Just took a few minutes to look through their web page. Very cool program; very, very cool.
The number of design factors it allows you input/deal with is very impressive; for all practical purposes, with a couple limitations I’ll highlight in a minute, seems to cover all the variables that matter.
In terms of it’s…..utility for boomilevers-
We have both tension in the tension member(s), and compression in the compression member(s).
Tension is much more straight-forward to deal with, so considering compression only. To keep things simple, assuming a single compression member.
Two major/basic approaches to this member – a) a truss- like a tower on it’s side, or a bridge loaded from the ends, or b) a constructed beam/column- like a box beam
The program is clearly well set up to deal with a), a truss/structure built with sticks/pieces of varying size and density. I can’t tell if it accommodates a constructed beam; but from what I could see, it looks like it may not. In that a constructed beam is a very viable approach to the compression member of a boom, if it can’t accommodate that, that’s a big hole….. An example I’m talking about would be a box beam- 4 “corner stringers”- for discussion purposes, let’s say a ½ inch apart, joined by “wall sheet”- so in cross section, ½ inch square- say 1/16th sq stringers, 1/64th thick x ½” wide wall sheets. Can such a construction be put into the program?
While there are other potential failure modes, the primary one for the compression member is column buckling failure- compression load along the long axis (axial loading)- in the case of a C-boom, around 40kg. When you axially load a thin column, at some load, it starts to bow out in the middle; with a tiny bit more load, it buckles/fails. Euler’s Buckling Equation describes this behavior, and with certain information allows you to calculate the buckling load a column will carry. For anyone interested, quite a bit of discussion on this in last year’s tower discussions (and Wikipedia provides a good presentation and discussion. The equation is:
FE = pi^2 x E x I / L^2
Where FE is the critical buckling load, L is the effective length (of the column), E is the (longitudinal) modulus of elasticity (also referred to as Young’s modulus), and I is the cross-sectional moment of inertia.
E is an inherent physical property of the wood, essentially how stiff, how resistant to bending under an axial load.
“I” (which you’ll see referred to in various discussions/sources as the moment of inertia, the cross-sectional moment of inertia, and the second moment of area) is, to state simply, a measure of the cross-sectional shape- how far material is from the axis of a column; how it is distributed around that axis. For two pieces of material/wood that are ‘the same’ (density/strength/stiffness), the one with the bigger cross section will be stiffer- have a higher I, and hence will have a higher FE; be a stronger column
As discussed at length over the years, E depends on and is…..some function of, density; the heavier/higher the density, the higher E is. What has not popped up in discussions on this board is a good data set for E; specifically E vs density, over the range of densities balsa comes in. Because wood is anisotropic- it’s grown, not manufactured – there is some level of variability between pieces, even if they are at the same density- so, in reality, for any density, there is a range of Es.
Resistance to bending, can be described in terms of something called "flexural stiffness. The variable turns out to be – as seen in Euler’s equation, the simple product of two factors, one reflecting the material present and the other its arrangement. The first is E. The second is I. So flexural stiffness (a.k.a. "bending modulus" or "flexural rigidity") is just E x I;
Looking at the “Success with ModelSmart3D” slide show series- #3, I see- as one would expect, the ability to plug in values for E and I.
Here’s where things begin to get interesting, and questions on the utility of this tool (beyond the apparent inability to handle/use/calculate E x I for a constructed beam) begin to emerge.
There’s a table (at slide 22) showing the program’s density range for balsa- from 12 to 24 lbs/cubic foot.
However, looking at the density range Specialized Balsa sells balsa over, we see a much larger range; for example, for 1/8 sq sticks, at 36” length, they’ll sell you sticks from 0.7 to 4.7grams. Converted to lb/cf, that’s 4.74 to 31.83 lb/cf…… I don’t know whether the program will accept densities outside the 12-24 range; if not, you can’t look at really light, or really strong wood options
Then, on the next slide (#23), we see a data entry box showing values for various physical properties, with a density entry of 17.2 lb/cf. The value for “E” (Young’s Modulus-the modulus of elasticity)- is shown as 676,000 psi (lb/ sq in).
Here’s where things get really interesting, and suggest fundamental ramifications beyond use of this program for booms. Being able to see only one value for E, I don’t know, and can only guess at the source for the data. It is suspiciously close to what is reflected in a data set that pops up early in a Google search. I don’t know the original source; it’s found on a number of web pages now. I’ve added conversion of densities to lbs/sf, Converting E from MPas (mega Pascals) to psi, we get 389 MPa = 56,420psi 460 MPa = 66,717psi 531 MPa =:77,015psi. Looks suspiciously like a one order of magnitude (decimal off one place) error, compared to the value in the program.
fm Balsa Wood Properties Guide
Lb/sf E (MPa) D-kg/m3
4.67 Lo 389 75
9.33 Med 460 150
14 Hi 531 225
There are also a lot of individual values for E to be found, and generally, the associated density is…..less than clear. They range from values consistent with the Balsa Properties Guide table to #s approaching twice the value the program’s showing.
Also, over the years, we have done some column testing – axially loading pieces of sticks, and measuring FE, which with weight (density) allows back calculation of E. Findings have been in the range of 10x the values seen in the BWPG table… hmmm….
And then this year, came across a very interesting research paper from 1956- work done by the U.S Forest Service. Ah, the wonders of the web!
http://scholarsarchive.library.oregonst ... sequence=1
See Table 1 and
most importantly, Fig 7.
Data from 27 samples/tests. E vs density plotted.
The density data in this report is expressed in specific gravity (SG). Water has a specific gravity of 1; it weighs 62.428 lbs/cu ft, so to convert SG to Lbs/cu ft, multiply SG x 62.428; e.g., an SG of 0.14 is 8.74 lbs/cu ft.
So the data range is from an SG of 0.08 to almost 0.185- ~5 to 11.5 lb/cu ft. To come up with Es for densities > 11.5 lbs/cf, you have to extrapolate into unmeasured territory, so certainty falls off…..at least a bit. Enough data points with a range of measured Es at/near a given density to see and understand the degree of variability in d vs E. Really cool.
There are a lot of reasons to think this data is good- accurate. If so, the value in the screen shot in the program is…..significantly off. Pulled from Fig 7, I see a range of E, at a density of 17.2 lb/sf between 1,102,000 and 1,448,000 psi. If that’s true, that would suggest the model at mid-5 grams – with corrected Es would be….lighter. In that mid 5gr range is at the “can win nationals” level, hard to believe a weight materially lighter. Interesting thoughts to ponder, huh?
