Proportions based on physics...statics

[Mark Singer]

Here are the calculations for a 10ft long table (beam) with a uniformly distributed load of 10 lbs/foot or 100 pounds total.
Firs taking Momentsa about R1=21.42
Then taking moments about the center of the table(beam) =21.5

So it is clear that these proportions yeild balanced moments and equal positive and negative stresses at the centerline and cantilever respectively


any engineers out there to check my calcs??? It been a few light years for me ...as they say in quantum physics

[Ken Garlock]

I can agree with your calculations, although I had to study the picture for a minute. I had to figure out that you were considering the load, although uniform, to be concentrated at the midpoint of each section and therefore giving an effective lever arm of 1/2 the actual length.

If I were building the bench I would have placed the supports at a distance of 1/4 from each end. Now I can see that the .21 is a better solution. I had always thought that the design and engineering were to separate and apart items, but your discussion shows that they are essentially one in the same.

Disclaimer: I am not an engineer, but I did know many in college I did have both a statics and dynamics course in college over 45 years ago, and long forgotten.

[Mark Singer]

I can agree with your calculations, although I had to study the picture for a minute. I had to figure out that you were considering the load, although uniform, to be concentrated at the midpoint of each section and therefore giving an effective lever arm of 1/2 the actual length.

If I were building the bench I would have placed the supports at a distance of 1/4 from each end. Now I can see that the .21 is a better solution. I had always thought that the design and engineering were to separate and apart items, but your discussion shows that they are essentially one in the same.

Disclaimer: I am not an engineer, but I did know many in college I did have both a statics and dynamics course in college over 45 years ago, and long forgotten.

Ken,
With your backround and mine we can send a cofee table to the moon

[Stephen Stokes]

Interesting thread. One question. How did you originally arrive at 0.207?

Stokes

[Mark Singer]

Interesting thread. One question. How did you originally arrive at 0.207?

Stokes

I used to work for a company that specialized in form and precast concrete design engineering many years ago when I was going to engieering school . This was long before I was an Architect... At this firm we analyized stress and designed reinforcing for different elements. One common problem is a tilt-up panel being lifted by a crane. Steel inserts are cast in the panel for erection by a crane. To equalize the sresses we used this and many other formulas. You can solve this formula for the distance (.207) that would make the positive center moment egual the cantilever moment. You use Xfor the distance of the cantilever and solve for X...the other distance is expressed as L minu(the entire distance)s x

[David Weaver]

My wife and i just went through kentuck knob a couple of weeks ago ( a frank lloyd wright house), and the entire roof is built like that. It creates quite an overhang on the outside of the house - to the point that all of the porches all the way around are covered. It's a great way to construct things and take advantage of the natural compression strength of wood in the direction of the grain.

[Tom Scott]

Mark,
Great thread. Everything you said seems to be right on.

To others, the stiffness won't affect the moments. The typical design proceedure for any structural element would be to analyze the load conditions and get the moments and shears within the element. Then with this information, find the section properties that satisfy all of your criteria (deflection, stress, etc.). So to carry this a step further, once you have the proportions of your furniture piece (a table in this instance) one should also proportion the structural element (the table top) accordingly. For instance, a really thin top would not look natural on a long table...and similarly, a thick top would not look correct for a really short table.

I just wish more architects I work with had an engineering background. Too many seem to think that a 20' cantilever from a free-standing column or wall (with no back-span) looks natural.

Tom (structural engineer by day)

[Rob Blaustein]

I was reading today in the latest Discover magazine an article about Fibonacci numbers. The short article observed that given a number 'n' of the Fibonacci sequence, if you divide it by the preceding number, it will approximate the 'golden ratio.' The larger the number in the sequence, the closer the ratio will be. The article didn't offer any supporting mathematics so it might just be a coincidence.

Ken--it's not a coincidence at least in the mathematical sense. Here is a site that describes why the ratios tend towards phi (the golden ratio): http://www.mcs.surrey.ac.uk/Personal...nacci/phi.html Scroll down to the section entitled "The Ratio of neighbouring Fibonacci Numbers tends to Phi" for a mathematical derivation. --Rob