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is this formula ok?

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I'm not familiar with that process (I've seen it,  but never really analyzed it). You can bet that if the units do not work, the expression is not correct. Where did you get this?


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Dr D., For most equations if the units don't work there is an error. This is not true all the time. The strength of concrete is where I ran into this. It is because the results are  arrived at  empirically. I looked at several sources all had the same equation. Finally I came across a post or a book, I can't recall, that explained why. I forget if the results was allowable force or a stress. But the square root of psi does not get you to either.

I get to work what are Civil projects. I find the phraseology puzzling at times. Like "the beam developing its full strength due to the load." The full strength should be X whether loaded or sitting in inventory. What this is understood to mean by civils, is the full bending strength. Or in other words will the beam experience failure in some other mode before the application reaches the allowable max bending stress with all factors of safety accounted for. 

But these examples aside, if the units don't work, don't assume it is as with the example above. Confirm the equations you are using from multiple sources if taken from a text or handbook.    

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JAG - If the units do not work, there has to be a dimensional constant (a constant that has dimensions, not a pure number) involved. This is not uncommon with empirical relationships, but it means that the whole equation is only valid in the original system of units.


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I know what you mean but that is not what I have discovered for shear strength of concrete.


Also attached a posted question with answers. One reply suggested the same as you. If there ever was a dimensional constant, it has been lost in time and the odd units accepted. If you have a better source  I would like to see it. I was sure there was an error but found the same relationship in a few sources. Then the replies from CE's.

What's up with the units in concrete design equations_ _ AskEngineers.pdf

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DrD, JAG, thank you for the responses.

I have got it from:

"Sheet Metal Forming Processes and Die Design"  By Vukota Boljanovic

I really think there is a mistake,

Knowing E: 210.000 MPa,  E square (ExE) would make always ZERO that division, considering YS, D and T very smaller numbers, don't you think?

It has no sense.

Furthermore, units do not work and there is no constant to fix it, like DrD said

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It should be E not E^2. Other than that it looks correct. Established books make mistakes (albeit rarely).

Here's for other potentially conflicting reference :D


I've seen very rare occasion where constants do have dimensional units. (I recall a book by Niemann on Design of Machine Elements, the original German edition)

Niemann & Hirt, Maschinenelemente 
Volume 1: Konstruktion und Berechnung von Verbindungen, Lagern, Wellen
Volume 2: Getriebe allgemein, Zahnradgetriebe - Grundlagen, Stirnradgetriebe
Volume 3: Schraubrad-, Kegelrad-, Schnecken-, Ketten-, Riemen-, Reibradgetriebe, Kupplungen, Bremsen, Freiläufe

Never seen it in American books or European books using SI units.

There are occasions that constants have dimensional units in practical standards/codes as well. But that's a different story.

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