Jim,
Thanks for going through those calcs, it's much appreciated.
Just a couple of questions:
Why did you choose 60% guy anchors instead of the commonly
recommended 80%? I agree though that 60% is probably in that
"sensible" range, but just barely.
I'm not quite sure how you so quickly came up with a number
for base bending moment in the guyed configuration. It seems
unlikely to me that it can be even 1/4 of the unguyed number,
unless the guys were left slack.
But even so, 5700 lbs compression vs. 19,000 compression
is quite an improvement, don't you think?
I do note that you're still worried about increased stress on
on the middle of the tower (column buckling). Are you speaking
of straight downward force collapsing the middle of the tower?
Or a bend, where the downward force helps it along once it gets
started?
Steve K8LX
Jim Lux wrote:
> At 09:16 AM 4/11/2005, Steve Maki wrote:
>
>>Jim Jarvis wrote:
>>
>>
>>>THAT SAID, a few short comments:
>>
>>
>>Since I was the one who led it astray (don't they all go astray?) - my
>>point is that unless I'm mistaken, adding a sensible guy system to a
>>small self support tower will generally increase load capability by a
>>large amount - keeping in mind long boom twisting issues of course.
>>
>>So the oft repeated flat out statements that self supporters are
>>compromised by guys should not be left unchallenged because it's
>>a wrong headed thing to say.
>>
>>You may argue on the insurance and legal issues all you want,
>>I'm only talking about the strength of the tower.
>>
>>Steve K8LX
>
>
>
> OK... some real numbers.. off the Rohn BX data sheets which I found on the
> web. Whether or not this is a tower anyone would actually use, or
> contemplate guying is sort of immaterial. It's representative...
>
> First off.. the limiting load on the actual lattice work sections is
> determined by.... drum roll.... buckling failure of the vertical members
> within the lattice. These are about 12.5" long, and have a radius of
> gyration of 0.505 inches (for the bottom section), for a slenderness ratio
> of 24.8.
>
> The allowable leg load for this tower section (BX-8) is 20,250 pounds. To
> compare to straight compression failure, the cross sectional area is .6043
> square inches, the material is spec'd as 45,000 psi yield cold rolled steel
> for a compressive failure limit of 27,194 pounds. That's almost 50% more
> than the failure load due to buckling.
>
> So, raw compression strength of the steel is NOT the issue here.
>
>
> Now... let's look at some guying strategies...
>
> Free standing, with the nominal 6 square ft antenna and 20psf wind on a
> BX-64..
>
> The total load in the leg is 19,260 pounds (fairly close to the max
> allowable, eh?), of which 19,100 pounds is the wind load and 160 pounds is
> the weight of the structure.
> (37,770 ft pound moment, 1.978 ft moment arm at base).
>
>
> Now, let's add three guys...
> Let's say we use 3/16" EHS as the guy material, and put the guy anchors 60%
> the tower height out. (so the angle between guy and tower is 30
> degrees...). The guys will be about 74 ft long (64/cos(30))
>
> The breaking strength is about 4000 pounds, it weighs 73 pounds/1000 ft.
> Each guy will weigh about 5-6 pounds, so we can probably neglect the guy
> weight. (it's small compared to 19,000 pounds)
>
> Now, it's been oft asserted that the guys should be tensioned to 10% of
> breaking strength. Sure, in this case, where you are using the guys as
> "safety cables" you might tension them less, but let's start there... The
> tension is, therefore, 400 pounds, per cable.
>
> The additional downforce is now 400*3*.866 pounds or about 1040 pounds. In
> the no wind situation, that's no big deal. To the tower, it's just like it
> weighs 1500 pounds instead of 476, and divided over the three legs,
> compared to the leg max allowable of 20,250, it's pretty small.
>
> Now, let's look at putting some wind load on the system. It's a tapered
> tower, and the calculations would be somewhat involved (because it's really
> an elastic system, both the tower and the guys would stretch, etc.)
>
> However, we'll approximate, using Rohn's moment calculation of 37,770 ft
> pounds. At the top of the 64 ft tower, this is about 590 pounds. So,
> assuming the wind comes from the direction of the guy, the guy is going to
> have to resist the 590 pounds.. assuming no deflection (so the angles
> remain the same) requiring a tension of 590/sin(30) = 1180 pounds. That's
> an increased downforce of about 1400 pounds, for a total of 2440
> pounds. Yes, it won't be quite that much, because the downwind guys will
> relax a bit, etc.
>
> -------------------
>
> Some load will still be transmitted as a bending moment to the base,
> loading the downwind leg. Whipping out the handbook (always dangerous, but
> it will give us a rough idea...)
>
> For a uniformly loaded canteliever beam, the maximum moment is at the base,
> and is 1/2 w*l^2 (w is the load per unit length)... conveniently, Rohn has
> calculated this for us, and it's the 37,770 ft lbs.
>
> Now lets assume that it's uniformly loaded, and the base is fixed, but the
> (top free end) is supported by a reaction force (from the guys). The peak
> moment is still at the base, and is 1/8 w*l^2, or one quarter of the
> unsupported case. That's about 9440 ft lbs. Using the same 1.987 ft
> baseline, that's a vertical load (on one leg) at the bottom of the section
> of 4752 lbs. Plus 158 pounds for the weight of the tower, plus about 800
> pounds for the resultant of the guys. We're up to around 5700 lbs.
>
> One would need to go through this for all the sections (because the max
> allowable for the sections varies from 5300 at the top to 20,250 at the
> bottom).
>
> So, if it were a uniform load (which it's not) and if the tower were of
> uniform stiffness (which it is not), it looks superficially safe. At least
> at the rated capacity...
>
>
> Of course, if you're just going to load it with the rated capacity, why
> bother putting guys on it. That tower is only rated with 6 square feet at
> 20 psf (70 mi/hr). If you think that by putting guys on it, you can safely
> handle 10 square feet at 90 mi/hr, you're dreaming... That's 2.5 times the
> wind load at the top... what was before a moment from the antenna of 8000
> ft pounds is now 20,000 ftlb. And, your guys are going to be exerting a
> downforce of about 4500 pounds.
>
> All bets are off for a casual analysis.
>
> -----
>
> All this foregoing analysis makes the fatal assumption that the structure
> is a rigid body (which is what all those guy and tower compression
> calculations assume), but it is NOT. It will flex.. Different parts are
> going to bend differently, and the stresses will divide in a way not
> intended by the mfr. If you look at the chart of expected loads vs the
> strength, there's not a huge margin anywhere in the system (it's a well
> balanced design from that standpoint.) The allowable loads at the splices
> neatly match the allowable loads on the vertical members at that
> joint. The load on the leg is typically about 90-95% of the allowable
> load on the leg.
>
> This isn't some sort of design where you're working at 20-30% of the
> ultimate capacity. Even with a simple rigid body analysis, you're pretty
> close to the edge. I haven't even looked at the loads on the diagonal
> braces (those look like they are loaded about about 30% of allowable), or
> the effect of torsion (clearly this is important, given the big warning
> about avoiding antennas with large twisting moments at the top of the sheet).
>
> Torsion raises the specter of eccentric loads on the vertical
> legs. Eccentric loads on columns dramatically reduce the maximum allowable
> load. The existing design assumes that the legs are loaded symmetrically
> and axially... Let this be a warning to those who would hang something off
> a leg (or bend the rolled profile or drill holes )that violates that
> assumption... there's not a lot of design margin.
>
> I suspect that if you start digging into the analysis, and actually looking
> at the distribution of loads as it flexes and is restrained by the guys,
> you'll find a serious column buckling problem in the middle.
>
>
>
>
> ----
>
> This analysis is truly a back of the envelope calculation... anyone is
> welcome to refine it, correct it, or provide counter examples...
>
>
> Jim, W6RMK
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> _______________________________________________
>
> See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless
> Weather Stations", and lot's more. Call Toll Free, 1-800-333-9041 with any
> questions and ask for Sherman, W2FLA.
>
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_______________________________________________
See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless Weather
Stations", and lot's more. Call Toll Free, 1-800-333-9041 with any questions
and ask for Sherman, W2FLA.
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