Designs

[coolio12]

What are some good methods on how to curve balsa wood?
i tried placing them in water and then curving, but the wood turned out to be very brittle and not very efficient...

[SLM]

Sorry, but I’m still not following your conclusion...

In your initial comment, I understood you to be saying that because the repaired and reinforced leg is so much stiffer, it carries significantly, or at least measurably, more than 3.75kg – yes? I’m not saying it won’t, but on the other hand, I don’t understand at this point why it would.

...-strength- under engineered, not over engineered. ...

This approach will, I believe, get you a lot closer to “optimum”, and get you there a lot quicker and more easily, than guessing/shooting in the dark, and building and breaking a whole lot of towers.

I am going to attempt to address the points I raised in two postings. First point: why and when change in member stiffness causes change in member forces.

Consider the simple tower shown below where A is the cross-sectional area of the vertical, and horizontal, members. Each diagonal member has a cross-sectional area of A/4.

Note the member forces in the tower. Each vertical member carries 88% of P and each diagonal member carries 15% of P where P is the magnitude of the two applied forces. Now, let’s stiffen the diagonal members by increasing their cross-sectional area from A/4 to A/2 and see what happens to the member forces.

Now, the vertical members carry 78% of P while the diagonal members carry 26% of P. One more time, let’s increase the stiffness of the diagonal members by increasing their cross-sectional area to A.

The share of P carried by the vertical members reduces to 65% while for the diagonal members it increases to 42%. The example illustrates the fact that a change in member stiffness could change the load distribution pattern in the structure.

Now let’s look at a counter example. The following tower is similar to the above tower, except for the missing diagonal member.

Here, however, the force pattern in the members does not change no matter how much you change the stiffness of any of the members. The vertical members carry 100% of P and the other members carry 0% of P. Why is that?

The reason is that the first tower has redundant members whereas the second tower does not. In structural engineering terminology, the first tower is considered statically indeterminate whereas the second tower is statically determinate. In a statically indeterminate structure, due to the presence of redundant members, the load at a joint is distributed among the members connected to the joint based on their relative stiffness. The stiffer the member the more % of the load it tends to carry. On the other hand, in a statically determinate structure the load can be distributed among the members in only one way, regardless of the relative stiffness of the members.

[SLM]

Sorry, but I’m still not following your conclusion...

...-strength- under engineered, not over engineered. ...

This approach will, I believe, get you a lot closer to “optimum”, and get you there a lot quicker and more easily, than guessing/shooting in the dark, and building and breaking a whole lot of towers.

The example used by Balsa Man implicitly assumes the tower is statically determinate. This indeed could be the case. But, my guess is that many towers end up being statically indeterminate because of diagonal bracings connecting the top of each leg to the base of an adjacent leg, or other similar configurations. So I am going to use a simple statically indeterminate structure to show why an increase in the stiffness of a few members could result in an over-designed tower. Consider the following structure.


In this example let’s assume each diagonal members has a cross-sectional area of A, and each of the other members has a cross-sectional area of 4A. To simplify the problem further, let’s take P = 100 N and A = 10 square mm. That is, each diagonal member has a cross-sectional area of 10 sq. mm and each of the other members has an area of 40 sq. mm. The analysis of the structure gives the following member forces.


Each diagonal member carries a compressive force of 17 N, each vertical member carries a compressive force of 85 N and the horizontal member carries a tensile force of 7 N.

Therefore,
axial compressive stress in each vertical member = Force/Area = 85/40 = 2.125 N/mm^2
axial compressive stress in each diagonal member = Force/Area = 17/10 = 1.7 N/mm^2

We need one more assumption. Let’s assume that balsa wood has a compressive strength of 2 N/mm^2. That is, when force/area in any compression member made of balsa exceeds 2 N/mm^2 the member fails. I am just making this number up to illustrate the point, the actual compressive strength of balsa is not 2 N/mm^2. So, using this assumed value, I can state that an optimally designed structure is one such that axial stress in every compression member reaches 2 N/mm^2 at the same time, that is, all the compression members fail simultaneously. Here is a simple diagram illustrating this point.



If a compression member is subjected to a stress higher than 2, then the member is over-stressed (or under-designed). If the stress in the member is less than 2, then the member is under-stressed (or over designed).

In the above example, the vertical members are over-stressed and the diagonal members are under-stressed. Let’s show this on the diagram.



The diagram indicates that while the diagonal members are over-designed by about 19%, the vertical ones are under-designed and would fail under the applied load. Say one or both of the vertical members fail and we decided to increase their cross-sectional area (stiffness) to 50 mm^2 to strengthen the members and to prevent their premature failure. As a result, the share of axial force in each member is going to change. Now, each vertical member carries 88 N and each diagonal member carries a force of 14 N. Consequently, stress in each member changes as follows:

axial compression in each vertical member = 88/50 = 1.76 N/mm^2
axial compressive force in each diagonal member = 14/10 = 1.40 N/mm^2.

Let’s place these values on the above diagram as well.



Notice that now both members are under-stressed. What is interesting here is not the fact that the vertical members are under-stressed, but that the stressed in the diagonal members has shifted further to the left (from 1.68 to 1.40), they are now under-stressed (over-designed) by about 43% (originally, they were under-stressed by 19%). Conclusion: By increasing the stiffness of the vertical members we have made the design of the diagonal members more conservative; compared to the original structure, they are excessively over-designed.


Note of caution: The significance of this inter-play between stiffness and over/under-designing towers depends on many factors including the tower’s geometry, determinacy and section properties of its members. It could be the case that for some towers this impact is negligible.

Furthermore, I agree with Balsa Man on the advantage of the non-destructive testing technique he has articulated over the ad-hoc approach of just building and testing. Any approximate technique (including theoretical calculations) that offers a solid basis for designing or modifying a tower, in my opinion, is superior to guessing.

[Balsa Man]

As so often in the past, SLM has provided us a beautifully detailed and presented analysis. As always, much appreciated.

Two intertwined things in the remainder of this post; a) continuing the fun, way down in the weeds, detailed, conceptual discussion with SLM, and b) some (personal) perspective on how advice on this board, and in coaching, fits into “the bigger picture.”

In any really complex problem – and we certainly have one here; in this case understanding; modeling, the forces in a wooden tower, taking into account both the dimensional and physical properties of all members, and a hanging, potentially moving load, any analysis is a) an approximation, and b) can encompass a single aspect (or member), a small of interacting aspects (or members), or the whole, dynamic structure. Approximations, by nature, make simplifying assumptions, either ignoring a factor or variable (because it’s very small compared to other variables), or assigning it what you know to be an approximate value that’s “close enough” to reality, so that you can do the analysis, and get the answer to the question you’re investigating to sufficient precision for your purposes. In reviewing what we’ve both had to say, there are differences in what we’re taking into account; what we’re assuming, and how we’re looking at the problem. I think I follow the analysis RJM has provided – I certainly don’t question (as in think there’s something wrong with) any aspect/result.

Diversion to point b): As I’ve said before, I am not a structural or any other kind of engineer; I have, over the years absorbed a fair amount of understanding of the engineering (from a number of engineers) around wooden structures – to a certain level, let me call it a practical level; understanding how key variables work, and how you can work with them – control them to “get to good results.” In coaching, an important aspect is…..how do I say this….balancing the level of intensity to time and interest realities. We see/deal with on this board (and within the teams we work with), a wide range of interest, commitment, intensity, and technical understanding. This goes from someone who has been building successfully for years and is really committed to finding that last few percent that will put them Nationals medaling range, to those that would be really happy to snag a Regional medal and are trying to figure out how to do that within the time they have around classes, orchestra, other clubs/activities, etc., and the rest of their lives, to folk that pop up on this board with questions like, “Gee, I got stuck with towers this year and don’t have a clue- where do I find instructions how to build one?” The level and nature of advice/guidance – what to focus on, what to ignore; how much time to invest in understanding, and various aspects of building (e.g., design, jig building building other construction tools, selecting wood, assembly, testing) – needs to be aligned with, most importantly, time available. My contributions to this particular discussion were from the time perspective; what’s a good – as in time-efficient - way for those in the “fairly serious to pretty darn serious” range to get a long way up the performance curve with a minimal time investment. How can you get pretty quickly to leg specs that are at least getting in the optimal range?

The technique/approach I’ve suggested:
-do a test build with legs of the same cross-section, spanning a range of density,
-test that build with a safety tower, so you can limit failure to a single break in a single member (leg),
-fix and reinforce the failed member, re-test, repeat as necessary till you get to a leg density that carries full load,
-and then build a tower using that leg density,

Is simply a way to get “pretty darn close”, pretty quickly, to a competitive tower (or bridge, or boomilever).

In this approach, and the analysis around it in my last post, the simplifications and assumptions include:
-That the inherent variability in wood means that any analysis – conceptual or testing – is only going to get you to/into a range. Inside that range, good wood selection skills will help narrow the “error bars”, but luck becomes a significant factor,
-That you’ve settled on the cross-section of the legs- the open question is what density,
-That density (at a given cross-section) is a sufficient indicator of the modulus of elacticity; that stiffness, within a reasonable range-10-ish percent, is a function of density,
-That you have enough experience/test data to have a cross-section, and a range of densities, and an exposed column length, that includes a leg that will carry full load,
-That the failure mode is limited to/driven by long-column buckling failure between bracing points (which implies the presumption that your column bracing scheme/approach is adequate to “pin” the bracing points along the long column (the leg), so that you functionally do have in the overall leg, a set of stacked, shorter columns, and that the transfer of axial leg forces to bracing system members that SLM lays out above is, for our purposes, negligible,
-Related to the assumption above is the assumption that the bracing system is…..adequately spec’d (i.e., over-engineered), such that column failure in a leg occurs before failure of a bracing member (if, in the testing approach outlined, the failure mode seen was to be bracing failure, the same fix/reinforce approach would be needed in that bracing component),
-That the leg density is sufficient to avoid compressive strength (a completely different parameter than column strength) issues/failure mode – that the wood is not so soft that the forces involved result in elastic shortening or crushing (inelastic compressive failure).

OK,, finally, back to point a)- SLMs and my analysis (and a fun discussion that I’m enjoying learning from):

My 5th assumption- around the bracing system – is an aspect where we are looking at the problem differently – focusing on different aspects, making different assumptions. The whole topic of what’s going on in bracing, what works how, and “best” is a separate, major consideration that’s been discussed, analyzed, and debated over a lot over the years. I recognize my perspective is….simplified, doesn’t account for/take into consideration all the static and dynamic forces involved in a loaded structure. SLM’s analysis (as I understand it so far) gets to the point/conclusion of over-engineering (i.e., ending up with excess weight due to leg stiffening) through consideration of the distribution of compressive force through both legs and diagonal bracing members. My analysis is simplified (correctly or not), a) by ignoring the weight of bracing, b) by focusing to/assuming the operative failure mode to be buckling column failure between bracing intervals, and c) by my….operative, experiential (and only somewhat theoretical) understanding of how and why the “compression ladders and tension Xs” bracing system we use “works.”
My operative understanding goes like this;

We’re talking about square cross-section compression members (legs). They are aligned such that their flat sides face each other. In a 4-legged tower, that means they are oriented such that their edge corners “point” to the middle of the tower- if you sliced across and looked down vertically, you would see four diamonds, out at some distance around the center, with one point of the diamond point toward the center, and the sides of two adjacent diamonds parallel to each other. The load on the tower results in axial compressive force on the legs- essentially equally distributed.

Looking at any individual leg, first without bracing in place, and then with it in place. The axial force at some level is going to induce buckling- at or near the center of the exposed length, it will start to bow. In a square cross-section, the direction of that buckling will be in one of four directions - toward one of the flat sides; the area moment of inertia (“I” in Euler’s Buckling equation) is less in those directions – those two planes - than it is in the planes across the diagonal of the cross-section.

If you put (ladder) bracing in at the midpoint – square cross-section pieces butted up against and joining the flat leg sides, they will resist the buckling of the legs toward each other. Up to some load, they will prevent buckling in that direction. The axial compressive force on each ladder, as long as the column/leg doesn’t actually move in deflection is very low, compared to the axial force along the leg (i.e., the ladders can be of a lot lower density wood than the legs, and “work.” If the bracing interval is “correct” (close enough for the stiffness of the leg so that the exposed column length will carry the design load), you’ve turned the longer leg section into two “stacked columns” sufficiently strong to carry the design load, relative to buckling failure of the legs toward each other- the inner sides of the “diamonds” are braced – they are not going to move, to fail moving toward each other.

Now, the other two buckling failure directions/planes are toward the outer flat faces of the legs/diamonds- the legs moving apart from each other. If you run thin strip Xs (as I’ve said before, we use 1/64th x ~1/16th fairly high density balsa for these) between the ladders (as shown in SLMs figures, above), those strips see tensile axial load when the legs try to buckle away from each other (and also if the whole structure starts to twist or rack). Just as the ladders prevent buckling of the legs toward each other, the Xs prevent buckling away from each other. With all 4 potential buckling failure directions constrained, the braced point doesn’t move.

As I’ve mentioned before, these X strips need to be put on taught, so, just as the legs can’t start to flex/deform in toward the ladders, they can’t because of the X-strips straightening out/stretching, start to flex/deform away. They work purely in tension (up to the point of overall significant structural deformation, which almost instantly leads to failure) - they, in conjunction with the ladders could be threads – like cable stays are used in “real” structures.

Yes, this is simplified. The much more complex matter of overall structural dynamics, stiffness, etc matters. But in the force ranges, and size of structures we’ve been dealing with, its worked to produce….competitive structural efficiencies. Chimney legs 55cm long will be pushing the experience envelope to a new level, though, for sure

See anything I’m materially missing or mis-understanding here?

[SLM]

... some (personal) perspective on how advice on this board...

I agree with Balsa Man’s perspective on how to use this forum. For the sake of continuing and expanding the discussion further, I would like to take this opportunity to add a few comments of my own and to solicit related comments from others, especially from coaches and mentors. Although this probably belongs to the “General Discussion” thread, for the sake of continuity I leave it here.

I think the impetus for academic competitions such as Science Olympiad is:

(1) to get students excited about science and engineering and
(2) to entice them to expand their understanding of the related topics while in high school.

I think focusing mainly on building the lightest tower without trying to develop a basic understanding of the underlying scientific or engineering concepts tends to ignore item 2 above. I tend to promote a balanced approached in this regard. I would like my students to be able to build a very light competition tower, and to demonstrate a valid understanding of the basic physics behind structural design. In the long run, medals and trophies don’t count much, although, in the short run they may create opportunities for students and even offer financial rewards, such as college scholarships, for a few. What counts in the long run, especially in engineering fields, is the ability to solve problems based on sound engineering principles, creativity and a few other factors. Engineering schools don’t care much about students’ ability to build the lightest balsa wood tower, although some schools do use similar competitions to get freshmen excited about structural engineering. What they value the most is the ability of students to grasp the fundamentals and be able to apply them effectively to solve meaningful problems. Based on my observations over the past few years, I do believe high school students, and even many middle school students, have the capacity to learn and then put to use some of the core issues pertaining to engineering design in the context of SO engineering events such as towers, assuming they have access to right resources. I firmly believe students who take advantage of this kind of learning opportunities in high school have a competitive advantage over their peers in college and beyond. Your thoughts?

[Balsa Man]

... some (personal) perspective on how advice on this board...

I agree with Balsa Man’s perspective on how to use this forum. For the sake of continuing and expanding the discussion further, I would like to take this opportunity to add a few comments of my own and to solicit related comments from others, especially from coaches and mentors. Although this probably belongs to the “General Discussion” thread, for the sake of continuity I leave it here.Based on my observations over the past few years, I do believe high school students, and even many middle school students, have the capacity to learn and then put to use some of the core issues pertaining to engineering design in the context of SO engineering events such as towers, assuming they have access to right resources. I firmly believe students who take advantage of this kind of learning opportunities in high school have a competitive advantage over their peers in college and beyond. Your thoughts?

Very much worth discussing. Let me, to help that, bring over something from the gravity vehicle board ;
"...Why? Because the big question is, indeed, “does this really matter.” The question of “what matters?” is, I would suggest, is the first and most important question for ANY event. It is the “sharp point” of good analysis.

When the rules come out, read, re-read, ponder. Put into your thinking pot, and stir around, three things; 1) the basic physics/engineering (from what you know, and enough research to get a....working understanding, and quite possibly some “proof of concept” experimentation); 2) the scoring system (how is it set up, how does it work, what “pays off” more and less – run some numbers- what happens to your score when you change the value of the various factors by a bit?); and 3) building practicalities and time consideration - think things through – get a handle, best you can, on “what would it take to make?”/”how long would that take?”. The ramp shape question we’ve been discussing is a fine example - how much time would it take, first to figure out how to actually construct a ramp with a surface that follows a b-curve, then to do it? How much time would it take to do a flat one with a bottom transition curve? Is the time difference worth what it will get you in points? Are there other aspects where the same, or maybe less time will get you more, or equal points?

We’ve been discussing this same fundamental, “what matters” question/issue over in the towers thread. The time we (kids, coaches, event supervisors, etc.) have to devote to Science-O, and a particular event, is limited by the other time demands in our lives; “t” is a finite resource.

The more effectively you focus your time to what matters most, the better you are going to do. No caveat words here; simple and absolute truth. A key to that is figuring out what are red herring, and what are....good eating fish."
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So, I couldn't agree more with you on the value and importance of problem solving skills - in the S-O competitive context, and that as a source and foundation for bringing those skills along with you as move into college, and then into the real, working world.

At the heart, really the foundation of, problem solving skills, are the "critical thinking skills" that allow good analysis; "grasp(ing) the fundamentals and be(ing) able to apply them effectively to solve meaningful problems."

Competitive advantage in college and beyond? Absolutely - big time. The payoff in college?- getting into the school you want, good grades, scholarships, the opportunity to take more/more advanced courses, the opportunity to get into undergrad reasearch opportunities, helping you get into grad school, or into a cool/fun/challenging/good-paying job. The payoff in the real working world? landing a good job - a job you want, and turning that into a successful career. Very much the case in the world of science and engineering, but I think it goes beyond; a well-honed, analytical mind, that thinks in terms and works in terms of problem-solving is a big advantage in any field, and in just about all aspects of life.

Focusing, then, briefly, to the competitive context of S-O, and the "real world" where engineers get jobs, two comments:
1) The constraints of competitive rules and time available are mirrored in the business and other constraints of the "real engineering world." How do you design a whatever so that it can be manufactured at a cost that will allow the company to make a profit (vs how to score the most points); how do you do that- say for a component of a larger project - in 60 days (vs how do I get it done before Regionals); how do I design it so that it will not fail, and kill somebody (vs how to make sure I get the scoring bonus for carrying full load)- the list goes on...
2) I can say for a fact, problem-solving, and critical thinking skills are a major thing we (a major consulting firm) look for in engineering employees - in new hiring, and in promotions. People with such skills well developed are pretty rare, and highly sought after; what more can I say.

[Balsa Man]

ok so for this year i have already began testing my towers and if i do say so myself they are turning out very well

Tower 1:
height: 68.4 cm
kg held: 15 kg
tower weight: 9.43 grams

Tower 2:
Height:69.6 cm
Kg held: 15 kg
Tower weight: 6.96 grams

1 is very good
2 is somewhere beyond seriously good

[SLM]

...the analysis around it in my last post, the simplifications and assumptions include:
- That the inherent variability in wood means that any analysis – conceptual or testing – is only going to get you to/into a range. Inside that range, good wood selection skills will help narrow the “error bars”, but luck becomes a significant factor,

Agreed.

-That you’ve settled on the cross-section of the legs- the open question is what density,

This is a valid assumption, but, personally, I would not take this variable (cross-sectional shape) out of the equation yet.

-That density (at a given cross-section) is a sufficient indicator of the modulus of elacticity; that stiffness, within a reasonable range-10-ish percent, is a function of density,

Agreed.

-That you have enough experience/test data to have a cross-section, and a range of densities, and an exposed column length, that includes a leg that will carry full load,

Agreed.

-That the failure mode is limited to/driven by long-column buckling failure between bracing points (which implies the presumption that your column bracing scheme/approach is adequate to “pin” the bracing points along the long column (the leg), so that you functionally do have in the overall leg, a set of stacked, shorter columns, and that the transfer of axial leg forces to bracing system members that SLM lays out above is, for our purposes, negligible,

I agree with the hypothesis. The conclusion, however, does not follow. The tower does not distinguish between main compression members and bracings. It only sees roads (members) for force transfer from one intersection (node) to the next. It does not matter how stacked the columns are, if both diagonals are present at each level and they contribute to the stiffness of their end joints, then they will carry some percentage of the axial load depending on their relative stiffness. The way to make their load carrying impact negligible, is to make their stiffness relative to the main member(s) negligible.

-Related to the assumption above is the assumption that the bracing system is…..adequately spec’d (i.e., over-engineered), such that column failure in a leg occurs before failure of a bracing member (if, in the testing approach outlined, the failure mode seen was to be bracing failure, the same fix/reinforce approach would be needed in that bracing component),

Agreed. However, for a bracing to be adequate its stiffness may have to be increased, which makes it also a pathway for force transfer between its end nodes.

-That the leg density is sufficient to avoid compressive strength (a completely different parameter than column strength) issues/failure mode – that the wood is not so soft that the forces involved result in elastic shortening or crushing (inelastic compressive failure).

Agreed.

[Balsa Man]

-(Balsa Man:)That the failure mode is limited to/driven by long-column buckling failure between bracing points (which implies the presumption that your column bracing scheme/approach is adequate to “pin” the bracing points along the long column (the leg), so that you functionally do have in the overall leg, a set of stacked, shorter columns, and that the transfer of axial leg forces to bracing system members that SLM lays out above is, for our purposes, negligible,

SLM:I agree with the hypothesis. The conclusion, however, does not follow. The tower does not distinguish between main compression members and bracings. It only sees roads (members) for force transfer from one intersection (node) to the next. It does not matter how stacked the columns are, if both diagonals are present at each level and they contribute to the stiffness of their end joints, then they will carry some percentage of the axial load depending on their relative stiffness. The way to make their load carrying impact negligible, is to make their stiffness relative to the main member(s) negligible.

Yes - and with the X/diagonals as we use them, (1/64th x 1/16th), even with fairly high density balsa, their stiffness is WAY less than - negligible relative to - the stiffness of the legs. As described, their function in bracing is in tension. One can see very easily when they see compression loading, and what happens- either by taking, say the chimney, and twisting it, or just before structure failure, when a leg, or part of a leg is moving/displacing- they visibly, and virtually instantaneously pop into bowing. As I noted, when we did a test build with the Xs done in string, it worked - zero stiffness/transmission of compressive force.

-(Balsa Man:) Related to the assumption above is the assumption that the bracing system is…..adequately spec’d (i.e., over-engineered), such that column failure in a leg occurs before failure of a bracing member (if, in the testing approach outlined, the failure mode seen was to be bracing failure, the same fix/reinforce approach would be needed in that bracing component),

(SLM:)Agreed. However, for a bracing to be adequate its stiffness may have to be increased, which makes it also a pathway for force transfer between its end nodes.

Here I was really talking about/thinking about failure in the ladders - should have said so - yes, for them, being under compression/having stiffness -> pathway. However, we never have experienced a failure in the Xs. As noted in the point above, X stiffness is negligible. They are, at a 64th x a 16th, both clearly over-engineered, and very light. maybe they get lighter this year

[Fletch1999]

Me and my partner made a tower, it was perfect exept the base was to small, it was humiliating, DONT DO THIS! IT SUKS!