Secret Metric Formula Conversions - Elastic Beam Equations 6

[CrunchBird]

If this has been answered, my apologies and thanks for pointing me to the right forum.

Find the area, given the allowable shear stress and load, A = Vfv. Find the section modulus, given the allowable bending stress and moment... and so on.

It's pretty easy if my forces are in Newtons and section properties are all in m, m^2, m^3 and so on. For example, I just convert from m^2 to mm^2 or cm^2 after I've gotten my answer in m^2. I've come across some direct computations, for example moment in N-m divided by MPa gives cm^3 - without including converting from m^2 to cm^2 by multiplying by 10^6 cm^3/m^3.

I've been working on deriving a cheat sheet on this, but so far I've confused myself to the point where I need assistance. Thanks for any suggestions/help/etc.!

 

[BAretired]

In the SI system, cm are out. Use either m or mm. For structural properties, mm are the norm.

It is best to start out with consistent units, then do your calculations without converting.

If you are given mass units in kg, convert to N or kN before starting.

A cheat sheet is not necessary if you follow through with consistent units.

BA

 

[csd72]

Yes, use N and mm, you will also find that MPa is equivalent to N/mm^2 which is handy.

so all kN become N x 10^3, m become mm x 10^3 e.t.c.

 

[CrunchBird]

OK, thanks BAretired and csd72!

"Handy" is the key.

Now, in the Arcelor sheet pile manual, section properties are given in cm^2, cm^3 and cm^4! And they have a beautiful example where moment in N-m/MPa = cm^3. It's almost supernatural; moment is "converted" from kN to NX10^3 yet allowable stress is kept at MPa.

This is the kind of "magic" computation I am looking for; that is, always remember that moment in N-m divided by MPa will give me cm^3. But... let's say I want to find moment of inertia, back-calculating from deflections - this is where my brain melts.

Now, it would be really rude of me to suggest that the Arcelor folks are doing it "wrong." But they've got all their section properties expressed as centimeters per meter. And since I have an AISC book with metric properties - expressed in millimeters I am thinking there's a good way to do direct computations with minimal powers of ten expressed.

 

[rb1957]

it's all "just" orders of magnitude (that's the beauty of the metric system)

for example stress = My/I, so I/y = M/stress so your pipe geometry specifies I/y (yes?) both in cm ... cm^4/cm = cm^3. on the RH side you have M/stress = Nm/MPa = 100Ncm/1E4(N/cm^2) = 0.01cm^3 ... clear as mud ?

say you have pipe with I/y = X cm^3 and S MPa allowable stress then the allowable moment is S*1E4/X Ncm = S*1E2/X Nm

or if you have a moment of M Nm and an allowable stress of S MPa then you'll need a pipe with I/y = M/(S*100) cm^3

 

[ishvaaag]

Arcelor may be following partly what was the "Technical System". Almost all structural steel properties were given on the kg, kgf and cm units, and except for cold formed or thin members I think it is still the real practice for most printed and non printed documentation in Spain and ample zones in Europe.

I found by experience that having Mathcad is precisely the recipe to forfeit doubts in unit matters, for it converts them consistently from whatever to whatever. I find myself using Mathcad to establish the correct input (or properly interpret output) for weights and pressures in SI units that are not something as identifiable as a lb or a kg, especially when something tera-tical like 10^13 (terathos or something so stand for monstruous, we rather avoid it) or whatever. So you can obtain quick assurance of what you are putting and getting. It also excels in finding some variable such say inertia from all else in the formula, whatever your input that respects dimensionality.

 

[CrunchBird]

Thanks, rb1957. Of course, my brain is ripping itself apart thanks to your answer, but you are on to something.

 

[rb1957]

careful with your brain cells ... they're the only ones you'll ever have

 

[hokie66]

Agree with BA and csd72. Using centimetres in engineering work is worse than sticking with feet and inches...in my opinion.

 

[apsix]

I also agree, but for some reason the Brits for one have always stated section properties (I, r, z etc) in cm, cm2 ...

Can anyone explain why?

cm are used in dressmaking.

 

[BigH]

hokie, et. al. - I agree that cm is out, but in Indonesia, every engineer I meet uses cm. Slump = 5; oops, 50 mm for me. It is maddening at times. Sadly, the only engineering unit in geotechnical that used metric before the conversion to SI was coefficient of permeability cm/sec and now I can't use that anymore either!

 

[hokie66]

I've always thought the French were responsible for the kg/cm^2 nonsense, but seems it is widespread.

 

[csd72]

Oh yes the french - They measure their drinks in cL (centilitres) and one set of french calculations I cheacked had results in dN (decca newtons).

 

[HgTX]

Centimeters may be out of fashion in various technical contexts, and might be not used in various contexts by user convention, but they are *not* out of the SI system. Contrary to popular belief, it is simply not the case that the SI got rid of any prefixes meaning 10^n where n is not a multiple of 3.

The horse's mouth:

http://www.bipm.org/en/si/prefixes.html

I'm not saying everyone needs to be using cm, but it is an incorrect statement to say they are out of the SI.

Hg

Eng-Tips policies: faq731-376

 

[BAretired]

HgTX is correct in stating that deci and centi are recognized prefixes in the SI system. However, the Canadian Metric Practice Guide recommends the use of prefixes representing 10 raised to a power that is a multiple of 3, a ternary power. Common structural design units would be:

Force - newton (N), kilonewton (kN)
Stress - pascal (Pa), kilopascal (kPa), megapascal (MPa)
Length - millimetre (mm), metre (m)
Mass - kilogram (kg), megagram (Mg)

BA

 

[drawoh]

CrunchBird,

When I do calculations nowadays, I set up a spreadsheet. The last page of my spreadsheet always is unit conversion factors. I systematically convert everything to a consistent system of units. This completely makes sense if you name the spreadsheet cells.

=25.5*lb/in^2

The result is entered in N/m^2, lb/ft^2, troy_oz/furlong^2.

I have gotten confused and wrong in the past by trying to combine Newtons and millimeters. Don't do it. Newtons and slugs are derived units. If you use them, you need to work in whatever unit system they were derived in.

JHG

 

[IDS]

drawoh - if you are able to share your spreadsheet I'd very much like to have a look at it.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[hokie66]

BA,
Megagram...that is a new one on me. We call 1000 kg a tonne.

 

[BAretired]

hokie,

It's a new one on me too, but I was quoting from the SI Summary in the CISC Handbook. Quoting further, it says "The tonne is a special unit, equal to 1000 kg (or 1 Mg)that will be used in the basic steel industry, but should not be used in structural design calculations."

Personally, I have never used either Mg or tonne in design calculations.

BA

 

[hokie66]

Not in our calculations, but tonne is used for weight of mass materials like steel, concrete, and fill. It is also loosely used for crane capacity, pile capacity, truck load, etc.