Significant Figures & and code interpretation 5

[Robvh1984]

I am a stickler to sound logic, e.g. significant figures, etc. However, My question arises from maybe a more philosophical standpoint (or poorly assumed to be). I see structural engineering as having 4 main components where variability may or will arise. 1.Loading 2.Engineering Analysis 3. Construction 4. Material Strength/general behavior.

All else equal, as engineers we have most control over the 1st and 2nd part of those 4 items as loadings may vary greatly with application (requiring our judgement) and analysis is literally performed by us. Therefore, as a young engineer, I prefer to use the code verbatim (i.e., if f'c=3000 I take it to mean that f'c has been measured to be precise to (1) significant figure(ignoring scatter of points). Then, for example, if I calculate the rupture strength (7.5f'c^.5) one calculates something on the order of 410.7919181288745850927273371006. I would say that the rupture strength is most nearly 400 psi, and I shall carry as many digits as I can from this intermediate calculation through my remaining calculations. I think my physics/chemistry professors would agree based on the standard mathematical laws or error propagation for arithmetic and single variable functions that this is valid.

However, My boss does not follow this logic when he performs calculations. He crudely & significantly rounds down whenever numbers dont seem to 'feel' right. Then in the end he selects sections with capacities as much as 20% greater than demanded by his rounded calculations. He justifies his methods of computing broadly based upon personal liability, loadings, and construction & material variability.

I find his methods to be unacceptable, as he applies this conservatism very broadly to everything he does. I understand our field is mostly experimental, but I feel that many of us (structural engineers) are so afraid of variability, we fly through analysis with grossly over estimated values and thus structural members.

In, short, how does everybody frame their logic in performing calculations as it relates to precision?



-Robert Miller, E.I.T.
KPA Structural Engineers

 

[sasa2k]

There are two different things here. One is a required numerical precision for your work and the other is a internal precision of your computing tool (calculator, slide rule, Mathcad, Excel, Maple, Mathematica, ...).

Just because Mathcad maintains 17-digit precision that doesn't mean your calculation will be more accurate than hand calculations using 3 significant digits.

The point is that by increasing the numerical precision to more than 3 significant digits you are not increasing the accuracy of your calculations.

 

[mtu1972]

It's easier for those of us who worked with slide rules to think in terms of 3 significant figures. With the stated list of variability -
"1.Loading 2.Engineering Analysis 3. Construction 4. Material Strength/general behavior."

I might rate them in the order of 1, 2 & 4 together, and then 3 (which I have very little control over).

I was always conservative with my load assumptions; which then meant that I did not have to get hung up on something being at 103% (or 105%) of allowable. Too many supervisors get so hung up on being less than 100%, or now days, never seeing anything turn red on the computer output.

I know which loads I started with and so trying to maximize design results always seemed ridiculous.

Picking steel sizes that are economic and/or more readily available; coordinating sizes so that connection detailing can be done more efficiently; and incorporating uniformity throughout the structure can all add material cost to a project, while reducing overall construction costs.

CIP concrete design is as much art as science. I love the flexibility it allows in solving problems.

As noted by others above, I always treated the clients money as if I was spending my own. Way too many engineers get hung up on feeling self-important and have no problem spending the Owner's money for "cheap concrete or steel" to pad the Safety Factors, etc.

gjc

 

[IRstuff]

"Just because Mathcad maintains 17-digit precision that doesn't mean your calculation will be more accurate than hand calculations using 3 significant digits. The point is that by increasing the numerical precision to more than 3 significant digits you are not increasing the accuracy of your calculations. "

No one said there was an increase in accuracy. What's being discussed is "increasing numerical precision" as if there something that had to be done differently. There isn't; the precision comes for free and costs nothing.

Since one calculation flows directly into the next, you would have go out of your way to decrease the precision at that point, so why would you?

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[dik]

For programs, I typically use 16 or 17 significant digits... but, it's not for the precision. Most programming languages default to double precision and there is no overhead in using the greater precision. In some instances code can actually execute faster...

One of my mentors was a little, bald headed, bearded, English professor (actually an electrical engineer), from the U of Southhampton. He used to do a skit, pretending to use a sliderule, and with a wonderful German accent, he used to mimic using a sliderule. He would say (in a German accent)... for example we will multiply 2 x 2... and he would proceed with two, und ve vill multiply it by 2, und the answer is 3.996... ve'll say 4... <G>

 

[BigH]

I'm a bit late on this - first comment, rjm5062 - I am not sure msquared, when he said his significant figure was his wife (which I would agree if it were my wife), I don't think he was even thinking of a W12x19 - at least I wouldn't!

There seems to be the slide-rule learned types vs the computer types (and those who think codes are absolute). In the end, one must think of what makes sense. As for footing design, I certainly would add a few extra square feet on the footing size (assuming a reasonable number of footings) rather than trying to cut it "close". A few hundred or even thousand of dollars on the foundation concrete is small insurance compared to what would happen if there was a sizing problem due to exactitude and the structure was almost completed.

When I see 3000 psi, I pretty well assume that they are talking about plus or minus a 100 psi. Only if someone wrote 3000. would I take it at four significant figures. I've seen this on my current job where the client's safety protocols required a "rest" platform if the ladder was more than 6 m high. So we end up with 6.2 m. Do we provide the platform or say, 6 m - could be up to 6.5 before we would "round" to 7.

I've been having a fit with our accountants who don't use the actual exchange rate on their calcuations (Indonesian rupiah - as stated on the credit card statement divided by the Canadian Dollars quoted as the expense - because the exchange rate quoted with the rupiah has truncated figures - and I always get the "bohica" over this!

 

[dik]

BigH... I agree with your concrete strength observation, and I think that 100 psi might be a little optomistic... I generally encounter several hundred psi over, as for the safety platform, I would have added one... maybe a couple of inches over as a construction tolerance (but not design), but 8" is a little much for construction tolerance... and at 6.45, you've added 18". for safety related issues, I generally don't 'max' things out... if for no other reason than for liability.

Dik

 

[paddingtongreen]

@rjm5062, You remind me of the teenager who noticed that as he became older, his father grew from being a stupid ignoramus to being a knowledgeable and intelligent man, at this moment, you know it all.

Lets be clear, if designing a beam, I first find the size the numbers require, then I consider it's fitness for purpose, is it wide enough for what sits on it etc,, it's fitness for decent connections (indecent connections cost money). If I'm at the top weight of a series of steel beams, I try to step up to the bottom of the next series, if it passes my other tests, above. Why do I do that? because a change in load can be covered by a weight change only, details still hold, if I have to change to another series later it may affect the detailer, the architect and/or other disciplines.

Most of the cost of structural members is in the fabrication and/or field labor, the raw materials are are a small part of the cost.

I advise all young structural engineers to look at the acceptable tolerances for structural members, thickness, out of true, sweep etc. Understand that when they reach the field they may be worse, but they are accepted. Take a look at the blemishes accepted under ASTM A6 and it's cousins in other jurisdictions.

This business is as much an art as it is a science. we do not build fine clockwork mechanisms.



Michael.
Timing has a lot to do with the outcome of a rain dance.