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Secret Metric Formula Conversions - Elastic Beam Equations
6

Secret Metric Formula Conversions - Elastic Beam Equations

Secret Metric Formula Conversions - Elastic Beam Equations

(OP)

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.!

RE: Secret Metric Formula Conversions - Elastic Beam Equations

2
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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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.

RE: Secret Metric Formula Conversions - Elastic Beam Equations

(OP)
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.

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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.

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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.

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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!

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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).

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

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RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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/
 

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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

RE: Secret Metric Formula Conversions - Elastic Beam Equations

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.

RE: Secret Metric Formula Conversions - Elastic Beam Equations

" I have gotten confused and wrong in the past by trying to combine Newtons and millimeters.  Don't do it."

I don't think that you'll get consensus on this, I do it, and as said above they combine nicely to equate to MPa.

RE: Secret Metric Formula Conversions - Elastic Beam Equations

apsix,

   I was working out the torque and the bending of a mirror rotating back and forth on a shaft.  I was doing a unit balance as I was advised to by one of my machine design teachers, and it did not work out.  Note how I have equations combining second moment of area and acceleration.  

   My solution was to systematically convert everything to MKS.  In general, your point is correct.  In my analysis, it might still be correct, but I have no intention of checking to find out.  A unit balance is an excellent error check.  It works better if I keep it simple.  

               JHG

RE: Secret Metric Formula Conversions - Elastic Beam Equations

Since codes almost always express loads in kN or kPa, rather than N and Pa, it is convenient to use tonne/m^3 for density, rather than kg.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Secret Metric Formula Conversions - Elastic Beam Equations

Why not change to unit weight and use kN/m3 - makes a lot more sense when you are dealing in kPa etc.  It is amazing how many mill test certificates I see use non-SI units for test results.

RE: Secret Metric Formula Conversions - Elastic Beam Equations

Quote:

Why not change to unit weight and use kN/m3

I usually do for my own calculations (if gravity is the only accelleration I have to worry about), but FEA programs like to have density in mass/volume, so I use tonne, m and kN (and kPa for stresses and pressures).

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Secret Metric Formula Conversions - Elastic Beam Equations

My $0.02 worth:

a) Always remember that mass and weight are NOT the same thing; try to avoid being loose / sloppy with "everyday" concepts like density (mass per unit volume; e.g. water = 1,000 kg/m^3 = 1 tonne per cubic metre) and unit weight (water = 9.8 kN/m^3).

b) Always use a fully consistent unit system throughout your calculations. If you are only doing static load calculations, you can often get away with being a bit sloppy with "mixed units", but it can sure come back to bite you when you get into dynamic analysis (where the time dimension comes into play), or when you have to deal with parameters with which you are not fully familiar (e.g. what is the correct conversion factor to get the heat flux in BTU per square foot per hour, if thermal conductivity is given in W/mK, temperature is in degrees Fahrenheit, area is in square feet, and thickness is in inches?)

c) There are quite a few common consistent unit systems; e.g. in metric, you can use base SI (m, kg, N, Pa, s, etc) or the N-mm system (mm, tonne, N, MPa, s, etc). Note, however, that when you deviate from base SI, some derived units can have "unusual" consistent units; e.g. in the N-mm system, the base unit for density is tonnes per cubic millimetre (which is a very small number for most common materials).

d) If in doubt, I strongly recommend you revert to basic SI units throughout; in this way, you can be confident that the consistent basic unit for ANY parameter in your analysis will be the corresponding base SI unit for that parameter.

Hope this helps!

RE: Secret Metric Formula Conversions - Elastic Beam Equations

I'm well aware of the tonne/m3 vs kN/m3 - being a geotechnical engineer, it is much easier for us to deal in kN/m3 than in tonne/m3.  Pressure at depth of 5 m with unit weight of 20kN/m3 = 100 kPa.  I don't have to go put in the gravity factor.  As jHardy1 points out - it is best to get the units right at the beginning.

RE: Secret Metric Formula Conversions - Elastic Beam Equations

"right" units are what ever you want to use ... i'd never use tonne/m^3 ... for me it's N, mm, and MPa

the key is to be consistent.  and if you're importing an odd unit (like IDS mentioned), i'd convert it immediately to the units i liked, and maybe convert my answer if particular units were required.

 

RE: Secret Metric Formula Conversions - Elastic Beam Equations

Quote:

"right" units are what ever you want to use ... i'd never use tonne/m^3 ... for me it's N, mm, and MPa


Which one of those do you use for mass?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Secret Metric Formula Conversions - Elastic Beam Equations

It has been noted previously that MPa is the same as N/mm2 which is very handy.  Another handy identity is that a load expressed in kN/m is the same as N/mm.

For a simple span of L with a uniform load of w, the bending moment is wL2/8.  If L is expressed in meters and w is kN/m, then M will be in kN-m.

Deflection is 5/384 * wL4/EI.  The load, w expressed in kN/m is the same when expressed in N/mm.  E is in MPa which is the same as N/mm2.  So, if span L is expressed in mm, the deflection comes out in consistent units, namely mm.  Another huge advantage of the SI metric system over the Imperial system.

BA

RE: Secret Metric Formula Conversions - Elastic Beam Equations

IMHO BA's post summarises the difficulty ... spans are big distances, better suited to big units (like m) but deflectiona are small, so small units (mm) are better.

the problem is that you have to be very careful (not saying BA isn't !) ... in one expression L is in m and the other it's in mm.  personally i keep the units the same and convert the answer, so a deflection of 0.01m = 10mm.

units of mass ... i avoid mass as much as i can ! but usually it's slugs ('cause i'm on the west side of the pond, and most of the time it's in, lbs, and psi/ksi)

RE: Secret Metric Formula Conversions - Elastic Beam Equations

@rb1957:

OMG! Someone who actually uses "slugs" as a unit of mass! I learnt about slugs at Uni (many,many years ago), but I honestly don't think I have ever come across someone who actually uses them!

w.r.t. the "right" units system - in Australia, conventional engineering drawing practice is to use mm for ALL construction dimensions (including member cross-section data, beam and slab spans, set-out dimensions, etc). About the only exception that I can think of is when dealing with large scale overall site plans etc, in which case the set-out coordinates are generally expressed in UTM (whole metres, with mm after the decimal point), and overall site dimensions / road changes / etc may well be specified in metres, but the mm will also be shown after the decimal point where applicable.

Where we make life a bit hard for ourselves, is that structural design calculations are generally done using kN, m and kNm, but we generally give member cross-section data in mm. By and large, it doesn't create any confusion, because it is generally pretty obvious by inspection whether a dimension is being given in metres or millimetres (or kilometres, when dealing with very large distances) - and of course the beauty of the metric system is that all you have to do to swap between units is shift the decimal point by 3 places one way or the other. I would much sooner work in metric units than have to deal with pounds, tons, feet, inches, 1/64 inch, etc.

While we understand the concept of other metric dimensions such as cm, dm, Dm, etc, you won't generally find them on any of our engineering drawings.

 

RE: Secret Metric Formula Conversions - Elastic Beam Equations

we only use them for inertial loads in FEM ... a 9g load you need mass density, slugs/in^3.

i'm trying to get the guys to understand they can use weight density, lbf/in^3, and then the load is 9 (instead of 9*32.174*12)

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