0.35 6.13
1.9 1.81 0.09 2.40 0.35 6.87
One can take this to an extreme: aluminum beverage cans have walls that
are about 0.0005" thick (thinner than household aluminum foil), or
actually thinner at the top and thicker at the bottom. But as anyone
who has demonstrated column buckling by standing on a can can tell you,
you get real subject to small imperfections..
If you make a solid bar, it weighs more, which increases the load on the
bottom just from the tower weight, too.
_______________________________________________
_______________________________________________
TowerTalk mailing list
TowerTalk@contesting.com
http://lists.contesting.com/mailman/listinfo/towertalk
|