Boomilever for 2013

[SLM]

...On another note, would testing the tension and compression members separately (think Towers; testing the base and the chimney separately to see if each could hold the required amount of weight) be a good idea? If so, any ideas on how would one do that since the load on the compression structure? Flipping the structure 90 degrees so it's upright (like a chimney of a tower) and then applying the load from the top down won't work, since on a boom the load isn't equally distributed.

It is a good idea to test the main pieces of balsa (or bass) for their tensile and compressive strengths before assembling the boom. A simple way to estimate the compressive strength of a wood stick is to place it perfectly vertically on a scale, then press down on the top end (while maintaining its vertical alignment) with your finger until the member starts to buckle, at which point the scale reading can be taken as the compressive strength of the member.

For tensile strength, I would use a spring scale, or a force gauge, to make the measurement. Attach (glue) a stronger (bigger) piece of wood to either end of the balsa stick, drill a hole at the center of each end piece for attaching a spring scale, attach a scale to either end, then pull on the free end of the scale subjecting the stick to a tensile force. You can continue pulling until either the member fails due to excessive tensile force (highly unlikely), or you have determined that the member has sufficient strength for the intended use.

However, keep in mind that in addition to tension and compression, the boom members are also subjected to bending. Stress due to bending in the main compression (or tension) member (if you are using a triangular boom) may be as high as 70% of the stress due to compression (or tension) alone. This means, if you are considering only the compression (or tension) force in the member as the basis for your design, you are under-designing it by a significantly large factor.

[jander14indoor]

<SNIP> A simple way to estimate the compressive strength of a wood stick is to place it perfectly vertically on a scale, then press down on the top end (while maintaining its vertical alignment) with your finger until the member starts to buckle, at which point the scale reading can be taken as the compressive strength of the member.<SNIP>

An important test, but that is NOT the compressive STRENGTH of the member. Its the BUCKLING LOAD. It does let you back calculate the compressive STIFFNESS of the material and project the buckling load to other size members. Calculate acceptable column free lengths, etc.

Note,

STRENGTH is the force per area it takes to permanently BREAK something. To test compresive STRENGTH you actually need a short and fat column that does not buckle under load before it breaks.

STIFFNESS is the resistance to deformation without breaking.

BUCKLING is a geometric instability of a shape under compression where you get failure at loads far below the compressive STRENGTH. The degree of weakening depends strongly on the free length of the object and its cross sectional shape (moment of inertia) as well as its STIFFNESS. Understanding this geometry effect is critical to understanding what's going on with the compressive member of the boom.

Jeff Anderson
Livonia, MI

[iwonder]

But why would someone need to know the compressive strength of a member, when in the majority of cases you will never reach that strength(I've done some testing on circular members that seems to have reached it)?

And I guess I'll go ahead and ask... Circular compressive members were talked about in other towers forums near te end of the year, I've done some testing and found that they can easily withstand the 50kg of compressive force(it seems to break in a ring by expanding outwards, which leads to believe it's compressive failure) but I can't quite picture were SLM is coming up with the stress from bending.

Maybe my model is to simple, but the only thing I can think of is that depending in your placement of the loading block the comoressuve force might not be equally distributed through the member, and how would this effect it? Or better yet, does anyone want to share a method to load a circular member equally? It seems that the circular style compression member is going to be the most efficient, if you can load it properly...

[SLM]

<SNIP> A simple way to estimate the compressive strength of a wood stick is to place it perfectly vertically on a scale, then press down on the top end (while maintaining its vertical alignment) with your finger until the member starts to buckle, at which point the scale reading can be taken as the compressive strength of the member.<SNIP>

An important test, but that is NOT the compressive STRENGTH of the member. Its the BUCKLING LOAD. ...

True, what I referred to in my post is buckling strength, not compressive strength. I suppose I was looking at it from the viewpoint of having the members tested to see if they could hold the load once the boom is built suggesting that the critical load capacity for each member can be determined using simple tests. I casually referred to the critical load for the tension member as tensile strength and that for the compression member as compressive strength. In reality an axially loaded member (whether in tension or compression) has multiple modes of failure each with its own unique technical name, clearly using the terms interchangeable could lead to confusion.

[SLM]

... Circular compressive members were talked about in other towers forums near te end of the year, I've done some testing and found that they can easily withstand the 50kg of compressive force(it seems to break in a ring by expanding outwards, which leads to believe it's compressive failure)

If the the member expands outward before any breaking takes place, then the failure is due to local buckling. If on the other hand, you don't see any outward expansion before the failure, then most probably stress in the member has exceeded its compressive strength.

... but I can't quite picture were SLM is coming up with the stress from bending.

The main members in the boom are subjected to bending moments due to the geometry of the structure and the location and direction of the load. You can determine the bending moments in each member by analyzing the boom as a frame structure use a structural analysis software. For example, consider the triangular boom shown below where the members are numbered 1, 2 and 3.


The analysis of the boom subjected to a downward force of 100 N yields the following member forces (For brevity only the significant forces in Members 2 and 3 are shown below).


The above diagram indicates that Member 2 carries an axial tensile force of 315 N. The member is also subjected to a bending moment of 12 N-cm at the upper end, bending moment at the lower end is zero. Member 2 carries an axial compressive force of 298 N and a bending moment of 13 N-cm at the left end.

When a structural member is subjected to bending moment, bending stresses develop in the member. For example, for Member 2 above, bending stress at the left end of the member (acting on the rectangular cross-section of the member) looks like this.


The diagram shows the top half of the member in tension and the bottom half of the member in compression. Intuitively, since the member bends downward the top fibers of the member (fibers along the top of the member) are going to stretch and the bottom fibers are going to shortened. This means the moment induces axial tensile stress along the top half of the section and axial compressive stress on the bottom half of the member, as shown above.

As for stress due to the axial tension force in the member, it is going to look something like this:


Here, tensile stress can be assumed to be constant across the section.

Since both axial force and bending moment are present in the member, the actual stress in the member is obtained by adding the above two diagrams, like this:


In conclusion, the presence of bending moment in a tension (or compression) member significantly increases stress in the member.

[jander14indoor]

Given your drawing, I'm having trouble seeing why there is any bending moment on the parts, depending on unstated assumptions.
Are the elements rigid or flexible, if flexible, how much (that affects the bending load).
Are the joints rigid or pinned. If pinned, there is NO bending load. If pinned, again, only bending if flexible elements and that depends on the material for how much bending load.

Example, I could make your top element out of string and there would be only tension, no bending load. Have to think a little more about the lower compression element, but I think string would eliminate any bending there too.

So again, please state the conditions fully with your analysis.

Note, agree fully with what you illustrate as the effect of bending when present in understanding the stresses on the members.

Thanks,

Jeff Anderson
Livonia, MI

[iwonder]

Thanks for the help... but I still don't see the bending moment in the tension member, but the compression member's moment is plainly obvious, I just didn't know what to call it.. lots to learn.

[SLM]

The assumptions are: The boom is made of balsa or bass and glue is used in the usual way to connect the members together.
Edit: And, all the members have the same cross-sectional shape and the same density.

As I've mentioned before, if the boom is made using wood and glue. That is, the members are joined together using glue, then the connections are rigid. That is, if member A is glued to member B, then A cannot rotate freely relative to B. When the joint rotates, both A and B rotate together. On the other hand, if I connect A and B using a pin (for example, put a pushpin through their ends) such that A can rotate relative to B freely, then I have a non-rigid (truss or pin) connection.

In the case of the triangular boom where glue is used in the usual way to connect the members, the connections are rigid, hence the members could be subjected to significant bending moments (depending on the position and orientation of the load), as illustrated in my example above. The only way to eliminate bending moment in the boom is make its connections of type pin.

Here is another perspective that should help us see why moments are present in the members. Imagine our boom is made of solid wood, a single piece of either rectangular or triangular wood that extends from the support surface to the point of application of the load. This boom, then, acts as a cantilever beam which is subjected to a downward concentrated load at the tip. Let 's assume the load magnitude is P and the length of the beam is L. Then, the moment at the base of the beam is P*L. Say, for our triangular solid beam, we carve out the middle part of the beam but leave the wood along the perimeter of the team intact. That is, we transform the solid triangular beam into a triangular boom conceptually consisting of three members only, very similar to the example I gave in my previous post. It is not plausible to suggest that the bending moment that was present in the solid beam disappears in this modified beam. Such a structure has to carry the bending moment produced by the load. The structure does it through its members.

[sciencegeek8]

This is my first year trying out for a new science olympiad team but we have to build a boomilever but I am only familiar with towers. any help on how to construct one? Should the top member be vertical or slanted, how does it attach to the wall, etc...

[iwonder]

There a gold mine if you read this topic, look at the aia's guide too.