Designs

[SLM]

There is, I believe a big downside to the rectangular configuration (with flat, parallel sides), though; overall tower stability. With the load on top of the tower 50cm above the base, only a tiny amount of bucket sway across (perpendicular to) the plane of the flat sides will create a force that will act to tip the tower over. Likewise, only a tiny amount of distortion out of the plane(s) of the flat sides will do the same. With all sides leaning in some toward the center you gain overall stability against both distortion and bucket sway.
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Here is a simple engineering analysis for determining the conditions under which a tower with a rectangular leg configuration (flat with parallel sides) losses its stability and tips over. To simplify the analysis, say the tower has the following overall dimensions.



Assuming that the individual members and connections are strong enough to hold the entire load, the tower could still fail by tipping over. This could happen for two reasons: (1) swaying of the bucket and (2) unsymmetrical construction of the tower. Let's look at each separately.

1. Swaying of the Bucket
If we look at the tower from side, and draw a diagram for the support points (where the tower rests on the table) and the load, we get something like this:



Now, if the bucket sways (say by angle "s" from the vertical axis), as shown below.



Then, a horizontal force would be formed at the top of the tower, as shown below.



This force causes the tower to tip over if: (50) (15 tan(s)) > (5)(7.5). Solving for s, we get s > 2.86. That is, if the bucket sways more than 2.86 degrees from the vertical axis, the tower would tip over.

2. Unsymmetrical Construction
Imagine a vertical line from top of the tower to its base. Note that the applied force, applied at the top of the tower, acts along this line. If the support points are not symmetrical relative to this line, as depicted below, then the tower could tip over.



As shown above, the load is off the center line by a distance e. In this case, the tower tips over if: 15 e > (7.5)(5). Or, e > 2.5 cm. That is, if the load is off-center by 2.5 cm, the tower tips over.

In this example, I've used a side distance of 5 cm between the legs. To improve the stability, this distance could be increased. For example, if we use a distance of 10 cm, then the tower would tip over if s (the sway angle) becomes greater than 5.7 degrees or e > 5 cm.

[lllazar]

Hey guys, i have a question more related to bridges, specifically toothpick bridges.

So i was just browsing vids on toothpick bridges and came across this one:

http://www.metacafe.com/watch/1079370/t ... hs_krissy/

I have a few questions about it

1. I just find it hard to believe that such skinny members could support such a large mass. Of course, it happened, can anyone explain how the base should be built - if it has to span 25 cm, what would be the best manner in which to make a large member with 6cmish toothpicks.

2. I think the secret in this is the brick that is used and the method of testing. After trying a few things with JHU bridge, i saw that the use of the brick more evenly distributes the force - for example, with the loading block style used in scioly and in my physics class, all the weight of the bucket is putting more force on the middle section of the bridge, where as in this video, the force is more evenly distributed throughout. Do you think that may have had a significant impact on the massive 82 pounds it held?
3. I built my test toothpick bridge for my physics class yesterday - i had a trapezoidal design. For the base and the top, i had 3 tooth pick by 2 tooth pick members, as in they were quite thick. Is this really necessary? Would 2x2 or even 3x1 be more efficient?

[SLM]

Hey guys, i have a question more related to bridges, specifically toothpick bridges.

So i was just browsing vids on toothpick bridges and came across this one:

http://www.metacafe.com/watch/1079370/t ... hs_krissy/

I have a few questions about it

1. I just find it hard to believe that such skinny members could support such a large mass. Of course, it happened, can anyone explain how the base should be built - if it has to span 25 cm, what would be the best manner in which to make a large member with 6cmish toothpicks.

2. I think the secret in this is the brick that is used and the method of testing. After trying a few things with JHU bridge, i saw that the use of the brick more evenly distributes the force - for example, with the loading block style used in scioly and in my physics class, all the weight of the bucket is putting more force on the middle section of the bridge, where as in this video, the force is more evenly distributed throughout. Do you think that may have had a significant impact on the massive 82 pounds it held?
3. I built my test toothpick bridge for my physics class yesterday - i had a trapezoidal design. For the base and the top, i had 3 tooth pick by 2 tooth pick members, as in they were quite thick. Is this really necessary? Would 2x2 or even 3x1 be more efficient?

If I remember correctly, most toothpicks are made of birch. Some species of birch are much stronger than bass and balsa. See Chapter 4 of the Wood handbook for a strength comparison between bass and birch.

Your are right, distributing the load over the top chord of the truss reduces some of the member forces. Here is a comparison between two load cases, in Case 1, a total load of 40 lbs is distributed over 4 nodes. In case 2, the same load is distributed over two nodes only. As you can see Load Case 2 does cause more sever force in some (not all) of the members. However, for this truss configuration, some of the members are unaffected by the load distribution pattern.





I think you need to run a few experiments to figure out a suitable size for each member. A couple of observations: The members along the bottom chord of the truss are in tension, hence less critical than the members along the top chord which could buckle due to compression force. However, since the compression members are relatively short (about 5 to 6 cm) buckling may not be a big factor after all. I may be wrong here, but a 3x2 trapezoidal member seems to be too strong for this truss. How about trying a 2x1 configuration and see how it holds up.

[lllazar]

Thank you very much SLM for that data and that explanation - i seriously overlooked the fact that Birch is indeed much stronger than balsa or bass...we'll see how the bridge does tomorrow at the practice test. I'm thinking right now that i change the 3x2 to 2x2 for the top compression and 1x2 for the bottom tension.

[phillies413]

What size wood are all of you using for the legs of the base and the legs of the top of the towers? 1/8 squared?

[lllazar]

We're using 1/8 squared for the base legs and the top vertical sections, 1/16 for everything else, at least to start off with. We're trying to eliminate as many confounding variables as we can so that we can change what truly should be changed, without any confusion.

[MHSSciOlympiad]

Any rules against using balsa sheet?

[Balsa Man]

Any rules against using balsa sheet?

Nope.

[Littleboy]

Any rules against using balsa sheet?

No the rules have no limit for thicknesses of wood. Sheets not cut are not advised due to making the bridge heavier than it needs to be. You don't want it heavy but do want it to hold most/all of the weight.

[Vizard007]

So, I was talking with my coach, and he told me a story on how the Japanese design houses without using a single screw or glue or anything. So, I was thinking, making a tower without glue at the joints? (The ones connecting the base with the "chimney", NOT the supports) Crazy idea? Or do you guys think it might work?